antimatter, feynman diagram, gravity
Daniel
backwards in time. so for example, a positron is an electron traveling
backwards in time, etc.
according to GR, matter curves space-time. would it be possible,
therefore, to say that traveling backwards in time is equivalent to
negative space-time curvature?
therefore, would anti-matter be gravitationally repulsive to ordinary
matter, due to the fact that it is curves space-time negatively (or in
feynman diagram, travels backward in time), but be grativtationally
attractive to anti-matter?
if so, then an galaxy of stars made of anti-matter would "repel" a
galaxy of stars made of ordinary matter, due to differing
gravitational interactions.
hence one of the problems of the standard model, why is there an
imbalance between antimatter and matter, would be easily solved. there
are equal amounts of matter and anti-matter in the universe, and it is
because of gravitational repulsion that the two do not come in
contact. after the big bang, matter and anti-matter were created in
exactly the same amounts, as predicted by the standard model, but b/c
of mutual gravitational repulsion, they flew apart.
[Moderator's note: Short answer: no. Antimatter is expected to
gravitate in the same way as ordinary matter. Note that an
attractive force, viewed backwards in time, is still an attractive
force. -TB]
Danny Ross Lunsford
Daniel wrote:
> according to feynman, antimatter is equivalent to matter running
> backwards in time. so for example, a positron is an electron traveling
> backwards in time, etc.
Yes, and it's clearly a balled-up picture...
> according to GR, matter curves space-time. would it be possible,
> therefore, to say that traveling backwards in time is equivalent to
> negative space-time curvature?
No because the equations are second order in time. However the real
issue is - can antimatter consistently be represented as negative mass
in GR? The Dirac equation alone (before Fermization and without further
interpretation) definitely states that antimatter has negative mass (an
equation doesn't know which way time is going, only if the two
directions are equivalent). Note that nothing bizarre is assumed here. A
negative mass electron is a positive mass positron. Tradition prefers
backward-in-time to negative-mass as a convention.
Banesh Hoffmann wrote a paper called "Negative Mass and the Quasars"
back in the 70s. Sorry I don't have a better reference - I saw it in a
book dedicated to Vaclav Hlavaty. While likely having not much to do
with actual quasars, it was very much to the point on the issue of
actual negative mass.
> [Moderator's note: Short answer: no. Antimatter is expected to
> gravitate in the same way as ordinary matter. Note that an
> attractive force, viewed backwards in time, is still an attractive
> force. -TB]
However, the experiment has never been done, so the jury is out,
physically speaking. Until a piece of antimatter can be made that lives
long enough to fall in a vacuum, we won't "really" know. The most direct
evidence so far comes from the burst of antineutrinos and neutrinos from
the Supernova 1987A.
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/antimatterFall.html
-drl
Uncle Al
>
> according to feynman, antimatter is equivalent to matter running
> backwards in time. so for example, a positron is an electron traveling
> backwards in time, etc.
>
> according to GR, matter curves space-time. would it be possible,
> therefore, to say that traveling backwards in time is equivalent to
> negative space-time curvature?
>
> therefore, would anti-matter be gravitationally repulsive to ordinary
> matter, due to the fact that it is curves space-time negatively (or in
> feynman diagram, travels backward in time), but be grativtationally
> attractive to anti-matter?
[snip]
Charge conjugation is an internal symmetry. Properties derived from
internal symmetries transform fields amongst themselves leaving
physical states (translation, rotation) invariant: U(1) symmetry in
electromagnetism, U(2) symmetry in electroweak theory, SU(3) in strong
force theory.
Antimatter falls identically to matter.
--
Uncle Al
http://www.mazepath.com/uncleal/qz.pdf
http://www.mazepath.com/uncleal/eotvos.htm
(Do something naughty to physics)
Oz
Danny Ross Lunsford <antima...@yahoo.NOSE-PAM.com> writes
>Daniel wrote:
>
>> according to feynman, antimatter is equivalent to matter running
>> backwards in time. so for example, a positron is an electron traveling
>> backwards in time, etc.
>
>Yes, and it's clearly a balled-up picture...
>
>> according to GR, matter curves space-time. would it be possible,
>> therefore, to say that traveling backwards in time is equivalent to
>> negative space-time curvature?
>
>No because the equations are second order in time. However the real
>issue is - can antimatter consistently be represented as negative mass
>in GR? The Dirac equation alone (before Fermization and without further
>interpretation) definitely states that antimatter has negative mass (an
>equation doesn't know which way time is going, only if the two
>directions are equivalent). Note that nothing bizarre is assumed here. A
>negative mass electron is a positive mass positron. Tradition prefers
>backward-in-time to negative-mass as a convention.
Hmm...
One can get terribly confused by negatives of negatives on these
situations. I am easily confused....
However there may be one scenario where the difference may make a
difference, or there again not.
If one postulated that spacetime and matter popped into existence at t=0
then is it plausible to consider that antimatter immediately started to
head in the -t direction and matter in the +t direction. Of course it
wouldn't be a simple process as each 'bunch' would continually be
producing both particles and antiparticles and there would be quite a
bit of mutual annihilation. One might imagine it as initially
symmetrical (in the time direction) but becoming increasingly biassed
towards antiparticles in the -t direction and particles in the +t
direction. After some (probably quite brief but busy) period one might
imagine each lobe would become separated (in time). Heuristically this
(until shot down in flames by Those Who Know) might be a mechanism for
explaining why we live in a (+ve) particulate universe where there isn't
much mass left.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
DEMON address no longer in use.
EjP
It's not really about lifetime, it's about energy. We routinely
store antiprotons for many days, but they're moving so fast that
gravity is negligible. In order to get any *individual* particles
(matter or antimatter) moving slowly enough that you can see
gravitational effects, they have to be very cold. Here's a paper
discussing some of the technical challenges in measuring the
graviational mass of anti-hydrogen
http://www.phy.duke.edu/~phillips/gravity/GravityExpt.html
-E
Esa A E Peuha
> However, the experiment has never been done, so the jury is out,
> physically speaking. Until a piece of antimatter can be made that lives
> long enough to fall in a vacuum, we won't "really" know.
Antimatter will certainly fall just like ordinary matter, regardless of
whether it has positive or negative mass. The question is whether
antimatter will attract (in case of positive mass) or repel (negative
mass) anything else.
--
Esa Peuha
student of mathematics at the University of Helsinki
http://www.helsinki.fi/~peuha/
Danny Ross Lunsford
> Charge conjugation is an internal symmetry. Properties derived from
> internal symmetries transform fields amongst themselves leaving
> physical states (translation, rotation) invariant: U(1) symmetry in
> electromagnetism, U(2) symmetry in electroweak theory, SU(3) in strong
> force theory.
Uncle Al is one of my heroes so it pains me to disagree with him :) But...
The unit pseudoscalar on spacetime is (in full tensorial form)
P = 1/24 epstensor_mnab gamma_m...gamma_b
This form is fixed by the interpretation of the gammas as forming a
local frame, the "square root" of the metric via Clifford
{ gamma_m, gamma_n } = 2 g_mn
Now the epsilon tensor is not just a permutation symbol - to make it a
tensor you have to prepend a factor of sqrt(det(g)). But det(g) is
negative, so the square root is imaginary. Thus epstensor_0123 = i and
P = i gamma_0..gamma_3
Under Hermitian conjugation
P* = -i gamma_3* ..gamma_0*
= i gamma_3 .. gamma_0 (gamma_i is anti-Hermitian)
= i gamma_0 .. gamma_3 = P
Writing the Dirac equation coupled to A
( gamma_m (dm + ieAm) + i M ) psi = 0
Pulling through P
( gamma_m (dm + ieAm) - i M ) P psi = 0
so P psi satisfies the same equation with the sign of the mass changed.
The adjoint is
psi* P gamma_0 ( gamma_m (dm - ieAm) + i M ) = 0
or
psibar P ( gamma_m (dm - ieAm) + i M ) = 0
There is a conserved current
J_m = psibar P gamma_m P psi = -psibar gamma_m psi
which is the original current reversed. That is, matter and antimatter
have been interchanged.
So, matter-antimatter conjugation is certainly associated with spacetime
symmetry. Note that the above description is given only in terms of
actual Lorentz-invariant objects.
-drl
Danny Ross Lunsford
> Danny Ross Lunsford <antima...@yahoo.NOSE-PAM.com> writes
> One can get terribly confused by negatives of negatives on these
> situations. I am easily confused....
>
> However there may be one scenario where the difference may make a
> difference, or there again not.
>
> If one postulated that spacetime and matter popped into existence at t=0
> then is it plausible to consider that antimatter immediately started to
> head in the -t direction and matter in the +t direction.
That is GREAT!! Of COURSE! It all ran off into the past!
Let's pray that the world does not have closed time loops - a whole
boatload of angry antimatter might be headed this way!
> Of course it wouldn't be a simple process as each 'bunch' would continually be
> producing both particles and antiparticles and there would be quite a
> bit of mutual annihilation. One might imagine it as initially
> symmetrical (in the time direction) but becoming increasingly biassed
> towards antiparticles in the -t direction and particles in the +t
> direction. After some (probably quite brief but busy) period one might
> imagine each lobe would become separated (in time). Heuristically this
> (until shot down in flames by Those Who Know) might be a mechanism for
> explaining why we live in a (+ve) particulate universe where there isn't
> much mass left.
I don't think there is a great mystery about the local lack of
antimatter. Hannes Alfven showed in simple terms that that
observationally, at best matter and its mirror are separated at the
level of galaxy clusters. An interesting aspect of his analysis - if you
have a tenuous gas of matter and one of antimatter and allow them to
interact, a boundary area of annihilation sets up and the radiation
pressure from it tends to keep them separated. An exactly analogous
thing happens when you drip water onto a hot surface - the water boils
at the surface of the drop and the outgassing of steam lifts the drop up
off the hot surface - allowing the water drop to live an unexpectedly
long time ("Leidenfrost effect").
The main problem with Alfven's symmetric cosmology - explaining the
thermalization of the annihilation radiation.
-drl
Danny Ross Lunsford
> No because the equations are second order in time. However the real
> issue is - can antimatter consistently be represented as negative mass
> in GR? The Dirac equation alone (before Fermization and without further
> interpretation) definitely states that antimatter has negative mass (an
> equation doesn't know which way time is going, only if the two
> directions are equivalent). Note that nothing bizarre is assumed here. A
> negative mass electron is a positive mass positron. Tradition prefers
> backward-in-time to negative-mass as a convention.
Just for completeness, let's verify this claim.
We work in the Dirac representation of the spacetime algebra. In this
representation a 4-spinor has "large" and "small" components, that is,
the top-half psi+ goes over to the 2-spinor that appears in the Pauli
non-relativistic theory, and the bottom half psi- is of order (v/c) in
comparison - specifically in the low-energy limit
psi- approx. = 1/2m s.(p - eA) psi+
(see Ryder, Quantum Field Theory 2nd edtion, section 2.6)
The Dirac equation coupled to an electromagnetic field is
[ gamma_m (dm + ieAm) + iM ] psi = 0
The unit pseudoscalar on spacetime is
P = 1/24 epstensor_mnab gamma_m...gamma_b
= sqrt(det(g)) eps_0123 gamma_0..gamma_3
= gamma_5
In the Dirac representation
gamma_5 = | 0 I |
| I 0 |
Pulling P through the Dirac equation we get
[ gamma_m (dm + ieAm) - iM ] P psi = 0
that is, P psi satisfies the same equation with the sign of the mass
reversed. Notice that P psi is just a 4-spinor with the "large" and
"small" components interchanged.
We take the complex conjugate of this equation, rearrange rows and
columns by twos so that the "large" half is back on top, and pull
through the matrix gamma_2 gamma_0 - we get
[ gamma_m (dm - ieAm) + iM ] gamma_2 gamma_0 psibarT = 0
where psibarT is the transpose of the adjoint spinor psibar. This
however is just the usual representation of the "charge conjugated"
Dirac equation up to a phase of i - the sign on the electromagnetic
field has changed sign as expected an we are back to positive mass.
Thus it would be entirely possible to work always in terms of negative
mass and avoid the problematic interpretation of "backward in time" that
gets algebraically introduced by plain complex conjugation.
If one takes this seriously, then one has to consider the Schwarzschild
solution with the integration constant corresponding to the mass of the
body taken to have the opposite sign. Matter and antimatter would then
definitely be distinguised gravitationally.
*Should* we take it seriously? I only point out that in one case, we
have a simple change in sign of the mass, and everything is sight is a
straightforward spacetime covariant based on the Dirac algebra, while in
the other, the unnatural looking charge-conjugation operator
C = i gamma_2 gamma_0
and the complex conjugate of the Dirac equation, must be introduced, not
to mention the problematic idea of "backward in time".
Moreover, when one goes over to Fermization (second quantization) the
action of the charge conjugation operator itself changes (sign change).
This is highly unsatisfactory.
-drl
Oz
>It's not really about lifetime, it's about energy. We routinely
>store antiprotons for many days, but they're moving so fast that
>gravity is negligible. In order to get any *individual* particles
>(matter or antimatter) moving slowly enough that you can see
>gravitational effects, they have to be very cold.
Wouldn't it be possible to use the same techniques of a neutron
spallation source to produce very slow antineutrons?
The only problem is that theory may well suggest that they would still
fall in the same manner as neutrons. If so (which would seem likely) a
null result would be expected either way.
Michael Varney
news:86pptat...@sirppi.helsinki.fi...
> Danny Ross Lunsford <antima...@yahoo.NOSE-PAM.com> writes:
>
> > However, the experiment has never been done, so the jury is out,
> > physically speaking. Until a piece of antimatter can be made that lives
> > long enough to fall in a vacuum, we won't "really" know.
>
> Antimatter will certainly fall just like ordinary matter
Are you certain? Physics is an experimental science, and until this
conjecture is experimentally verified, it cannot be stated with certainty.
>, regardless of
> whether it has positive or negative mass. The question is whether
> antimatter will attract (in case of positive mass) or repel (negative
> mass) anything else.
This is not the question.
Danny Ross Lunsford
EjP wrote:
> It's not really about lifetime, it's about energy. We routinely
> store antiprotons for many days, but they're moving so fast that
> gravity is negligible. In order to get any *individual* particles
> (matter or antimatter) moving slowly enough that you can see
> gravitational effects, they have to be very cold. Here's a paper
> discussing some of the technical challenges in measuring the
> graviational mass of anti-hydrogen
> http://www.phy.duke.edu/~phillips/gravity/GravityExpt.html
Great! Are you going to do this experiment? I would think it would be
very exciting. Good luck!
-drl
Oz
Esa A E Peuha <esa....@helsinki.fi> writes
>Antimatter will certainly fall just like ordinary matter, regardless of
>whether it has positive or negative mass.
I presume this is just a statement saying all bodies follow a geodesic.
>The question is whether
>antimatter will attract (in case of positive mass) or repel (negative
>mass) anything else.
I am unclear about this though. Will a large antimatter body repel
ordinary matter or attract it, similarly for antimatter. Its all those
double and triple negatives that confuse the heck out of me. You suggest
that they behave gravitationally differently but your first statement
(above) suggests they don't.
Its the old saw about negative mass being attracted by a negative force
results in attraction. Makes my head hurt ....
One has a horrible feeling that even devising a test to determine if
negative mass exists might be difficult.
Uncle Al
>
> Uncle Al wrote:
>
> > Charge conjugation is an internal symmetry. Properties derived from
> > internal symmetries transform fields amongst themselves leaving
> > physical states (translation, rotation) invariant: U(1) symmetry in
> > electromagnetism, U(2) symmetry in electroweak theory, SU(3) in strong
> > force theory.
>
> Uncle Al is one of my heroes so it pains me to disagree with him :) But...
You are not disagreeing, you are disproving. Quality counts towards
everybody's bottom line.
I'm a good sport! I don't doubt Lorentz invariance, too. Metric
theories of gravitation are parity-symmetric. Affine theories of
gravitation can be parity-antisymmetric. If you have successfully
demonstrated that matter-antimatter comparison is deeper than the
classical internal symmetry, right on!
How do you secure the boojum (or rather, the antiboojum) and do the
test to sufficient accuracy?
I have described and calculated a novel Equivalence Principle test
using left-handed vs. right-handed single crystal alpha-quartz test
masses of identical chemical composition and macroscopic form
(spherical balls, equal diameter and height right cylinders, or
facetted cylinders with three identical moments of inertia ) in an
unmodified existing Eotvos balance,
http://www.mazepath.com/uncleal/qz.pdf
(Graphs are presented for paired 3.44x10^17-atom single crystal test
masses. We currently have data to 7.33x10^17 atoms or 0.26 mm
diameter. We hope to hit 9x10^18 atoms and 0.60 mm diameter in the
current 16 Opteron-848 cluster run, then quit forever. If anybody has
a 128-bit precision math library and a teraFL0PS cluster supercomputer
with a month of slack time, we can do some *serious* diameters.)
How would you fabricate and test an antimatter body? Other physics
constrains the maximum Equivalence Principle violation to no more than
100 parts-per-trillion difference/average. Even claiming 10
parts-per-trillion will be met with loud doubt absent convincing
measurements. Matter interferometers are only good to about 1000
parts-per-million (with an "m" not a "t;" Colella-Overhauser-Werner
and Bonse-Wroblewski neutron interferometers; Kasevich-Chu atom
interferometer) Manufacturing and containing a gram of antimatter
will be infeasible for cost and safety (43 kilotonne blast plus EPA
sanctions).
Oz
>Thus it would be entirely possible to work always in terms of negative
>mass and avoid the problematic interpretation of "backward in time" that
>gets algebraically introduced by plain complex conjugation.
Ooohhh... that'll raise some eyebrows...
>If one takes this seriously, then one has to consider the Schwarzschild
>solution with the integration constant corresponding to the mass of the
>body taken to have the opposite sign. Matter and antimatter would then
>definitely be distinguised gravitationally.
Ooooohhh ... not mainstream (but in many ways nice).
Note that this matches well with Charles Francis' formulation of
teleparallel quantum gravity and the naive particle-antiparticle BB
radiation.
>*Should* we take it seriously?
Er, um, I have enough problem here anyway ...
>I only point out that in one case, we
>have a simple change in sign of the mass, and everything is sight is a
>straightforward spacetime covariant based on the Dirac algebra, while in
>the other, the unnatural looking charge-conjugation operator
>
>C = i gamma_2 gamma_0
>
>and the complex conjugate of the Dirac equation, must be introduced, not
>to mention the problematic idea of "backward in time".
>
>Moreover, when one goes over to Fermization (second quantization) the
>action of the charge conjugation operator itself changes (sign change).
>This is highly unsatisfactory.
Am I to interpret this as a statement that its mathematically more
elegant to take antiparticles as having negative mass but moving forward
in time?
If so, why is it considered somewhat crankish?
Oz
>Antimatter will certainly fall just like ordinary matter, regardless of
>whether it has positive or negative mass.
I presume this is just a statement saying all bodies follow a geodesic.
>The question is whether
>antimatter will attract (in case of positive mass) or repel (negative
>mass) anything else.
I am unclear about this though. Will a large antimatter body repel
ordinary matter or attract it, similarly for antimatter. Its all those
double and triple negatives that confuse the heck out of me. You suggest
that they behave gravitationally differently but your first statement
(above) suggests they don't.
Its the old saw about negative mass being attracted by a negative force
results in attraction. Makes my head hurt ....
One has a horrible feeling that even devising a test to determine if
negative mass exists might be difficult.
--
Oz
>Oz wrote:
>
>> Danny Ross Lunsford <antima...@yahoo.NOSE-PAM.com> writes
>
>> One can get terribly confused by negatives of negatives on these
>> situations. I am easily confused....
>>
>> However there may be one scenario where the difference may make a
>> difference, or there again not.
>>
>> If one postulated that spacetime and matter popped into existence at t=0
>> then is it plausible to consider that antimatter immediately started to
>> head in the -t direction and matter in the +t direction.
>
>That is GREAT!! Of COURSE! It all ran off into the past!
Well, I have suggested it before. Seems quite a nice idea to me.
>Let's pray that the world does not have closed time loops - a whole
>boatload of angry antimatter might be headed this way!
We ought to see quite a few photons well in advance, so some warning
might be forthcoming.
