Gravity effect on observed speed of light

[atyy]

I didn't see any problem with section 8, which was based on the amplitude transform derived in section 7.

It seems to me that what my earlier derivation shows is the IF E=g(f), g must be linear, but that if E is independent of f, the argument shows nothing.

In Einstein's section 8 is the volume transformed correctly? Is it the volume of a light sphere?

The Energy E in section 8 is not my naive understanding of energy. I would expect E ~ A². But he defined E ~ AS.

I've actually never read this section

 

[harrylin]

To make the classical vs. quantum relation between energy, frequency, and amplitude concrete, consider a concrete example:

Imagine in one frame we have 3 pulses of light, each with energy E0, amplitude A0, and frequency f1, f2, and f3. Classically, there is no relation between E and f. Now the quantum situation is simply that pulse 1 has E0/hf1 photons, pulse 2 has E0/hf2 photons, etc.

Now apply a Lorentz transform. We have the following relations:

E0' is related to A0' the same as E0 is to A0.
E0'/E0 = f1'/f1 = f2'/f2 = f3'/f3 (1)

As a result of (1), E0'/hf1' = E0/hf1, so the number of photons is preserved. However, from a classical point of view, there remains no relation between E and f.

Earlier you wrote: "light energy and frequency [are] proportionally changed, purely from SR and Maxwell".

I still think that that is correct!

In shorthand, for the change of speed, dE~df. And as E=0 when f=0, also E~f for the case under consideration.
This tells me that if we move away at such a speed that the received frequency is half of that in rest, the energy that we can absorb is also half of that in rest.

Proportional does not necessarily mean causal. That is a mistake that is (was) notoriously made in medical studies.

Regards,
Harald

 

[harrylin]

In Einstein's section 8 is the volume transformed correctly? Is it the volume of a light sphere?

The Energy E in section 8 is not my naive understanding of energy. I would expect E ~ A². But he defined E ~ AS.

I've actually never read this section

You overlooked a square, right?
He has that the [energy] ~ [amplitude per volume]² * [volume].
Looks good to me!

 

[PAllen]

Earlier you wrote: "light energy and frequency [are] proportionally changed, purely from SR and Maxwell".

I still think that that is correct!

Yes, I agree.

In shorthand, for the change of speed, dE~df. And as E=0 when f=0, also E~f for the case under consideration.

Here there is an issue. f=0 is no longer a wave, and power radiation arguments completely break down. Classically, any f > 0 can be associated with any E > 0. Quantum mechanics comes along and says for any E there is a maximum f =(E/h), and for any f, there is a minimum E = hf. But within the broad range where quantization is insignificant (hf << E), then the classical picture is essentially correct: for a give f, the energy of a light pulse can be whatever you want.

This tells me that if we move away at such a speed that the received frequency is half of that in rest, the energy that we can absorb is also half of that in rest.

correct, despite the disagreement above.

Proportional does not necessarily mean causal. That is a mistake that is (was) notoriously made in medical studies.

Regards,
Harald

In this case, proportional is wrong as regards light pulses or corresponding sections of traveling waves. All that is true is for a given light pulse, Energy and frequency change in proportion, *not* that the energy is proportional to the frequency.

[Edit: I guess we can agree that *for a given body of light*, E is proportional to f *under the operations of change of motion of an observer or measuring device*. But it is not proportional in any other sense. A different body of light can have the same f and any other E desired (classically).]

 

[harrylin]

[..]
In this case, proportional is wrong as regards light pulses or corresponding sections of traveling waves. All that is true is for a given light pulse, Energy and frequency change in proportion, *not* that the energy is proportional to the frequency.

[Edit: I guess we can agree that *for a given body of light*, E is proportional to f *under the operations of change of motion of an observer or measuring device*. But it is not proportional in any other sense. A different body of light can have the same f and any other E desired (classically).]

Yes, nothing else is implied than that of a given light pulse, the observed E~f.

 

[harrylin]

E/E0=f/f0 => E ~ f.
Thus I would say, QM knows SR! [..]

Correction: I should not have written that, as the similarity is just in the equations and not in their physical meanings as we now elaborated: SR's E~f has little to do with QM's E=hf.

But also, I had forgotten that E=hf was proposed in 1901 already - so SR knew about QM!

 

[atyy]

You overlooked a square, right?
He has that the [energy] ~ [amplitude per volume]² * [volume].
Looks good to me!

Yes, the volume factor is necessary. What I didn't understand was why we are allowed to have the volume factor, eg. for a plane wave solution. Apparently, some approproate volume can be used if you have an approximately monochromatic wavepacket. It's limited enough in space that its volume is objective, but unlimited enough that its wavelength is well defined. So we really need a bullet of light, exactly what the semiclassical photon is. At least this is what I gathered from comments in Brau's "Modern problems in classical electrodynamics", but I haven't seen a detailed calculation.

 

[harrylin]

Yes, the volume factor is necessary. What I didn't understand was why we are allowed to have the volume factor, eg. for a plane wave solution. Apparently, some approproate volume can be used if you have an approximately monochromatic wavepacket. It's limited enough in space that its volume is objective, but unlimited enough that its wavelength is well defined. So we really need a bullet of light, exactly what the semiclassical photon is. At least this is what I gathered from comments in Brau's "Modern problems in classical electrodynamics", but I haven't seen a detailed calculation.

Oops I had put the square at the wrong place, it should have been:
[energy] ~ [(amplitude)² per volume] * [volume].

But I wonder if you actually read that chapter, as Einstein took there the example of a sphere that encloses a wave:

"We may therefore say that this surface permanently encloses the same light complex. We inquire as to the quantity of energy enclosed by this surface, viewed in system k, that is, as to the energy of the light complex relatively to the system k."