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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.

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]

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

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?

>

> 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)

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.

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

to

It's not really about lifetime, it's about energy. We routinely

store antiprotons for many days, but they're moving so fast that

gravity is negligible. In order to get any *individual* particles

(matter or antimatter) moving slowly enough that you can see

gravitational effects, they have to be very cold. Here's a paper

discussing some of the technical challenges in measuring the

graviational mass of anti-hydrogen

http://www.phy.duke.edu/~phillips/gravity/GravityExpt.html

-E

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/

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.

The adjoint is

psi* P gamma_0 ( gamma_m (dm - ieAm) + i M ) = 0

or

psibar P ( gamma_m (dm - ieAm) + i M ) = 0

There is a conserved current

J_m = psibar P gamma_m P psi = -psibar gamma_m psi

which is the original current reversed. That is, matter and antimatter

have been interchanged.

So, matter-antimatter conjugation is certainly associated with spacetime

symmetry. Note that the above description is given only in terms of

actual Lorentz-invariant objects.

-drl

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

boatload of angry antimatter might be headed this way!

> Of course it wouldn't be a simple process as each 'bunch' would continually be

> producing both particles and antiparticles and there would be quite a

> bit of mutual annihilation. One might imagine it as initially

> symmetrical (in the time direction) but becoming increasingly biassed

> towards antiparticles in the -t direction and particles in the +t

> direction. After some (probably quite brief but busy) period one might

> imagine each lobe would become separated (in time). Heuristically this

> (until shot down in flames by Those Who Know) might be a mechanism for

> explaining why we live in a (+ve) particulate universe where there isn't

> much mass left.

I don't think there is a great mystery about the local lack of

antimatter. Hannes Alfven showed in simple terms that that

observationally, at best matter and its mirror are separated at the

level of galaxy clusters. An interesting aspect of his analysis - if you

have a tenuous gas of matter and one of antimatter and allow them to

interact, a boundary area of annihilation sets up and the radiation

pressure from it tends to keep them separated. An exactly analogous

thing happens when you drip water onto a hot surface - the water boils

at the surface of the drop and the outgassing of steam lifts the drop up

off the hot surface - allowing the water drop to live an unexpectedly

long time ("Leidenfrost effect").

The main problem with Alfven's symmetric cosmology - explaining the

thermalization of the annihilation radiation.

-drl

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

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

to

EjP <nos...@hackers.are.bad> writes

>It's not really about lifetime, it's about energy. We routinely

>store antiprotons for many days, but they're moving so fast that

>gravity is negligible. In order to get any *individual* particles

>(matter or antimatter) moving slowly enough that you can see

>gravitational effects, they have to be very cold.

>It's not really about lifetime, it's about energy. We routinely

>store antiprotons for many days, but they're moving so fast that

>gravity is negligible. In order to get any *individual* particles

>(matter or antimatter) moving slowly enough that you can see

>gravitational effects, they have to be very cold.

Wouldn't it be possible to use the same techniques of a neutron

spallation source to produce very slow antineutrons?

The only problem is that theory may well suggest that they would still

fall in the same manner as neutrons. If so (which would seem likely) a

null result would be expected either way.

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

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.

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

to

EjP wrote:

> It's not really about lifetime, it's about energy. We routinely

> store antiprotons for many days, but they're moving so fast that

> gravity is negligible. In order to get any *individual* particles

> (matter or antimatter) moving slowly enough that you can see

> gravitational effects, they have to be very cold. Here's a paper

> discussing some of the technical challenges in measuring the

> graviational mass of anti-hydrogen

> http://www.phy.duke.edu/~phillips/gravity/GravityExpt.html

Great! Are you going to do this experiment? I would think it would be

very exciting. Good luck!

-drl

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.

I am unclear about this though. Will a large antimatter body repel

ordinary matter or attract it, similarly for antimatter. Its all those

double and triple negatives that confuse the heck out of me. You suggest

that they behave gravitationally differently but your first statement

(above) suggests they don't.

Its the old saw about negative mass being attracted by a negative force

results in attraction. Makes my head hurt ....

One has a horrible feeling that even devising a test to determine if

negative mass exists might be difficult.

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...

>

> 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).

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

radiation.

>*Should* we take it seriously?

Er, um, I have enough problem here anyway ...

>I only point out that in one case, we

>have a simple change in sign of the mass, and everything is sight is a

>straightforward spacetime covariant based on the Dirac algebra, while in

>the other, the unnatural looking charge-conjugation operator

>

>C = i gamma_2 gamma_0

>

>and the complex conjugate of the Dirac equation, must be introduced, not

>to mention the problematic idea of "backward in time".

>

>Moreover, when one goes over to Fermization (second quantization) the

>action of the charge conjugation operator itself changes (sign change).

>This is highly unsatisfactory.

Am I to interpret this as a statement that its mathematically more

elegant to take antiparticles as having negative mass but moving forward

in time?

If so, why is it considered somewhat crankish?

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.

I am unclear about this though. Will a large antimatter body repel

ordinary matter or attract it, similarly for antimatter. Its all those

double and triple negatives that confuse the heck out of me. You suggest

that they behave gravitationally differently but your first statement

(above) suggests they don't.