>> Of course it wouldn't be a simple process as each 'bunch' would continually be
>> producing both particles and antiparticles and there would be quite a
>> bit of mutual annihilation. One might imagine it as initially
>> symmetrical (in the time direction) but becoming increasingly biassed
>> towards antiparticles in the -t direction and particles in the +t
>> direction. After some (probably quite brief but busy) period one might
>> imagine each lobe would become separated (in time). Heuristically this
>> (until shot down in flames by Those Who Know) might be a mechanism for
>> explaining why we live in a (+ve) particulate universe where there isn't
>> much mass left.
>
>I don't think there is a great mystery about the local lack of
>antimatter. Hannes Alfven showed in simple terms that that
>observationally, at best matter and its mirror are separated at the
>level of galaxy clusters. An interesting aspect of his analysis - if you
>have a tenuous gas of matter and one of antimatter and allow them to
>interact, a boundary area of annihilation sets up and the radiation
>pressure from it tends to keep them separated.
Sounds highly plausible, except that this radiation should be quite
evident, particularly in the early universe.
>An exactly analogous
>thing happens when you drip water onto a hot surface - the water boils
>at the surface of the drop and the outgassing of steam lifts the drop up
>off the hot surface - allowing the water drop to live an unexpectedly
>long time ("Leidenfrost effect").
It also hovercrafts round at high speed.
>The main problem with Alfven's symmetric cosmology - explaining the
>thermalization of the annihilation radiation.
His model doesn't seem to have much in common with my suggestion.
I am proposing it for the *very* early universe, certainly before
10^-12s. At this time radiation pressure would (I guess) be
insignificant compared to the energy of the particles. I would expect
particles and antiparticles to have very short mean free paths (in 4-D)
so the universe initially expanded symmetrically (that is equally in the
+t and -t) directions, it would be (looking from 5-D) a hypersphere.
However there would be a drift of antiparticles in the -t direction and
a drift of particles in the +t direction. The whole time, in each small
volume, particles and antiparticles would be being produced but
progressively the +t direction would be depleted in antiparticles, and
the -t in particles to produce two lobes. I expect it to end up as some
horrible diffusion-like equation. Something roughly analogous a ball of
hot plasma in an intense electrical field where ionisation is repeatedly
happening until the paths start to line up with the electric field.
Hah! Could a distant bunch of negative mass give us an accelerating
expansion? I don't know, seems unlikely.
Oz
>It's not really about lifetime, it's about energy. We routinely
>store antiprotons for many days, but they're moving so fast that
>gravity is negligible. In order to get any *individual* particles
>(matter or antimatter) moving slowly enough that you can see
>gravitational effects, they have to be very cold.
Wouldn't it be possible to use the same techniques of a neutron
spallation source to produce very slow antineutrons?
The only problem is that theory may well suggest that they would still
fall in the same manner as neutrons. If so (which would seem likely) a
null result would be expected either way.
--
Esa A E Peuha
> Esa A E Peuha <esa....@helsinki.fi> writes
>
> >Antimatter will certainly fall just like ordinary matter, regardless of
> >whether it has positive or negative mass.
>
> I presume this is just a statement saying all bodies follow a geodesic.
Yes.
> >The question is whether
> >antimatter will attract (in case of positive mass) or repel (negative
> >mass) anything else.
>
> I am unclear about this though. Will a large antimatter body repel
> ordinary matter or attract it, similarly for antimatter.
Since antimatter is not known to have negative mass, I'll use PMM
(positive mass matter) and NMM (negative mass matter) to avoid any
confusion. Now PMM will attract anything gravitationally, and NMM will
repel everything, so if you have equal amounts of PMM and NMM
interacting only by gravitation next to each other, then the PMM will
accelerate away from the NMM and the NMM will follow the PMM. However
if these matters have also electric charge (and the gravitational
interaction can be ignored), things can look different; if they have the
same charge, the PMM will still accelerate away from the NMM and the NMM
will still accelerate towards the PMM (because for the NMM force and
acceleration vectors must point to opposite directions), but if they
have opposite charges, the NMM will run away and the PMM will follow.
> One has a horrible feeling that even devising a test to determine if
> negative mass exists might be difficult.
Actually it's pretty easy to see that at least antiparticles of ordinary
particles have positive mass; if, for example, the positron had negative
mass, we would see vast amounts of positrons chased by electrons at very
near light speed, since positron-electron pairs are known to be created
by cosmic radiation and other reasons. Also, positrons and antiprotons
are known to form antihydrogen atoms (or is that hydrogen antiatoms)
which would be impossible if they had negative masses.
Danny Ross Lunsford
Esa A E Peuha wrote:
> Since antimatter is not known to have negative mass, I'll use PMM
> (positive mass matter) and NMM (negative mass matter) to avoid any
> confusion.
Unfortunately that doesn't work - the sign on the mass is a matter of
convention and the issue becomes - it is legitimate to use both
conventions at once, as is usually done? That is, there is a very
definite operation on a negative energy solution to the Dirac equation
that inverts the sign on the mass of a jabber and dresses it up as a
positive-energy antijabber - and one uses *both* conventions at the same
time in the subsequent development. All of the odd, paradoxical behavior
in the Dirac theory can be traced back to this choice.
> Now PMM will attract anything gravitationally, and NMM will
> repel everything...
Hang on, this is not at all clear. If gravity is polar with respect to
matter and antimatter, then the polarity can't be the simple kind found
in the vector field theory (electrodynamics). So it may be that
antimatter gravitationally repels other antimatter, while the mutual
gravitational interaction of matter and antimatter is a total unknown -
there is no place in GR for introducing the distinction (one would have
to have a theory in which the volume element itself was a dynamical
variable because the distinction of matter and antimatter is ultimately
a consequence of spacetime parity).
> Actually it's pretty easy to see that at least antiparticles of ordinary
> particles have positive mass; if, for example, the positron had negative
> mass, we would see vast amounts of positrons chased by electrons at very
> near light speed, since positron-electron pairs are known to be created
> by cosmic radiation and other reasons.
The "chasing" behavior is based on the tacit assumption that for
antimatter, Minertial = Mgravitational. Because there is no place in the
usual formalism of GR for the idea of matter-antimatter and mutual
creation-annihilation, we just don't know - the experiment really has to
be done to guide the formalism.
> ... Also, positrons and antiprotons
> are known to form antihydrogen atoms (or is that hydrogen antiatoms)
> which would be impossible if they had negative masses.
This is certainly not true - we can reconvene and call the existing
hydrogen "antihydrogen" and lament that we have no koinohydrogen to play
with. In introducing the local charge conjugation operator iy2y0 one has
tacitly assumed that it is possible to redefine the two everywhere
globally (I'm working on localizing this to see if any new information
emerges).
-drl
Danny Ross Lunsford
Oz wrote:
> Am I to interpret this as a statement that its mathematically more
> elegant to take antiparticles as having negative mass but moving forward
> in time?
Well it's certainly more in the spirit of invariant theory. When you
take the complex conjugate of the Dirac eqn you are in effect
interchanging the past and future light cones. This erases the effect of
parity in the full Lorentz group as far as time is concerned, so to get
it back you have to pick a bivector (in spacetime, 2 directions) which
then defines a plane in spacetime normal to it, and then one gets back
parity by reflection in this plane. But, this is a kind of choice of
gauge and for every possible frame you have to pick another one - the
common choice is what is called the charge conjugation operator
mentioned before i gamma_2 gamma_0. It is far more natural to work
directly with negative mass, so parity has a frame-independent
representation.
Is it crankish? No one thinks about these things any more, everyone
assumes they know everything there is to be known about the Dirac
equation. Call it "eccentric" then.
-drl
Danny Ross Lunsford
> If one postulated that spacetime and matter popped into existence at t=0
> then is it plausible to consider that antimatter immediately started to
> head in the -t direction and matter in the +t direction.
You know, this is disturbing me Oz. In fact this might be an amazing
insight. How can one reconcile the Big Bang scenario with the simple
logical fact that at t=0 there is no past to go into? The only possible
way out is a time-symmetric cosmology with the valid mirror image of a
gradually accelerating collapse to nothingness, with the end phase being
deflationary. This is clearly impossible, so the choices are 1) backward
in time is untenable 2) t=0 is impossible.
-drl
Esa A E Peuha
> "Esa A E Peuha" <esa....@helsinki.fi> wrote in message
> news:86pptat...@sirppi.helsinki.fi...
> > Danny Ross Lunsford <antima...@yahoo.NOSE-PAM.com> writes:
> >
> > > However, the experiment has never been done, so the jury is out,
> > > physically speaking. Until a piece of antimatter can be made that lives
> > > long enough to fall in a vacuum, we won't "really" know.
> >
> > Antimatter will certainly fall just like ordinary matter
>
> Are you certain? Physics is an experimental science, and until this
> conjecture is experimentally verified, it cannot be stated with certainty.
Of course the result of any experiment can't be predicted with absolute
certainty. However, if the experiment shows that antimatter does fall
up, it violates general relativity on a very fundamental level. Now
general relativity has been tested by hundreds of experiments (with
which no other known theory of gravity completely agrees), so it would
be extremely surprising if antimatter did fall up.
Oz
>Since antimatter is not known to have negative mass, I'll use PMM
>(positive mass matter) and NMM (negative mass matter) to avoid any
>confusion. Now PMM will attract anything gravitationally, and NMM will
>repel everything, so if you have equal amounts of PMM and NMM
>interacting only by gravitation next to each other, then the PMM will
>accelerate away from the NMM and the NMM will follow the PMM.
Ahh, yes. I remember a long thread about this some years ago.
>However
>if these matters have also electric charge (and the gravitational
>interaction can be ignored), things can look different; if they have the
>same charge, the PMM will still accelerate away from the NMM and the NMM
>will still accelerate towards the PMM (because for the NMM force and
>acceleration vectors must point to opposite directions), but if they
>have opposite charges, the NMM will run away and the PMM will follow.
Hmmm. Not the sort of behaviour one usually expects.
>> One has a horrible feeling that even devising a test to determine if
>> negative mass exists might be difficult.
>
>Actually it's pretty easy to see that at least antiparticles of ordinary
>particles have positive mass; if, for example, the positron had negative
>mass, we would see vast amounts of positrons chased by electrons at very
>near light speed, since positron-electron pairs are known to be created
>by cosmic radiation and other reasons. Also, positrons and antiprotons
>are known to form antihydrogen atoms (or is that hydrogen antiatoms)
>which would be impossible if they had negative masses.
So perhaps better to take antiparticles as particles going backwards in
time? Or are you able to show that this has flaws too?
<sigh>
John Baez
Oz <o...@farmeroz.port995.com> wrote:
>Esa A E Peuha <esa....@helsinki.fi> writes
>>Antimatter will certainly fall just like ordinary matter, regardless of
>>whether it has positive or negative mass.
Right! - as long as general relativity applies, that is.
>I presume this is just a statement saying all bodies follow a geodesic.
Right, and it's worth noting this pattern:
the geodesic is timelike <=> mass^2 > 0 (tardyons)
the geodesic is lightlike <=> mass^2 = 0 (luxons)
the geodesic is spacelike <=> mass^2 < 0 (tachyons)
So, you can tell a little about the mass of a particle by the
sort of geodesic it follows, but not the *sign* of its mass.
>>The question is whether antimatter will attract (in case of positive
>>mass) or repel (negative mass) anything else.
>I am unclear about this though. Will a large antimatter body repel
>ordinary matter or attract it, similarly for antimatter. Its all those
>double and triple negatives that confuse the heck out of me.
Right, they're confusing - and I never worked them out myself until we
discussed this a couple of times here on sci.physics.research. But now
I know how it goes. As long as general relativity applies:
A positive-mass body will curve spacetime in a way that bends geodesics
"towards" it, so it will *attract* other bodies regardless of the sign
of their mass.
A negative-mass body will curve spacetime in a way that bends geodesics
"away from" it, so it will *repel* other bodies regardless of the sign
of their mass.
Now you've got all the necessary knowledge to take a crack at this:
PUZZLE:
Figure out what happens if you have two planets near each
other: Earth and Anti-Earth, the first with positive mass, the
second with an "equal but opposite" negative mass.
(We've already discussed *everything* here. We've even been through
a discussion before about how "equal and opposite" is a slightly stupid
thing to say - but we all know what it means.)
>Its the old saw about negative mass being attracted by a negative force
>results in attraction. Makes my head hurt ....
Yes, but it's not much worse than - x - = +... which of course some
people never get around to grokking.
>One has a horrible feeling that even devising a test to determine if
>negative mass exists might be difficult.
This is an interesting question, but you should do the puzzle
first.
By the way, it currently seems like I'll be in Oxford this July 7-9,
to speak at the Workshop on Gerbes: Recent Developments and Future
Perspectives, at Oxford, organized by Nuno Reis. So, maybe we can
get together while I'm there. (There's a chance this workshop won't
actually happen, due to funding issues, but regardless of that I'll
be in Cambridge from July 1st to September 8th, modulo a few side-trips.)
-------------------------------------------------------------------------
Puzzle #19:
As of February 2004, five of the ten richest people in the world had
the same last name. What is it?
If you give up, try:
John Baez
http://math.ucr.edu/home/baez/quantum/
Quantum Quandaries: A Category-Theoretic Perspective
John C. Baez
To appear in _Structural Foundations of Quantum Gravity_,
eds. Steven French, Dean Rickles and Juha Saatsi, Oxford U. Press.
Abstract:
General relativity may seem very different from quantum theory, but work
on quantum gravity has revealed a deep analogy between the two. General
relativity makes heavy use of the category nCob, whose objects are
(n-1)-dimensional manifolds representing "space" and whose morphisms
are n-dimensional cobordisms representing "spacetime". Quantum theory
makes heavy use of the category Hilb, whose objects are Hilbert spaces
used to describe "states", and whose morphisms are bounded linear operators
used to describe "processes". Moreover, the categories nCob and Hilb
resemble each other far more than either resembles Set, the category
whose objects are sets and whose morphisms are functions. In particular,
both Hilb and nCob but not Set are *-categories with a noncartesian
monoidal structure. We show how this accounts for many of the famously
puzzling features of quantum theory: the failure of local realism, the
impossibility of duplicating quantum information, and so on. We argue
that these features only seem puzzling when we try to treat Hilb as
analogous to Set rather than nCob, so that quantum theory will make
more sense when regarded as part of a theory of spacetime.
This will probably show up at http://www.arxiv.org/abs/quant-ph/0404040
pretty soon. (Yay! I got the coolest arxiv number this year!)
Michael Varney
> "Michael Varney" <varney@colorado_no_spam.edu> writes:
>
> > "Esa A E Peuha" <esa....@helsinki.fi> wrote in message
> > news:86pptat...@sirppi.helsinki.fi...
> > > Danny Ross Lunsford <antima...@yahoo.NOSE-PAM.com> writes:
> > >
> > > > However, the experiment has never been done, so the jury is out,
> > > > physically speaking. Until a piece of antimatter can be made that
lives
> > > > long enough to fall in a vacuum, we won't "really" know.
> > >
> > > Antimatter will certainly fall just like ordinary matter
> >
> > Are you certain? Physics is an experimental science, and until this
> > conjecture is experimentally verified, it cannot be stated with
certainty.
>
> Of course the result of any experiment can't be predicted with absolute
> certainty. However, if the experiment shows that antimatter does fall
> up, it violates general relativity on a very fundamental level.
Which is why it is an important experiment to perform.
> Now
> general relativity has been tested by hundreds of experiments (with
> which no other known theory of gravity completely agrees), so it would
> be extremely surprising if antimatter did fall up.
It would be surprising. However, the experiment needs to be done, and to
state with certainty that antimatter will fall like matter is an incorrect
thing to do in science.
---
Michael Varney
Department of Physics
University of Colorado, Boulder
http://rintintin.colorado.edu/~varney
Doug Sweetser
I was thinking about this sort of thing recently:
> the geodesic is timelike <=> mass^2 > 0 (tardyons)
> the geodesic is lightlike <=> mass^2 = 0 (luxons)
> the geodesic is spacelike <=> mass^2 < 0 (tachyons)
See, there are perfectly fine paths in spacetime that are spacelike
separated from an observer:
\t| / x
\|/ |
R--------|
/|\ x
/ | \
The arbitrary choice of the origin makes all the events on that
worldline spacelike separated from the origin. The relativistic
velocity of the x--x worldline is zero, and could be created by a real
particle.
What happens if this spacetime graph is transformed to the classical
realm? The 45 degree lines end up going flat. In the limit of this
process, the nice defined slope of the x--x worldline becomes
undefined. Uncool.
I had an alternate idea, and want to see if someone else has thought of
this before. The Minkowski metric is an indefinite metric. It is that
darn negative distance squared that doesn't make sense, particularly
for a pure mathematician. So let's try and aid the mathematicians in
the audience. We apply a simple rule: if |t| > |R|, the point gets
plotted in spacetime as always. This should fill up the past and
future timelike light cones. If |t| < |R|, then we plot the points in
the complex-valued tangent space:
it| / x
\|/ |
iR--------|
/|\ x
/ | \
Now the metric will be a positive definite number because
(it)^2 - (iR)^2 = -|t|^2 + |R|^2 > 0
Note, the observer cannot travel a distance iR to get to these points.
Yet gamma and beta are well defined real numbers because they are
ratios of two imaginary numbers.
The Minkowski metric is a metric, not a pseudo metric, so long as this
rule of accounting in enforced for timelike events graphed in
spacetime, and spacelike events graphed in the complex-valued tangent
space.
doug
quaternions.com
Oz
>In article <iHM3pEEX...@btopenworld.com>,
>Oz <o...@farmeroz.port995.com> wrote:
>
> and triple negatives that confuse the heck out of me.
>
>Right, they're confusing - and I never worked them out myself until we
>discussed this a couple of times here on sci.physics.research. But now
>I know how it goes. As long as general relativity applies:
>
>A positive-mass body will curve spacetime in a way that bends geodesics
>"towards" it, so it will *attract* other bodies regardless of the sign
>of their mass.
>
>A negative-mass body will curve spacetime in a way that bends geodesics
>"away from" it, so it will *repel* other bodies regardless of the sign
>of their mass.
That strikes me as very reasonable. Of course we must be careful to
distinguish between a positive and negative inertia, too. In this sort
of scenario I don't think we can assume mass and inertia will
necessarily be either the same, or a different, sign. Fortunately in GR
when following a geodesic, there is no acceleration so this can be
conveniently swept under the carpet.
>Now you've got all the necessary knowledge to take a crack at this:
Oh .. my .. god! He never changes! Straight into homework.
>PUZZLE:
>
> Figure out what happens if you have two planets near each
> other: Earth and Anti-Earth, the first with positive mass, the
> second with an "equal but opposite" negative mass.
I expect we will have the 'accelerate across the universe' scenario...
This needs some thought. I trust you are not expecting me to solve an
equivalent of schild metric for this scenario?
If so you are out of luck.
I assume embedded in an otherwise empty flat spacetime. For convenience
I will consider the masses as point particles.
Now what?
Well, there will be a point halfway between the two which will be
locally flat. Eh? No, that can't be right. A test particle on the
repulsive body will fall straight down and hit the attractive one, since
it will be repelled by the repulsive and attracted by the attractive.
So if both bodies were dust then the repulsive one would expand and the
attractive one would collapse. If they were solid enough to resist
gravitational forces then they clearly would accelerate across the
universe, trailing their gravitational fields behind them. If they were
orbiting each other as well, then they would have a complex circular
path (probably).
What if they were different sized masses?
Well a -m particle would orbit a large +m particle, but presumably in
its immediate vicinity space would be less curved. I think this means it
has a slightly larger orbit. The two bodies will orbit round a centre of
mass that will be outside the line between them. This will be a patch of
flat spacetime. For an infinitely small orbiting mass, the only patch of
flat spacetime (not at inf) will be the saddle on the major body,
clearly a -ve mass will push this further away from the -ve particle.
As their masses tend to being equal and opposite then this patch will
recede to infinity and we get the 'follow my leader' scenario again.
My head hurts ....
>>Its the old saw about negative mass being attracted by a negative force
>>results in attraction. Makes my head hurt ....
>
>Yes, but it's not much worse than - x - = +... which of course some
>people never get around to grokking.
>
>>One has a horrible feeling that even devising a test to determine if
>>negative mass exists might be difficult.
I note that time-reversing the above scenarios reverses -ve and +ve
mass.
>By the way, it currently seems like I'll be in Oxford this July 7-9,
>to speak at the Workshop on Gerbes: Recent Developments and Future
>Perspectives, at Oxford, organized by Nuno Reis. So, maybe we can
>get together while I'm there.
Should be fine.
I can't contact you, but you can contact me using reply-to of this post.
