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Aug 14, 2010, 9:05:16 PM8/14/10

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A New Limit on Photon Mass

A new limit on photon mass, less than 10-51 grams or 7 x 10-19

electron volts, has been established by an experiment in which light

is aimed at a sensitive torsion balance; if light had mass, the

rotating balance would suffer an additional tiny torque. This

represents a 20-fold improvement over previous limits on photon mass.

Photon mass is expected to be zero by most physicists, but this is an

assumption which must be checked experimentally. A nonzero mass would

make trouble for special relativity, Maxwell's equations, and for

Coulomb's inverse-square law for electrical attraction.

The work was carried out by Jun Luo and his colleagues at Huazhong

University of Science and Technology in Wuhan, China

(jun...@mail.hust.edu.cn, 86-27-8755-6653). They have also carried out

a measurement of the universal gravitational constant G (Luo et al.,

Physical Review D, 15 February 1999) and are currently measuring the

force of gravity at the sub-millimeter range (a departure from

Newton's inverse-square law might suggest the existence of extra

spatial dimensions) and are studying the Casimir force, a quantum

effect in which nearby parallel plates are drawn together. (Luo et

al., Physical Review Letters, 28 February 2003)

A new limit on photon mass, less than 10-51 grams or 7 x 10-19

electron volts, has been established by an experiment in which light

is aimed at a sensitive torsion balance; if light had mass, the

rotating balance would suffer an additional tiny torque. This

represents a 20-fold improvement over previous limits on photon mass.

Photon mass is expected to be zero by most physicists, but this is an

assumption which must be checked experimentally. A nonzero mass would

make trouble for special relativity, Maxwell's equations, and for

Coulomb's inverse-square law for electrical attraction.

The work was carried out by Jun Luo and his colleagues at Huazhong

University of Science and Technology in Wuhan, China

(jun...@mail.hust.edu.cn, 86-27-8755-6653). They have also carried out

a measurement of the universal gravitational constant G (Luo et al.,

Physical Review D, 15 February 1999) and are currently measuring the

force of gravity at the sub-millimeter range (a departure from

Newton's inverse-square law might suggest the existence of extra

spatial dimensions) and are studying the Casimir force, a quantum

effect in which nearby parallel plates are drawn together. (Luo et

al., Physical Review Letters, 28 February 2003)

Aug 15, 2010, 1:20:52 PM8/15/10

to

physics wrote:

> A New Limit on Photon Mass

> A new limit on photon mass, less than 10-51 grams or 7 x 10-19

> electron volts, has been established by an experiment in which light

> is aimed at a sensitive torsion balance; if light had mass, the

> rotating balance would suffer an additional tiny torque. This

> represents a 20-fold improvement over previous limits on photon mass.

> Photon mass is expected to be zero by most physicists, but this is an

> assumption which must be checked experimentally. A nonzero mass would

> make trouble for special relativity,

> A New Limit on Photon Mass

> A new limit on photon mass, less than 10-51 grams or 7 x 10-19

> electron volts, has been established by an experiment in which light

> is aimed at a sensitive torsion balance; if light had mass, the

> rotating balance would suffer an additional tiny torque. This

> represents a 20-fold improvement over previous limits on photon mass.

> Photon mass is expected to be zero by most physicists, but this is an

> assumption which must be checked experimentally. A nonzero mass would

> make trouble for special relativity,

Why for relativity?

QED with massive photons is still renormalizable and relativistic.

Arnold Neumaier

Aug 15, 2010, 1:20:53 PM8/15/10

to

> ...

> Photon mass is expected to be zero by most physicists, but this is an

> assumption which must be checked experimentally. A nonzero mass would

> make trouble for special relativity, Maxwell's equations, and for

> Coulomb's inverse-square law for electrical attraction.

> ...

> Photon mass is expected to be zero by most physicists, but this is an

> assumption which must be checked experimentally. A nonzero mass would

> make trouble for special relativity, Maxwell's equations, and for

> Coulomb's inverse-square law for electrical attraction.

This kind of experiment is a waste of time except as a way of training

the

experimenters in making careful measurements.

Special relativity is not in trouble; it is an observed fact that the

speed of

light in vacuum does not vary with reference frame. This could not

possibly be so if

photons had a nonzero mass or a proper time. The mass of a photon

must be exactly

zero; any rationale which postulates a transition region, a

continuity, from

zero to minute but nonzero mass is math fiction, not science.

One might as well remeasure the mass of the electron, to see whether

it was zero or not.

Think of the trouble that would cause for electronics!

Aug 15, 2010, 1:49:05 PM8/15/10

to

jw...@BasicISP.net wrote:

> On Aug 14, 6:05 pm, physics <phy...@gmail.com> wrote:

>> A New Limit on Photon Mass

>> ...

>> Photon mass is expected to be zero by most physicists, but this is an

>> assumption which must be checked experimentally. A nonzero mass would

>> make trouble for special relativity, Maxwell's equations, and for

>> Coulomb's inverse-square law for electrical attraction.

>> ...

>

> This kind of experiment is a waste of time except as a way of training

> the

> experimenters in making careful measurements.

>

> Special relativity is not in trouble; it is an observed fact that the

> speed of

> light in vacuum does not vary with reference frame.

> On Aug 14, 6:05 pm, physics <phy...@gmail.com> wrote:

>> A New Limit on Photon Mass

>> ...

>> Photon mass is expected to be zero by most physicists, but this is an

>> assumption which must be checked experimentally. A nonzero mass would

>> make trouble for special relativity, Maxwell's equations, and for

>> Coulomb's inverse-square law for electrical attraction.

>> ...

>

> This kind of experiment is a waste of time except as a way of training

> the

> experimenters in making careful measurements.

>

> Special relativity is not in trouble; it is an observed fact that the

> speed of

> light in vacuum does not vary with reference frame.

This is demonstable only within a certain accuracy.

> This could not possibly be so if

> photons had a nonzero mass or a proper time.

If photons have mass, the relativity principle simply reads:

''There is a finite limit speed for particles, which is achieved if

the particle is massless, and which is asymptotically approached as

a massive particle acquires more and more momentum.''

Only this is required for a consistent standard model + relativitry.

Arnold Neumaier

Aug 15, 2010, 4:30:27 PM8/15/10

to

"jw...@BasicISP.net" <jw...@BasicISP.net> writes:

> On Aug 14, 6:05 pm, physics <phy...@gmail.com> wrote:

>> A New Limit on Photon Mass

>> ...

