# antimatter, feynman diagram, gravity

35 views

### Daniel

Mar 30, 2004, 12:42:32 PM3/30/04
to
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?

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

Mar 30, 2004, 2:15:29 PM3/30/04
to

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

Mar 31, 2004, 5:35:30 PM3/31/04
to
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.
>
> 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

Apr 1, 2004, 5:17:20 AM4/1/04
to

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

Apr 1, 2004, 10:15:50 AM4/1/04
to

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

Apr 1, 2004, 10:25:50 AM4/1/04
to
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, 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

Apr 2, 2004, 5:45:47 PM4/2/04
to
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...

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.

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

Apr 2, 2004, 5:46:26 PM4/2/04
to
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!

Let's pray that the world does not have closed time loops - a whole

> 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

-drl

### Danny Ross Lunsford

Apr 2, 2004, 5:50:35 PM4/2/04
to
Danny Ross Lunsford wrote:

> 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

Apr 3, 2004, 7:23:37 PM4/3/04
to

>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

Apr 3, 2004, 7:24:15 PM4/3/04
to
"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.

>, 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

Apr 4, 2004, 8:36:38 AM4/4/04
to

EjP wrote:

> 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

Apr 4, 2004, 8:36:43 AM4/4/04
to

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.

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

Apr 5, 2004, 2:49:34 PM4/5/04
to
Danny Ross Lunsford wrote:
>
> 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

Apr 5, 2004, 2:50:26 PM4/5/04
to
Danny Ross Lunsford <antima...@yahoo.NOSE-PAM.com> writes

>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

>*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

Apr 5, 2004, 2:50:41 PM4/5/04
to
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.

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

Apr 5, 2004, 2:51:33 PM4/5/04
to
Danny Ross Lunsford <antima...@yahoo.NOSE-PAM.com> writes
>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

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

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

Apr 5, 2004, 2:51:57 PM4/5/04
to

>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

Apr 5, 2004, 3:09:36 PM4/5/04
to
Oz <aco...@btopenworld.com> writes:

> 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.
>
> 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

Apr 6, 2004, 10:08:18 AM4/6/04
to

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

Apr 6, 2004, 10:08:30 AM4/6/04
to

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

Apr 6, 2004, 1:55:46 PM4/6/04
to
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? 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

Apr 6, 2004, 1:56:46 PM4/6/04
to

> "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

Apr 6, 2004, 5:53:39 PM4/6/04
to
Esa A E Peuha <esa....@helsinki.fi> writes

>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.

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

Apr 7, 2004, 3:12:52 PM4/7/04
to
In article <iHM3pEEX...@btopenworld.com>,
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.

>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:

http://math.ucr.edu/home/baez/puzzles/19.html

### John Baez

Apr 7, 2004, 3:12:58 PM4/7/04
to
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

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

Apr 7, 2004, 3:13:24 PM4/7/04
to
"Esa A E Peuha" <esa....@helsinki.fi> wrote in message
news:86pisge...@sirppi.helsinki.fi...

>
> > "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

### Doug Sweetser

Apr 8, 2004, 2:27:06 PM4/8/04
to
Hello:

> 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

Apr 8, 2004, 2:27:11 PM4/8/04
to
John Baez <ba...@galaxy.ucr.edu> writes

>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.

>>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

Apr 8, 2004, 2:28:08 PM4/8/04
to
Danny Ross Lunsford <antima...@yahoo.nose-pam.com> wrote:
> 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

Apr 8, 2004, 6:35:10 PM4/8/04
to
Danny Ross Lunsford <antima...@yahoo.NOSE-PAM.com> writes:

> 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

Apr 8, 2004, 6:39:50 PM4/8/04
to
John Baez wrote:

>>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

Apr 8, 2004, 6:42:02 PM4/8/04
to
"Michael Varney" <varney@colorado_no_spam.edu> wrote in message news:<y5Lcc.48\$fE1....@news.uswest.net>...

> > 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

Apr 9, 2004, 5:14:18 PM4/9/04
to
<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

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

Apr 11, 2004, 11:44:14 AM4/11/04
to

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

Apr 11, 2004, 11:44:32 AM4/11/04
to

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

Apr 13, 2004, 5:44:20 PM4/13/04
to
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
>
> 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

Apr 13, 2004, 5:42:34 PM4/13/04
to
ba...@math-ws-n09.math.ucr.edu (John Baez) writes:

>Some of you may enjoy this paper, or at least be infuriated by it:

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

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

Apr 13, 2004, 5:45:45 PM4/13/04
to
car...@no-physics-spam.ucdavis.edu writes

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

Apr 14, 2004, 3:18:10 AM4/14/04
to
Danny Ross Lunsford wrote:

> 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

Apr 14, 2004, 8:36:02 AM4/14/04
to

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

Apr 15, 2004, 7:02:11 AM4/15/04
to

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."

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

Apr 15, 2004, 11:17:24 AM4/15/04
to
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.

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

Apr 15, 2004, 11:16:47 AM4/15/04
to
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.

>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.
>

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

Apr 16, 2004, 2:28:22 AM4/16/04
to
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 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

Apr 17, 2004, 5:08:20 AM4/17/04
to
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,
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

Apr 17, 2004, 5:09:03 AM4/17/04
to
k_ig...@lycos.com (Igor Khavkine) wrote:
`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

Apr 18, 2004, 3:50:56 AM4/18/04
to
In article <c5fcj8\$6ua\$1...@glue.ucr.edu>, John Baez <ba...@galaxy.ucr.edu>
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:
>>>
>>>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.

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.
>>
>
>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

Apr 18, 2004, 3:51:04 AM4/18/04
to
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.

Regards

--
Charles Francis

### Arnold Neumaier

Apr 19, 2004, 1:29:45 PM4/19/04
to
John Baez wrote:
> 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

Apr 19, 2004, 1:51:25 PM4/19/04
to
k_ig...@lycos.com (Igor Khavkine) writes:

> 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

Apr 19, 2004, 2:08:22 PM4/19/04
to sci-physic...@moderators.isc.org
In article <c4s9pi\$c8g\$1...@lfa222122.richmond.edu>, Oz
<aco...@btopenworld.com> writes

>Danny Ross Lunsford <antima...@yahoo.NOSE-PAM.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

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

Apr 19, 2004, 2:08:44 PM4/19/04
to sci-physic...@moderators.isc.org
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

>
>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

Apr 19, 2004, 2:10:57 PM4/19/04
to
on 17/04/2004 10:08 am, Ken S. Tucker at dyna...@vianet.on.ca wrote:

> 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

Apr 19, 2004, 2:10:30 PM4/19/04
to sci-physic...@moderators.isc.org
In article <ZM6JLBCV...@btopenworld.com>, Oz
<o...@farmeroz.port995.com> writes
>John Baez <ba...@galaxy.ucr.edu> writes

>>
>>Now you've got all the necessary knowledge to take a crack at this:
>
>Oh .. my .. god! He never changes! Straight into homework.

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

Apr 19, 2004, 2:12:44 PM4/19/04
to
Charles Francis <cha...@clef.demon.co.uk> writes

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.