>(There's a chance this workshop won't
>actually happen, due to funding issues, but regardless of that I'll
>be in Cambridge from July 1st to September 8th, modulo a few side-trips.)
Will be outside claire's termtime I think.
car...@no-physics-spam.ucdavis.edu
> Oz wrote:
> > If one postulated that spacetime and matter popped into existence at t=0
> > then is it plausible to consider that antimatter immediately started to
> > head in the -t direction and matter in the +t direction.
> You know, this is disturbing me Oz. In fact this might be an amazing
> insight. How can one reconcile the Big Bang scenario with the simple
> logical fact that at t=0 there is no past to go into?
If you are sticking with standard general relativity (with a Lorentzian
metric), t=0 is a singularity, anyway, so it's not clear that you should
expect any reconciliation. If you accept the Hartle-Hawking picture of
quantum cosmology, though, in which the metric near t=0 is Riemannian,
there's a nice answer -- in fact, the geometry naturally picks out the
decomposition into positive and negative frequencies. See Gibbons and
Pohle, "Complex Numbers, Quantum Mechanics and the Beginning of Time,"
gr-qc/9302002.
Steve Carlip
Esa A E Peuha
> Unfortunately that doesn't work - the sign on the mass is a matter of
> convention and the issue becomes - it is legitimate to use both
> conventions at once, as is usually done?
That depends on the context. GR itself has no problem with having
matter with negative mass.
> > Now PMM will attract anything gravitationally, and NMM will
> > repel everything...
>
> Hang on, this is not at all clear.
It is perfectly clear in GR.
> If gravity is polar with respect to
> matter and antimatter, then the polarity can't be the simple kind found
> in the vector field theory (electrodynamics). So it may be that
> antimatter gravitationally repels other antimatter, while the mutual
> gravitational interaction of matter and antimatter is a total unknown -
> there is no place in GR for introducing the distinction
What do you mean? In GR, any given object either attracts everything or
repels everything gravitationally, so the gravitational interaction
between matter and antimatter is definitely predicted no matter what we
assume about the mass of antimatter (even if it turns out to be wrong).
> (one would have
> to have a theory in which the volume element itself was a dynamical
> variable because the distinction of matter and antimatter is ultimately
> a consequence of spacetime parity).
I don't understand; the volume element dx /\ dy /\ dz does change sign
when spacetime parity is reversed (if that's what you mean).
> > Actually it's pretty easy to see that at least antiparticles of ordinary
> > particles have positive mass; if, for example, the positron had negative
> > mass, we would see vast amounts of positrons chased by electrons at very
> > near light speed, since positron-electron pairs are known to be created
> > by cosmic radiation and other reasons.
>
> The "chasing" behavior is based on the tacit assumption that for
> antimatter, Minertial = Mgravitational.
In the case of gravitation, yes, but electric force only involves the
inertial mass. Since the electric force between an electron and a
positron is several orders of magnitude greater than the gravitational
force, it is quite clear that positron must have the same sign of
inertial mass as electron.
> Because there is no place in the
> usual formalism of GR for the idea of matter-antimatter and mutual
> creation-annihilation, we just don't know - the experiment really has to
> be done to guide the formalism.
I agree that the experiment should be done, but if it turns out that
antimatter falls up, then we will have no theory of gravity that can
agree with all experiments, and no idea how to construct one.
> > ... Also, positrons and antiprotons
> > are known to form antihydrogen atoms (or is that hydrogen antiatoms)
> > which would be impossible if they had negative masses.
>
> This is certainly not true - we can reconvene and call the existing
> hydrogen "antihydrogen" and lament that we have no koinohydrogen to play
> with.
Antihydrogen has been observed at Fermilab in 1997.
Danny Ross Lunsford
>>I am unclear about this though. Will a large antimatter body repel
>>ordinary matter or attract it, similarly for antimatter. Its all those
>>double and triple negatives that confuse the heck out of me.
>
> Right, they're confusing - and I never worked them out myself until we
> discussed this a couple of times here on sci.physics.research. But now
> I know how it goes. As long as general relativity applies:
>
> A positive-mass body will curve spacetime in a way that bends geodesics
> "towards" it, so it will *attract* other bodies regardless of the sign
> of their mass.
>
> A negative-mass body will curve spacetime in a way that bends geodesics
> "away from" it, so it will *repel* other bodies regardless of the sign
> of their mass.
This is consistent with taking the other sign for 2M in the
Schwarzschild solution. I suppose that was done.
> Now you've got all the necessary knowledge to take a crack at this:
>
> PUZZLE:
>
> Figure out what happens if you have two planets near each
> other: Earth and Anti-Earth, the first with positive mass, the
> second with an "equal but opposite" negative mass.
>
> (We've already discussed *everything* here. We've even been through
> a discussion before about how "equal and opposite" is a slightly stupid
> thing to say - but we all know what it means.)
Without looking up the answer, if it's going to be realistic then the
two have to be capable of erasing each other into some kind of
radiation. So they must be capable of forming some odd topogical
relation. This is like a magnetic pole in the vicinity of an electric one.
> -------------------------------------------------------------------------
> Puzzle #19:
>
> As of February 2004, five of the ten richest people in the world had
> the same last name. What is it?
This was too easy.
-drl
Ulmo
> > Now
> > general relativity has been tested by hundreds of experiments (with
> > which no other known theory of gravity completely agrees), so it would
> > be extremely surprising if antimatter did fall up.
>
> It would be surprising. However, the experiment needs to be done, and to
> state with certainty that antimatter will fall like matter is an incorrect
> thing to do in science.
>
It's also incorrect to make up a conjecture that violates well
established physics, and then refuse to believe it's not true unless
someone physically performs an experiment. The mass of an antiparticle
is identical to its corresponding particle, and there is no reason to
think they are effected by gravity any differently. You could just as
easily theorize that an elephant covered with peanut butter will fall
up when thrown off a cliff, and if someone remarks that that would
violate general relativity, retort "It would be surprising. However,
the experiment needs to be done, and to state with certainty that
elephants covered with peanut butter will fall like other objects is
an incorrect thing to do in science."
David
CCRyder
<ul...@cheerful.com> wrote:
Let's take just your first sentence's assertion and leave out the
elephant stuff.
If I could cite an instance of well established physics which is
believed by nearly everyone ever exposed to even the most mediocre
physics course and suggest or conjecture that the interpretation of the
data which has led people to believe in a certain behavior of matter
can be reanalyzed to yield a completely different hypothesis
(concerning this behavior) yet still provide the same data set then
would you change your mind?
Particularly if the extrapolation of the new hypothesis yields a
completely new physics that also is consistent with all known data and
physical phenomena?
To suppose that 'well established physics' is necessarily correct may
be precisely why physics as a discipline is mired in confusion and
complexity, and is presently not a finished science.
CCRyder
Danny Ross Lunsford
CCRyder wrote:
> If I could cite an instance of well established physics which is
> believed by nearly everyone ever exposed to even the most mediocre
> physics course and suggest or conjecture that the interpretation of the
> data which has led people to believe in a certain behavior of matter
> can be reanalyzed to yield a completely different hypothesis
> (concerning this behavior) yet still provide the same data set then
> would you change your mind?
>
> Particularly if the extrapolation of the new hypothesis yields a
> completely new physics that also is consistent with all known data and
> physical phenomena?
>
> To suppose that 'well established physics' is necessarily correct may
> be precisely why physics as a discipline is mired in confusion and
> complexity, and is presently not a finished science.
Well it's only natural to keep probing at the foundations. There is a
lot of subtle behavior in something like the Dirac equation. And there
are examples of statements in the texts that are plain wrong - for
example identifying the particle velocity as the operator Alpha and then
scratching the head when the eigenvalues come out to be +-c. It never
hurts to poke around in the basement.
-drl
Oz
Esa A E Peuha <esa....@helsinki.fi> writes
>What do you mean? In GR, any given object either attracts everything or
>repels everything gravitationally, so the gravitational interaction
>between matter and antimatter is definitely predicted no matter what we
>assume about the mass of antimatter (even if it turns out to be wrong).
OK, that's fine. We don't want to break GR as well!
Let's for the moment investigate what a body that repels everything
might look like. I have been castigated by a moderator who says that,
time-reversed or no: attractive bodies attract. The logic of this is to
time reverse a film. Bodies still follow the normal newtonian path,
which is completely true. I know this, I am not thinking straight.
A large repulsive body would have no stable orbits, its not a matter of
time reversal since that just means backwards orbits. A negative-mass
universe would be totally different from a positive mass universe,
although I guess electric and nuclear combinations will still form,
larger, gravitationally bound ones will not. There would be no stars and
very little interaction. I'm not even sure how one would interpret
energy, which on the face of it would be negative. One imagines that
this would produce an energy-free annihilation between a +ve and -ve
mass electron, which is not what we see.
That said, and all the other implausible scenarios that go with allowing
-ve mass matter, I am forced to conclude that the evidence for its
existence is on the 'very unlikely' side of 'very doubtful'.
Er ... if that's not a double negative too ...
Now I am confused again. Ross has claimed that antiparticles can be
considered as negative matter or time reversed (I hope not both
simultaneously). Given the implausibility of it being negative mass
matter, is it reasonable to take antiparticles as simply time-reversed
particles, since the other alternative doesn't look good at all?
Danny Ross Lunsford
> Some of you may enjoy this paper, or at least be infuriated by it:
>
> http://math.ucr.edu/home/baez/quantum/
>
> Quantum Quandaries: A Category-Theoretic Perspective
>
> John C. Baez
This is very nice!
A thing that always bugs me - quantum mechanics is really projective at
base, but using it requires positing an isometry. Now in ordinary
projective geometry this is accomplished by specifying a quadratic form
(a metric). If one considers all the projective transformations that
preserve this quadratic form, one gets a way to form projective
invariants that behave like metric invariants. One forms the cross ratio
of 4 points, two of which are given, and two of which are defined by the
intersection points of the line through the given points and the
quadratic form. One now has four points on a line and forms the "Klein
angle" as the imaginary log of their cross-ratio:
W = i log XR(A,S;B,S')
This is the closest you can get to physically sensing i :)
This allows a completely consistent definition of an isometry group and
associated metric geometry. The additive aspects of metric geometry come
from the additivity of exponents in a product!
Now people unconsciously apply just this process when orienting
themselves in space. They pick a quadratic form - the things that are
farthest away. One ignores the logical sense which says the tracks will
never converge and instead redefines the world so that convergence is
possible in an "ideal domain".
There must be an analogy in QM to "establishing the invariant quadratic
form". Something like insisting on the probability that SOMETHING
happens is 1.
-drl
r...@maths.tcd.ie
>Some of you may enjoy this paper, or at least be infuriated by it:
>http://math.ucr.edu/home/baez/quantum/
It makes very entertaining and educating reading. The last time I
looked at categories I gave up after a while because it seemed
cute but useless. Maybe I'll have another look.
>In particular,
>both Hilb and nCob but not Set are *-categories with a noncartesian
>monoidal structure. We show how this accounts for many of the famously
>puzzling features of quantum theory: the failure of local realism, the
>impossibility of duplicating quantum information, and so on. We argue
>that these features only seem puzzling when we try to treat Hilb as
>analogous to Set rather than nCob, so that quantum theory will make
>more sense when regarded as part of a theory of spacetime.
That claim is rather ambitious - from what I can see your solution
to the puzzles is merely to say just think about Hilbert spaces
and it'll be fine, which is the "shut up and calculate" approach
in disguise. You have definitely pinpointed one of the surprising
and perhaps disturbing aspects of quantum mechanics with the observation
that the product structure is noncartesian, although I think this
product discrepancy is known, if not understood so clearly, to anybody
who thinks about quantum mechanics.
The similarity of Hilb to relations rather than functions is
philosophically interesting as well, but I would say that overall,
the most puzzling features of quantum mechanics do not come from
its mathematical structures, but from from the thing which is not
expressed anywhere in the mathematics - the fact that individual
measurements have individual results, rather than mere amplitudes
of results.
"It is as if classical logic continued to apply to us, while the
mysterious rules of quantum theory apply only to the physical systems
we are studying. But of course this is not true: we are part of the
world being studied."
Here's a comment that most physicists won't like and will consider
useless philosophical rubbish, but which is true nonetheless: our
bodies are physical systems - parts of the world being studied, but
our minds are not.
R.
Oz
It has taken me a while to figure out what you might be saying.
Are you saying that time-reversed particles will head towards a
singularity and so you can't have the rather nice 4-spere symmetry at
the early stages of the universe because nothing can cross from -t to +t
and vice-versa (assuming a singularity at t=0)? I put this in typical
crude Oz-style.
I'm not quite sure that is necessarily precisely correct (he says in
fear and trepidation), although it took me several minutes to work out
why I thought it so. Naturally my explanation will be a tad confused,
and probably unclear, but no matter.
Obviously if matter is to move through t=0 then it had better not go
through (0,0,0,0), but 'round' the singularity. That is when it gets
back to t=0, there had better be some space to get round
[space=/=(0,0,0)].
I assume backward-moving particles have their proper time reversed.
I'm not sure (as in I don't know) if reversing the proper time of a
bunch of particles (but not others) will result in everything returning
to where it was some time previously.
However I doubt, in a quantum mechanical world, whether a particle going
backwards is guaranteed to perfectly reverse all its quantum-mechanical
interactions. Well, it doesn't seem to going forwards, anyway: there is
a great deal of random processes that make this unlikely. There will be
a plethora of quantum mechanical processes between creation and the
'return' of a backwards-moving particle (which has likely only existed
for femtosecs or very much less).
That hopefully being so, then a particle going past t=0 is unlikely to
see everything conveniently coming together in perfect unison to
precisely produce a singularity. In fact I would hazard a guess that
it's very highly improbable. Sure it will go through a high-density
region, but not a singularity. There will be some space to go round.
I probably haven't expressed this well or accurately.
island
> John Baez wrote:
> > PUZZLE:
That assumes that an 'antiplanet' has the same characteristics as an
antiparticle, but antiparticles don't have the characteristics of
negative mass.
A negative mass object produces negative pressure because, like John
said... "a negative-mass body will curve spacetime in a way that bends
geodesics "away from" it"... which means that negative mass produces the
same effects as a positive cosmological constant.
~
Quoting from the Sci.Astro faqs:
http://www.astro.ucla.edu/~wright/cosmo_constant.html
"The magnitude of the negative pressure needed for energy conservation
is easily found to be P = -u = -rho*c2 where P is the pressure, u is the
vacuum energy density, and rho is the equivalent mass density using E =
m*c2.
But in General Relativity, pressure has weight, which means that the
gravitational acceleration at the edge of a uniform density sphere is
not given by
g = GM/R2 = (4*pi/3)*G*rho*R
but is rather given by
g = (4*pi/3)*G*(rho+3P/c2)*R
Now Einstein wanted a static model, which means that g = 0, but he also
wanted to have some matter, so rho > 0, and thus he needed P < 0. In
fact, by setting
rho(vacuum) = 0.5*rho(matter)
he had a total density of 1.5*rho(matter) and a total pressure of
-0.5*rho(matter)*c2 since the pressure from ordinary matter is
essentially zero (compared to rho*c2). Thus rho+3P/c2=0 and the
gravitational acceleration was zero,
g = (4*pi/3)*G*(rho(matter)-2*rho(vacuum))*R = 0
allowing a static Universe."
/quote
That's the reason why we get all those weird, contrdictory answers when
we try to posit an antimass particle into our world, because there
'ain't no such animal', because an antiparticle doesn't have -rho.
Both, Positrons and Electrons, are produced at the event horizon of a
Black Hole from virtual particle pairs. As with electric charge, this
means that the *normal* distribution of negative energy electrons does
not contribute to pair creation. Only *departures* from the normal
distribution in a vacuum will isolate enough vacuum energy to produce
virtual particle pairs. These pairs can be converted into real
particles if enough energy is introduced, but they do not have -rho if
they represent localized departures from the norm.
General relativity tells us that gravitation is essentially curvature
due to the energy contained in a region and pair production changes this
energy to the positve mass of particle pairs, so the 'departure' is
maintained in this manner. These departures cannot produce negative
curvature, so they cannot have negative mass, because the energy density
of these particles does *not* represent the background density.
The anti-electron has the same gravitational properties as an electron,
and the electron has a greater chance for survival, (thus maintaining
the departure, *indefinitely*), since it might be a long time before it
meets an antiparticle if its counterpart antiparticle gets sucked into
the black hole.
There will be a contribution -e for each occupied state of positive
energy and a contribution -e for each unoccupied state of negative
energy, because negative pressure increases in proportion to the hole
that the departures represent.
In other words, *both* particles leave "holes", not just one.
More from the faq:
-Einstein's Greatest Blunder
"However, there is a basic flaw in this Einstein static model: it is
unstable - like a pencil balanced on its point. For imagine that the
Universe grew slightly: say by 1 part per million in size. Then the
vacuum energy density stays the same, but the matter energy density goes
down by 3 parts per million. This gives a net negative gravitational
acceleration, which makes the Universe grow even more! If instead the
Universe shrank slightly, one gets a net positive gravitational
acceleration, which makes it shrink more! Any small deviation gets
magnified, and the model is fundamentally flawed."
That's not correct if the increase in mass-energy is offset by the
increase in negative pressure that results from the "departure", because
the vacuum expands naturally, as a function of rarefaction that results
from pair production, so the number of particles in the universe always
equals the square of the ratio of the electric and the gravitational
force between two electrons, as the number of particles in the universe
increases, while G remains constant.
Tension between ordinary matter and the vacuum increases when you
increase mass energy, while at the same time increasing negative
pressure by way of particle pair production.
"In addition to this flaw of instability, the static model's premise of
a static Universe was shown by Hubble to be incorrect. This led Einstein
to refer to the cosmological constant as his greatest blunder, and to
drop it from his equations. But it still exists as a possibility -- a
coefficient that should be determined from observations or fundamental
theory."
There is no instability if vacuum expansion is offset by an increase in
mass energy, as previuously described.
-The Quantum Expectation
"The equations of quantum field theory describing interacting particles
and anti-particles of mass M are very hard to solve exactly. With a
large amount of mathematical work it is possible to prove that the
ground state of this system has an energy that is less than infinity.
But there is no obvious reason why the energy of this ground state
should be zero. One expects roughly one particle in every volume equal
to the Compton wavelength of the particle cubed, which gives a vacuum
density of
rho(vacuum) = M4c3/h3 = 1013 [M/proton mass]4 gm/cc
For the highest reasonable elementary particle mass, the Planck mass of
20 micrograms, this density is more than 1091 gm/cc. So there must be a
suppression mechanism at work now that reduces the vacuum energy density
by at least 120 orders of magnitude."
One particle in every volume equal to the Compton wavelength of the
particle cubed'... describes the "depature", *not* the normal
distribution, which, a rough guess would put at about 120 orders of
magnitude greater.
"It never hurts to poke around in the basement"
-drl
"I think it'll be something that we've all missed"
-John Baez
"Such a variation lies outside ordinary general relativity, but can be
incorporated by a fairly simple modification of the theory"
-Steve Carlip
Danny Ross Lunsford
island wrote:
>>Without looking up the answer, if it's going to be realistic then the
>>two have to be capable of erasing each other into some kind of
>>radiation. So they must be capable of forming some odd topogical
>>relation. This is like a magnetic pole in the vicinity of an electric one.
>
> That assumes that an 'antiplanet' has the same characteristics as an
> antiparticle, but antiparticles don't have the characteristics of
> negative mass.
Well we don't know this yet :) We have to do that experiment...
> A negative mass object produces negative pressure because, like John
> said... "a negative-mass body will curve spacetime in a way that bends
> geodesics "away from" it"... which means that negative mass produces the
> same effects as a positive cosmological constant.
The usual Schwarzschild solution looks like (pardon sign and factor errors)
g44 = 1 - 2Gm/r
gij = -delta_ij - (2Gm yi yj/(r - 2Gm)
where yi = xi / r.
Formally replacing m->-m is again a solution to Rmn=0 with the -assumed-
wrong correspondence with the potential of Newtonian theory (because m
is in fact just an integration constant). Such a solution has no horizon
because g44 is always positive, so it certainly seems
curvature-distinguished from the usual solution. One would have to
repeat the work of Hoffmann, Infeld, and Einstein on ponderomotive
theory to find out how such a solution really behaves in the Newtonian
limit. Someone must have done this but I've never seen it...
-drl
Mike Stay
You compared Hilb and nCob in this paper, but it looks like any of the
matrix-mechanics-over-rigs structures from your fall 2003 qg notes
ought to work in the same way. Is that right?