>> Photon mass is expected to be zero by most physicists, but this is an

>> assumption which must be checked experimentally. A nonzero mass would

>> make trouble for special relativity, Maxwell's equations, and for

>> Coulomb's inverse-square law for electrical attraction.

>> ...

>

> This kind of experiment is a waste of time except as a way of training

> the experimenters in making careful measurements.

It does that, for sure. Were there only coresponding activities that

trained the theoretians in making careful claims.

> Special relativity is not in trouble; it is an observed fact that the

> speed of light in vacuum does not vary with reference frame.

And those are the observations that give the current (or previous)

limits for the photon mass. How well do you think is the constancy of

the speed of light established?

> This could not possibly be so if photons had a nonzero mass or a

> proper time. The mass of a photon must be exactly zero; any rationale

> which postulates a transition region, a continuity, from zero to

> minute but nonzero mass is math fiction, not science.

Here is a training activity as alleged above: Devise an experiment (can

be a Gedankenexperiment, but real experiments are preferred) that allows

to distinguish through a measurement a photon mass of 1e-100 eV from 0

eV.

--

Space - The final frontier

Aug 16, 2010, 5:03:33 AM8/16/10

to

physics wrote:

[...]

[...]

Relativity would not care, as it is not a theory of light.

All that would happen is Maxwell --> Proca, and a decoupling between the

speed of light and the maximum speed on a Lorentzian manifold.

Aug 16, 2010, 9:19:01 AM8/16/10

to

<jw...@BasicISP.net> wrote in message

news:f6ee99d6-24dc-40ae...@t2g2000yqe.googlegroups.com...

> On Aug 14, 6:05 pm, physics <phy...@gmail.com> wrote:

>> A New Limit on Photon Mass

>> ...

>> Photon mass is expected to be zero by most physicists, but

>> this is an

>> assumption which must be checked experimentally. A nonzero

>> mass would

>> make trouble for special relativity, Maxwell's equations, and

>> for

>> Coulomb's inverse-square law for electrical attraction.

>> ...

>

> This kind of experiment is a waste of time except as a way of

> training

> the

> experimenters in making careful measurements.

>

news:f6ee99d6-24dc-40ae...@t2g2000yqe.googlegroups.com...

> On Aug 14, 6:05 pm, physics <phy...@gmail.com> wrote:

>> A New Limit on Photon Mass

>> ...

>> Photon mass is expected to be zero by most physicists, but

>> this is an

>> assumption which must be checked experimentally. A nonzero

>> mass would

>> make trouble for special relativity, Maxwell's equations, and

>> for

>> Coulomb's inverse-square law for electrical attraction.

>> ...

>

> This kind of experiment is a waste of time except as a way of

> training

> the

> experimenters in making careful measurements.

>

No, it isn't. All postulation must be checked to the be method

of measurements. Only if the basis of physics is confirmed within

experimental limits can the theories based on those postulations

can be trusted. The more precise and the more accurate we can

measure fundamental physical constants the more confidence we

have in our explanation of world and universe.

This experiment is in the same league as measuring the decay rate

of a proton or the change in time of the gravitational constant.

Aug 16, 2010, 11:41:13 AM8/16/10

to

jw...@BasicISP.net wrote:

> On Aug 14, 6:05 pm, physics <phy...@gmail.com> wrote:

>> A New Limit on Photon Mass ... Photon mass is expected to be zero by most

>> physicists, but this is an assumption which must be checked experimentally.

>> A nonzero mass would make trouble for special relativity, Maxwell's

>> equations, and for Coulomb's inverse-square law for electrical attraction.

>> ...

>

> This kind of experiment is a waste of time except as a way of training the

> experimenters in making careful measurements.

> On Aug 14, 6:05 pm, physics <phy...@gmail.com> wrote:

>> A New Limit on Photon Mass ... Photon mass is expected to be zero by most

>> physicists, but this is an assumption which must be checked experimentally.

>> A nonzero mass would make trouble for special relativity, Maxwell's

>> equations, and for Coulomb's inverse-square law for electrical attraction.

>> ...

>

> This kind of experiment is a waste of time except as a way of training the

> experimenters in making careful measurements.

No. It is always appropriate to test physical theories to improved accuracy. One

never knows where surprises might turn up (see neutrinos below).

> Special relativity is not in trouble; it is an observed fact that the speed

> of light in vacuum does not vary with reference frame. This could not

> possibly be so if photons had a nonzero mass or a proper time.

Observations of the constancy of the speed of light have a limit in their

accuracy, and that is ENORMOUSLY less accurate than these more direct

measurements of the photon mass. I don't know exactly, but in terms of a limit

on the photon mass it must be many billions of times greater (c.f. neutrinos below).

> The mass of

> a photon must be exactly zero; any rationale which postulates a transition

> region, a continuity, from zero to minute but nonzero mass is math fiction,

> not science.

Not true. There are viable physical theories in which the photon has a nonzero mass.

Sanity check: just a few years ago it was generally accepted that neutrinos had

zero mass. Today from oscillation measurements it is known that at least two of

them have nonzero mass, and it is suspected that all of them do. Note the lower

limits on neutrino masses are ~10^15 times larger than the limit on the photon

mass, yet neutrinos and light moved with the same speed to within ~10 parts per

billion from SN1987A -- that is comparable to the accuracy with which the speed

of light was known prior to the redefinition in 1983.

> One might as well remeasure the mass of the electron, to see whether it was

> zero or not. Think of the trouble that would cause for electronics!

This is not a valid analogy.

As I said before, Special Relativity would not be affected by a non-zero photon

mass, as Einstein's second postulate is not required in a modern derivation

(using group theory one obtains three related theories, two of which are solidly

refuted experimentally and the third is SR). So today's foundations of modern

physics would not be threatened.

Tom Roberts

Aug 16, 2010, 12:06:52 PM8/16/10

to

==== Moderator's note ==================================================

The photon mass is determined to be 0 to a phantastic degree of

accuracy, but it's not absolutely known to be exactly 0. The upper

limit, according to the just appeared review of particle physics is

m<10^(-18) eV/c^2.

========================================================================

On Aug 16, 8:41 am, Tom Roberts <tjroberts...@sbcglobal.net> wrote:

> jw...@BasicISP.net wrote:

>

You are missing the point. The the photon mass HAS BEEN measured

with infinite precision already!

