The Mysterious, Impossible Box: Questions & Answers

[Dale]

My mistake. Pax.

I've been trying out the argument in the accelerating frame, as I half-gave above, but I have a qualitative, not a quantitative solution as yet. And I'm assumming I can derive the blue shift, delta lambdda over lamba, for an accelerating frame, from first principles, rather than looking it up somewhere.

Did I mention that I agree; in the accelerating frame a standing wave is only a good approximation where the acceleration times box-height product is small?

If you ever figure that out I would definitely be interested in seeing the results. I can do basic Newtonian mechanics directly in non-inertial frames, but for other physics I always have to transform to an inertial frame.

 

[Dale]

"If you are pushing on a box of light to accelerate it then a photon leaving the front of the box will be blueshifted by the time it reaches the back of the box, and a photon leaving the back of the box will be redshifted by the time it reaches the front."

Shouldn't it be the opposite?
That the photon leaving the front of the box traveling against its box 'direction' towards the back wall, as seen from an observer, should be redshifted as its following a declining energy gradient, and that the photon emitted from the back towards the front wall then should be blueshifted as its walking an upgrade slope as seen from the observer.

Or am I getting this totally wrong?
Are you placing the observer inside this frame so that the thought observers would be traveling with it and in the photons reference frame?

One observing from the back wall, sort of, and one observing from the front wall.
But then there shouldn't be any 'slope' (in any direction -+) should it?
They are at rest inside their frame of reference, or?
Where would that 'excess energy' of that 'blue shifted' photon hitting the back wall f. ex come from if they share the same reference frame?

I should have been more specific about how the red and blue shifts are measured. They are measured by detectors mounted on the front and back wall of the box.

In an inertial reference frame the Doppler shift is simply related to the relative velocity between the source at the time of emission and the detector at the time of reception. If the relative velocity is towards each other then it is blueshifted and if the relative velocity is away then it is redshifted (it is also redshifted if the relative velocity is transverse).

In this case, consider an inertial frame where the front wall is at rest at the time of emission. By the time the light reaches the detector at the back wall the box will have accelerated such that the back wall is traveling towards the point of emission. Therefore it is blueshifted. The reverse holds in considering the case where the rear wall is at rest at the time of emission.

Btw, this is a minor point, but photons do not have a reference frame.

 

[Yor_on]

I should have been more specific about how the red and blue shifts are measured. They are measured by detectors mounted on the front and back wall of the box.

In an inertial reference frame the Doppler shift is simply related to the relative velocity between the source at the time of emission and the detector at the time of reception. If the relative velocity is towards each other then it is blueshifted and if the relative velocity is away then it is redshifted (it is also redshifted if the relative velocity is transverse).

In this case, consider an inertial frame where the front wall is at rest at the time of emission. By the time the light reaches the detector at the back wall the box will have accelerated such that the back wall is traveling towards the point of emission. Therefore it is blueshifted. The reverse holds in considering the case where the rear wall is at rest at the time of emission.

Btw, this is a minor point, but photons do not have a reference frame.

Yes, that was how I after pondering some thought that you might mean:)
But my point there is that inside that elevator: accelerating at one G constantly all objects would be at rest relative each other?
So how would there be any red/blueshift as seen from 'inside' the reference frame?
I get stuck there:)

The explanation might either be that I'm bicycling in the blue younder (No big surprise there:) or that when describing it you look at it 'from the outside' seeing that black box moving relative the detector, in which case, as I see it, if you were placed so that you could see the detectors you would observe a redshift when observing from behind that moving frame and blueshifted when observing it coming towards you.

But it do seem as your description has its own reality to it, even though I can't see how I should see it for the moment:)

As for photons having no frame I presume you are thinking of its velocity? 'c'.
That always will be the same?

But they will become either blue or redshifted when observed from another reference frame.
And inside that 'moving' box with a light bulb situated in the middle and two detectors rigged up at each side of it, in the direction of the box velocity, you say that it will be redshifted as the box moves 'toward' the lightsource?

So by that reasoning it seems to me that we will have a reference for where no velocity exist?
We only have to observe a lightsource while remaining inside that box.
If the light then shows the same frequency as observed from all (360 degrees all over, slice by slice all directions:) sides, should then this frame be seen as unmoving?

If you see how I think here.

 

[Dale]

Yes, that was how I after pondering some thought that you might mean:)
But my point there is that inside that elevator: accelerating at one G constantly all objects would be at rest relative each other?
So how would there be any red/blueshift as seen from 'inside' the reference frame?
I get stuck there:)

As I said to Phrak, I don't know how to work the problem quantitatively in that frame. But it is not really necessary since all frames must agree on all experimental results. That said, qualitatively it is easy to see that in the non-inertial frame there is a potential energy, so as a photon goes down it gains energy and is therefore blueshifted and as it goes up it loses energy and is therefore redshifted.

As for photons having no frame I presume you are thinking of its velocity? 'c'.
That always will be the same?

Correct. An object's frame is the frame where its velocity is 0, and a photon's velocity is c in all frames, so there is no frame where a photon's velocity is 0.

 

[Phrak]

As I said to Phrak, I don't know how to work the problem quantitatively in that frame. But it is not really necessary since all frames must agree on all experimental results. That said, qualitatively it is easy to see that in the non-inertial frame there is a potential energy, so as a photon goes down it gains energy and is therefore blueshifted and as it goes up it loses energy and is therefore redshifted.

I'm not sure if you were responding to me or not. I'm nearly incapable with my current schedule of doing any physics in most days of the week, other than pondering, but if I quantize the energy and momentum, it seems to yield a solution in the accelerating frame--not the full quantization but a requirment of that E/omega and p/k be constants. It shouldn't depend on quantum mechanics; it's got to be crazy or wrong.

 

[atyy]

I'm not sure if you were responding to me or not. I'm nearly incapable with my current schedule of doing any physics in most days of the week, other than pondering, but if I quantize the energy and momentum, it seems to yield a solution in the accelerating frame--not the full quantization but a requirment of that E/omega and p/k be constants. It shouldn't depend on quantum mechanics; it's got to be crazy or wrong.

Apparently if you quantize in flat spacetime, there's the Unruh effect in which the ground state in the accelerated frame is not the same as the ground state in the inertial frame.

 

[Dale]

What does quantization have to do with any of this? I mean, reflection is not a quantized phenomenon.

 

[Dale]

I'm not sure if you were responding to me or not.

I was responding to Yor On

 

[Phrak]

What does quantization have to do with any of this? I mean, reflection is not a quantized phenomenon.

I'll have to get back at you later.

 

[Yor_on]

Dale, thanks for your patience here:)
If one look at Earth and that experiment(s:) defining the speed of light.
And especially those testing for that elusive 'ether'.

And looked at Earth as a moving object, rotating, orbiting the sun, and traveling with the solar system at a speed of??
Shouldn't that show itself as red and blue shift when making those experiments.
Or is it that we are 'at rest' relative those experiments that explains it?

 

[Phrak]

pervect does light in a box. https://www.physicsforums.com/showthread.php?t=116769"

 

[mrpeach32]

Wow, I never thought it would get this many replies, I stopped looking after my last reply. Very interested stuff, everyone, thanks!