Today I went to a lecture by V.S. Sunder, since the abstract sounded
so similar to what you wrote in this paper. Here it is:
"In recent work with my colleague Vijay Kodiyalam, we showed that
there is a bijective correspondence between Vaughan Jones' `subfactor
planar algebras' on the one hand, and what may be called `unitary
topological quantum field theories' defined on a category `D' on the
other, where the objects of `D' are suitably `decorated closed
oriented 1-manifolds' and the morphisms are similarly decorated
classes of cobordisms between a pair of objects.
Since the subject is slightly technical, it will help to give the talk
in two parts, with the first part devoted to a discussion of Vaughan's
planar algebras, and the second part to our work."
(I had to giggle at "slightly technical" after reading the first
paragraph, but he was right. It was mostly drawing nice pictures of
tangles.) I got it down to the end, but I missed the punchline. His
paper isn't online, so I'll have to see if I can figure it out during
the second lecture.
Anyway, here's what I got:
A tangle T has
1) An outer disk D0 minus an ordered (possibly empty) list of
subdisks.
2) A bunch of curves that divide up the interior into
checkerboard-colorable regions (equivalently, the boundaries of the
disks have an even number of curves ending on them).
3) A set of distinguished points: each disk boundary with at least one
curve intersecting it has one point, where white goes to black when
going clockwise around the disk, that is distinguished (denoted * in
the diagram)
4) "color": take the number of curves intersecting the outside edge
and divide by 2.
And a few other things I'll get to below.
So here is an example of a tangle:
---------------
-----...............-----
*--.........................--\
D0 ///|............................---\\
// |......................../--/ \\
// |....................---/ \\
// |................/--/ \\
/ /-----\........---/ \
/ // \\..---/ \
/ | +- \
/-------+ D1 | \
|........| | |
|.........| | |
|......../-*\ // ----------- |
|......../ \---+-/ //...........\\ |
|.......| |.| //...............\\ |
|.........\ /..| /...................\ |
|..........\---/...| |.....................| |
|..................| |........-----........| |
|..................| |.......// \\.......| |
|..................| |......| |......| |
|..................| |......| D3 |......| |
|..................| |......| |......| |
|............./----+\ |......\\ //......| |
|..........// \\ |........-----........| |
|.........| | \.................../ |
+--------* | \\...............// |
| | D2 | \\...........// |
| | | ----------- |
\ \\ // /
\ \---+-/..\\ /
\ |......\\ /
\ |........\\ /
\\ |..........\\ //
\\ |............\\ //
\\ |..............\\ //
\\\ |................\\ ///
\+-.................\\ --/
-----..............\-----
---------------
Subdisks are "inputs" and the outer boundary is the "output" of the
tangle. There's a natural way to compose tangles: if the input and
output are colored the same, match up the *'s and the curves.
Here is a tangle M(3):
---*--+--+---
----- |..| |...-----
///- |..| |........-\\\
// |..| |............\\
// |..| |..............\\
// |..| |................\\
/ *--+--+-.................\
// // \\................\\
/ / \.................\
/ | |.................\
| | D1 |................|
| | |.................|
| | |..................|
| | |...................|
| \ /.....................|
| \\ //......................|
| +--+--+-........................|
| |..| |.........................|
| |..| |.........................|
| -*--+--|.........................|
| //- -\\.......................|
| // \\.....................|
| / \...................|
| | |...................|
| | |.................|
| | D2 |................|
\ | |................/
\ | |.............../
\\ | |..............//
\ \ /............./
\\ \\ //............//
\\ \\- -//............//
\\ +-+-+--.............//
\\\- |.| |...........-///
----- |.| |......-----
--+-+-+------
It takes two 3-colored tangles X, Y as input and outputs a 3-colored
tangle. We can call it multiplication and denote the output as XY.
Annular tangles have one subdisk. An annular tangle A(m,n) is a
tangle with an m-colored input and an n-colored output. Here is the
identity(3,3) tangle:
-*--+--+---
/--- |..| |...---\
// |..| |.......\\
// |..| |.........\\
/ |..| |...........\
/ *--+--+-...........\
/ // \\..........\
| // \\.........|
| / \........|
| | |.........|
| | |........|
| | |........|
| | |........|
| | |.........|
| \ /........|
| \\ //.........|
\ \\ //........../
\ +---+--+.........../
\ |...| |........../
\\ |...| |........//
\\ |...| |......//
\--- |...| |..---/
-+---+--+--
Then there are tangles with no subdisks. A function from a
zero-dimensional vector space to an n-dimensional one is really just
scalar multiplication. So here's 1(3):
----+----+
//*-....| |--\\
// |.....| |....\\
/ |.....| |......\
/ |.....| |.......\
/ |.....| |........\
| |.....| |.........|
| |.....| |..........|
| |.....| |..........|
| |.....| |..........|
| |.....| |..........|
| |.....| |..........|
| |.....| |..........|
| |.....| |.........|
\ |.....| |......../
\ |.....| |......./
\ |.....| |....../
\\ |.....| |....//
\\+-....| |--//
----+----+
There's a conjugation operator * that's the following steps: reflect,
then move all the *'s counterclockwise (in the original drawing,
clockwise in the reflected one) one position on the disk boundary. So
M*(3) is (note the subdisk labels)
---*--+--+---
----- |..| |...-----
///- |..| |........-\\\
// |..| |............\\
// |..| |..............\\
// |..| |................\\
/ *--+--+-.................\
// // \\................\\
/ / \.................\
/ | |.................\
| | D2 |................|
| | |.................|
| | |..................|
| | |...................|
| \ /.....................|
| \\ //......................|
| +--+--+-........................|
| |..| |.........................|
| |..| |.........................|
| -*--+--|.........................|
| //- -\\.......................|
| // \\.....................|
| / \...................|
| | |...................|
| | |.................|
| | D1 |................|
\ | |................/
\ | |.............../
\\ | |..............//
\ \ /............./
\\ \\ //............//
\\ \\- -//............//
\\ +-+-+--.............//
\\\- |.| |...........-///
----- |.| |......-----
--+-+-+------
I.e. (XY)* = Y*X*.
We get an algebra out of tangles with no subdisks by making the disks
into squares with the * in the upper left, and half the curve
endpoints on top, half on bottom. So 1(3) also looks like this:
| | |
+------*------+-------+--------+
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
| |......| |........|
+------+------+-------+--------+
| | |
Multiplication is just stacking these; inputs are on top, outputs on
bottom.
Sometimes you get loops:
| | |
+-*----+------+------+
| |....| |......|
| \__/ |......|
| /......|
| /.......|
| /........|
| /.........|
| /..........|
| /...__......|
| /.../ \.....|
| |...| |....|
+------+---+----+----+
| | | <----- like this
+------*---+----+----+
| |...| |....|
| \...\__/.....|
| \...........|
| \..........|
| \.........|
| \........|
| \.......|
| ___ \......|
| /...\ |.....|
| |.....| |.....|
+--+-----+-----+-----+
| | |
When you do, you multiply by a constant, delta. This was the
important part that I missed. Something special happens when delta is
of the form
delta = cos 4pi/n (I think)
which has something to do with Vaughan Jones' subfactor planar
algebras. I didn't get all the details, and now I can't remember.
Does anyone know?
Next week I'll see how this works with cobordisms and TQFT's.
P.S. ASCII art courtesy of Email Effects. Great stuff, even includes
figlet fonts. http://www.sigsoftware.com/emaileffects/
--
Mike Stay
Igor Khavkine
> A positive-mass body will curve spacetime in a way that bends geodesics
> "towards" it, so it will *attract* other bodies regardless of the sign
> of their mass.
>
> A negative-mass body will curve spacetime in a way that bends geodesics
> "away from" it, so it will *repel* other bodies regardless of the sign
> of their mass.
>
> Now you've got all the necessary knowledge to take a crack at this:
>
> PUZZLE:
>
> Figure out what happens if you have two planets near each
> other: Earth and Anti-Earth, the first with positive mass, the
> second with an "equal but opposite" negative mass.
Going on what's written above, I think Anti-Earth will be attracted
to Earth, while Earth will be repelled by Anti-Earth. As a result,
they will both start moving, Earth running away from Anti-Earth and
Anti-Earth trying to catch up. This situation is rather strange since
the overall momentum of the system is not conserved so something
is fishy here. (Yes, I know that momentum need not be conserved in GR,
but lets assume weak fields, and whatever niceties that allow it). This
effect is in principle observable, but I have not heard any such
observations.
Also, if negative masses repell each other, we wouldn't find any really
large clumps of it around, since they would be unstable.
Igor
John Baez
Oz <o...@farmeroz.port995.com> wrote:
>John Baez <ba...@galaxy.ucr.edu> writes:
>>As long as general relativity applies:
>>
>>A positive-mass body will curve spacetime in a way that bends geodesics
>>"towards" it, so it will *attract* other bodies regardless of the sign
>>of their mass.
>>
>>A negative-mass body will curve spacetime in a way that bends geodesics
>>"away from" it, so it will *repel* other bodies regardless of the sign
>>of their mass.
In short:
a positive-mass body attracts EVERYTHING;
a negative-mass body repels EVERYTHING.
>That strikes me as very reasonable. Of course we must be careful to
>distinguish between a positive and negative inertia, too. In this sort
>of scenario I don't think we can assume mass and inertia will
>necessarily be either the same, or a different, sign.
I'm assuming general relativity holds. Given that, the equivalence
principle says mass and inertia are the same. If we don't assume
general relativity holds, all bets are off - we just have to do the
experiment.
>Fortunately in GR
>when following a geodesic, there is no acceleration so this can be
>conveniently swept under the carpet.
Yes: that's a more elegant way of saying the equivalence principle holds.
>>Now you've got all the necessary knowledge to take a crack at this:
>Oh .. my .. god! He never changes! Straight into homework.
Heh - but this is an easy one, just for old time's sake.
>>PUZZLE:
>>
>> Figure out what happens if you have two planets near each
>> other: Earth and Anti-Earth, the first with positive mass, the
>> second with an "equal but opposite" negative mass.
>I expect we will have the 'accelerate across the universe' scenario...
>
>This needs some thought. I trust you are not expecting me to solve an
>equivalent of schild metric for this scenario?
No, I don't expect miracles - just a little logic!
>I assume embedded in an otherwise empty flat spacetime. For convenience
>I will consider the masses as point particles.
Good.
>Now what?
Now solve the problem.
>Well, there will be a point halfway between the two which will be
>locally flat. Eh? No, that can't be right. A test particle on the
>repulsive body will fall straight down and hit the attractive one, since
>it will be repelled by the repulsive and attracted by the attractive.
Hmm, you've certainly managed to make it more complicated by
introducing this unnecessary "test particle". Now *I'm* confused!
>So if both bodies were dust then the repulsive one would expand and the
>attractive one would collapse.
You assumed they were points a minute ago, so there's no
need to worry about what would happen if they were made of dust -
though you're perfectly right about what *would* happen!
>If they were solid enough to resist
>gravitational forces then they clearly would accelerate across the
>universe, trailing their gravitational fields behind them.
Right! Excellent!
The positive mass Earth attracts the negative mass Anti-Earth.
The negative mass Anti-Earth repels the positive mass Anti-Earth.
Since they have "equal and opposite mass", they both accelerate
in the same direction at the same rate.
So, the Anti-Earth chases the Earth faster and faster, approaching
the speed of light... but never catches it.
And energy is conserved, since the total kinetic energy is zero
no matter how fast they're going!
>If they were orbiting each other as well, then they would have a
>complex circular path (probably).
Oh??
This is fun to think about, but I'm highly dubious of this idea of
particles of opposite mass "orbiting" each other. Do you see why?
>What if they were different sized masses?
This is even *more* fun.
>Well a -m particle would orbit a large +m particle, but presumably in
>its immediate vicinity space would be less curved.
You can do all these problems with Newtonian gravity as long as
nothing goes too fast and none of your point masses get too close.
You should do them this way before worrying about fancy "spacetime
curvature" effects.
>I think this means it
>has a slightly larger orbit. The two bodies will orbit round a centre of
>mass that will be outside the line between them. This will be a patch of
>flat spacetime. For an infinitely small orbiting mass, the only patch of
>flat spacetime (not at inf) will be the saddle on the major body,
>clearly a -ve mass will push this further away from the -ve particle.
I'm not sure what you mean here - let's keep things simple and
Newtonian for a while; we'll have enough fun that way.
In the Newtonian approximation, the center of mass of our two particles
will move along a straight line at constant speed. This is conservation
of momentum, so it holds no matter what the signs of the masses - under
our default assumption that GR still works.
But: what's the center of mass of a positive mass particle and a
negative mass particle?
>As their masses tend to being equal and opposite then this patch will
>recede to infinity and we get the 'follow my leader' scenario again.
>
>My head hurts ....
Yeah, it's tough. The math works just as well when you change
the signs in these problems. The hard part, but the fun part,
is to solve them using "intuition".
>>By the way, it currently seems like I'll be in Oxford this July 7-9,
>>to speak at the Workshop on Gerbes: Recent Developments and Future
>>Perspectives, at Oxford, organized by Nuno Reis. So, maybe we can
>>get together while I'm there.
>Should be fine.
>I can't contact you, but you can contact me using reply-to of this post.
Okay, I'll contact you shortly after I arrive in Cambridge on July 1st.
alistair
>> other: Earth and Anti-Earth, the first with positive mass, the
>> second with an "equal but opposite" negative mass.
If you had a universe made of just two large masses, one negative mass
and the other positive,the two masses would oscillate towards and away
from one another perpetually (unless they started out static at
maximum separation, in which case they would keep at a fixed
distance).
Ken S. Tucker
Sorry to interrupt, this is fun, in view of symmetry.
>In article <ZM6JLBCV...@btopenworld.com>,
>Oz <o...@farmeroz.port995.com> wrote:
>>John Baez <ba...@galaxy.ucr.edu> writes:
>>>As long as general relativity applies:
>>So if both bodies were dust then the repulsive one would expand and the
>>attractive one would collapse.
>
>You assumed they were points a minute ago, so there's no
>need to worry about what would happen if they were made of dust -
>though you're perfectly right about what *would* happen!
Using Old Newton's Force = - G (M) (m) /r^2 the universe
would behave the same if one used (-M) and (-m) in Newtons,
so I think there is no easy way to decide if mass/energy is positive
or negative. So I think a negative energy "dust cloud" would
condense as a positive energy cloud.
To satisfy GR, we should presume a photon, born
from negative energy would possess negative energy,
and deflect in the the negative mass universe as it would
presuming positive mass. (?)
IOW's could we do an experiment to determine the
polarization of the scalar "mass"?
Ken S. Tucker
PS: snippable, there is interesting symmetry in the
+/- mass universe. But if you really want a repulsive
dust cloud you would need (i = sqrt(-1))
F' = - G(Mi)(mi)/r^2 = + G(M)(m)/r^2
(last term is repulsive because of the +)
and it looks like that universe would be equal to
ours if the "arrow of time" were to reverse to
convert F' to F.
kst
Dushan Mitrovich
`ba...@galaxy.ucr.edu (John Baez) wrote in message news:<c4vns4$il1$1...@glue.ucr.edu>...
`
`> A positive-mass body will curve spacetime in a way that bends geodesics
`> "towards" it, so it will *attract* other bodies regardless of the sign
`> of their mass.
`>
`> A negative-mass body will curve spacetime in a way that bends geodesics
`> "away from" it, so it will *repel* other bodies regardless of the sign
`> of their mass.
`> Now you've got all the necessary knowledge to take a crack at this:
`>
`> PUZZLE:
`>
`> Figure out what happens if you have two planets near each
`> other: Earth and Anti-Earth, the first with positive mass, the
`> second with an "equal but opposite" negative mass.
` Going on what's written above, I think Anti-Earth will be attracted
` to Earth, while Earth will be repelled by Anti-Earth. As a result,
` they will both start moving, Earth running away from Anti-Earth and
` Anti-Earth trying to catch up. This situation is rather strange since
` the overall momentum of the system is not conserved so something
` is fishy here. (Yes, I know that momentum need not be conserved in GR,
` but lets assume weak fields, and whatever niceties that allow it). This
` effect is in principle observable, but I have not heard any such
` observations.
What 'overall momentum'? The total mass is zero.
- Dushan Mitrovich
Charles Francis
writes
>In article <ZM6JLBCV...@btopenworld.com>,
>Oz <o...@farmeroz.port995.com> wrote:
>
>>John Baez <ba...@galaxy.ucr.edu> writes:
>
>>>As long as general relativity applies:
>>>
>>>"towards" it, so it will *attract* other bodies regardless of the sign
>>>of their mass.
>>>
>>>A negative-mass body will curve spacetime in a way that bends geodesics
>>>"away from" it, so it will *repel* other bodies regardless of the sign
>>>of their mass.
Huh, I've missed something. Mass is generally a magnitude, hence
positive.
>
>In short:
>
>a positive-mass body attracts EVERYTHING;
>a negative-mass body repels EVERYTHING.
Well, if you say so.
>
>>>PUZZLE:
>>>
>>> Figure out what happens if you have two planets near each
>>> other: Earth and Anti-Earth, the first with positive mass, the
>>> second with an "equal but opposite" negative mass.
>
>>If they were solid enough to resist
>>gravitational forces then they clearly would accelerate across the
>>universe, trailing their gravitational fields behind them.
>
>Right! Excellent!
Is it?
>The positive mass Earth attracts the negative mass Anti-Earth.
>The negative mass Anti-Earth repels the positive mass Anti-Earth.
>
But since active gravitational mass is normally the same as passive
gravitational mass the positive mass Earth should attract the negative
mass anti-Earth negatively. I.e. it repels it, so we have the opposite
of em, like masses attract, unlike repel.
>negative mass particle?
>
>>As their masses tend to being equal and opposite then this patch will
>>recede to infinity and we get the 'follow my leader' scenario again.
>>
>>My head hurts ....
>
>Yeah, it's tough. The math works just as well when you change
>the signs in these problems. The hard part, but the fun part,
>is to solve them using "intuition".
Certainly math which isn't formalised intuition is no fun. And not much
use either in my book.
Regards
--
Charles Francis
Charles Francis
<o...@farmeroz.port995.com> writes
>So perhaps better to take antiparticles as particles going backwards in
>time? Or are you able to show that this has flaws too?
No, it has no mathematical flaws. It's quite simple mathematically.
Regards
--
Charles Francis
Arnold Neumaier
> In article <ZM6JLBCV...@btopenworld.com>,
> Oz <o...@farmeroz.port995.com> wrote:
>
>
>>John Baez <ba...@galaxy.ucr.edu> writes:
>
>
>>>As long as general relativity applies:
>>>
>>>A positive-mass body will curve spacetime in a way that bends geodesics
>>>"towards" it, so it will *attract* other bodies regardless of the sign
>>>of their mass.
>>>
>>>A negative-mass body will curve spacetime in a way that bends geodesics
>>>"away from" it, so it will *repel* other bodies regardless of the sign
>>>of their mass.
>
>
> In short:
>
> a positive-mass body attracts EVERYTHING;
> a negative-mass body repels EVERYTHING.
This sounds paradoxical - it would mean a positive-mass body attracts
a negative-mass body, while the latter repels the former.
Probably they are chasing after each other???
But shouldn't we have actio = reactio? So:
Do they get closer to each other or farther apart if initially they
are at rest with respect to each other?
To which extent is the general relativistic 2-body problem solved?
Arnold Neumaier
Esa A E Peuha
> Going on what's written above, I think Anti-Earth will be attracted
> to Earth, while Earth will be repelled by Anti-Earth. As a result,
> they will both start moving, Earth running away from Anti-Earth and
> Anti-Earth trying to catch up.
Right.
> This situation is rather strange since
> the overall momentum of the system is not conserved so something
> is fishy here.
Wrong. Total momentum is most definitely conserved: momentum of Earth
is m_Ev and momentum of Anti-Earth is m_Av, so total momentum is
(m_E + m_A)v which is zero since m_E + m_A is zero.
Charles Francis
<aco...@btopenworld.com> writes>Ooohhh... that'll raise some eyebrows...
>
>>If one takes this seriously, then one has to consider the Schwarzschild
>>solution with the integration constant corresponding to the mass of the
>>body taken to have the opposite sign. Matter and antimatter would then
>>definitely be distinguised gravitationally.
Actually not. I like to think of (m,0,0,0) as representing the rest
momentum of a particle. An antiparticle has negative m, so is
represented by a vector pointing backwards in time. The active
gravitational effect is the same as for a positive m particle
represented by a vector pointing forwards in time.