If a photon had ANY mass, it would by definition be associated

with an inertial rest frame. Therefore, the speed of propagation

of photons would vary with the velocity of the source, relative

to any other rest frame. The velocity of light would very obviously

add or subtract from the easily measured velocities of other objects,

such as satellites, planets, or stars.

But, the speed of light is known to be at least approximately constant

in all rest frames,

well within the margin of error which holds for objects moving

with various velocities. The mass can not be nonzero, whether

or not the speed of light is exactly the same in all frames.

Aug 16, 2010, 1:15:30 PM8/16/10

to

On Aug 15, 7:20 pm, Arnold Neumaier <Arnold.Neuma...@univie.ac.at>

wrote:

wrote:

Obviously that would invalidate the light postulate of SRT; but that

already happened with GRT. Such "trouble" is both real and small.

Harald

Aug 16, 2010, 3:07:07 PM8/16/10

to

"jw...@BasicISP.net" <jw...@BasicISP.net> writes:

> ==== Moderator's note ==================================================

> The photon mass is determined to be 0 to a phantastic degree of

> accuracy, but it's not absolutely known to be exactly 0. The upper

> limit, according to the just appeared review of particle physics is

> m<10^(-18) eV/c^2.

> ========================================================================

>

> On Aug 16, 8:41 am, Tom Roberts <tjroberts...@sbcglobal.net> wrote:

>> jw...@BasicISP.net wrote:

>>

>

> You are missing the point. The the photon mass HAS BEEN measured

> with infinite precision already!

If you could name the relevant publication, many of us would appreciate

it.

Aug 17, 2010, 3:27:01 AM8/17/10

to

Thus spake "jw...@BasicISP.net" <jw...@BasicISP.net>

>

>==== Moderator's note ==================================================

>The photon mass is determined to be 0 to a phantastic degree of

>accuracy, but it's not absolutely known to be exactly 0. The upper

>limit, according to the just appeared review of particle physics is

>m<10^(-18) eV/c^2.

>========================================================================

>

>On Aug 16, 8:41 am, Tom Roberts <tjroberts...@sbcglobal.net> wrote:

>> jw...@BasicISP.net wrote:

>>

>

>You are missing the point. The the photon mass HAS BEEN measured

>with infinite precision already!

>

>If a photon had ANY mass, it would by definition be associated

>with an inertial rest frame.

>

>==== Moderator's note ==================================================

>The photon mass is determined to be 0 to a phantastic degree of

>accuracy, but it's not absolutely known to be exactly 0. The upper

>limit, according to the just appeared review of particle physics is

>m<10^(-18) eV/c^2.

>========================================================================

>

>On Aug 16, 8:41 am, Tom Roberts <tjroberts...@sbcglobal.net> wrote:

>> jw...@BasicISP.net wrote:

>>

>

>You are missing the point. The the photon mass HAS BEEN measured

>with infinite precision already!

>

>If a photon had ANY mass, it would by definition be associated

>with an inertial rest frame.

This seems to be your misconception. It is true that Einstein originally

formulated sr wrt the speed of light. Since then it has been recognised

that sr should be formulated wrt a limiting speed, sometimes called the

maximal speed of information. When sr is formulated like this it still

holds but has no physical dependency on light and the photon does not

have to have zero mass.

Regards

--

Charles Francis

moderator sci.physics.foundations.

charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and

braces)

Aug 17, 2010, 9:56:24 PM8/17/10

to

physics <phy...@gmail.com> wrote:

> A New Limit on Photon Mass

> A new limit on photon mass, less than 10-51 grams or 7 x 10-19

> electron volts, has been established by an experiment in which light

> is aimed at a sensitive torsion balance; if light had mass, the

> rotating balance would suffer an additional tiny torque. This

> represents a 20-fold improvement over previous limits on photon mass.

The experiment has no value beyond a demonstration

of experimental skills.

It teaches us nothing new about the universe.

The limit corresponds (in more relevant units)

to a photon mass of about 2 mHz, or about 1 AU^-1

We already have far more stringent limits on the photon mass

from solar system physics,

(solar magnetopause, and interstellar magneto-hydrodynamics,

which tell us that the range of the EM force is far larger than 1 AU,

hence the photon mass is much smaller than that.

> Photon mass is expected to be zero by most physicists, but this is an

> assumption which must be checked experimentally.

Physists expect nothing of the kind.

They use the simplest adequate model,

which for the time being has zero photon mass.

> A nonzero mass would

> make trouble for special relativity, Maxwell's equations, and for

> Coulomb's inverse-square law for electrical attraction.

No problem for special relativity,

and we know how Maxwell's equations

and Coulombs law will be modified.

Jan

Aug 17, 2010, 10:01:55 PM8/17/10

to

I'll try once more.

It has nothing to do with the exact speed of light, nor with

propagation of

information. We are not talking about information, but about light.

The infinite precision only depends upon the empirical fact that

the velocity of light does not add to the velocity of an object

sending or receiving light.

It also depends upon the assumption that light consists of photons.

If a photon had mass, then its velocity would depend on existence

of a rest frame for that photon. If such a rest frame existed,

then the velocity of light would add to that of the object at

its points of creating and annihilation. But this never is observed.

Surely, no one is questioning the idea of vector addition?

Therefore, photons have no rest frame, no proper time, nor

any mass.

The experiment described may indeed be valuable as training

for the researchers who carried it out, and it may be

valuable as a paradigm of precision, but it did not

reveal anythng new about the mass of the photon.

As for the information issue, one has to keep in mind

that the speed itself isn't the issue, but rather the mass

(or, value of the rest mass in some inertial frame).

Under reasonable assumptions, it eaasily can be proven

deductively tha all massless particles travel at the

same speed. If this is of interest, then you may

try reading http://www.siuc.edu/~pulfrich/Pulfrich_Pages/lit_nonp/phys_astro/2007_cSpeed/LimitingVelocity.html

Aug 18, 2010, 6:32:57 AM8/18/10

to

jw...@BasicISP.net wrote:

> I'll try once more.

>

> It has nothing to do with the exact speed of light, nor with

> propagation of

> information. We are not talking about information, but about light.

>

> The infinite precision only depends upon the empirical fact that

> the velocity of light does not add to the velocity of an object

> sending or receiving light.

> I'll try once more.

>

> It has nothing to do with the exact speed of light, nor with

> propagation of

> information. We are not talking about information, but about light.

>

> The infinite precision only depends upon the empirical fact that

> the velocity of light does not add to the velocity of an object

> sending or receiving light.