Its the old saw about negative mass being attracted by a negative force

results in attraction. Makes my head hurt ....

One has a horrible feeling that even devising a test to determine if

negative mass exists might be difficult.

--

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!

>Oz wrote:

>

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

>

>> One can get terribly confused by negatives of negatives on these

>> situations. I am easily confused....

>>

>> However there may be one scenario where the difference may make a

>> difference, or there again not.

>>

>> If one postulated that spacetime and matter popped into existence at t=0

>> then is it plausible to consider that antimatter immediately started to

>> head in the -t direction and matter in the +t direction.

>

>That is GREAT!! Of COURSE! It all ran off into the past!

Well, I have suggested it before. Seems quite a nice idea to me.

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

>boatload of angry antimatter might be headed this way!

We ought to see quite a few photons well in advance, so some warning

might be forthcoming.

>> Of course it wouldn't be a simple process as each 'bunch' would continually be

>> producing both particles and antiparticles and there would be quite a

>> bit of mutual annihilation. One might imagine it as initially

>> symmetrical (in the time direction) but becoming increasingly biassed

>> towards antiparticles in the -t direction and particles in the +t

>> direction. After some (probably quite brief but busy) period one might

>> imagine each lobe would become separated (in time). Heuristically this

>> (until shot down in flames by Those Who Know) might be a mechanism for

>> explaining why we live in a (+ve) particulate universe where there isn't

>> much mass left.

>

>I don't think there is a great mystery about the local lack of

>antimatter. Hannes Alfven showed in simple terms that that

>observationally, at best matter and its mirror are separated at the

>level of galaxy clusters. An interesting aspect of his analysis - if you

>have a tenuous gas of matter and one of antimatter and allow them to

>interact, a boundary area of annihilation sets up and the radiation

>pressure from it tends to keep them separated.

Sounds highly plausible, except that this radiation should be quite

evident, particularly in the early universe.

>An exactly analogous

>thing happens when you drip water onto a hot surface - the water boils

>at the surface of the drop and the outgassing of steam lifts the drop up

>off the hot surface - allowing the water drop to live an unexpectedly

>long time ("Leidenfrost effect").

It also hovercrafts round at high speed.

>The main problem with Alfven's symmetric cosmology - explaining the

>thermalization of the annihilation radiation.

His model doesn't seem to have much in common with my suggestion.

I am proposing it for the *very* early universe, certainly before

10^-12s. At this time radiation pressure would (I guess) be

insignificant compared to the energy of the particles. I would expect

particles and antiparticles to have very short mean free paths (in 4-D)

so the universe initially expanded symmetrically (that is equally in the

+t and -t) directions, it would be (looking from 5-D) a hypersphere.

However there would be a drift of antiparticles in the -t direction and

a drift of particles in the +t direction. The whole time, in each small

volume, particles and antiparticles would be being produced but

progressively the +t direction would be depleted in antiparticles, and

the -t in particles to produce two lobes. I expect it to end up as some

horrible diffusion-like equation. Something roughly analogous a ball of

hot plasma in an intense electrical field where ionisation is repeatedly

happening until the paths start to line up with the electric field.

Hah! Could a distant bunch of negative mass give us an accelerating

expansion? I don't know, seems unlikely.

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

to

EjP <nos...@hackers.are.bad> writes

>It's not really about lifetime, it's about energy. We routinely

>store antiprotons for many days, but they're moving so fast that

>gravity is negligible. In order to get any *individual* particles

>(matter or antimatter) moving slowly enough that you can see

>gravitational effects, they have to be very cold.

>It's not really about lifetime, it's about energy. We routinely

>store antiprotons for many days, but they're moving so fast that

>gravity is negligible. In order to get any *individual* particles

>(matter or antimatter) moving slowly enough that you can see

>gravitational effects, they have to be very cold.

Wouldn't it be possible to use the same techniques of a neutron

spallation source to produce very slow antineutrons?

The only problem is that theory may well suggest that they would still

fall in the same manner as neutrons. If so (which would seem likely) a

null result would be expected either way.

--

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.

>

> I am unclear about this though. Will a large antimatter body repel

> ordinary matter or attract it, similarly for antimatter.

Since antimatter is not known to have negative mass, I'll use PMM

(positive mass matter) and NMM (negative mass matter) to avoid any

confusion. Now PMM will attract anything gravitationally, and NMM will

repel everything, so if you have equal amounts of PMM and NMM

interacting only by gravitation next to each other, then the PMM will

accelerate away from the NMM and the NMM will follow the PMM. However

if these matters have also electric charge (and the gravitational

interaction can be ignored), things can look different; if they have the

same charge, the PMM will still accelerate away from the NMM and the NMM

will still accelerate towards the PMM (because for the NMM force and

acceleration vectors must point to opposite directions), but if they

have opposite charges, the NMM will run away and the PMM will follow.

> One has a horrible feeling that even devising a test to determine if

> negative mass exists might be difficult.