>
>Ooooohhh ... not mainstream (but in many ways nice).
>Note that this matches well with Charles Francis' formulation of
>teleparallel quantum gravity and the naive particle-antiparticle BB
>radiation.
Ouch. I didn't think so.
>
>>*Should* we take it seriously?
Yes, but we have to be *very* careful about signs.
>
>Am I to interpret this as a statement that its mathematically more
>elegant to take antiparticles as having negative mass but moving forward
>in time?
No, you can't do that. They have negative mass moving backwards in time,
and this manifests as positive mass moving forwards in time.
Regards
--
Charles Francis
Charles Francis
<o...@farmeroz.port995.com> writes
>I assume backward-moving particles have their proper time reversed.
Yes.
>I'm not sure (as in I don't know) if reversing the proper time of a
>bunch of particles (but not others) will result in everything returning
>to where it was some time previously.
?
>
>However I doubt, in a quantum mechanical world, whether a particle going
>backwards is guaranteed to perfectly reverse all its quantum-mechanical
>interactions.
Something about weak interactions, but otherwise it's perfect
>
>That hopefully being so, then a particle going past t=0 is unlikely to
>see everything conveniently coming together in perfect unison to
>precisely produce a singularity.
I don't see why not, except that I doubt it is possible to talk of time
and space in the same way near the singularity. That is to say I expect
the physics to break down *before* you get to the mathematical
singularity.
Regards
--
Charles Francis
Tim S
> ba...@galaxy.ucr.edu (John Baez) wrote in message
> news:<c5fcj8$6ua$1...@glue.ucr.edu>...
>
> Sorry to interrupt, this is fun, in view of symmetry.
>
>> In article <ZM6JLBCV...@btopenworld.com>,
>> Oz <o...@farmeroz.port995.com> wrote:
>>> John Baez <ba...@galaxy.ucr.edu> writes:
>>>> As long as general relativity applies:
>
>>> So if both bodies were dust then the repulsive one would expand and the
>>> attractive one would collapse.
>>
>> You assumed they were points a minute ago, so there's no
>> need to worry about what would happen if they were made of dust -
>> though you're perfectly right about what *would* happen!
>
> Using Old Newton's Force = - G (M) (m) /r^2 the universe
> would behave the same if one used (-M) and (-m) in Newtons,
No! The _force_ would be the same, but the acceleration would be different.
There's only one m in F=ma.
Tim
Charles Francis
>John Baez <ba...@galaxy.ucr.edu> writes
>>
>>Now you've got all the necessary knowledge to take a crack at this:
>
Now you see where I get it from.
>
>So if both bodies were dust then the repulsive one would expand and the
>attractive one would collapse. If they were solid enough to resist
>gravitational forces then they clearly would accelerate across the
>universe, trailing their gravitational fields behind them. If they were
>orbiting each other as well, then they would have a complex circular
>path (probably).
I think there is a missing minus sign. A negative mass particle moves
backwards in time, according to the rest momentum vector, (m,0,0,0). But
the active gravitational mass (effect on curvature) depends on the
magnitude of this vector.
>>>One has a horrible feeling that even devising a test to determine if
>>>negative mass exists might be difficult.
antiparticles are observed.
Regards
--
Charles Francis
Oz
Its an odd thing, but I find this an interesting concept.
However, whenever I try and discuss it here there is a dearth of replies
as if the experts are in some way afraid of it.
I suspect the reason may be that one of necessity seem to have to reject
a minkowski spacetime if you are to include QM, and this is surely by
its very nature a qm 'feature'. I am not very convinced, in fact I have
convinced myself of the reverse, that the worldines of 'backward
running' particles do NOT see global time reversed. The trouble is that
this also implies that particles taking a different (relativistic) path
probably don't see all other paths taking a time-reversible (or do I
mean trajectory-reversible?) path either (in a curved spacetime).
In a way its just an extension of the problems of having global
anything-much in a curved spacetime. Does a 'global time' in GR even
make sense even before you allow backward-time-running particles? I
suspect not.
That has quite interesting possibilities, but I don't know enough to
refine, or even accurately say, what it is I am trying to say in the
clear unambiguous way that so many experts require.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
DEMON address no longer in use.
BTOPENWORLD address about to cease.
>>Use o...@farmeroz.port995.com (whitelist check on first post)<<
Matthew Donald
John Baez wrote
> Some of you may enjoy this paper, or at least be infuriated by
> it:
> http://math.ucr.edu/home/baez/quantum/
> Quantum Quandaries: A Category-Theoretic Perspective
It has now also appeared as quant-ph/0404040
I both did enjoy it and I was infuriated by it.
At
http://www.poco.phy.cam.ac.uk/~mjd1014/readings.html
I keep a page with comments on some of the papers available
from the physics e-print archive which are relevant, or
significant, or recommended in the broad context of my
many-minds interpretation of quantum theory. Here's what I've
written for that page about John's paper:
> J.C. Baez, ``Quantum Quandaries: a Category-Theoretic
> Perspective'' quant-ph/0404040.
>
> Baez describes similarities between a category significant for
> quantum theory and one significant for general relativity. The
> similarities are at the level of abstract mathematical structure.
> Baez claims that the mathematics ``accounts for many of the
> famously puzzling features of quantum theory''. This is correct
> only in the sense that the mathematics provides a framework
> within which those puzzling features somehow arise. It does not
> address the most puzzling questions: specific questions like
> ``Precisely what might we see happening next?'' and ``Precisely
> how is what we might see restricted by what we are, or by what
> we do?''.
You'll see from this that I am largely in agreement with the
comments made by R (r...@maths.tcd.ie)
-- but only largely -- in as far as R wrote
> I would say that overall, the most puzzling features of
> quantum mechanics do not come from its mathematical
> structures, but from the thing which is not expressed
> anywhere in the mathematics - the fact that individual
> measurements have individual results, rather than mere
> amplitudes of results.
I would have said ``the fact that individual measurements appear
to us to have individual results''.
R also quoted some of the passage in which John most
``infuriated'' me:
> the famously counter-intuitive behavior of the microworld
> suggests that not only set theory but even classical logic is not
> optimized for understanding quantum systems. While there are
> no real paradoxes, and one can compute everything to one's
> heart's content, one often feels that one is grasping these
> systems `indirectly', like a nuclear power plant operator
> handling radioactive material behind a plate glass window with
> robot arms. This sense of distance is reflected in the endless
> literature on `interpretations of quantum mechanics', and also in
> the constant invocation of the split between `observer' and
> `system'. It is as if classical logic continued to apply to us,
> while the mysterious rules of quantum theory apply only to the
> physical systems we are studying. But of course this is not
> true: we are part of the world being studied.
The trouble with statements like this is knowing what it could
mean for classical logic not to apply to us.
Saying that some sort of quantum logic applies hardly answers
the question. If you try to unpack an answer, then I think you
will end up contributing to the ``endless literature''.
Originally, quantum logic suggested that the Boolean algebra of
conventional logic ought to be replaced by the non-Boolean
algebra of projections on a Hilbert space. This is an interesting
and insightful analogy. But what exactly does it do for us?
The part of the endless literature called ``consistent
histories'' tries to analyse classes of sequences of projections
constituting situations in which we could continue to apply
classical logic. It fails because there are far too many
such situations. This means, in particular, that there is no way
of knowing what the possible continuations of a given history
should be, unless a specific set of future possibilities is
somehow given a priori.
In this context, invoking quantum logic, which will widen, rather
than restrict, the set of possible histories, seems to me to be
unhelpful.
In his paper, Baez
> suggests that the interpretation of quantum theory will
> become easier, not harder, when we finally succeed in
> merging it with general relativity.
My take is a bit different. I suspect that the interpretative
problems of quantum gravity will only become addressable if
we first address the problems of the interpretation of
conventional quantum theory.
One of the ways that this might happen is that we might come to
accept that the interpretation of quantum theory has to be
applied to entities (``observers'') which are local both in space
and in time. This might allow us to accept that conventional
ideas about space and time only need to be applied to the
observations of individual local observers. (If we accept, for
example, that the big bang didn't ``happen'', because there was no
when for it to happen in and that it exists only as a singularity in
extrapolations from our observations, then it might become
easier to contemplate superpositions of ``initial'' temporal
singularities.)
In Baez's paper, there is a suggestion that locality might
amount to triviality:
> a passage of time in which no topology change occurs has no
> effect at all on the state of the universe. This seems
> paradoxical at first, since it seems we regularly observe things
> happening even in the absence of topology change. However,
> this paradox is easily resolved: a topological quantum field
> theory describes a world without local degrees of freedom. In
> such a world, nothing local happens, so the state of the universe
> can only change when the topology of space itself changes.
Although John goes on to describe this as a ``peculiarity of
topological quantum field theory'', in fact, his paper doesn't talk
about ``observation'' at all. And in a flat space many-worlds
theory also, nothing happens without observation. The
Heisenberg state of the universe just is.
Later Baez says
> unitary time evolution is not a built-in feature of quantum
> theory but rather the consequence of specific assumptions
> about the nature of spacetime
Am I right in thinking that natural assumptions (Hadamard
states, for example) imply local unitarity? (I'll read that as
locally ``nothing is happening without observation''.)
It seems to me that the analogy between nCob and Hilb is mainly
likely to be helpful in talking about global structure. But the
puzzling features of quantum theory are local.
Matthew Donald (matthew...@phy.cam.ac.uk)
web site:
http://www.poco.phy.cam.ac.uk/~mjd1014
``a many-minds interpretation of quantum theory''
*****************************************
Zig
>>>Figure out what happens if you have two planets near each
>>>other: Earth and Anti-Earth, the first with positive mass, the
>>>second with an "equal but opposite" negative mass.
>
> The positive mass Earth attracts the negative mass Anti-Earth.
> The negative mass Anti-Earth repels the positive mass Anti-Earth.
>
> Since they have "equal and opposite mass", they both accelerate
> in the same direction at the same rate.
>
> So, the Anti-Earth chases the Earth faster and faster, approaching
> the speed of light... but never catches it.
>
> And energy is conserved, since the total kinetic energy is zero
> no matter how fast they're going!
>
>
>
>
> You can do all these problems with Newtonian gravity as long as
> nothing goes too fast and none of your point masses get too close.
>
> You should do them this way before worrying about fancy "spacetime
> curvature" effects.
>
OK, hang on here! I tried this with Newton's Universal Law of
Gravitation, and did not get the result you claim.
F_12=-GM_1M_2/r^2*hat{r}_12
where F_12 is the force particle 1 exerts on particle 2, M_1 is the mass
of particle 1, M_2 is the mass of particle 2, and hat{r}_12 is the unit
vector r2-r1/|r2-r1| pointing from r1 to r2
i have a mass 1 of +m at x=0 and mass 2 -m at x=r. for the force
particle 1 exerts on particle 2, hat{r}_12=hat{x}, and F12=Gm^2/r^2
on the other hand, for the force particle 2 exerts on particle one, the
unit vector hat{r}_21=-hat{x}, so i get the negative of the previous
result: F_21=-Gm^2/r^2
in other words, the two particles don't go in the same direction, they
go in opposite directions (as Newton's third law requires). The
difference between this case and the normal positive mass case is that
the two particles repel, instead of attract. Like masses attract,
opposite masses repel. It's Coulomb's Law with an extra minus sign
thrown in.
[Moderator's note: It's incorrect to say that the two particles "go"
in opposite directions. The forces are in opposite directions, but
since the inertial masses have opposite signs, the accelerations are
in the same direction. -TB]
Italo Vecchi
>
> In short:
>
> a positive-mass body attracts EVERYTHING;
> a negative-mass body repels EVERYTHING.
>
Huh. So in a negative mass world masses repel each other, as do
positive and negative charges (positive force on negative mass), while
same sign charges attract each other(negative force on negative mass).
It's like a movie playing backwards.
IV
Oz
>In article <c5hn29$uj1$1...@lfa222122.richmond.edu>, Oz
><o...@farmeroz.port995.com> writes
>
>>I assume backward-moving particles have their proper time reversed.
>
>Yes.
>
>>I'm not sure (as in I don't know) if reversing the proper time of a
>>bunch of particles (but not others) will result in everything returning
>>to where it was some time previously.
>
>?
>>
>>However I doubt, in a quantum mechanical world, whether a particle going
>>backwards is guaranteed to perfectly reverse all its quantum-mechanical
>>interactions.
>
>Something about weak interactions, but otherwise it's perfect
How do we know? One presumes that for a time-reversed particle,
backwards time seems precisely the same as particles see forward time.
Since the behaviour of an individual particle is not precisely
predictable in forward time, why should it be so for backwards-running
particles? Quantum behaviour is inherently unpredictable, and should be
so in both time directions.
So, if we are to have time-reversed particles then QM should break the
perfection of the past. That is, I think I am groping myself towards
believing that spacetime itself is somehow local to a body (or
particle). I don;t see how else you can generalise QM with reversed-time
particles making forward and backwards symmetrical.
The problem we have is that we have no real idea of the detail, since
(to a high degree of perfection) we live in a world entirely populated
by forward-travelling particles.
Its a bit of a mindbender, but surely someone has seriously considered
it before.
>>That hopefully being so, then a particle going past t=0 is unlikely to
>>see everything conveniently coming together in perfect unison to
>>precisely produce a singularity.
>
>I don't see why not,
Well, it breaks the unpredictability of QM. Why should QM be
unpredictable in our time direction, but predictable in a reversible
direction?
Charles Francis
<o...@farmeroz.port995.com> writes
>Charles Francis <cha...@clef.demon.co.uk> writes
>>In article <c4v8t3$dk2$1...@lfa222122.richmond.edu>, Oz
>><o...@farmeroz.port995.com> writes
>>>So perhaps better to take antiparticles as particles going backwards in
>>>time? Or are you able to show that this has flaws too?
>>
>>No, it has no mathematical flaws. It's quite simple mathematically.
>
>Its an odd thing, but I find this an interesting concept.
>
>However, whenever I try and discuss it here there is a dearth of replies
>as if the experts are in some way afraid of it.
Yes, but I don't really know why, except that it is the fashion to shy
away from interpretation. They like to think the formulae are enough for
a scientific theory. I don't. I think we need interpretation.
>
>I suspect the reason may be that one of necessity seem to have to reject
>a minkowski spacetime if you are to include QM,
No, we can do relativistic qm if we tip toe through the nasties. It's
curved space-times that cause fundamental problems.
>. I am not very convinced, in fact I have
>convinced myself of the reverse, that the worldines of 'backward
>running' particles do NOT see global time reversed.
I don't see how you get that. To me that is what "backward running"
means.
> The trouble is that
>this also implies that particles taking a different (relativistic) path
>probably don't see all other paths taking a time-reversible (or do I
>mean trajectory-reversible?) path either (in a curved spacetime).
Let's stick with flat space-times here. That should be pretty good as
space-time is locally Minkowski and qm generally deals in local effects.
In this case paths are time reversible, and in time reversal particles
get switched to antiparticles.
>
>In a way its just an extension of the problems of having global
>anything-much in a curved spacetime. Does a 'global time' in GR even
>make sense even before you allow backward-time-running particles? I
>suspect not.
The only "global time" in gr is cosmological time, which is really just
proper time for particles emanating straight from the big bang. But
really its just a load of proper times, not a global time.
Regards
--
Charles Francis
John Baez
Igor Khavkine <k_ig...@lycos.com> wrote:
>ba...@galaxy.ucr.edu (John Baez) wrote in message
>news:<c4vns4$il1$1...@glue.ucr.edu>...
>> PUZZLE:
>>
>> Figure out what happens if you have two planets near each
>> other: Earth and Anti-Earth, the first with positive mass, the
>> second with an "equal but opposite" negative mass.
>
Going on what's written above, I think Anti-Earth will be attracted
>to Earth, while Earth will be repelled by Anti-Earth. As a result,
>they will both start moving, Earth running away from Anti-Earth and
>Anti-Earth trying to catch up.
Right!
>This situation is rather strange since
>the overall momentum of the system is not conserved so something
>is fishy here.
Eh? Momentum is indeed conserved. In the Newtonian limit, it's just
mass times velocity; the Earth and Anti-Earth have the same velocity
but opposite mass, so the momentum is zero!
In the Newtonian limit the kinetic energy of this funny system is also
zero, and the potential energy doesn't change because the distance
between Earth and anti-Earth remains constant - so energy is conserved too.
John Baez
Tim S <T...@timsilverman.demon.co.uk> wrote:
>on 17/04/2004 10:08 am, Ken S. Tucker at dyna...@vianet.on.ca wrote:
>> Using Old Newton's Force = - G (M) (m) /r^2 the universe
>> would behave the same if one used (-M) and (-m) in Newtons,
>> I think there is no easy way to decide if mass/energy is positive
>> or negative. So I think a negative energy "dust cloud" would
>> condense as a positive energy cloud.
Whoops! Actually a negative mass dust cloud would *expand*, not collapse
like a positive mass one does. The reason is...
>The _force_ would be the same, but the acceleration would be different.
>There's only one m in F=ma.
Right!
If you have two negative masses, they REPEL each other,
since we get two minus signs from the masses in F = GMm/r^2,
but a third when we work out the acceleration using F = ma.
Triple negatives seem tricky, so it may help to remember
what I wrote earlier in this thread:
a positive-mass body attracts EVERYTHING;
a negative-mass body repels EVERYTHING.
And again, if we use GR this is just the equivalence principle in action:
A positive-mass body will curve spacetime in a way that bends geodesics
"towards" it, so it will *attract* other bodies regardless of the sign
of their mass.
A negative-mass body will curve spacetime in a way that bends geodesics
"away from" it, so it will *repel* other bodies regardless of the sign
of their mass.
Next puzzle... I may have asked Oz this already:
PUZZLE: in Newtonian gravity, how does a small negative mass
"orbit" a big positive mass? What curve does it trace out?
John Baez
Arnold Neumaier <Arnold....@univie.ac.at> wrote:
>John Baez wrote:
>> a positive-mass body attracts EVERYTHING;
>> a negative-mass body repels EVERYTHING.
>This sounds paradoxical - it would mean a positive-mass body attracts
>a negative-mass body, while the latter repels the former.
>Probably they are chasing after each other???
Right. It **sounds** paradoxical - that's why I'm talking about it!
But it's not; it's just weird.
Of course, the fact that we never see such runaway motions is evidence
that there aren't negative masses!
Quite generally, anything with unbounded negative energy runs the risk
of causing motions with speeds that approach infinity. The simplest
example is the negative *potential* energy of two positive point
masses in Newtonian mechanics: they can speed up indefinitely as
they fall into each other. But negative masses give negative
*kinetic* energy, and that causes other funny effects.
>But shouldn't we have actio = reactio? So:
>Do they get closer to each other or farther apart if initially they
>are at rest with respect to each other?
They stay the same distance apart, at least in Newtonian mechanics,
where the question is completely unambiguous because we don't need
to worry about Lorentz transforms.
>To which extent is the general relativistic 2-body problem solved?
It's a huge open problem which needs to be solved by supercomputers
for people to analyze the gravitational wave data that may eventually
come out of LIGO. People are really struggling to solve it.
But everything I've been discussing becomes easy to understand
in the Newtonian limit.
Oz
>PUZZLE: in Newtonian gravity, how does a small negative mass
>"orbit" a big positive mass? What curve does it trace out?
I think I already answered this. Although I used my usual randomly
talking around the problem method (which does generate some 'feel' for
what is going on) the answer is simple.
In essence the large positive mass will dominate and result in
attraction. The small negative mass will orbit in a newtonian manner.
However the common centre will move from being between the two masses,
to one on ... ohh ascii art is easier:
O = large +ve mass
- = small -ve mass (sketch #1)
+ = small +ve mass (sketch #2)
x = centre of rotation
viewed perp to axis of orbit
x O - sketch #1 -ve mass
O x + sketch #2 +ve mass
Adjust appropriately using normal newtonian methods for elliptical
orbits.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use o...@farmeroz.port995.com (whitelist check on first posting)<<
Richard Saam
>In article <BCA6E161...@timsilverman.demon.co.uk>,
>Tim S <T...@timsilverman.demon.co.uk> wrote:
>
>
>
>>on 17/04/2004 10:08 am, Ken S. Tucker at dyna...@vianet.on.ca wrote:
>>
>>
>
>
>Whoops! Actually a negative mass dust cloud would *expand*, not collapse
>like a positive mass one does. The reason is...
>
>
>
>>The _force_ would be the same, but the acceleration would be different.
>>There's only one m in F=ma.