As any empirical fact, this can be checked experimentally only up

to some tiny possible deviations.

> It also depends upon the assumption that light consists of photons.

>

> If a photon had mass, then its velocity would depend on existence

> of a rest frame for that photon. If such a rest frame existed,

> then the velocity of light would add to that of the object at

> its points of creating and annihilation. But this never is observed.

Observations are never exact, so sufficiently small deviations

(and hence a sufficiently small mass of the photon) cannot

be observed. The point of such experiments is precisely to

imporve the limit on how small these deviations must be.

If actual deviations would be found by an accurate enough

experiment, it would make a difference to physics.

> Surely, no one is questioning the idea of vector addition?

The question is how accurately Nature respects this vector addition.

> Therefore, photons have no rest frame, no proper time, nor

> any mass.

This only holds if you _define_ photons to be massless particles.

The question then would become whether these theoretical photons

describe Nature exactly. But the testing problem would remain the same.

> Under reasonable assumptions, it eaasily can be proven

> deductively that all massless particles travel at the

> same speed.

Yes, and currently, this speed is called the speed of light.

Would the photon be found to have a slight mass, this speed would

simply be renamed to ''limit speed'' or something like that,

photons could come to rest, but not much else would change.

Aug 18, 2010, 6:47:22 AM8/18/10

to

There is one more difference between a massless and a massive vector field,

and that's the fact that a massive field has three physical field degrees of

freedom. In the rest frame of a single particle (the usual choice of the

"standard momentum" for massive particles in the representation theory of

the Poincare group) these are the three spin components of the particle (the

little group is SO(3), and thus one has usual spin, defined by the behavior

of the states of particles at rest under the rotation group, i.e. (2s+1)

spin states).

and that's the fact that a massive field has three physical field degrees of

freedom. In the rest frame of a single particle (the usual choice of the

"standard momentum" for massive particles in the representation theory of

the Poincare group) these are the three spin components of the particle (the

little group is SO(3), and thus one has usual spin, defined by the behavior

of the states of particles at rest under the rotation group, i.e. (2s+1)

spin states).

For massless particles, however, the little group is generated by boosts in

direction of the light-like (!) standard momentum (usually the z axis) and

two independent "null rotations". This group is equivalent to ISO(2), the

affine group of the Euclidean 2D plane. In order not to have continuous

spin-like intrinsic degrees of freedom of massless particles, one assumes

that the null rotations are represented trivially, which implies that

massless vector fields (and such of higher spin) admit corresponding local

gauge transformations and are thus gauge fields. The physical degrees of

freedom are the two helicity states \pm s.

I've never thought about it carefully, but wouldn't indeed a finite mass of

photons, no matter how tiny it might be (the most recent PDB lists 10^-18 eV

as upper limit) change the thermodynamics of black-body radiation? At a

given temperature one would have a larger photon density by a factor of 3/2.

Shouldn't this have been observed then by now?

Arnold Neumaier wrote:

--

Hendrik van Hees

Justus-Liebig Universität Gießen

D-35392 Gießen

http://theorie.physik.uni-giessen.de/~hees/

Aug 18, 2010, 3:24:01 PM8/18/10

to

On 08/18/2010 06:47 AM, Hendrik van Hees wrote:

> There is one more difference between a massless and a massive vector field,

> and that's the fact that a massive field has three physical field degrees of

> freedom.

...> There is one more difference between a massless and a massive vector field,

> and that's the fact that a massive field has three physical field degrees of

> freedom.

> I've never thought about it carefully, but wouldn't indeed a finite mass of

> photons, no matter how tiny it might be (the most recent PDB lists 10^-18 eV

> as upper limit) change the thermodynamics of black-body radiation? At a

> given temperature one would have a larger photon density by a factor of 3/2.

> Shouldn't this have been observed then by now?

Must the Photon Mass be Zero?

L. Bass, E. Schrödinger

http://www.jstor.org/stable/99679

Discusses exactly this question. (answer:no)

The longitudinal degrees of freedom couple to matter so weakly, they can

never come to thermal equilibrium. Any practical cavity is effectively

transparent to to longitudinally polarized photons. In the m=0 limit

they don't interact at all, making them non-physical.

The effects of photon mass on black body radiation are (according to

http://link.aps.org/doi/10.1103/PhysRevA.32.623) much too small for any

reasonable experiment to detect (given existing upper bounds).

Ralph Hartley

Aug 18, 2010, 7:06:53 PM8/18/10

to

Thus spake "jw...@BasicISP.net" <jw...@BasicISP.net>

>I'll try once more.

>

>It has nothing to do with the exact speed of light, nor with

>propagation of

>information. We are not talking about information, but about light.

>I'll try once more.

>

>It has nothing to do with the exact speed of light, nor with

>propagation of

>information. We are not talking about information, but about light.

Actually we are talking about the structure of spacetime, by which we

may mean a mathematical structure, i.e. R$, whose elements can be found

from a particular class of physical processes, namely, measurements of

time and position. Those processes only make sense given a maximal speed

of information. To the best of our knowledge this is equal to the speed

of light, but because all measurement has finite accuracy, we cannot say

with absolute certainty that the two are equal.

>

>The infinite precision only depends upon the empirical fact that

>the velocity of light does not add to the velocity of an object

>sending or receiving light.

That is an empirical fact known only with finite precision. Experiments

like the one describe improve the precision with which it is known.

>

>It also depends upon the assumption that light consists of photons.

This is quite another matter. We don't need an assumption here. Both the

theoretical and empirical evidence are conclusive.

Aug 18, 2010, 7:06:54 PM8/18/10

to

Arnold Neumaier wrote:

> jw...@BasicISP.net wrote:

> jw...@BasicISP.net wrote:

>> If a photon had mass, then its velocity would depend on existence

>> of a rest frame for that photon. If such a rest frame existed,

>> then the velocity of light would add to that of the object at

>> its points of creating and annihilation. But this never is observed.

>

> Observations are never exact, so sufficiently small deviations

> (and hence a sufficiently small mass of the photon) cannot

> be observed. The point of such experiments is precisely to

> imporve the limit on how small these deviations must be.

A thorough analysis of the problems involved in determining the mass of

the photon is given in the paper

L.-C. Tu, J. Luo, and G.T. Gillies,

The mass of the photon

Rep. Prog. Phys. 68 (2005), 77--130.