Actually it's pretty easy to see that at least antiparticles of ordinary

particles have positive mass; if, for example, the positron had negative

mass, we would see vast amounts of positrons chased by electrons at very

near light speed, since positron-electron pairs are known to be created

by cosmic radiation and other reasons. Also, positrons and antiprotons

are known to form antihydrogen atoms (or is that hydrogen antiatoms)

which would be impossible if they had negative masses.

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

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

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

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

to

"Michael Varney" <varney@colorado_no_spam.edu> writes:

> "Esa A E Peuha" <esa....@helsinki.fi> wrote in message

> news:86pptat...@sirppi.helsinki.fi...

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

> >

> > > However, the experiment has never been done, so the jury is out,

> > > physically speaking. Until a piece of antimatter can be made that lives

> > > long enough to fall in a vacuum, we won't "really" know.

> >

> > Antimatter will certainly fall just like ordinary matter

>

> Are you certain? Physics is an experimental science, and until this

> conjecture is experimentally verified, it cannot be stated with certainty.

Of course the result of any experiment can't be predicted with absolute

certainty. However, if the experiment shows that antimatter does fall

up, it violates general relativity on a very fundamental level. 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.

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.

Ahh, yes. I remember a long thread about this some years ago.

>However

>if these matters have also electric charge (and the gravitational

>interaction can be ignored), things can look different; if they have the

>same charge, the PMM will still accelerate away from the NMM and the NMM

>will still accelerate towards the PMM (because for the NMM force and

>acceleration vectors must point to opposite directions), but if they

>have opposite charges, the NMM will run away and the PMM will follow.

Hmmm. Not the sort of behaviour one usually expects.

>> One has a horrible feeling that even devising a test to determine if

>> negative mass exists might be difficult.

>

>Actually it's pretty easy to see that at least antiparticles of ordinary

>particles have positive mass; if, for example, the positron had negative

>mass, we would see vast amounts of positrons chased by electrons at very

>near light speed, since positron-electron pairs are known to be created

>by cosmic radiation and other reasons. Also, positrons and antiprotons

>are known to form antihydrogen atoms (or is that hydrogen antiatoms)

>which would be impossible if they had negative masses.

So perhaps better to take antiparticles as particles going backwards in

time? Or are you able to show that this has flaws too?

<sigh>

Apr 7, 2004, 3:12:52 PM4/7/04

to

In article <iHM3pEEX...@btopenworld.com>,

Oz <o...@farmeroz.port995.com> wrote:

Oz <o...@farmeroz.port995.com> wrote:

>Esa A E Peuha <esa....@helsinki.fi> writes

>>Antimatter will certainly fall just like ordinary matter, regardless of

>>whether it has positive or negative mass.

Right! - as long as general relativity applies, that is.

>I presume this is just a statement saying all bodies follow a geodesic.

Right, and it's worth noting this pattern:

the geodesic is timelike <=> mass^2 > 0 (tardyons)

the geodesic is lightlike <=> mass^2 = 0 (luxons)

the geodesic is spacelike <=> mass^2 < 0 (tachyons)

So, you can tell a little about the mass of a particle by the

sort of geodesic it follows, but not the *sign* of its mass.

>>The question is whether antimatter will attract (in case of positive

>>mass) or repel (negative mass) anything else.

>I am unclear about this though. Will a large antimatter body repel

>ordinary matter or attract it, similarly for antimatter. Its all those

>double and triple negatives that confuse the heck out of me.

Right, they're confusing - and I never worked them out myself until we

discussed this a couple of times here on sci.physics.research. But now

I know how it goes. As long as general relativity applies:

A positive-mass body will curve spacetime in a way that bends geodesics

"towards" it, so it will *attract* other bodies regardless of the sign

of their mass.

A negative-mass body will curve spacetime in a way that bends geodesics

"away from" it, so it will *repel* other bodies regardless of the sign

of their mass.

Now you've got all the necessary knowledge to take a crack at this:

PUZZLE:

Figure out what happens if you have two planets near each

other: Earth and Anti-Earth, the first with positive mass, the

second with an "equal but opposite" negative mass.

(We've already discussed *everything* here. We've even been through

a discussion before about how "equal and opposite" is a slightly stupid

thing to say - but we all know what it means.)

>Its the old saw about negative mass being attracted by a negative force

>results in attraction. Makes my head hurt ....

Yes, but it's not much worse than - x - = +... which of course some

people never get around to grokking.

>One has a horrible feeling that even devising a test to determine if

>negative mass exists might be difficult.

This is an interesting question, but you should do the puzzle

first.

By the way, it currently seems like I'll be in Oxford this July 7-9,

to speak at the Workshop on Gerbes: Recent Developments and Future

Perspectives, at Oxford, organized by Nuno Reis. So, maybe we can

get together while I'm there. (There's a chance this workshop won't

actually happen, due to funding issues, but regardless of that I'll

be in Cambridge from July 1st to September 8th, modulo a few side-trips.)

-------------------------------------------------------------------------

Puzzle #19:

As of February 2004, five of the ten richest people in the world had

the same last name. What is it?

If you give up, try:

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!)

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...> "Michael Varney" <varney@colorado_no_spam.edu> writes:

>

> > "Esa A E Peuha" <esa....@helsinki.fi> wrote in message

> > news:86pptat...@sirppi.helsinki.fi...