>>
>>
>
>Right!
>
>
What are the implications for an expanding universe? Are there negative
mass dust clouds here and there?
Richard Saam
Ken S. Tucker
Hi Dr. Baez et al, I commited a stupid error above (maybe).
((in Ken Tucker posts)).
The quantities Mass, Time, Length are all relative,
but, "c", "h", "q" are invariants, (speed of light, Planck's
constant, fundamental charge) and I think in any
universe, whether positive or negative matter,
we should find c=h=1 and q^2 =1.
For example, using the units of "h" = energy*time
and energy =mass*c^2, then 1*h = mass*time =1.
Here we should denote the common varibles M,R,T
as being those (Mass, Radius,Time) we use in our familiar
universe.
Hence in a unverse of negative matter, using "h=1"
we should find,
h = m*t =1
where m = -M and t=-T
Let's look at acceleration, given in OUR universe
by A= R/T^2, that becomes a= r/t^2 in the negative
universe, because t^2 =T^2 and r=-R thus,
A = - a.
Hence in the negitive mass universe, Newton suggests
A = M/R^2 in our universe
is transformed too,
a = m/r^2 in the negative universe.
I don't want to make a mistake, so I'll transform
this way,
m=-M , A= -a and r^2 = R^2,,,
to get,
M*A = m*a = F = f.
Sorry, about the detail, I was just trying to compare
the polarity of the scalar "m", with our usual "M".
Regards
Ken S. Tucker
John Baez
Charles Francis <cha...@clef.demon.co.uk> wrote:
> In article <c5fcj8$6ua$1...@glue.ucr.edu>, John Baez <ba...@galaxy.ucr.edu>
>writes
>>a positive-mass body attracts EVERYTHING;
>>a negative-mass body repels EVERYTHING.
>Well, if you say so.
Perhaps "if" I say so, but not simply "because" I do. :-)
>>>>PUZZLE:
>>>>
>>>> Figure out what happens if you have two planets near each
>>>> other: Earth and Anti-Earth, the first with positive mass, the
>>>> second with an "equal but opposite" negative mass.
>>>If they were solid enough to resist
>>>gravitational forces then they clearly would accelerate across the
>>>universe, trailing their gravitational fields behind them.
>>Right! Excellent!
>Is it?
Yes - because then, the fact that this crazy behavior is not
seen is evidence that there are no negative-mass objects.
Oz
>In article <c614qs$d1u$1...@lfa222122.richmond.edu>, Oz
><o...@farmeroz.port995.com> writes
>>I suspect the reason may be that one of necessity seem to have to reject
>>a minkowski spacetime if you are to include QM,
>
>No, we can do relativistic qm if we tip toe through the nasties. It's
>curved space-times that cause fundamental problems.
Minkowski spacetime allows relativistic speeds anyway, so of course.
No, its not that that is the problem. We are happy to see unpredictable
and random effects when these are in the future, but minkowski spactime
predicts the past perfectly (and by implication, the future). Its
basically newtonian in structure, that is global. QM though, ought to
predict that a time reversed particle also show indeterminancy. That
would mean that the past is variable.
This brings up a whole load of very interesting problems. One thing is
for sure, we can't go back in time and repeat an experiment to see if we
get the same result. If we did, then we might not be surprised if we got
a different result, in fact we would expect it (well, I would).
hah! Actually its not really any different concept than 'predicting'
which silver ion gets to become deionised in a photographic film in a
diffraction pattern. The probability of any one is miniscule, but the
probability of one on the film is near 100%. Similarly a changed result
of a time reversed interaction is unlikely to have more than a minute
effect on the future, it would look like some kind of noise or low-level
indeterminancy in the future (perhaps something like h).
One could consider the ramifications further, but I don't think its
intractable. After all essentially everything locally is travelling the
in same direction and the same speed in time so will have no effect on
'the local past'.
>>. I am not very convinced, in fact I have
>>convinced myself of the reverse, that the worldines of 'backward
>>running' particles do NOT see global time reversed.
>
>I don't see how you get that. To me that is what "backward running"
>means.
Backward running ought to be a local phenomenon, pretty well everything
is. It should not and need not have any relationship to any 'global
time'.
>>In a way its just an extension of the problems of having global
>>anything-much in a curved spacetime. Does a 'global time' in GR even
>>make sense even before you allow backward-time-running particles? I
>>suspect not.
>
>The only "global time" in gr is cosmological time, which is really just
>proper time for particles emanating straight from the big bang. But
>really its just a load of proper times, not a global time.
Not really. Minkowski puts global time co-ordinates down along with
global space ones. Its a fixed four dimensional co-ordinate system. No
room for indeterminancy.
Tim S
>
> Next puzzle... I may have asked Oz this already:
>
> PUZZLE: in Newtonian gravity, how does a small negative mass
> "orbit" a big positive mass? What curve does it trace out?
That's easy: 2-body orbits are conic sections, so it must be a hyperbola.
With the big body at the focus of the other branch.
Tim
robert bristow-johnson
on 04/20/2004 02:35:
> In article <c612a9$d0e$1...@lfa222122.richmond.edu>,
> Arnold Neumaier <Arnold....@univie.ac.at> wrote:
>
>> John Baez wrote:
>
>>> a positive-mass body attracts EVERYTHING;
>>> a negative-mass body repels EVERYTHING.
>
>> This sounds paradoxical - it would mean a positive-mass body attracts
>> a negative-mass body, while the latter repels the former.
>> Probably they are chasing after each other???
>
> Right. It **sounds** paradoxical - that's why I'm talking about it!
> But it's not; it's just weird.
>
> Of course, the fact that we never see such runaway motions is evidence
> that there aren't negative masses!
okay, if that is the case, then from what principle does your "a
positive-mass body attracts EVERYTHING; a negative-mass body repels
EVERYTHING" statement come from? from a Newtonian POV it seems nonsensical
because of Newton's 3rd law. if it were like static E&M except for a sign
change (like signed masses attract, unlike signed masses repel), that could
make sense since both would be attracting or repelling each other.
so where (from what parent theory) does that principle come from, John?
r b-j
Dushan Mitrovich
`>> Figure out what happens if you have two planets near each
`>> other: Earth and Anti-Earth, the first with positive mass, the
`>> second with an "equal but opposite" negative mass.
`>
`> Going on what's written above, I think Anti-Earth will be attracted
`> to Earth, while Earth will be repelled by Anti-Earth. As a result,
`> they will both start moving, Earth running away from Anti-Earth and
`> Anti-Earth trying to catch up.
`
` Right!
Suppose there were a spherical shell of identical mass-antimass pairs,
with their alignments (pointing from antimass to mass) all directed at
the center of the sphere. It would look the same as a massive shell ac-
celerated inward by the gravitational field of a central mass. I don't
know what to do with this picture, but find it sort of interesting.
- Dushan Mitrovich
John Baez
Mike Stay <st...@datawest.net> wrote:
>You compared Hilb and nCob in this paper, but it looks like any of the
>matrix-mechanics-over-rigs structures from your fall 2003 qg notes
>ought to work in the same way. Is that right?
Right. Since this paper was written for philosophers of
physics, I figured I'd better not bombard them with *too*
much math, like matrix mechanics over an arbitrary *-rig.
*-rig?
Well, a rig is just a "ring without negatives", like the
natural numbers or {F,T} with "or" as plus and "and" as times.
We can do a lot of matrix mechanics using matrices with
coefficients in an arbitrary rig, and in this paper I note
that if we use {F,T} our matrices are just what people usually
call "binary relations". These matrices say whether or not a
transition is *possible*, instead of giving a transition *amplitude*.
However, for the formalism to nicely include complex matrix
mechanics - the example that actually comes up in quantum theory! -
we really want a *-structure on our rig, i.e. an operation satisfying
(a+b)* = a* + b* 0* = 0
(ab)* = b* a* 1* = 1
This fills the role played by complex conjugation in complex
matrix mechanics. I forget if I got around to talking about
this in the fall 2003 quantum gravity seminar:
http://www.math.ucr.edu/home/baez/qg-fall2003/
... but I should have.
Any commutative rig becomes a *-rig if we define a* = a;
the real numbers and natural numbers and {F,T} should be thought
of as *-rigs of this degenerate sort. It's interesting that
Nature has chosen a *-rig of a more interesting sort.
>Today I went to a lecture by V.S. Sunder, since the abstract sounded
>so similar to what you wrote in this paper. Here it is:
>
>"In recent work with my colleague Vijay Kodiyalam, we showed that
>there is a bijective correspondence between Vaughan Jones' `subfactor
>planar algebras' on the one hand, and what may be called `unitary
>topological quantum field theories' defined on a category `D' on the
>other, where the objects of `D' are suitably `decorated closed
>oriented 1-manifolds' and the morphisms are similarly decorated
>classes of cobordisms between a pair of objects.
Cool! I've been interested in Jones' planar algebras for a while,
but perhaps because he doesn't use enough n-category theory, his
definition of a "planar algebra" sounds rather ad hoc and contrived.
Unfortunately, I've never had the energy to translate his definition
into the language of n-category theory to see exactly how much modification
it needs (if any) to appear beautiful and "inevitable".
Jones is a very good mathematician, so presumably planar algebras
*are* beautiful and inevitable, at least after a little tweaking or
generalization, if one looks at them the right way.
Sunder sounds like he's struggling to do this.
But....
>Anyway, here's what I got:
>
>A tangle T has
>
>1) An outer disk D0 minus an ordered (possibly empty) list of
>subdisks.
>2) A bunch of curves that divide up the interior into
>checkerboard-colorable regions (equivalently, the boundaries of the
>disks have an even number of curves ending on them).
>3) A set of distinguished points: each disk boundary with at least one
>curve intersecting it has one point, where white goes to black when
>going clockwise around the disk, that is distinguished (denoted * in
>the diagram)
>4) "color": take the number of curves intersecting the outside edge
>and divide by 2.
>
>And a few other things I'll get to below.
Ugh... these rather complex "decorations" are precisely the sort
of things that seem ad hoc and complicated about planar algebras!
I think there has to be some better way to understand all this stuff
using a bit categories or n-categories. But I'd need to understand
what all these decorations *accomplish* to figure this out.
>So here is an example of a tangle:
---------------
-----...............-----
*--.........................--\
D0 ///|............................---\\
// |......................../--/ \\
// |....................---/ \\
// |................/--/ \\
/ /-----\........---/ \
/ // \\..---/ \
/ | +- \
/-------+ D1 | \
|........| | |
|.........| | |
|......../-*\ // ----------- |
|......../ \---+-/ //...........\\ |
|.......| |.| //...............\\ |
|.........\ /..| /...................\ |
|..........\---/...| |.....................| |
|..................| |........-----........| |
|..................| |.......// \\.......| |
|..................| |......| |......| |
|..................| |......| D3 |......| |
|..................| |......| |......| |
|............./----+\ |......\\ //......| |
|..........// \\ |........-----........| |
|.........| | \.................../ |
+--------* | \\...............// |
| | D2 | \\...........// |
| | | ----------- |
\ \\ // /
\ \---+-/..\\ /
\ |......\\ /
\ |........\\ /
\\ |..........\\ //
\\ |............\\ //
\\ |..............\\ //
\\\ |................\\ ///
\+-.................\\ --/
-----..............\-----
---------------
Cool! It looks like a Yin-Yang symbol on steroids!
>When you do, you multiply by a constant, delta. This was the
>important part that I missed. Something special happens when delta is
>of the form
>
>delta = cos 4pi/n (I think)
>
>which has something to do with Vaughan Jones' subfactor planar
>algebras. I didn't get all the details, and now I can't remember.
>Does anyone know?
The "hyperfinite type II_1 factor" is an incredibly cool algebra
that shows up in von Neumann's classification of operator algebras
(see below). Just as modules of the complex numbers are called
"complex vector spaces" and these can have dimension 0,1,2,3,...,
the hyperfinite type II_1 finite factor has modules which have some
sort of "dimension" that can be any nonnegative real number! This
was shown by von Neumann and Murray back in the 1930's or 1940's.
The hyperfinite type II_1 factor has copies of itself sitting inside
itself, and one of Jones' great achievements (for which he won the
Fields medal) was to figure out what dimensions these could have.
The allowed dimensions are numbers pretty much like your numbers
cos(4 pi / n) - though like you I forget the exact formula. I'm
fuzzy about the details, but I'm sure this is what's lurking behind
the appearance of that number delta!
Best,
jb
...........................................................................
Also available at http://math.ucr.edu/home/baez/week175.html
December 29, 2001
This Week's Finds in Mathematical Physics (Week 175)
John Baez
[stuff deleted]
In case you don't know: Alain Connes is a Fields medalist, who won the
prize mainly for two things: his work on Von Neumann algebras, and his
work on noncommutative geometry. Now I'll talk a bit about von Neumann
algebras, since you'll need to understand a bit about them to follow the
rest of my description of the paper by Michael Mueger that I have
been slowly explaining throughout "week173" and "week174".
So: what's a von Neumann algebra? Before I get technical and you all
leave, I should just say that von Neumann designed these algebras to be
good "algebras of observables" in quantum theory. The simplest example
consists of all n x n complex matrices: these become an algebra if you
add and multiply them the usual way. So, the subject of von Neumann
algebras is really just a grand generalization of the theory of matrix
multiplication.
But enough beating around the bush! For starters, a von Neumann algebra
is a *-algebra of bounded operators on some Hilbert space of countable
dimension - that is, a bunch of bounded operators closed under addition,
multiplication, scalar multiplication, and taking adjoints: that's the *
business. However, to be a von Neumann algebra, our *-algebra needs one
extra property! This extra property is cleverly chosen so that we can
apply functions to observables and get new observables, which is
something we do all the time in physics.
More precisely, given any self-adjoint operator A in our von Neumann
algebra and any measurable function f: R -> R, we want there to be a
self-adjoint operator f(A) that again lies in our von Neumann algebra.
To make sure this works, we need our von Neumann algebra to be "closed"
in a certain sense. The nice thing is that we can state this closure
property either algebraically or topologically.
In the algebraic approach, we define the "commutant" of a bunch of
operators to be the set of operators that commute with all of them.
We then say a von Neumann algebra is a *-algebra of operators that's
the commutant of its commutant.
In the topological approach, we say a bunch of operators T_i converges
"weakly" to an operator T if their expectation values converge to that
of T in every state, that is,
<psi, T_i psi> -> <psi, T psi>
for all unit vectors psi in the Hilbert space. We then say a von
Neumann algebra is an *-algebra of operators that is closed in the
weak topology.
It's a nontrivial theorem that these two definitions agree!
While classifying all *-algebras of operators is an utterly hopeless
task, classifying von Neumann algebras is almost within reach - close
enough to be tantalizing, anyway. Every von Neumann algebra can be
built from so-called "simple" ones as a direct sum, or more generally a
"direct integral", which is a kind of continuous version of a direct
sum. As usual in algebra, the "simple" von Neumann algebras are defined
to be those without any nontrivial ideals. This turns out to be
equivalent to saying that only scalar multiples of the identity commute
with everything in the von Neumann algebra.
People call simple von Neumann algebras "factors" for short. Anyway,
the point is that we just need to classify the factors: the process
of sticking these together to get the other von Neumann algebras is
not tricky.
The first step in classifying factors was done by von Neumann and
Murray, who divided them into types I, II, and III. This classification
involves the concept of a "trace", which is a generalization of the
usual trace of a matrix.
Here's the definition of a trace on a von Neumann algebra. First, we say
an element of a von Neumann algebra is "nonnegative" if it's of the form
xx* for some element x. The nonnegative elements form a "cone": they
are closed under addition and under multiplication by nonnegative
scalars. Let C be the cone of nonnegative elements. Then a "trace" is
a function
tr: C -> [0, +infinity]
which is linear in the obvious sense and satisfies
tr(xy) = tr(yx)
whenever both xy and yx are nonnegative.
Note: we allow the trace to be infinite, since the interesting von
Neumann algebras are infinite-dimensional. This is why we define
the trace only on nonnegative elements; otherwise we get "infinity minus
infinity" problems. The same thing shows up in the measure theory,
where we start by integrating nonnegative functions, possibly getting
the answer +infinity, and worry later about other functions.
Indeed, a trace very much like an integral, so we're really studying a
noncommutative version of the theory of integration. On the other hand,
in the matrix case, the trace of a projection operator is just the
dimension of the space it's the projection onto. We can define a
"projection" in any von Neumann algebra to be an operator with p* = p
and p^2 = p. If we study the trace of such a thing, we're studying a
GENERALIZATION OF THE CONCEPT OF DIMENSION. It turns out this can be
infinite, or even nonintegral!
We say a factor is "type I" if it admits a nonzero trace for which the
trace of a projection lies in the set {0,1,2,...,+infinity}. We say it's
"type I_n" if we can normalize the trace so we get the values {0,1,...,n}.
Otherwise, we say it's "type I_infinity", and we can normalize the trace
to get all the values {0,1,2,...,+infinity}.
It turn out that every type I_n factor is isomorphic to the algebra of
n x n matrices. Also, every type I_infinity factor is isomorphic to the
algebra of all bounded operators on a Hilbert space of countably infinite
dimension.
Type I factors are the algebras of observables that we learn to love in
quantum mechanics. So, the real achievement of von Neumann was to begin
exploring the other factors, which turned out to be important in quantum
field theory.
We say a factor is "type II_1" if it admits a trace whose values on
projections are all the numbers in the unit interval [0,1]. We say it
is "type II_infinity" if it admits a trace whose value on projections
is everything in [0,infinity].
Playing with type II factors amounts to letting dimension be a
continuous rather than discrete parameter!
Weird as this seems, it's easy to construct a type II_1 factor. Start
with the algebra of 1 x 1 matrices, and stuff it into the algebra of
2 x 2 matrices as follows:
( x 0 )
x |-> ( )
( 0 x )
This doubles the trace, so define a new trace on the algebra of 2 x 2
matrices which is half the usual one. Now keep doing this, doubling the
dimension each time, using the above formula to define a map from the
2^n x 2^n matrices into the 2^{n+1} x 2^{n+1} matrices, and normalizing
the trace on each of these matrix algebras so that all the maps are
trace-preserving. Then take the UNION of all these algebras... and
finally, with a little work, complete this and get a von Neumann algebra!
One can show this von Neumann algebra is a factor. It's pretty
obvious that the trace of a projection can be any fraction in the
interval [0,1] whose denominator is a power of two. But actually,
*any* number from 0 to 1 is the trace of some projection in this
algebra - so we've got our paws on a type II_1 factor.
This isn't the only II_1 factor, but it's the only one that contains a
sequence of finite-dimensional von Neumann algebras whose union is dense
in the weak topology. A von Neumann algebra like that is called
"hyperfinite", so this guy is called "the hyperfinite II_1 factor".
It may sound like something out of bad science fiction, but the
hyperfinite II_1 factor shows up all over the place in physics!
First of all, the algebra of 2^n x 2^n matrices is a Clifford algebra,
so the hyperfinite II_1 factor is a kind of infinite-dimensional
Clifford algebra. But the Clifford algebra of 2^n x 2^n matrices is
secretly just another name for the algebra generated by creation and
annihilation operators on the fermionic Fock space over C^{2n}.
Pondering this a bit, you can show that the hyperfinite II_1 factor is
the smallest von Neumann algebra containing the creation and
annihilation operators on a fermionic Fock space of countably infinite
dimension.
In less technical lingo - I'm afraid I'm starting to assume you know
quantum field theory! - the hyperfinite II_1 factor is the right algebra
of observables for a free quantum field theory with only fermions.
For bosons, you want the type I_infinity factor.
There is more than one type II_infinity factor, but again there is
only one that is hyperfinite. You can get this by tensoring the type
I_infinity factor and the hyperfinite II_1 factor. Physically, this
means that the hyperfinite II_infinity factor is the right algebra of
observables for a free quantum field theory with both bosons and fermions.
The most mysterious factors are those of type III. These can be simply
defined as "none of the above"! Equivalently, they are factors for
which any nonzero trace takes values in {0,infinity}. In a type III
factor, all projections other than 0 have infinite trace. In other
words, the trace is a useless concept for these guys.
As far as I'm concerned, the easiest way to construct a type III factor
uses physics. Now, I said that free quantum field theories had
different kinds of type I or type II factors as their algebras of
observables. This is true if you consider the algebra of *all*
observables. However, if you consider a free quantum field theory on
(say) Minkowski spacetime, and look only at the observables that you can
cook from the field operators on some bounded open set, you get a
subalgebra of observables which turns out to be a type III factor!