See also

AS Goldhaber, MM Nieto

Photon and graviton mass limits

Reviews of Modern Physics, 2010

arxiv:0809.1003

Aug 18, 2010, 7:06:53 PM8/18/10

to

Hendrik van Hees wrote:

> There is one more difference between a massless and a massive vector field,

> and that's the fact that a massive field has three physical field degrees of

> freedom. In the rest frame of a single particle (the usual choice of the

> "standard momentum" for massive particles in the representation theory of

> the Poincare group) these are the three spin components of the particle [...]> There is one more difference between a massless and a massive vector field,

> and that's the fact that a massive field has three physical field degrees of

> freedom. In the rest frame of a single particle (the usual choice of the

> "standard momentum" for massive particles in the representation theory of

>

> massless vector fields (and such of higher spin) admit corresponding local

> gauge transformations and are thus gauge fields. The physical degrees of

> freedom are the two helicity states \pm s.

>

> I've never thought about it carefully, but wouldn't indeed a finite mass of

> photons, no matter how tiny it might be (the most recent PDB lists 10^-18 eV

> as upper limit) change the thermodynamics of black-body radiation?

It would change it by a tiny amount only. There is no discontinuity.

> At a given temperature one would have a larger photon density by a factor of 3/2.

Why? This would assume that all modes are equivalent.

But the transverse state would be very little populated only.

The reason is that for almost massless particles, the transverse mode is

suppressed by a factor proportional to its mass. (Or even mass square?

I'd need to check; haven't done such calculations for a long time.)

This can be seen by writing the massive representation in the Jacob-Wick

helicity form, where the massless limit can be taken. The massless case

is just a conventional limit of the massive case, without any

discontinuity when the mass approaches zero.

Jacob M & Wick G C.

On the general theory of collisions for particles with spin.

Ann.Phys. 7:404-428, 1959.

Thus what is known about black body radiation gives just like any other

effect only an upper bound on the photon mass.

Arnold Neumaier

Aug 19, 2010, 1:56:15 AM8/19/10

to

On 08/17/2010 10:01 PM, jw...@BasicISP.net wrote:

> If a photon had mass, then its velocity would depend on existence

> of a rest frame for that photon. If such a rest frame existed,

> then the velocity of light would add to that of the object at

> its points of creating and annihilation.

Also higher energy (blue) photons would go slightly faster than lower

energy (red) ones. Light from an approaching source would be faster, and

therefore appear bluer. The Doppler shift is about the same for zero

mass and very small mass.

> Surely, no one is questioning the idea of vector addition?

This remark makes me suspect that you may have forgotten that the

relativistic formula for adding velocities is s=(a+b)/(1+ab/c^2) not

s=a+b. If one of the two velocities is very close c (and the other is

not as close) then the sum will be very close to c as well.

Ralph Hartley

Aug 19, 2010, 4:09:55 AM8/19/10

to

Arnold Neumaier <Arnold....@univie.ac.at> wrote:

[Moderator's note: Huge amount of quoted text snipped. -P.H.]

> > Therefore, photons have no rest frame, no proper time, nor

> > any mass.

>

> This only holds if you _define_ photons to be massless particles.

> The question then would become whether these theoretical photons

> describe Nature exactly. But the testing problem would remain the same.

>

> > Under reasonable assumptions, it eaasily can be proven

> > deductively that all massless particles travel at the

> > same speed.

>

> Yes, and currently, this speed is called the speed of light.

> Would the photon be found to have a slight mass, this speed would

> simply be renamed to ''limit speed'' or something like that,

> photons could come to rest, but not much else would change.

(if so) How would you go about decelerating a photon?

Jan

Aug 19, 2010, 4:10:26 AM8/19/10

to

jw...@BasicISP.net wrote:

> I'll try once more.

> It has nothing to do with the exact speed of light, nor with

> propagation of

> information. We are not talking about information, but about light.

> The infinite precision only depends upon the empirical fact that

> the velocity of light does not add to the velocity of an object

> sending or receiving light.

> I'll try once more.

> It has nothing to do with the exact speed of light, nor with

> propagation of

> information. We are not talking about information, but about light.

> The infinite precision only depends upon the empirical fact that

> the velocity of light does not add to the velocity of an object

> sending or receiving light.

But turned into a limit on photon mass, this is at least some TRILLIONS

of times less stringent than the measurement being discussed. That comes

from estimates based on the neutrino/photon speed difference from

SN1987A and the lower limit on neutrino masses from oscillation

measurements.

If the light emitted from a source moving with velocity v toward the

observer has a speed c+kv in the observer's frame, then these

experiments place a limit on k. See

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#moving-source_tests

for a list of experiments. The best limit on k is k < 2E-9.

That is by no means "infinite precision".

> It also depends upon the assumption that light consists of photons.

> If a photon had mass, then its velocity would depend on existence

> of a rest frame for that photon. If such a rest frame existed,

> then the velocity of light would add to that of the object at

> its points of creating and annihilation. But this never is observed.

You are ASSUMING that SR is valid. that does not constitute an

experimental test in any way.

> Surely, no one is questioning the idea of vector addition?

Yes, among other things we are. That's what experimental physicists do:

test theories. Your notion of "vector addition" is merely a theory of

how such things ought to behave.

BTW in SR velocity vectors do NOT add via vector addition. Rather,

they are composed via the Lorentz composition of velocities formula.

> Therefore, photons have no rest frame, no proper time, nor

> any mass.

You make quite strong assumptions not in evidence. Your claim is

worthless.

> Under reasonable assumptions, it eaasily can be proven

> deductively tha all massless particles travel at the

> same speed.

It is not "reasonable" to ASSUME that SR or GR is EXACTLY correct. This

is an experimental issue, not one to be solved from your armchair by

assuming some particular physical theory is true.

Tom Roberts

Aug 19, 2010, 7:11:01 AM8/19/10

to

On 19 août, 10:09, nos...@de-ster.demon.nl (J. J. Lodder) wrote:

>

> (if so) How would you go about decelerating a photon?

>

> (if so) How would you go about decelerating a photon?

The only case of photon acceleration/deceleration known to me is the

photon propagation in a transparent non-uniform medium, i.e., in a

medium with real and variable n(r).

Aug 19, 2010, 3:35:13 PM8/19/10

to

Since it is uncharged, it is not easy. There is no conservation law,

and photons are easily absorbed, so it is likely to be destroyed long

before it has a small speed. The ''could'' was meant as a possibility

allowed by the theory, not as something we can actually do.

