Special relativity

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Can't exactly do a two column proof on a thread, but I've done the mathematical steps top and the logic below each numbered step. If anyone would like to point out any errors in the steps I've done, please do so.

Questions:

1. Does light have mass that increases with increasing frequency (and thus decreases with increasing wavelength)?

2. E = mc^2 is used to determine the energy contained within a quantity of matter, is a photon to be considered matter (which is defined as having both size and mass) or energy?

3. Does a photon have "mass" when it is traveling and does it convert that "mass" into the kinetic energy required for its propagation?
Since I can't type lambda I'll use "L".


1. L = h/(mv)
De Broglie's theorem

2. v = c
Specified to light

3. L = h/(mc)
Substitution
_________

4. f = v/L
Frequency-wavelength relationship

5. v = c
Specifying case to light

6. f = c/L
Substitution

_________

7. E = hf
Relationship of light's energy to its frequency

8. E = hc/L
Substitution

9. L = hc/E
Solved for L
_________

10. L = h/(mc) = hc/E
Transitive property (if a=b & b=c, then a=c)

11. 1/(mc) = c/E
Cancellation

12. Emc*(1/mc) = (c/E)*Emc
Rearrange

13. E = mc^2
Solved for E.

Last edited by iamnotaparakeet on 17 Mar 2008, 8:50 am, edited 2 times in total.

Also I noticed,

1. E = hc/L
(from line # 8 above)

2. E = mc^2
(from line # 13)

3. hc/L = mc^2
Transitive property

4. h/L = mc
Cancellation

5. m = h/(Lc)
Solved for mass
________

6. E = hf
(line # 7 above)

7. E = mc^2
(line # 13)

8. mc^2 = hf
Transitive

9. m = hf/c^2
Solved for mass
_________

10. m = h/(Lc) = hf/c^2
Transitive

11. 1/L = f/c
Cancellation

12. f = c/L
Solved for frequency, this is the same equation as in line # 6 in the previous post.

Anyone have anything to say?

answering question 3 cause it was most obvious to me - photons have relative mass so the kinetic energy would still be 0.5mv*v

Nice

Though I'll point out that you'd be hard pressed to find a professional physicist who works in relativity, in this era, to say that a photon has "mass"

The "modern" view of all of this is to declare that mass is a non-relativistic quantity, that the mass is always the rest mass regardless of choice of reference frame, and that it is instead momentum that is the relativistic quantity. While in some cases this makes things less clear, it on the whole seems to work more cleanly.

It also avoids the confusion of thought experiments like "if I go fast enough do I turn into a black hole" which sometimes arise when trying to think of relativistic mass, but are in fact manifestly unanswerable within special relativity (or worse, SR gives the wrong answer) and that require general relativity (where mass and such are treated somewhat differently altogether)

I suppose that would be brought about by the equation of:

mass(final) = mass(initial) / gamma

Where as gamma becomes infinitely small, mass(final) becomes infinite?

So they address the issue by saying that momentum (mass*velocity) exists, but mass doesn't? How exactly does that work out and is this experimentally determined? I thought in a cyclotron that they have mechanisms for handling the increased mass of the electrons. Were they unnecessary?

The more energy the more "mass" (or its relativistic equivalent).

That is why X-rays and Gamma rays do more damage than visible light.

ruveyn

You problem cannot really be tackled without general relativity (which was invented to take care of the inconveniences resulting from special relativity alone).

To answer your first question; photons do not have a mass per se. Yes, I do mean rest mass. Particles with rest mass do have a DeBroglie wavelength, but it is not the same as a wave packet.

2. Light is not considered matter. E=mcc is the energy equivalent of mass, or in other words, the energy bound as mass.

3. No.

Electrons do have a rest mass, and that mass increases with the speed of the electron. If an electron were to approach the speed of light, its mass would increase until the force accelerating the electron is no longer accelerating the electron. This is far before any black hole is generated. Even if a black hole was constructed from a single electron, it would radiate into emptyness is a short time.

No particle moving slower than light can achieve faster-than-light speeds by acceleration. It has been proposed that particles moving faster-than-light cannot achieve speeds slower than light through deceleration. To my knowledge, the ftl-theory is not complete regarding the behavior of colliding particles, but it seems that stl and ftl particles do not interact with particles of the other domain. Both might interact with massless elemental particles moving at the speed of light. There are no known particles moving faster-than-light.

How do you reconcile Einstein's theory of relativity which assumes locality with the outcome of experiments that show Bell's Inequality is false. In other words, distant events are superluminally correlated, a contradiction to Einstein's assumption that light speed in a vacuum is the upper bound.

See -Einstein's Mistakes- by Hans Ohanian. Not a crank book. He gives journal, page and references to mistakes the Einstein made. For example, he shows that Einstein never properly proved E = m*c^2, where m is the rest mass of an object. It was correctly proven by von Laue later on. Einstein was also wrong about quantum theory and about locality. Reality is not local as the double-delay experiments which falsify Bell's Inequality show. There are no hidden variables that will reproduce the predictions of quantum theory.

ruveyn