In fact, this isn't just true for free field theories. According to a
theorem of axiomatic quantum field theory, pretty much all the usual
field theories on Minkowski spacetime have type III factors as their
algebras of "local observables" - observables that can be measured in
a bounded open set.
Okay, so much for the crash course on von Neumann algebras! Next time
I'll hook this up to Mueger's work on 2-categories.
In the meantime, here are some references on von Neumann algebras in
case you want to dig deeper. For the math, try these:
5) Masamichi Takesaki, Theory of Operator Algebras I, Springer,
Berlin, 1979.
6) Richard V. Kadison and John Ringrose, Fundamentals of the
Theory of Operator Algebras, 4 volumes, Academic Press, New York,
1983-1992.
7) Shoichiro Sakai, C*-algebras and W*-algebras, Springer, Berlin,
1971.
A W*-algebra is basically just a von Neumann algebra, but defined
"intrinsically", in a way that doesn't refer to a particular
representation as operators on a Hilbert space.
For applications to physics, try these:
8) Gerard G. Emch, Algebraic Methods in Statistical Mechanics and Quantum
Field Theory, Wiley-Interscience, New York, 1972.
9) Rudolf Haag, Local Quantum Physics: Fields, Particles, Algebras,
Springer, Berlin, 1992.
10) Ola Bratelli and Derek W. Robinson, Operator Algebras and Quantum
Statistical Mechanics, 2 volumes, Springer, Berlin, 1987-1997.
John Baez
Richard Saam <rds...@att.net> wrote:
>What are the implications for an expanding universe? Are there negative
>mass dust clouds here and there?
Nobody has ever seen them, and I doubt they exist. For one,
as we've seen here, negative mass stuff would do incredibly weird
things - so it probably doesn't exist, or we'd notice! For two,
a negative-mass dust cloud would automatically spread apart and
dissolve under the effects of gravity! There'd be no reason for
it to form in the first place.
The physics of negative mass particles is mainly good for
stretching our brains and having a little fun.
Aaron Bergman
>
> The physics of negative mass particles is mainly good for
> stretching our brains and having a little fun.
Can you write down a lagrangian for a negative mass particle?
Aaron
--
Aaron Bergman
<http://zippy.ph.utexas.edu/~abergman/>
Stephen Riley
writes
>They stay the same distance apart, at least in Newtonian mechanics,
>where the question is completely unambiguous because we don't need
>to worry about Lorentz transforms.
So looking at this in 1 dimension, their separation remains constant but
they accelerate away together at a constant rate in the direction of the
positive mass, forever. This assumes equal magnitude masses with each
initially at rest relative to the other?
But, staying in 1D for simplicity, what if one body were less massive
than the other, even slightly? If for example there's a large positive
mass and a smaller negative mass; the same force acts between them so
there's a net attraction and they do eventually collide and don't
accelerate forever. They annihilate, or collide and come back where they
started. If instead the larger mass were negative, acceleration between
them (repulsion in this case) is proportional to the inverse square of
the distance, so while they do accelerate forever this tends to zero. So
there are three extremes, in the first case bodies collide, in the
second acceleration approaches zero, and in the third case, where masses
are equal, acceleration is constant. But the third case is unstable in
that if things do not start out with each body still wrt to the other
one of the other two cases results, from conservation of energy, because
the bodies continue to separate or approach at this initial relative
speed. So we probably wouldn't see runaway acceleration?
In the first case they collide - the collision formulas still work since
the denominator only goes to zero for equal (and opposite signed)
masses. But what if one mass was hurled at another opposite signed mass
of equal magnitude? Another force would be required to stop equal (and
opposite) masses hitting each other otherwise the collision formulas
blow up, which presumably means energy and/or momentum wouldn't be
conserved. Any self respecting universe allow that surely :) If in the
unlikely event that any of the above is correct, what would that force
look like?
--
Stephen Riley
Boo
>
> PUZZLE: in Newtonian gravity, how does a small negative mass
> "orbit" a big positive mass? What curve does it trace out?
I'll bite : It must still be an elipse (one minus sign that appears in
both equations hence a remains unchanged). Presumeably the point about
which both planets mutually orbit is on the opposite side of the larger
mass from usual though ?
--
Boo
Ulmo
So that's very strong evidence against the existence of wormholes
since wormholes would require negative mass to exist.
David
eb...@lfa221051.richmond.edu
robert bristow-johnson <r...@surfglobal.net> wrote:
>okay, if that is the case, then from what principle does your "a
>positive-mass body attracts EVERYTHING; a negative-mass body repels
>EVERYTHING" statement come from?
I won't pretend to speak for John B., but personally, I'd say that this
principle comes from
1. The equivalence principle
2. The fact that a positive-mass object attracts another positive-mass
object
3. Newton's 3rd Law.
I know you don't like this, because you say
>from a Newtonian POV it seems nonsensical
>because of Newton's 3rd law.
I'm not quite sure why you think that, though. Perhaps there's just a
semantic issue here? In the sentence "a negative-mass body repels
everything," the word "repels" doesn't mean "exerts a force that
points away from itself"; it means "causes the other body to
accelerate away from it."
In a world consisting only of positive-mass objects, those two
are equivalent, but with negative masses, they're not.
Let's write down all the directions in an explicit case. Say
we have a positive mass at the origin, and a negative mass
to the right of it (on the positive x axis). Then the directions
of all the relevant quantities are
Force on positive-mass object: Left
Force on negative-mass object: Right
Acceleration of positive-mass object: Left
Acceleration of negative-mass object: Left
Note that there's no problem with Newton's 3rd Law: the forces
are equal and opposite. The positive-mass object attracts
the negative-mass object (that is, it causes the negative-mass
object to accelerate towards it). The negative-mass object
repels the positive-mass object (that is, it causes the positive-mass
object to accelerate away from it).
Given the assumptions above, there's no other way it could be. At the
risk of belaboring the obvious, here's why. (In case it's not clear,
in every sentence below, the word "it" refers to the subject of the
sentence. That is, "A exerts a force on B that points away from it"
means "A exerts a force on B that points away from A.")
A. A positive mass causes another positive mass to accelerate towards
it.
B. A positive mass causes anything to accelerate towards it.
(Equivalence Principle: everything accelerates the same way under a
gravitational force.) In particular, a positive mass causes a
negative mass to accelerate towards it.
C. A positive mass exerts a force on a negative mass that points away
from it. This comes from the definition of mass. If m is negative,
then F = ma implies that F and a point in opposite directions.
D. A negative mass exerts a force on a positive mass that points away
from it. (Newton's 3rd Law)
E. A negative mass causes a positive mass to accelerate away from it.
(F = ma)
F. A negative mass causes anything to accelerate away from it.
(Equivalence Principle)
Statements B and F are the ones that can also be phrased
>"a positive-mass body attracts EVERYTHING; a negative-mass body
>repels EVERYTHING"
(with or without the shouting).
-Ted
--
[E-mail me at na...@domain.edu, as opposed to na...@machine.domain.edu.]
John Baez
robert bristow-johnson <r...@surfglobal.net> wrote:
>>> John Baez wrote:
>>>> a positive-mass body attracts EVERYTHING;
>>>> a negative-mass body repels EVERYTHING.
>from what principle does your "a
>positive-mass body attracts EVERYTHING; a negative-mass body repels
>EVERYTHING" statement come from?
In Newtonian mechanics it comes from
F = Gmm'/r^2
and
F = ma
In general relativity it comes from Einstein's equations, which
say:
The rate at which a small initially comoving ball of freely falling
test particles begins to shrink is proportional to its volume times:
the energy density at the center of the ball, plus the pressure in
the x direction at that point, plus the pressure in the y direction,
plus the pressure in the z direction.
A blob with negative mass and negligible pressure would thus repel
freely falling particles in its vicinity, regardless of their mass.
I believe you can also see this sort of thing by taking the Schwarzschild
solution, sticking in a negative value of m, and working out the geodesics
in this metric.
>from a Newtonian POV it seems nonsensical because of Newton's 3rd law.
Eh? Conservation of momentum *demands* that if a positive-mass
particle attracts a negative-mass one, the negative-mass particle
repels the positive-mass one. It has nothing to say about whether
two negative-mass particles will attract or repel each other, but
F = Gmm'/r^2
and
F = ma
say they repel each other.
>if it were like static E&M except for a sign
>change (like signed masses attract, unlike signed masses repel), that could
>make sense since both would be attracting or repelling each other.
Newtonian gravity is *not* like electrostatics, since m shows up twice
in
F = Gmm'/r^2
and
F = ma
but only once in
F = Gqq'/r^2
and
F = ma.
John Baez
Aaron Bergman <aber...@physics.utexas.edu> wrote:
>In article <c68tqt$84l$1...@glue.ucr.edu>, John Baez wrote:
>> The physics of negative mass particles is mainly good for
>> stretching our brains and having a little fun.
>Can you write down a lagrangian for a negative mass particle?
Ah, now this is getting really interesting! If you can
write down one for a positive mass particle, I can switch
the sign and get one for a negative mass particle. But
sometimes you can't do this!
Are we talking Newtonian classical point particles, special-relativistic
classical point particles, general relativistic classical point
particles, quantum mechanics, or quantum field theory? All the
variations are interesting, but I'll just think about two.
If we're talking Newtonian classical point particles, the
Lagrangian is
mv^2/2 - V(q)
The sign of m here really affects things: if we make it negative,
we get particles that accelerate the opposite way than we're used to!
If we're talking about a massive spin-0 quantum field, the
Lagrangian doesn't say anything about whether the particle
in question has positive or negative mass, because all that
shows up in the formula is m^2.
In this case, we can consistently quantize this Lagrangian in two
different ways. One way gives particles with positive rest
mass; the other gives particles with negative rest mass!
Depending on which we choose, we get two unitarily inequivalent
representations of the Poincare group on the single-particle Hilbert
space. Either choice is equally good, since they are equivalent
by an *antiunitary* operator. The trouble starts when we try
to cook up theories that allow positive-mass particles to interact
with negative-mass ones.
Danny Ross Lunsford
> The physics of negative mass particles is mainly good for
> stretching our brains and having a little fun.
Has the work on "ponderomotive theory" of Einstein, Infeld, and Hoffmann
been done for negative mass test particles?
-drl
Danny Ross Lunsford
> Ah, now this is getting really interesting! If you can
> write down one for a positive mass particle, I can switch
> the sign and get one for a negative mass particle. But
> sometimes you can't do this!
What about a mass that is positive *and* negative?
Here's a relativistic wave equation:
(ym dm - y5 m) psi = 0
To see that it is formally equivalent to the usual equation, make a
transformation of basis
ym -> y'm = iy5 ym
so
{y'm, y'n} = -{y5 ym, y5 yn} = 2 gmn
A suitable S leading from one basis to the other is
S = 1/root2(1 + iy5) S-1 = 1/root2(1 - iy5)
S ym S-1 = 1/2(1 + iy5) ym (1 - iy5)
= 1/2(ym + i[y5,ym] - ym)
= iy5 ym
The transformed spinor is
psi' = 1/root2(1 + iy5) psi
and
(i y5 y'm dm - m y5) psi' = 0
or
(y'm dm + im) psi' = 0
Geometrically, however, the "pseudo" Dirac equation is a very different
animal. In order to be fully Lorentz invariant the mass has to change
sign under spacetime parity. If you really "believe" that antimatter is
negative mass, then this is "correct" equation!
-drl
Aaron Denney
> Nobody has ever seen them, and I doubt they exist. For one,
> as we've seen here, negative mass stuff would do incredibly weird
> things - so it probably doesn't exist, or we'd notice! For two,
> a negative-mass dust cloud would automatically spread apart and
> dissolve under the effects of gravity! There'd be no reason for
> it to form in the first place.
What about charged negative-mass particles? If they have like charges,
shouldn't they glom together rapidly?
--
Aaron Denney
-><-
Charles Francis
writes
>
>>if it were like static E&M except for a sign
>>change (like signed masses attract, unlike signed masses repel), that could
>>make sense since both would be attracting or repelling each other.
>
>Newtonian gravity is *not* like electrostatics, since m shows up twice
>in
>
>F = Gmm'/r^2
>
>and
>
>F = ma
I make that thrice!
>but only once in
>
>F = Gqq'/r^2
>
>and
>
>F = ma.
>
The only trouble is we already know that the transformation m -> -m
takes matter to antimatter and t to -t, so there is an extra minus of
which you take no account, and as a result negative inertial mass
manifests as positive.
--
Charles Francis
Charles Francis
>In article <UYfIiCF6...@clef.demon.co.uk>,
>Charles Francis <cha...@clef.demon.co.uk> wrote:
>
>> In article <c5fcj8$6ua$1...@glue.ucr.edu>, John Baez <ba...@galaxy.ucr.edu>
>>writes
>
>>>a positive-mass body attracts EVERYTHING;
>>>a negative-mass body repels EVERYTHING.
>
>>Well, if you say so.
>
>Perhaps "if" I say so, but not simply "because" I do. :-)
>
>>>>>PUZZLE:
>>>>>
>>>>> Figure out what happens if you have two planets near each
>>>>> other: Earth and Anti-Earth, the first with positive mass, the
>>>>> second with an "equal but opposite" negative mass.
>
>>>>If they were solid enough to resist
>>>>gravitational forces then they clearly would accelerate across the
>>>>universe, trailing their gravitational fields behind them.
>
>>>Right! Excellent!
>
>>Is it?
>
>Yes - because then, the fact that this crazy behavior is not
>seen is evidence that there are no negative-mass objects.
>
scooting it would rapidly get destroyed. In any case absence of
observation is not necessarily evidence of absence. I would rather see a
theoretical demonstration. As I recall D'Inverno shows the equivalence
of inertial mass with active and passive gravitational mass, and since
we know negative mass is time reversed and manifests as positive mass,
that ought to be enough.
--
Charles Francis
Charles Francis
<o...@farmeroz.port995.com> writes
>Charles Francis <cha...@clef.demon.co.uk> writes
>>In article <c614qs$d1u$1...@lfa222122.richmond.edu>, Oz
>><o...@farmeroz.port995.com> writes
>
>>>I suspect the reason may be that one of necessity seem to have to reject
>>>a minkowski spacetime if you are to include QM,
>>
>>No, we can do relativistic qm if we tip toe through the nasties. It's
>>curved space-times that cause fundamental problems.
>
>Minkowski spacetime allows relativistic speeds anyway, so of course.
>
>No, its not that that is the problem. We are happy to see unpredictable
>and random effects when these are in the future, but minkowski spactime
>predicts the past perfectly (and by implication, the future). Its
>basically newtonian in structure, that is global. QM though, ought to
>predict that a time reversed particle also show indeterminancy. That
>would mean that the past is variable.
It only means that what we can know of the present does not determine
the past. Maybe that is what you meant.
>
>This brings up a whole load of very interesting problems. One thing is
>for sure, we can't go back in time and repeat an experiment to see if we
>get the same result. If we did, then we might not be surprised if we got
>a different result, in fact we would expect it (well, I would).
The universe can't be two different things at the same time so if we
could go back we must get the same result. But certainly we should never
have been be surprised if we repeat an experiment and get a different
result at different time.
>
>hah! Actually its not really any different concept than 'predicting'
>which silver ion gets to become deionised in a photographic film in a
>diffraction pattern.
Yes, its just the same. Laws of motion are time reversible - although
collapse takes place at a different stage of the motion (i.e. the end,
whether you are going forwards or backwards)
>>>. I am not very convinced, in fact I have
>>>convinced myself of the reverse, that the worldines of 'backward
>>>running' particles do NOT see global time reversed.
>>
>>I don't see how you get that. To me that is what "backward running"
>>means.
>
>Backward running ought to be a local phenomenon, pretty well everything
>is. It should not and need not have any relationship to any 'global
>time'.
Global time is a local phenomenon. It is just a set of proper times for
particles on particular world lines from the big bang. By backward
running we mean backward running wrt other local matter. This other
matter has been on a roughly ok world line from the big bang, so can be
synchronised with global time.
>>>In a way its just an extension of the problems of having global
>>>anything-much in a curved spacetime. Does a 'global time' in GR even
>>>make sense even before you allow backward-time-running particles? I
>>>suspect not.
>>
>>The only "global time" in gr is cosmological time, which is really just
>>proper time for particles emanating straight from the big bang. But
>>really its just a load of proper times, not a global time.
>
>Not really. Minkowski puts global time co-ordinates down along with
>global space ones.
That is taking Minkowski too far. He only applies locally, and does not
apply at all at a singularity like the big bang.
--
Charles Francis
Kefka G
>>> John Baez wrote:
>>
>>>> a positive-mass body attracts EVERYTHING;
>>>> a negative-mass body repels EVERYTHING.
>>
>>> This sounds paradoxical - it would mean a positive-mass body attracts
>>> a negative-mass body, while the latter repels the former.
>>> Probably they are chasing after each other???
>>
>> Right. It **sounds** paradoxical - that's why I'm talking about it!
>> But it's not; it's just weird.
>>
>> Of course, the fact that we never see such runaway motions is evidence
>> that there aren't negative masses!
>
>okay, if that is the case, then from what principle does your "a
>positive-mass body attracts EVERYTHING; a negative-mass body repels
>EVERYTHING" statement come from? from a Newtonian POV it seems nonsensical
>because of Newton's 3rd law. if it were like static E&M except for a sign
>change (like signed masses attract, unlike signed masses repel), that could
>make sense since both would be attracting or repelling each other.
>
>so where (from what parent theory) does that principle come from, John?
>
I'm not John, but I think confusion regarding Newton's third law arises because
of the following - the third law is, indeed, satisfied, it's just that a
positive force on a negative mass object induces a negative acceleration. In
other words, a "push" is effectively a "pull" when we're dealing with negative
mass. Yes, the resulting physics is somewhat pathological, but it is good to
note that in classical E/M, we have much the same problem - when we assume
point charges exist, we're forced to assume that the "bare" mass of a particle
is negative so that we end up with a finite total mass. This leads to the well
known runaway solutions when we calculate the self force of a point charge.
These end up conserving energy precisely because of the negative bare mass -
the increase of energy in the fields is balanced by a decrease of energy in the
particle. We generally choose to ignore these solutions, preferring the
acausal ones (see Rohrlich's 1965 book for a better explanation).
-Eric
Aaron Bergman
wrote:
> Depending on which we choose, we get two unitarily inequivalent
> representations of the Poincare group on the single-particle Hilbert
> space. Either choice is equally good, since they are equivalent
> by an *antiunitary* operator. The trouble starts when we try
> to cook up theories that allow positive-mass particles to interact
> with negative-mass ones.
I don't see offhand how you're going to tell the difference between the
ordinary theory and the 'negative mass' theory run backwards in time.
Aaron
Ken S. Tucker
Pardon my knee-jerk, let's look at the geodesics
of any material particle, (from the standpoint of GR),
with any scalar polarity, (m, -m, sqrt(-1)*m)...).
An easy definition of a material particle in classical
geodesic motion is one where an accelometer on the
geodesic would read zero, aka free-fall.
Suppose we were to construct our accelometer using
*negative matter*, we should expect that accelometer
to read zero, as does an accelometer constructed from
positive matter. This is in respect of Equivalence.
My point is, the material of the construction is
unimportant, since they will both read zero.
Hence, I think, GR would work independant of the
relative mass scalar polarity.
Interesting, Ken S. Tucker
Oz
> In message <c697gh$gqb$1...@lfa222122.richmond.edu>, Oz
><o...@farmeroz.port995.com> writes
>>Charles Francis <cha...@clef.demon.co.uk> writes
>>>In article <c614qs$d1u$1...@lfa222122.richmond.edu>, Oz
>>><o...@farmeroz.port995.com> writes
>>
>>>>I suspect the reason may be that one of necessity seem to have to reject
>>>>a minkowski spacetime if you are to include QM,
>>>
>>>No, we can do relativistic qm if we tip toe through the nasties. It's
>>>curved space-times that cause fundamental problems.
>>
>>Minkowski spacetime allows relativistic speeds anyway, so of course.
>>
>>No, its not that that is the problem. We are happy to see unpredictable
>>and random effects when these are in the future, but minkowski spactime
>>predicts the past perfectly (and by implication, the future). Its
>>basically newtonian in structure, that is global. QM though, ought to
>>predict that a time reversed particle also show indeterminancy. That
>>would mean that the past is variable.
>
>It only means that what we can know of the present does not determine
>the past. Maybe that is what you meant.
Possibly, I was being more explicit.