(Your question is like how would you go about picking an ounce of

solar matter from the center of the sun.)

Aug 20, 2010, 1:55:12 AM8/20/10

to

jw...@BasicISP.net wrote on Tue, 17 Aug 2010 22:01:55 -0400:

> I'll try once more.

>

> It has nothing to do with the exact speed of light, nor with

> propagation of information. We are not talking about information, but

> about light.

>

> The infinite precision only depends upon the empirical fact that the

> velocity of light does not add to the velocity of an object sending or

> receiving light.

>

> It also depends upon the assumption that light consists of photons.

>

> If a photon had mass, then its velocity would depend on existence of a

> rest frame for that photon. If such a rest frame existed, then the

> velocity of light would add to that of the object at its points of

> creating and annihilation. But this never is observed.

>

> Surely, no one is questioning the idea of vector addition?

>

> Therefore, photons have no rest frame, no proper time, nor any mass.

(...)

First, the idea of measuring something with "infinite precision" as

you claim is unreal, because it would mean recording infinite data

(0.000000000000000000000000000000000000...) among other issues.

Second, the statistics behind the current measurements of phton

properties is understood and the upper limit stated. The relevant

article is

Review of Particle Physics 2008: Physics Letters B 667(1-5), 1-6.

Amsler, C. et al. (Particle Data Group).

giving the upper limit for mass

m < 10^(-18) eV/c^2

and the next limit for the charge of photon

q < 10^(-35) e

--

http://www.canonicalscience.org/

BLOG:

http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html

Aug 20, 2010, 1:56:13 AM8/20/10

to

Bob_for_short wrote:

Yes, but this is due to changes in the nature of the photon.

Photons in matter are effective photons, dressed differently than

in vacuum.

Their lower speed has nothing to do with photon mass, since effective

photons are still massless.

Aug 21, 2010, 11:05:44 PM8/21/10

to

On 20 ao?t, 07:56, Arnold Neumaier <Arnold.Neuma...@univie.ac.at>

wrote:

> Bob_for_short wrote:

wrote:

> Bob_for_short wrote:

I don't think that the "nature" of photon may be changed in a

transparent medium, if we mean the photon electric and magnetic

fields. But in a medium we see that a photon is not a free "particle"

but a collective excitation mode. I think that "vacuum" for photon is

just a uniform medium and photon itself is its deviation from

uniformity.

Of course, slowly propagating photons are still massless.

Aug 22, 2010, 3:16:57 PM8/22/10

to

Arnold Neumaier <Arnold....@univie.ac.at> wrote:

What you can do is run along with it

at a very relativistic speed. (Einstein's thought experiment)

This however also downshifts the photon frequency to zero.

So you would need a zero temperature container as well.

(or a perfectly reflecting one) [1]

My idea for building a photon cooler (without running so fast) would be

to reflect the photon a great many times from receding mirrors. Should

work, very much in principle,

Jan

[1] Since a Kelvin is about 20 GHz a microHertz photon will be

obliterated by noise at 10^{-16} K

Aug 22, 2010, 3:17:28 PM8/22/10

to

On Aug 19, 4:11 am, Bob_for_short <vladimir.kalitvian...@wanadoo.fr>

wrote:

wrote:

Although LIGHT can change velocity in a nonvacuum medium,

a photon can not. The speed of light declines in water or glass,

for example, because photons propagating in those media are

repeatedly absorbed by atoms; generally, for each such photon,

a new photon is reemitted with the same momentum. Of course,

sometimes the photon is absorbed and its momentum goes toward

modifying the momentum (and energy) of the atom.

The atom takes time to reemit a photon, causing the average

speed to decline below c. Photons always travel

only exactly at speed c; they can not change during propagation

because they have no proper time.

Photons have specific wavelengths, but they do not oscillate

during propagation -- their phase is effectively spatial, only,

and it differs at annihilation as a function of distance only,

not as a function of proper time.

Aug 22, 2010, 3:18:28 PM8/22/10

to

Bob_for_short wrote:

> On 20 ao?t, 07:56, Arnold Neumaier <Arnold.Neuma...@univie.ac.at>

> wrote:

>> Bob_for_short wrote:

>>> On 19 ao?t, 10:09, nos...@de-ster.demon.nl (J. J. Lodder) wrote:

>>>> (if so) How would you go about decelerating a photon?

>>> The only case of photon acceleration/deceleration known to me is the

>>> photon propagation in a transparent non-uniform medium, i.e., in a

>>> medium with real and variable n(r).

>> Yes, but this is due to changes in the nature of the photon.

>>

>> Photons in matter are effective photons, dressed differently than

>> in vacuum.

>>

>> Their lower speed has nothing to do with photon mass, since effective

>> photons are still massless.

>

> I don't think that the "nature" of photon may be changed in a

> transparent medium, if we mean the photon electric and magnetic

> fields.

> On 20 ao?t, 07:56, Arnold Neumaier <Arnold.Neuma...@univie.ac.at>

> wrote:

>> Bob_for_short wrote:

>>> On 19 ao?t, 10:09, nos...@de-ster.demon.nl (J. J. Lodder) wrote:

>>>> (if so) How would you go about decelerating a photon?

>>> The only case of photon acceleration/deceleration known to me is the

>>> photon propagation in a transparent non-uniform medium, i.e., in a

>>> medium with real and variable n(r).

>> Yes, but this is due to changes in the nature of the photon.

>>

>> Photons in matter are effective photons, dressed differently than

>> in vacuum.

>>

>> Their lower speed has nothing to do with photon mass, since effective

>> photons are still massless.

>

> I don't think that the "nature" of photon may be changed in a

> transparent medium, if we mean the photon electric and magnetic

> fields.

I didn't assign any particular (or changing) ''nature'' to the photon.

For me, a photon is the lowest quantum excitiation of an

electromagnetic field. The electromagnetic field in a transparent

non-uniform medium is an effective field with different equations than

the free field; so it is also dressed differently than an e/m field

in vacuum.

> But in a medium we see that a photon is not a free "particle"

> but a collective excitation mode.

This makes the photon in a medium quite a different object than in

vacuum.

> I think that "vacuum" for photon is

> just a uniform medium and photon itself is its deviation from

> uniformity.

It is a quantum excitation of the medium.

> Of course, slowly propagating photons are still massless.

And that was the real point of my mail.