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

> > >

> > > > However, the experiment has never been done, so the jury is out,

> > > > physically speaking. Until a piece of antimatter can be made that

lives

> > > > long enough to fall in a vacuum, we won't "really" know.

> > >

> > > Antimatter will certainly fall just like ordinary matter

> >

> > Are you certain? Physics is an experimental science, and until this

> > conjecture is experimentally verified, it cannot be stated with

certainty.

>

> Of course the result of any experiment can't be predicted with absolute

> certainty. However, if the experiment shows that antimatter does fall

> up, it violates general relativity on a very fundamental level.

Which is why it is an important experiment to perform.

> Now

> general relativity has been tested by hundreds of experiments (with

> which no other known theory of gravity completely agrees), so it would

> be extremely surprising if antimatter did fall up.

It would be surprising. However, the experiment needs to be done, and to

state with certainty that antimatter will fall like matter is an incorrect

thing to do in science.

---

Michael Varney

Department of Physics

University of Colorado, Boulder

http://rintintin.colorado.edu/~varney

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

to

Hello:

I was thinking about this sort of thing recently:

> the geodesic is timelike <=> mass^2 > 0 (tardyons)

> the geodesic is lightlike <=> mass^2 = 0 (luxons)

> the geodesic is spacelike <=> mass^2 < 0 (tachyons)

See, there are perfectly fine paths in spacetime that are spacelike

separated from an observer:

\t| / x

\|/ |

R--------|

/|\ x

/ | \

The arbitrary choice of the origin makes all the events on that

worldline spacelike separated from the origin. The relativistic

velocity of the x--x worldline is zero, and could be created by a real

particle.

What happens if this spacetime graph is transformed to the classical

realm? The 45 degree lines end up going flat. In the limit of this

process, the nice defined slope of the x--x worldline becomes

undefined. Uncool.

I had an alternate idea, and want to see if someone else has thought of

this before. The Minkowski metric is an indefinite metric. It is that

darn negative distance squared that doesn't make sense, particularly

for a pure mathematician. So let's try and aid the mathematicians in

the audience. We apply a simple rule: if |t| > |R|, the point gets

plotted in spacetime as always. This should fill up the past and

future timelike light cones. If |t| < |R|, then we plot the points in

the complex-valued tangent space:

it| / x

\|/ |

iR--------|

/|\ x

/ | \

Now the metric will be a positive definite number because

(it)^2 - (iR)^2 = -|t|^2 + |R|^2 > 0

Note, the observer cannot travel a distance iR to get to these points.

Yet gamma and beta are well defined real numbers because they are

ratios of two imaginary numbers.

The Minkowski metric is a metric, not a pseudo metric, so long as this

rule of accounting in enforced for timelike events graphed in

spacetime, and spacelike events graphed in the complex-valued tangent

space.

doug

quaternions.com

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.

>In article <iHM3pEEX...@btopenworld.com>,

>Oz <o...@farmeroz.port995.com> wrote:

>

> and triple negatives that confuse the heck out of me.

>

>Right, they're confusing - and I never worked them out myself until we

>discussed this a couple of times here on sci.physics.research. But now

>I know how it goes. As long as general relativity applies:

>

>A positive-mass body will curve spacetime in a way that bends geodesics

>"towards" it, so it will *attract* other bodies regardless of the sign

>of their mass.

>

>A negative-mass body will curve spacetime in a way that bends geodesics

>"away from" it, so it will *repel* other bodies regardless of the sign

>of their mass.

That strikes me as very reasonable. Of course we must be careful to

distinguish between a positive and negative inertia, too. In this sort

of scenario I don't think we can assume mass and inertia will

necessarily be either the same, or a different, sign. Fortunately in GR

when following a geodesic, there is no acceleration so this can be

conveniently swept under the carpet.

>Now you've got all the necessary knowledge to take a crack at this:

Oh .. my .. god! He never changes! Straight into homework.

>PUZZLE:

>

> Figure out what happens if you have two planets near each

> other: Earth and Anti-Earth, the first with positive mass, the

> second with an "equal but opposite" negative mass.

I expect we will have the 'accelerate across the universe' scenario...

This needs some thought. I trust you are not expecting me to solve an

equivalent of schild metric for this scenario?

If so you are out of luck.

I assume embedded in an otherwise empty flat spacetime. For convenience

I will consider the masses as point particles.

Now what?

Well, there will be a point halfway between the two which will be

locally flat. Eh? No, that can't be right. A test particle on the

repulsive body will fall straight down and hit the attractive one, since

it will be repelled by the repulsive and attracted by the attractive.

So if both bodies were dust then the repulsive one would expand and the

attractive one would collapse. If they were solid enough to resist

gravitational forces then they clearly would accelerate across the

universe, trailing their gravitational fields behind them. If they were

orbiting each other as well, then they would have a complex circular

path (probably).

What if they were different sized masses?

Well a -m particle would orbit a large +m particle, but presumably in

its immediate vicinity space would be less curved. I think this means it

has a slightly larger orbit. The two bodies will orbit round a centre of

mass that will be outside the line between them. This will be a patch of

flat spacetime. For an infinitely small orbiting mass, the only patch of

flat spacetime (not at inf) will be the saddle on the major body,

clearly a -ve mass will push this further away from the -ve particle.

