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*From*: Moses Fayngold <moshfarlan@yahoo.com>*Date*: Sun, 3 Oct 2010 15:55:26 -0700 (PDT)

Here I want to approach the question about massless photon raised in the

previous discussion, from 2 other perspectives different from those discussed

before (someone on this List has said that it is always good to have more than

one ways to answer or address a question).

First of all I would slightly reformulate the question, introducing the term

"invariant speed" instead of speed of light or a graviton. Let c stand for the

invariant speed. Then we could ask: "If there exists a particle moving with

invariant speed, what is its mass m?" (For brevity, "m" here stands for the

invariant or rest mass).

Answer 1.

For any non-zero m, by definition of the rest mass, we can find a frame

comoving with the particle in question. In this frame, the particle's speed is

zero. Clearly, the invariant speed cannot be zero. Therefore the particle in

question cannot have a non-zero m.

Answer 2.

Interestingly enough, it directly involves QM, since now we will use the wave

aspect of matter. If the particle in question is in a state with definite

4-momentum P = (E/c, p), it is described by the monochromatic de Broglie's wave

Aexp (kx - wt), with the phase velocity u = w/k. In another reference frame

(RF), w and k would have other numerical values, but, by definition, their ratio

must remain the same (otherwise, it would be possible to "cook up" wave packets

with different group velocities, which would contradict the condition that the

particle has the invariant speed). Thus, we must have u = w/k = const = c. It

follows that the dispersion equation for this particle must be (w/c)^2 - k^2 =

0.

Now, when we switch to another RF, E and p undergo exactly the same Lorentz

transformation as w and k (this similarity was one of the factors that inspired

de Broglie to introduce his famous equations.) Therefore, there must be also u =

E/p = const = c, and accordingly, (E/c)^2 - p^2 = 0.

This is the dispersion equation for a massless particle, so there must be m = 0.

Moses Fayngold,

NJIT

________________________________

From: Derek McKenzie <derek_s_mckenzie@hotmail.com>

To: phys-l@carnot.physics.buffalo.edu

Sent: Fri, October 1, 2010 8:02:35 PM

Subject: Re: [Phys-l] Absolute four-momentum of massless particles

Ok - I've finally got on top of the arguments in this thread (or at least those

relating to my questions about massless particles)...

On 09/30/2010 08:23 PM, Derek McKenzie wrote:

On what basis do we declare a particle to have zero mass anyway?

What means "declare"? Strictly speaking, I reckon you

can declare anything you want.

At the other extreme, if you want to /prove/ that the

photon mass is zero, then you're probably out of luck.

According to Popper's view, which is nowadays a rather

conventional view in the scientific community, no theory

ever gets proved right. Roughly speaking: wrong theories

can be disproved, but valid theories always remain open

to further testing.

It was precisely because you can't 'prove' things in physics that I used the

word 'declare'. The physics community (more or less unanimously) concur that a

photon has zero mass, so they declare it to be the case (albeit possibly

temporarily). Nothing deep was meant by the word. Perhaps I should have asked

'What makes physicists 'believe' a given particle has zero mass?'.

Your description of the photon case was very enlightening, but my question is a

different one (sorry I didn't express it properly). Firstly, I do realize that

relativity does not require photons to travel at the speed c (c being defined

here as the geometrical constant in the theory of relativity). But the argument

accepted in the community is that IF a particle (who cares whether it's a photon

or a neutrino) travels at speed c (again, I mean here the geometrical c), THEN

it has to be massless (and conversely). This assumption is not usually justified

in texts - perhaps because it is supposed to be totally obvious.

Is the idea that IF a particle has a timelike worldline, THEN it has a well

defined four velocity and therefore a well-defined P = mU, and therefore the

latter must be zero? In other words, a time-like particle of zero mass would

have no momentum or energy in any frame. Is that all there is to it?

Derek

The

popular argument seems to be that assigning any positive mass leads

to a contradiction, but that only convinces me that the mass is

either zero for that particle OR meaningless.

We can do much better than that. A massless photon

means that electromagnetism is an infinite-range

interaction. A positive mass would dictate the range

of the interaction via the Yukawa formula. To say

the same thing in slightly different words, you would

see a departure from the 1/r^2 law.

This has been checked experimentally on the laboratory

length-scale and on cosmological length scales. In

all cases that have been checked, the exponent n in

the 1/r^n law is 2 within the precision of measurement,

and some of the measurements are good to one part in

10^12. Reference: Jackson; also

http://en.wikipedia.org/wiki/Photon#Experimental_checks_on_photon_mass

There is no 11th commandment that requires the photom

mass to be zero. Maybe tomorrow somebody will discover

that the photon has a mass ... but if so, it must be

reeeally small.

Note that neutrinos were for many years believed to be

massless, but are now believed to have a very small but

nonzero mass. This demonstrates that it is possible to

reclassify a particle from massless to non-massless.

Such a reclassification is not hard to carry out; it's

not like we've never seen a massive particle before.

On the other hand, such a reclassification is very

unusual and newsworthy.

_______________________________________________

Forum for Physics Educators

Phys-l@carnot.physics.buffalo.edu

https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

_______________________________________________

Forum for Physics Educators

Phys-l@carnot.physics.buffalo.edu

https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

**Follow-Ups**:**Re: [Phys-l] Why is the photon massless?***From:*Derek McKenzie <derek_s_mckenzie@hotmail.com>

**References**:**Re: [Phys-l] Absolute four-momentum of massless particles***From:*Derek McKenzie <derek_s_mckenzie@hotmail.com>

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