Aug 22, 2010, 8:28:39 PM8/22/10

to

On Aug 22, 3:17 pm, "jw...@BasicISP.net" <jw...@BasicISP.net> wrote:

>

> Although LIGHT can change velocity in a nonvacuum medium,

> a photon can not. The speed of light declines in water or glass,

> for example, because photons propagating in those media are

> repeatedly absorbed by atoms; generally, for each such photon,

> a new photon is reemitted with the same momentum.

>

> Although LIGHT can change velocity in a nonvacuum medium,

> a photon can not. The speed of light declines in water or glass,

> for example, because photons propagating in those media are

> repeatedly absorbed by atoms; generally, for each such photon,

> a new photon is reemitted with the same momentum.

In this model, how is coherence maintained? I would think that the

time interval between absorption and emmission of the photon is a

quantum - i.e., random - process that coherence would be destroyed.

Aug 23, 2010, 4:16:57 PM8/23/10

to

On 22 August, 21:17, "jw...@BasicISP.net" <jw...@BasicISP.net> wrote:

> On Aug 19, 4:11 am, Bob_for_short <vladimir.kalitvian...@wanadoo.fr>

> wrote:

>

> > On 19 august, 10:09, nos...@de-ster.demon.nl (J. J. Lodder) wrote:

>

> > > (if so) How would you go about decelerating a photon?

>

> > The only case of photon acceleration/deceleration known to me is the

> > photon propagation in a transparent non-uniform medium, i.e., in a

> > medium with real and variable n(r).

>

> Although LIGHT can change velocity in a nonvacuum medium,

> a photon can not.

> On Aug 19, 4:11 am, Bob_for_short <vladimir.kalitvian...@wanadoo.fr>

> wrote:

>

> > On 19 august, 10:09, nos...@de-ster.demon.nl (J. J. Lodder) wrote:

>

> > > (if so) How would you go about decelerating a photon?

>

> > The only case of photon acceleration/deceleration known to me is the

> > photon propagation in a transparent non-uniform medium, i.e., in a

> > medium with real and variable n(r).

>

> Although LIGHT can change velocity in a nonvacuum medium,

> a photon can not.

So, according to you, there is no time delay in photon propagation

through a medium layer. The why the LIGHT has this "retardation" if it

consists of non interaction photons?

> The speed of light declines in water or glass,

> for example, because photons propagating in those media are

> repeatedly absorbed by atoms; generally, for each such photon,

> a new photon is re-emitted with the same momentum.

I think it is plainly wrong about atoms. It is the medium (lots of

bound atoms) that has some EMF energy levels that take part in the

propagation. In particular, in the window of transparency nothing is

absorbed and re-emitted or even "interacts" with the medium. It is

better to think in terms of the medium proper EMF modes with somewhat

different from vacuum properties.

> The atom takes time to re-emit a photon, causing the average

> speed to decline below c.

Rubbish. Nothing can force an excited atom to re-emit a photon in the

same direction. Next, nothing can forme an excited atom to re-emit a

photon with the same delay. Delays are random: exp(-t/T). Finally, in

the theoretical description it is not atomic levels that are involved

but those of the medium. In other words, a medium is not a simple

collection of non interacting atoms.

Arnold Neumaier wrote:

>> Yes, but this is due to changes in the nature of the photon.

> I didn't assign any particular (or changing) ''nature'' to the photon.

Choose one of the statements to be self-consistent.

>> Photons in matter are effective photons, dressed differently than

>> in vacuum.

And in vacuum they are ineffective or what?

> For me, a photon is the lowest quantum excitation of an

> electromagnetic field.

Better, it is the first excited mode of the EMF in a given situation.

> The electromagnetic field in a transparent

> non-uniform medium is an effective field with different equations than

> the free field; so it is also dressed differently than an e/m field

> in vacuum.

Dressing means that there is something undressed, bare. But bare

photon is a purely theoretical bla-bla involved in the renormalization

ideology and it has nothing to do with always physical photons in

physics. Everybody agrees that EMF equations in a medium are different

(involve n(r) =/= 1) but the nature of equations remains practically

the same. As a result, the space frequency of a photon changes but not

the frequency omega in exp(-i*omega*t) (in a still medium, of course).

The omega determines the photon energy.

Concerning the photon mass, there is no such a thing in a theory even

in resonators with the frequency spectrum starting at finite omega > 0.

Aug 23, 2010, 6:01:45 PM8/23/10

to

Thus spake Bob_for_short <vladimir.k...@wanadoo.fr>

>> The atom takes time to re-emit a photon, causing the average

>> speed to decline below c.

>

>Rubbish. Nothing can force an excited atom to re-emit a photon in the

>same direction.

>> The atom takes time to re-emit a photon, causing the average

>> speed to decline below c.

>

>Rubbish. Nothing can force an excited atom to re-emit a photon in the

>same direction.

Actually conservation laws can do exactly that. Remember this is not an

excitation mode of the atom.

> Next, nothing can forme an excited atom to re-emit a photon with the

>same delay.

No one suggested it did.

>Delays are random: exp(-t/T). Finally, in the theoretical description

>it is not atomic levels that are involved but those of the medium. In

>other words, a medium is not a simple collection of non interacting

>atoms.

No, clearly it is a complex collection of interacting atoms. It is atoms

nonetheless, and must get its behaviour from the behaviour of atoms and

their constitituents.

Aug 23, 2010, 6:02:01 PM8/23/10

to

Thus spake Lester Welch <lester...@gmail.com>The explanation requires that one understands wave functions as

conveyors of information, not as physical waves. We have no way of

knowing, even in principle, when a photon is absorbed or by which

electron. The wave function does not then describe the behaviour of an

individual photon or photons, but rather the net effect.

conveyors of information, not as physical waves. We have no way of

knowing, even in principle, when a photon is absorbed or by which

electron. The wave function does not then describe the behaviour of an

individual photon or photons, but rather the net effect.

Aug 24, 2010, 3:06:59 AM8/24/10

to

Here's my call on that:

LIGHT coherence is maintained because in a transparent medium such as

glass, all the atoms are about the same, to the extent that almost none

are absorbing (without reemitting). Because it is transparent,

reemission of photons preserves their momentum p, and with time delay

about the same for each atom.

It is true that absorption and reemission of a single photon is an event

requiring quantum-mechanical analysis. However, coherence of light is

determined by expectancies, <p>, not p of individual photons.

Transmission of light through any medium always introduces some

dispersion of phase, some loss of coherence. If you want, you can view

this as the Second Law in action.