As their masses tend to being equal and opposite then this patch will

recede to infinity and we get the 'follow my leader' scenario again.

My head hurts ....

>>Its the old saw about negative mass being attracted by a negative force

>>results in attraction. Makes my head hurt ....

>

>Yes, but it's not much worse than - x - = +... which of course some

>people never get around to grokking.

>

>>One has a horrible feeling that even devising a test to determine if

>>negative mass exists might be difficult.

I note that time-reversing the above scenarios reverses -ve and +ve

mass.

>By the way, it currently seems like I'll be in Oxford this July 7-9,

>to speak at the Workshop on Gerbes: Recent Developments and Future

>Perspectives, at Oxford, organized by Nuno Reis. So, maybe we can

>get together while I'm there.

Should be fine.

I can't contact you, but you can contact me using reply-to of this post.

>(There's a chance this workshop won't

>actually happen, due to funding issues, but regardless of that I'll

>be in Cambridge from July 1st to September 8th, modulo a few side-trips.)

Will be outside claire's termtime I think.

Apr 8, 2004, 2:28:08 PM4/8/04

to

Danny Ross Lunsford <antima...@yahoo.nose-pam.com> wrote:

> Oz 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

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.

Apr 8, 2004, 6:39:50 PM4/8/04

to

John Baez wrote:

>>I am unclear about this though. Will a large antimatter body repel

>>ordinary matter or attract it, similarly for antimatter. Its all those

>>double and triple negatives that confuse the heck out of me.

>

> Right, they're confusing - and I never worked them out myself until we

> discussed this a couple of times here on sci.physics.research. But now

> I know how it goes. As long as general relativity applies:

>

> A positive-mass body will curve spacetime in a way that bends geodesics

> "towards" it, so it will *attract* other bodies regardless of the sign

> of their mass.

>

> A negative-mass body will curve spacetime in a way that bends geodesics

> "away from" it, so it will *repel* other bodies regardless of the sign

> of their mass.

This is consistent with taking the other sign for 2M in the

Schwarzschild solution. I suppose that was done.

> Now you've got all the necessary knowledge to take a crack at this:

>

> PUZZLE:

>

> Figure out what happens if you have two planets near each

> other: Earth and Anti-Earth, the first with positive mass, the

> second with an "equal but opposite" negative mass.

>

> (We've already discussed *everything* here. We've even been through

> a discussion before about how "equal and opposite" is a slightly stupid

> thing to say - but we all know what it means.)

Without looking up the answer, if it's going to be realistic then the

two have to be capable of erasing each other into some kind of

radiation. So they must be capable of forming some odd topogical

relation. This is like a magnetic pole in the vicinity of an electric one.

> -------------------------------------------------------------------------

> Puzzle #19:

>

> As of February 2004, five of the ten richest people in the world had

> the same last name. What is it?

This was too easy.

-drl

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.

>

> > 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

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

to

In article <53ca460a.04040...@posting.google.com>, Ulmo

<ul...@cheerful.com> wrote:

<ul...@cheerful.com> wrote:

Let's take just your first sentence's assertion and leave out the

elephant stuff.

If I could cite an instance of well established physics which is

believed by nearly everyone ever exposed to even the most mediocre

physics course and suggest or conjecture that the interpretation of the

data which has led people to believe in a certain behavior of matter

can be reanalyzed to yield a completely different hypothesis

(concerning this behavior) yet still provide the same data set then

would you change your mind?

Particularly if the extrapolation of the new hypothesis yields a

completely new physics that also is consistent with all known data and

physical phenomena?

To suppose that 'well established physics' is necessarily correct may

be precisely why physics as a discipline is mired in confusion and

complexity, and is presently not a finished science.

CCRyder

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

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?

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

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:

>http://math.ucr.edu/home/baez/quantum/

It makes very entertaining and educating reading. The last time I

looked at categories I gave up after a while because it seemed

cute but useless. Maybe I'll have another look.

>In particular,

>both Hilb and nCob but not Set are *-categories with a noncartesian

>monoidal structure. We show how this accounts for many of the famously

>puzzling features of quantum theory: the failure of local realism, the

>impossibility of duplicating quantum information, and so on. We argue

>that these features only seem puzzling when we try to treat Hilb as

>analogous to Set rather than nCob, so that quantum theory will make

>more sense when regarded as part of a theory of spacetime.

That claim is rather ambitious - from what I can see your solution

to the puzzles is merely to say just think about Hilbert spaces

and it'll be fine, which is the "shut up and calculate" approach

in disguise. You have definitely pinpointed one of the surprising

and perhaps disturbing aspects of quantum mechanics with the observation

that the product structure is noncartesian, although I think this

product discrepancy is known, if not understood so clearly, to anybody

who thinks about quantum mechanics.

The similarity of Hilb to relations rather than functions is

philosophically interesting as well, but I would say that overall,

the most puzzling features of quantum mechanics do not come from

its mathematical structures, but from from the thing which is not

expressed anywhere in the mathematics - the fact that individual

measurements have individual results, rather than mere amplitudes

of results.