>>This brings up a whole load of very interesting problems. One thing is
>>for sure, we can't go back in time and repeat an experiment to see if we
>>get the same result. If we did, then we might not be surprised if we got
>>a different result, in fact we would expect it (well, I would).
>
>The universe can't be two different things at the same time so if we
>could go back we must get the same result.
Why? If we repeated 'going back and doing the same experiment' many
times, I think we would end up with the standard probabilistic result.
However individual events would differ. I can't see why, from the
viewpoint of a reversed-time particle, the past should not look as we
see the future, that is to some degree undetermined.
In general I doubt this matters much, since the macroscopic view is one
born of an immense multitude of interactions where the average result is
in practice 'reality'. It really doesn't bother 'the future' precisely
which pattern of dots, in which order, produced that diffraction
pattern, only that a diffraction pattern was produced.
Furthermore its clear that anything happening before the universe was at
t=0 can never affect us. Any changes can never propagate to the present.
I have a gut feel, well it would be interesting to think carefully
about, that a reversed particle interacting differently in the past
would result in a change propagating forward in time which may not
precisely reach us in the present. This would be much more a viewpoint
that makes 'many worlds' a viable process to examine.
>But certainly we should never
>have been be surprised if we repeat an experiment and get a different
>result at different time.
I can see no reason why this should not be true of an experiment
performed in the past, as it is one performed in the future. That is
both should be random.
>>hah! Actually its not really any different concept than 'predicting'
>>which silver ion gets to become deionised in a photographic film in a
>>diffraction pattern.
>
>Yes, its just the same. Laws of motion are time reversible - although
>collapse takes place at a different stage of the motion (i.e. the end,
>whether you are going forwards or backwards)
The laws of motion are reversible, absolutely.
From this we get very many irreversible laws for bulk matter (we are
bulk matter). If we lived in an antimatter-time-reversed universe we
could not know, the laws of physics would remain the same.
As a matter of fact, we live in a universe where antiparticles have
tremendously short lifetimes and are hugely rare. Are you sure the
irreversibility of time is not an assumption born of the fact that
everything we see is travelling (fast) in the same time direction?
>>>>. I am not very convinced, in fact I have
>>>>convinced myself of the reverse, that the worldines of 'backward
>>>>running' particles do NOT see global time reversed.
>>>
>>>I don't see how you get that. To me that is what "backward running"
>>>means.
>>
>>Backward running ought to be a local phenomenon, pretty well everything
>>is. It should not and need not have any relationship to any 'global
>>time'.
>
>Global time is a local phenomenon. It is just a set of proper times for
>particles on particular world lines from the big bang. By backward
>running we mean backward running wrt other local matter. This other
>matter has been on a roughly ok world line from the big bang, so can be
>synchronised with global time.
This is certainly so for matter travelling +vely in time.
None of it can go backwards. This need not be so of reversed-time
particles.
>>>>In a way its just an extension of the problems of having global
>>>>anything-much in a curved spacetime. Does a 'global time' in GR even
>>>>make sense even before you allow backward-time-running particles? I
>>>>suspect not.
>>>
>>>The only "global time" in gr is cosmological time, which is really just
>>>proper time for particles emanating straight from the big bang. But
>>>really its just a load of proper times, not a global time.
>>
>>Not really. Minkowski puts global time co-ordinates down along with
>>global space ones.
>
>That is taking Minkowski too far. He only applies locally, and does not
>apply at all at a singularity like the big bang.
Yes, a good point. A backwards-running particle should, as in the other
thread, see black holes as white holes. This rather screws up ted's
statement that you can't tell if a film is being run backwards or
forwards. For a black hole, you most certainly can.
We thus, delightfully, run into an impasse.
Hang on tho, its a bit more subtle than this. [Gosh this is fun].
Throughout I have assumed an antiparticle in this viewpoint has +ve
mass, at least in the sense that it bends spacetime the same as a
particle. That, at least, seems to be OK experimentally.
So there is no difference between an 'antiparticle' black hole and a
'particle' black hole, except they evolve in opposite time directions.
If you don't accept this difference then you will run into an internal
contradiction. Doubtless this separation is completely anathema to GR,
but lets stick with it for a while.
Firstly its easy to tell you have an antiparticle black hole, its one
emitting lots of particles (or absorbing lots of antiparticles) as it
evolves backwards. Since I am accepting backwards-travelling particles
then of course I have to accept backwards-travelling black holes, so
this is not a problem. In an antimatter universe, where everything
travels backwards, of course they look like 'ordinary' black holes to
the denizens there.
Secondly the hawking radiation modelled as a particle-antiparticle pair
production where the antiparticle is absorbed, allowing the particle to
be emitted looks slightly more reasonable. We just have to be careful
not to start invoking negative mass, at least in an unphysical way.
Probably I should stop at this point....
alistair
energy?
And if so, do these gravitons carry momentum in the same direction
that they are moving?
Charles Francis
In message <SnP7R0F4...@farmeroz.port995.com>, Oz
>Charles Francis <cha...@clef.demon.co.uk> writes
>> In message <c697gh$gqb$1...@lfa222122.richmond.edu>, Oz
>><o...@farmeroz.port995.com> writes
>
>>>for sure, we can't go back in time and repeat an experiment to see if we
>>>get the same result. If we did, then we might not be surprised if we got
>>>a different result, in fact we would expect it (well, I would).
>>
>>The universe can't be two different things at the same time so if we
>>could go back we must get the same result.
>
>Why? If we repeated 'going back and doing the same experiment' many
>times, I think we would end up with the standard probabilistic result.
>However individual events would differ.
Perhaps it is a confusion over words. Surely the only way I understand
to go back in time is to reoccupy the same consciousness and redo the
sae experiment. It is then only one experiment, seen again. Otherwise it
would be a different experiment, at the same time but a different place.
In this case the result need not be the same.
> I can't see why, from the
>viewpoint of a reversed-time particle, the past should not look as we
>see the future, that is to some degree undetermined.
It does.
>
>In general I doubt this matters much, since the macroscopic view is one
>born of an immense multitude of interactions where the average result is
>in practice 'reality'. It really doesn't bother 'the future' precisely
>which pattern of dots, in which order, produced that diffraction
>pattern, only that a diffraction pattern was produced.
>
>Furthermore its clear that anything happening before the universe was at
>t=0 can never affect us. Any changes can never propagate to the present.
>I have a gut feel, well it would be interesting to think carefully
>about, that a reversed particle interacting differently in the past
>would result in a change propagating forward in time which may not
>precisely reach us in the present. This would be much more a viewpoint
>that makes 'many worlds' a viable process to examine.
I think it is a version of the idea discussed on uba, that at the big
bang the universe could split into disconnected regions, conceivable but
untestable at the present time. Mind you there is no good reason for
calling one of these disconnected regions t<0, since there is no way to
compare time between one region and another, and there is no way to say
that only two such regions exist. One may as well call the regions red,
blue yellow, or anything else.
>
>
>The laws of motion are reversible, absolutely.
>From this we get very many irreversible laws for bulk matter (we are
>bulk matter).
That is mostly down to thermodynamics. Even entropy would be reversible
if you could know a final condition, and know that the prior state was
not determined in anyway.
> If we lived in an antimatter-time-reversed universe we
>could not know, the laws of physics would remain the same.
>
>As a matter of fact, we live in a universe where antiparticles have
>tremendously short lifetimes and are hugely rare.
Positrons can be kept in storage rings almost indefinitely.
>Are you sure the
>irreversibility of time is not an assumption born of the fact that
>everything we see is travelling (fast) in the same time direction?
Yes. It is something we can prove from statistical mechanics. It is down
to knowledge of initial conditions, not matter or antimatter. If the
universe is fated for final collapse I would expect entropy to be
reversed during the dying phase.
>
>>>>>. I am not very convinced, in fact I have
>>>>>convinced myself of the reverse, that the worldines of 'backward
>>>>>running' particles do NOT see global time reversed.
>>>>
>>>>I don't see how you get that. To me that is what "backward running"
>>>>means.
>>>
>>>Backward running ought to be a local phenomenon, pretty well everything
>>>is. It should not and need not have any relationship to any 'global
>>>time'.
>>
>>Global time is a local phenomenon. It is just a set of proper times for
>>particles on particular world lines from the big bang. By backward
>>running we mean backward running wrt other local matter. This other
>>matter has been on a roughly ok world line from the big bang, so can be
>>synchronised with global time.
>
>This is certainly so for matter travelling +vely in time.
>None of it can go backwards. This need not be so of reversed-time
>particles.
It would be the same. Remember a backward running electron appears to us
exactly like a forward running positron, so proper time for time
reversed particles behaves just as for forward running particles..
>Yes, a good point. A backwards-running particle should, as in the other
>thread, see black holes as white holes.
Which other thread? Gravity looks just the same under time reversal, so
a black hole remains a black hole.
>This rather screws up ted's
>statement that you can't tell if a film is being run backwards or
>forwards. For a black hole, you most certainly can.
I don't think so.
>Throughout I have assumed an antiparticle in this viewpoint has +ve
>mass, at least in the sense that it bends spacetime the same as a
>particle. That, at least, seems to be OK experimentally.
>
>So there is no difference between an 'antiparticle' black hole and a
>'particle' black hole, except they evolve in opposite time directions.
>If you don't accept this difference then you will run into an internal
>contradiction. Doubtless this separation is completely anathema to GR,
>but lets stick with it for a while.
>
>Firstly its easy to tell you have an antiparticle black hole, its one
>emitting lots of particles (or absorbing lots of antiparticles) as it
>evolves backwards.
That's the wrong way about. I believe an antiparticle black hole will
emit antiparticles by Hawking radiation.
>Secondly the hawking radiation modelled as a particle-antiparticle pair
>production where the antiparticle is absorbed, allowing the particle to
>be emitted looks slightly more reasonable. We just have to be careful
>not to start invoking negative mass, at least in an unphysical way.
>
The only reason the antiparticle is absorbed is if it is a particle
black hole. It is the negative energy particle which is absorbed,
allowing that negative energy particles can exist in qft for very short
time durations.
Regards
--
Charles Francis
Oz
>
><o...@farmeroz.port995.com> writes
>>
>>Why? If we repeated 'going back and doing the same experiment' many
>>times, I think we would end up with the standard probabilistic result.
>>However individual events would differ.
>
>Perhaps it is a confusion over words. Surely the only way I understand
>to go back in time is to reoccupy the same consciousness and redo the
>sae experiment. It is then only one experiment, seen again. Otherwise it
>would be a different experiment, at the same time but a different place.
>In this case the result need not be the same.
But what if you do the same experiment at the same time and place?
Is there any reason to expect the precise same result?
GR says yes, QM says no.
The interaction of individual particles is a QM event, so I say no.
>> I can't see why, from the
>>viewpoint of a reversed-time particle, the past should not look as we
>>see the future, that is to some degree undetermined.
>
>It does.
It cannot be determined by our viewpoint but undetermined from an
antiparticles'. Hmm, maybe it can, but philosophically treacherous.
>I think it is a version of the idea discussed on uba, that at the big
>bang the universe could split into disconnected regions, conceivable but
>untestable at the present time. Mind you there is no good reason for
>calling one of these disconnected regions t<0, since there is no way to
>compare time between one region and another, and there is no way to say
>that only two such regions exist. One may as well call the regions red,
>blue yellow, or anything else.
Of course.
>>The laws of motion are reversible, absolutely.
>>From this we get very many irreversible laws for bulk matter (we are
>>bulk matter).
>
>That is mostly down to thermodynamics. Even entropy would be reversible
>if you could know a final condition, and know that the prior state was
>not determined in anyway.
Que? In QM I don't think its so that knowing the final states precisely
allows you to state the initial states precisely. You can only do it to
some level of accuracy.
>> If we lived in an antimatter-time-reversed universe we
>>could not know, the laws of physics would remain the same.
>>
>>As a matter of fact, we live in a universe where antiparticles have
>>tremendously short lifetimes and are hugely rare.
>
>Positrons can be kept in storage rings almost indefinitely.
But only by isolating them from our universe.
This is a terribly rare situation.
>>Are you sure the
>>irreversibility of time is not an assumption born of the fact that
>>everything we see is travelling (fast) in the same time direction?
>
>Yes. It is something we can prove from statistical mechanics. It is down
>to knowledge of initial conditions, not matter or antimatter. If the
>universe is fated for final collapse I would expect entropy to be
>reversed during the dying phase.
See my comment on 'antimatter black holes'.
>>This is certainly so for matter travelling +vely in time.
>>None of it can go backwards. This need not be so of reversed-time
>>particles.
>
>It would be the same. Remember a backward running electron appears to us
>exactly like a forward running positron, so proper time for time
>reversed particles behaves just as for forward running particles..
Hmm. Good point. I need to ponder this again.
So what that means is a backwards-running universe looks like a forward-
running anti-universe.
OK, my whole argument shot down in flames......
There is one implication though. That is that time is something a
particle carries.
Charles Francis
<o...@farmeroz.port995.com> writes
>Charles Francis <cha...@clef.demon.co.uk> writes
>>
>><o...@farmeroz.port995.com> writes
>>>
>>>Why? If we repeated 'going back and doing the same experiment' many
>>>times, I think we would end up with the standard probabilistic result.
>>>However individual events would differ.
>>
>>Perhaps it is a confusion over words. Surely the only way I understand
>>to go back in time is to reoccupy the same consciousness and redo the
>>sae experiment. It is then only one experiment, seen again. Otherwise it
>>would be a different experiment, at the same time but a different place.
>>In this case the result need not be the same.
>
>But what if you do the same experiment at the same time and place?
>Is there any reason to expect the precise same result?
>GR says yes, QM says no.
History says yes. QM has no bearing on that.
>>> I can't see why, from the
>>>viewpoint of a reversed-time particle, the past should not look as we
>>>see the future, that is to some degree undetermined.
>>
>>It does.
>
>It cannot be determined by our viewpoint but undetermined from an
>antiparticles'. Hmm, maybe it can, but philosophically treacherous.
Yes.
>
>>I think it is a version of the idea discussed on uba, that at the big
>>bang the universe could split into disconnected regions, conceivable but
>>untestable at the present time. Mind you there is no good reason for
>>calling one of these disconnected regions t<0, since there is no way to
>>compare time between one region and another, and there is no way to say
>>that only two such regions exist. One may as well call the regions red,
>>blue yellow, or anything else.
>
>Of course.
>
>>>The laws of motion are reversible, absolutely.
>>>From this we get very many irreversible laws for bulk matter (we are
>>>bulk matter).
>>
>>That is mostly down to thermodynamics. Even entropy would be reversible
>>if you could know a final condition, and know that the prior state was
>>not determined in anyway.
>
>Que? In QM I don't think its so that knowing the final states precisely
>allows you to state the initial states precisely. You can only do it to
>some level of accuracy.
You can only do it to the same extent as vice versa, probabilistically.
>
>>>This is certainly so for matter travelling +vely in time.
>>>None of it can go backwards. This need not be so of reversed-time
>>>particles.
>>
>>It would be the same. Remember a backward running electron appears to us
>>exactly like a forward running positron, so proper time for time
>>reversed particles behaves just as for forward running particles..
>
>Hmm. Good point. I need to ponder this again.
>So what that means is a backwards-running universe looks like a forward-
>running anti-universe.
Precisely.
>
>OK, my whole argument shot down in flames......
>
>There is one implication though. That is that time is something a
>particle carries.
>
That is something of which I am quite convinced. It ties together a lot
of ideas that people have thought about for some time, "many fingered
time", the importance of proper time. But I think it becomes clear when
put like that, that time is a property of matter, matter does not exist
in time.
--
Charles Francis
Oz
>>But what if you do the same experiment at the same time and place?
>>Is there any reason to expect the precise same result?
>>GR says yes, QM says no.
>
>History says yes. QM has no bearing on that.
History is by definition macroscopic and gr-like.
>>>It would be the same. Remember a backward running electron appears to us
>>>exactly like a forward running positron, so proper time for time
>>>reversed particles behaves just as for forward running particles..
>>
>>Hmm. Good point. I need to ponder this again.
>>So what that means is a backwards-running universe looks like a forward-
>>running anti-universe.
>
>Precisely.
>>
>>OK, my whole argument shot down in flames......
>>
>>There is one implication though. That is that time is something a
>>particle carries.
>>
>That is something of which I am quite convinced. It ties together a lot
>of ideas that people have thought about for some time, "many fingered
>time", the importance of proper time. But I think it becomes clear when
>put like that, that time is a property of matter, matter does not exist
>in time.
I am much tempted by this idea, it seems to fit.
But then you have to consider that space is also a property of matter.
God only knows what *that* would do to my crank index.
Oh, well, at least I have a better grasp of time and antiparticles, so
the thread has not been wasted.
Charles Francis
<o...@farmeroz.port995.com> writes
>Charles Francis <cha...@lluestfarmpoultry.co.uk> writes
>>In message <vhbUQJBx$ilA...@farmeroz.port995.com>, Oz
>><o...@farmeroz.port995.com> writes
>
>>>But what if you do the same experiment at the same time and place?
>>>Is there any reason to expect the precise same result?
>>>GR says yes, QM says no.
>>
>>History says yes. QM has no bearing on that.
>
>History is by definition macroscopic and gr-like.
History is that which happened. That which happened, happened,
irrespective of the physical laws underlying it.
>>>There is one implication though. That is that time is something a
>>>particle carries.
>>>
>>That is something of which I am quite convinced. It ties together a lot
>>of ideas that people have thought about for some time, "many fingered
>>time", the importance of proper time. But I think it becomes clear when
>>put like that, that time is a property of matter, matter does not exist
>>in time.
>
>I am much tempted by this idea, it seems to fit.
>But then you have to consider that space is also a property of matter.
Indeed. But whereas time is an elemental property, pertaining to each
individual particle, distance is emergent, requiring a system of
interactions between several particles.
Regards
--
Charles Francis
Gordon D. Pusch
Tim S <T...@timsilverman.demon.co.uk> writes:
> on 20/04/2004 7:35 am, John Baez at ba...@galaxy.ucr.edu wrote:
>
>>
>> Next puzzle... I may have asked Oz this already:
>>
>> PUZZLE: in Newtonian gravity, how does a small negative mass
>> "orbit" a big positive mass? What curve does it trace out?
>
> That's easy: 2-body orbits are conic sections, so it must be a hyperbola.
> With the big body at the focus of the other branch.
...Actually, that would be what you'd get if a small mass was "orbiting" a
large negative one.
For a small negative mass orbiting a large positive one, the orbit of the
small negative mass would be a normal ellipse around the postive mass body;
what would be a bit odd is that the positive mass body would be _between_
the small negative mass and the center of mass of the combined system,
which would still be at one of the foci of the ellipse...
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
John Baez
Aaron Bergman <aber...@physics.utexas.edu> wrote:
>In article <c6chsp$n0k$1...@glue.ucr.edu>, ba...@galaxy.ucr.edu (John Baez)
>wrote:
>> Depending on which we choose, we get two unitarily inequivalent
>> representations of the Poincare group on the single-particle Hilbert
>> space. Either choice is equally good, since they are equivalent
>> by an *antiunitary* operator.
>I don't see offhand how you're going to tell the difference between the
>ordinary theory and the 'negative mass' theory run backwards in time.
Right: time reversal is the antiunitary operator I was referring to
above.
However, there is a real difference between the theory of two species
of equal-mass particles, and the theory of two species of particles
of opposite mass! In the latter case the spectrum of the Hamiltonian
is the whole real line, while in the former the spectrum lies in a
half-line. This is for free particles. But....
John Baez
Charles Francis <cha...@clef.demon.co.uk> wrote:
>In message <c6cg9f$mg2$1...@glue.ucr.edu>, John Baez <ba...@galaxy.ucr.edu>
>writes
>>Newtonian gravity is *not* like electrostatics, since m shows up twice
>>in
>>
>>F = Gmm'/r^2
>>
>>and
>>
>>F = ma
>I make that thrice!
The concept of mass shows up thrice, but m shows up twice:
Thus, when you reverse the sign of just the mass m, the particle whose
mass was m feels the same acceleration.
But, if you switch the signs of *all* masses in a gravitational
problem, all accelerations switch sign.
Both the previous two sentences would work the other way if we
were doing electrostatics and said "charge" and "q" instead of
"mass" and "m":
When you reverse the sign of just the charge q, the particle whose
charge was q feels the opposite acceleration.
But: if you switch the signs of *all* charges in a electrostatics
problem, all accelerations stay the same.
Has someone pointed out yet that this is related to the fact that
photons have odd spin while gravitons have even spin?