Also, one can not have "coherence" except for light of a given

wavelength. This means that momentary absorption and reemission always

takes place in the same energy eigenstate of all atoms involved. It is

the eigenstate that keeps the delay identical for all transmission

through the medium, thus preserving coherence (at a reduced wavelength,

frequency being constant, while the light is in the medium).

Aug 25, 2010, 12:35:30 PM8/25/10

to

There is an alternate explanation which does not assume

interaction of the photons with atoms of a transparent

medium:

interaction of the photons with atoms of a transparent

medium:

Photons have no inertial rest frame; therefore they can not

be accelerated relative to anything; thus, they always travel

at speed c. However, c might vary in a transparent medium

such as water or glass:

We know that c = sqrt(epsilon_0*mu_0)^-1 in vacuum;

suppose that the permittivity and/or permeability of the

transparent medium was higer than in vacuum, which

would make c lower. Then, we could assume that a

photon leaving a transparent medium was identical to

one which entered it and just never interacted at all.

The reason I favor brief absorption and reemission

over change in c, is that I know that any atom

can be manipulated by "laser tweezers" -- shining

a laser on a surface to which an atom adheres

exerts a force on the atom and can move it. This

is because of interaction of the photons with the

electric fields of the atom's electrons. So, I

don't see how a photon could get through a

sheet of glass with billions of atoms, all

bound by electric charges, without intercting.

Also, why does adding a dense substance such as lead

to glass increase its refractive index? As density

goes up, generally refractive index goes up.

The greater density is from the atomic nuclei, not

its electrons. The electrons in a higher-Z material

are on the average farther from its nucleus than for

a lower=Z atom; thus, speeds of electronic relaxation

would average lower; therefore, reemission after

absorption would be slower, increasing the refractive

index.

Finally, a mirror reflects light back; this can't

possibly be because of a change in c but rather involves

transfer of momentum to the mirror. The reflected

photons can't possibly be the same as the ones

incident on the mirror.

Sep 4, 2010, 5:03:47 PM9/4/10

to

[ Mod. note: Note to poster, please include distinguishing marks around

quoted text, as is done in most other posts, to avoid confusion of

attribution. Quotation marks were restored. -ik ]

quoted text, as is done in most other posts, to avoid confusion of

attribution. Quotation marks were restored. -ik ]

On Aug 25, 12:35 pm, jw wrote:

>

> There is an alternate explanation which does not assume interaction of the photons with atoms of a transparent medium:

> Photons have no inertial rest frame; therefore they can not be

> accelerated relative to anything; thus, they always travel

> at speed c. However, c might vary in a transparent medium such as

> water or glass:

> We know that c = sqrt(epsilon_0*mu_0)^-1 in vacuum; suppose that the

> permittivity and/or permeability of the transparent medium was higher

> than in vacuum, which

> would make c lower. Then, we could assume that a photon leaving a

> transparent medium was identical to one which entered it and just

> never interacted at all.

> The reason I favor brief absorption and re-emission over change in c,

> is that I know that any atom can be manipulated by "laser tweezers" --

> shining a laser on a surface to which an atom adheres exerts a force

> on the atom and can move it. This is because of interaction of the

> photons with the electric fields of the atom's electrons. So, I

> don't see how a photon could get through a

> sheet of glass with billions of atoms, all

> bound by electric charges, without interacting. >

All of the above assumes that a photon is a particle that exists and

transmits through the empty space in a vacuum. That assumption stems

from Einstein's theory, not from Max Planck. In Planck's theory there

are two different quanta;

1. A quantum of action, h = 2pirmc'; and

2. A quantum of energy, e_0.

Though different from each other, they are related by the equation,

e_0 = hf,

in which f, the frequency of the waves of h,

depends on the state of motion of the observer.

The meaning of h = 2pirmc' is this:

Let there be a resonator in a black box. In Planck's paper, he took

the resonator as stationary, thus at absolute zero degrees K.

Even so, inside such an atom a circulating wave system called an

"electron" exists. It moves therein at c' = cFs, where Fs is the fine

structure constant and c is the speed of light in a vacuum.

If such a wave system and its trapping material medium escapes from

an atom -- say during a quantum emission -- the remaining weight of

the atom is m_grams less than it had been. This "mass" (actually

weight) is attributed to the electron.

Given that the orbital path of such an electron is 2pir long, in

which r is the average length of the radius of an atom under the

specified conditions, then the quantity of action, h, is equal to

2pir *m * (c' = cFs).

When such a quantity of matter with its trapped wave system escapes

from an atom, it is an increase in the local density of the

surrounding material field. Such a +grad d causes a local increase in

pressure, thus a =grad s exists. Since a pressure disequilibrium

cannot remain present in the compressible material filling the local

field, it will radiate away in all directions, until grad s = 0 for

any value of grad d.

> Also, why does adding a dense substance such as lead to glass increase its refractive index? As density goes up, generally refractive index goes up.

> The greater density is from the atomic nuclei, not its electrons.

> The electrons in a higher-Z material are on the average farther from

> its nucleus than for a lower=Z atom; thus, speeds of electronic

> relaxation would average lower; therefore, re-emission after

> absorption would be slower, increasing the refractive index. >

Light is not made of separate particles, it is waves of pressure

transmitted by the matter in the local field. the speed of each wave

depends on how one elects to measure it. (If you use the usual

method, you measure how many feet -- or miles or km -- it travels per

second. Since that is a function of the density of the traversed

medium, the results will be variable.) However, if you measure the

quantity of matter traversed per second, the result will be a constant

regardless of the variable density of the luminiferous medium.

Even though there are zillions of tiny atoms per cc in a material

field, between any group of them there is always a space filled by

continuous matter. If its density is less than theirs, light waves

will move faster through that space than through the atom-filled

places. If they can get through it, the medium will be transparent. If

you add lead to glass, thereby increasing the local density, that will

increase the refractive index.

> Finally, a mirror reflects light back; this can't possibly be because of a change in c but rather involves transfer of momentum to the mirror. The reflected photons can't possibly be the same as the ones incident on the mirror. >

Momentum is mass times velocity. If a light wave had any rest mass

at all, it would be infinitely great when moving at c; thus would

eradicate anything it hit. Since that never happens, there is no such

thing as the "mass" of a quantum of energy; which Einstein called "a

photon". For reasons I won't get into here, Planck was right;

although a quantity of energy e_0 IS emitted and/or absorbed by an

atom, no such quantum exists during transmission.

glird

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