"It is as if classical logic continued to apply to us, while the

mysterious rules of quantum theory apply only to the physical systems

we are studying. But of course this is not true: we are part of the

world being studied."

Here's a comment that most physicists won't like and will consider

useless philosophical rubbish, but which is true nonetheless: our

bodies are physical systems - parts of the world being studied, but

our minds are not.

R.

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.

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

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

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."

(I had to giggle at "slightly technical" after reading the first

paragraph, but he was right. It was mostly drawing nice pictures of

tangles.) I got it down to the end, but I missed the punchline. His

paper isn't online, so I'll have to see if I can figure it out during

the second lecture.

Anyway, here's what I got:

A tangle T has

1) An outer disk D0 minus an ordered (possibly empty) list of

subdisks.

2) A bunch of curves that divide up the interior into

checkerboard-colorable regions (equivalently, the boundaries of the

disks have an even number of curves ending on them).

3) A set of distinguished points: each disk boundary with at least one

curve intersecting it has one point, where white goes to black when

going clockwise around the disk, that is distinguished (denoted * in

the diagram)

4) "color": take the number of curves intersecting the outside edge

and divide by 2.

And a few other things I'll get to below.

So here is an example of a tangle:

---------------

-----...............-----

*--.........................--\

D0 ///|............................---\\

// |......................../--/ \\

// |....................---/ \\

// |................/--/ \\

/ /-----\........---/ \

/ // \\..---/ \

/ | +- \

/-------+ D1 | \

|........| | |

|.........| | |

|......../-*\ // ----------- |

|......../ \---+-/ //...........\\ |

|.......| |.| //...............\\ |

|.........\ /..| /...................\ |

|..........\---/...| |.....................| |

|..................| |........-----........| |

|..................| |.......// \\.......| |

|..................| |......| |......| |

|..................| |......| D3 |......| |

|..................| |......| |......| |

|............./----+\ |......\\ //......| |

|..........// \\ |........-----........| |

|.........| | \.................../ |

+--------* | \\...............// |

| | D2 | \\...........// |

| | | ----------- |

\ \\ // /

\ \---+-/..\\ /

\ |......\\ /

\ |........\\ /

\\ |..........\\ //

\\ |............\\ //

\\ |..............\\ //

\\\ |................\\ ///

\+-.................\\ --/

-----..............\-----

---------------

Subdisks are "inputs" and the outer boundary is the "output" of the

tangle. There's a natural way to compose tangles: if the input and

output are colored the same, match up the *'s and the curves.

Here is a tangle M(3):

---*--+--+---

----- |..| |...-----

///- |..| |........-\\\

// |..| |............\\

// |..| |..............\\

// |..| |................\\

/ *--+--+-.................\

// // \\................\\

/ / \.................\

/ | |.................\

| | D1 |................|

| | |.................|

| | |..................|

| | |...................|

| \ /.....................|

| \\ //......................|

| +--+--+-........................|

| |..| |.........................|

| |..| |.........................|

| -*--+--|.........................|

| //- -\\.......................|

| // \\.....................|

| / \...................|

| | |...................|

| | |.................|

| | D2 |................|

\ | |................/

\ | |.............../

\\ | |..............//

\ \ /............./

\\ \\ //............//

\\ \\- -//............//

\\ +-+-+--.............//

\\\- |.| |...........-///

----- |.| |......-----

--+-+-+------

It takes two 3-colored tangles X, Y as input and outputs a 3-colored

tangle. We can call it multiplication and denote the output as XY.

Annular tangles have one subdisk. An annular tangle A(m,n) is a

tangle with an m-colored input and an n-colored output. Here is the

identity(3,3) tangle:

-*--+--+---

/--- |..| |...---\

// |..| |.......\\

// |..| |.........\\

/ |..| |...........\

/ *--+--+-...........\

/ // \\..........\

| // \\.........|

| / \........|

| | |.........|

| | |........|

| | |........|

| | |........|

| | |.........|

| \ /........|

| \\ //.........|

\ \\ //........../

\ +---+--+.........../

\ |...| |........../

\\ |...| |........//

\\ |...| |......//

\--- |...| |..---/

-+---+--+--

Then there are tangles with no subdisks. A function from a

zero-dimensional vector space to an n-dimensional one is really just

scalar multiplication. So here's 1(3):

----+----+

//*-....| |--\\

// |.....| |....\\

/ |.....| |......\

/ |.....| |.......\

/ |.....| |........\

| |.....| |.........|

| |.....| |..........|

| |.....| |..........|

| |.....| |..........|

| |.....| |..........|

| |.....| |..........|

| |.....| |..........|

| |.....| |.........|

\ |.....| |......../

\ |.....| |......./

\ |.....| |....../

\\ |.....| |....//

\\+-....| |--//

----+----+

There's a conjugation operator * that's the following steps: reflect,

then move all the *'s counterclockwise (in the original drawing,

clockwise in the reflected one) one position on the disk boundary. So

M*(3) is (note the subdisk labels)

---*--+--+---

----- |..| |...-----

///- |..| |........-\\\

// |..| |............\\

// |..| |..............\\

// |..| |................\\

/ *--+--+-.................\

// // \\................\\

/ / \.................\

/ | |.................\

| | D2 |................|

| | |.................|

| | |..................|

| | |...................|

| \ /.....................|

| \\ //......................|

| +--+--+-........................|

| |..| |.........................|

| |..| |.........................|

| -*--+--|.........................|

| //- -\\.......................|

| // \\.....................|

| / \...................|

| | |...................|

| | |.................|

| | D1 |................|

\ | |................/

\ | |.............../

\\ | |..............//

\ \ /............./

\\ \\ //............//

\\ \\- -//............//

\\ +-+-+--.............//

\\\- |.| |...........-///

----- |.| |......-----

--+-+-+------

I.e. (XY)* = Y*X*.

We get an algebra out of tangles with no subdisks by making the disks

into squares with the * in the upper left, and half the curve

endpoints on top, half on bottom. So 1(3) also looks like this:

| | |

+------*------+-------+--------+

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

| |......| |........|

+------+------+-------+--------+

| | |

Multiplication is just stacking these; inputs are on top, outputs on

bottom.

Sometimes you get loops:

| | |

+-*----+------+------+

| |....| |......|

| \__/ |......|

| /......|

| /.......|

| /........|

| /.........|

| /..........|

| /...__......|

| /.../ \.....|

| |...| |....|

+------+---+----+----+

| | | <----- like this

+------*---+----+----+

| |...| |....|

| \...\__/.....|

| \...........|

| \..........|

| \.........|

| \........|

| \.......|

| ___ \......|

| /...\ |.....|

| |.....| |.....|

+--+-----+-----+-----+

| | |

When you do, you multiply by a constant, delta. This was the

important part that I missed. Something special happens when delta is

of the form

delta = cos 4pi/n (I think)

which has something to do with Vaughan Jones' subfactor planar

algebras. I didn't get all the details, and now I can't remember.

Does anyone know?

Next week I'll see how this works with cobordisms and TQFT's.

P.S. ASCII art courtesy of Email Effects. Great stuff, even includes

figlet fonts. http://www.sigsoftware.com/emaileffects/

--

Mike Stay

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

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

to

In article <ZM6JLBCV...@btopenworld.com>,

Oz <o...@farmeroz.port995.com> wrote:

Oz <o...@farmeroz.port995.com> wrote:

>John Baez <ba...@galaxy.ucr.edu> writes:

>>As long as general relativity applies:

>>

>>A positive-mass body will curve spacetime in a way that bends geodesics

>>"towards" it, so it will *attract* other bodies regardless of the sign

>>of their mass.

>>

>>A negative-mass body will curve spacetime in a way that bends geodesics

>>"away from" it, so it will *repel* other bodies regardless of the sign

>>of their mass.

In short:

a positive-mass body attracts EVERYTHING;

a negative-mass body repels EVERYTHING.

>That strikes me as very reasonable. Of course we must be careful to

>distinguish between a positive and negative inertia, too. In this sort

>of scenario I don't think we can assume mass and inertia will

>necessarily be either the same, or a different, sign.

I'm assuming general relativity holds. Given that, the equivalence

principle says mass and inertia are the same. If we don't assume

general relativity holds, all bets are off - we just have to do the

experiment.

>Fortunately in GR

>when following a geodesic, there is no acceleration so this can be

>conveniently swept under the carpet.

Yes: that's a more elegant way of saying the equivalence principle holds.

>>Now you've got all the necessary knowledge to take a crack at this:

>Oh .. my .. god! He never changes! Straight into homework.

Heh - but this is an easy one, just for old time's sake.

>>PUZZLE:

>>

>> Figure out what happens if you have two planets near each

>> other: Earth and Anti-Earth, the first with positive mass, the

>> second with an "equal but opposite" negative mass.

>I expect we will have the 'accelerate across the universe' scenario...

>

>This needs some thought. I trust you are not expecting me to solve an

>equivalent of schild metric for this scenario?

No, I don't expect miracles - just a little logic!

>I assume embedded in an otherwise empty flat spacetime. For convenience

>I will consider the masses as point particles.

Good.

>Now what?

Now solve the problem.

>Well, there will be a point halfway between the two which will be

>locally flat. Eh? No, that can't be right. A test particle on the

>repulsive body will fall straight down and hit the attractive one, since

>it will be repelled by the repulsive and attracted by the attractive.

Hmm, you've certainly managed to make it more complicated by

introducing this unnecessary "test particle". Now *I'm* confused!

>So if both bodies were dust then the repulsive one would expand and the

>attractive one would collapse.

You assumed they were points a minute ago, so there's no

need to worry about what would happen if they were made of dust -

though you're perfectly right about what *would* happen!

>If they were solid enough to resist

>gravitational forces then they clearly would accelerate across the

>universe, trailing their gravitational fields behind them.

Right! Excellent!

The positive mass Earth attracts the negative mass Anti-Earth.

The negative mass Anti-Earth repels the positive mass Anti-Earth.

Since they have "equal and opposite mass", they both accelerate

in the same direction at the same rate.

So, the Anti-Earth chases the Earth faster and faster, approaching

the speed of light... but never catches it.

And energy is conserved, since the total kinetic energy is zero

no matter how fast they're going!

>If they were orbiting each other as well, then they would have a

>complex circular path (probably).

Oh??

This is fun to think about, but I'm highly dubious of this idea of

particles of opposite mass "orbiting" each other. Do you see why?

>What if they were different sized masses?

This is even *more* fun.

>Well a -m particle would orbit a large +m particle, but presumably in

>its immediate vicinity space would be less curved.

You can do all these problems with Newtonian gravity as long as

nothing goes too fast and none of your point masses get too close.

You should do them this way before worrying about fancy "spacetime

curvature" effects.

>I think this means it

>has a slightly larger orbit. The two bodies will orbit round a centre of

>mass that will be outside the line between them. This will be a patch of

>flat spacetime. For an infinitely small orbiting mass, the only patch of

>flat spacetime (not at inf) will be the saddle on the major body,

>clearly a -ve mass will push this further away from the -ve particle.

I'm not sure what you mean here - let's keep things simple and

Newtonian for a while; we'll have enough fun that way.

In the Newtonian approximation, the center of mass of our two particles

will move along a straight line at constant speed. This is conservation

of momentum, so it holds no matter what the signs of the masses - under

our default assumption that GR still works.

But: what's the center of mass of a positive mass particle and a

negative mass particle?

>As their masses tend to being equal and opposite then this patch will

>recede to infinity and we get the 'follow my leader' scenario again.

>

>My head hurts ....

Yeah, it's tough. The math works just as well when you change

the signs in these problems. The hard part, but the fun part,

is to solve them using "intuition".

>>By the way, it currently seems like I'll be in Oxford this July 7-9,

>>to speak at the Workshop on Gerbes: Recent Developments and Future

>>Perspectives, at Oxford, organized by Nuno Reis. So, maybe we can

>>get together while I'm there.

>Should be fine.

>I can't contact you, but you can contact me using reply-to of this post.

Okay, I'll contact you shortly after I arrive in Cambridge on July 1st.

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.

>> 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).

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

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.

`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

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:

>>>

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.

>>>"towards" it, so it will *attract* other bodies regardless of the sign

>>>of their mass.

>>>

>>>A negative-mass body will curve spacetime in a way that bends geodesics

>>>"away from" it, so it will *repel* other bodies regardless of the sign

>>>of their mass.

Huh, I've missed something. Mass is generally a magnitude, hence

positive.

>

>In short:

>

>a positive-mass body attracts EVERYTHING;

>a negative-mass body repels EVERYTHING.

Well, if you say so.

>

>>>PUZZLE:

>>>

>>> Figure out what happens if you have two planets near each

>>> other: Earth and Anti-Earth, the first with positive mass, the

>>> second with an "equal but opposite" negative mass.

>

>>If they were solid enough to resist

>>gravitational forces then they clearly would accelerate across the

>>universe, trailing their gravitational fields behind them.

>

>Right! Excellent!

Is it?

>The positive mass Earth attracts the negative mass Anti-Earth.

>The negative mass Anti-Earth repels the positive mass Anti-Earth.

>

But since active gravitational mass is normally the same as passive

gravitational mass the positive mass Earth should attract the negative

mass anti-Earth negatively. I.e. it repels it, so we have the opposite

of em, like masses attract, unlike repel.

>negative mass particle?

>

>>As their masses tend to being equal and opposite then this patch will

>>recede to infinity and we get the 'follow my leader' scenario again.

>>

>>My head hurts ....

>

>Yeah, it's tough. The math works just as well when you change

>the signs in these problems. The hard part, but the fun part,

>is to solve them using "intuition".

Certainly math which isn't formalised intuition is no fun. And not much

use either in my book.

Regards

--

Charles Francis

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?

<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

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.

> 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

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.

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>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.

<aco...@btopenworld.com> writes>Ooohhh... that'll raise some eyebrows...

>

>>If one takes this seriously, then one has to consider the Schwarzschild

>>solution with the integration constant corresponding to the mass of the

>>body taken to have the opposite sign. Matter and antimatter would then

>>definitely be distinguised gravitationally.

Actually not. I like to think of (m,0,0,0) as representing the rest

momentum of a particle. An antiparticle has negative m, so is

represented by a vector pointing backwards in time. The active

gravitational effect is the same as for a positive m particle

represented by a vector pointing forwards in time.

>

>Ooooohhh ... not mainstream (but in many ways nice).

>Note that this matches well with Charles Francis' formulation of

>teleparallel quantum gravity and the naive particle-antiparticle BB

>radiation.

Ouch. I didn't think so.

>

>>*Should* we take it seriously?

Yes, but we have to be *very* careful about signs.

>

>Am I to interpret this as a statement that its mathematically more

>elegant to take antiparticles as having negative mass but moving forward

>in time?

No, you can't do that. They have negative mass moving backwards in time,

and this manifests as positive mass moving forwards in time.

Regards

--

Charles Francis

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

<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

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

Apr 19, 2004, 2:10:30 PM4/19/04