Time dilation and the photon clock

[JesseM]

So here's another thought:

In the perspective of the photon, it is the box itsself that is vibrating back and fourth. From the photons perspective, gamma=sqrt(0) so therefore the height of the box is 0, no? So that would mean that the clock is constantly ticking, correct?

Actually, since gamma = 1/sqrt(1 - v^2/c^2), if you plug in v=c you get gamma=1/sqrt(0), division by zero. In SR a photon does not have its own rest frame, so it isn't really meaningful to talk about the "photon's perspective".

 

[Stellar1]

ahh, yes, sorry, it is 1/0 in that case. So in that case the length would be infinite and it would never tick...?

What is SR? Special relativity I take it? Why does it matter that a photon does not have its own rest frame?

 

[JesseM]

ahh, yes, sorry, it is 1/0 in that case. So in that case the length would be infinite and it would never tick...?

Again, the equations for length contraction and time dilation only make sense when you are talking about length and time as measured in a given inertial frame, it is meaningless to use them outside this context, and a photon does not have an inertial rest frame.

What is SR? Special relativity I take it? Why does it matter that a photon does not have its own rest frame?

Yes, SR = special relativity. As I said, the time dilation equation and length contraction equation are specifically derived based on the assumption that you are talking about time and length as measured by a system of rulers and clocks that are moving inertially, you can't have a ruler/clock system that's moving at the speed of light, so there is no physical meaning to plugging v=c into those equations.

 

[Stellar1]

Why does a photon not have an inertial rest frame?

 

[JesseM]

Why does a photon not have an inertial rest frame?

Because a given observer's inertial frame is based on rulers and clocks at rest relative to that observer...it's impossible to accelerate rulers and clocks up to light speed.

Another way of seeing that a photon cannot have an inertial frame is that one of the two postulates of SR is that the laws of physics must be the same in every inertial frame, but in all slower-than-light frames photons always move at c, so if there was a frame where a photon could be at rest this postulate would be violated.

 

[yuiop]

So here's another thought:

In the perspective of the photon, it is the box itsself that is vibrating back and fourth. From the photons perspective, gamma=sqrt(0) so therefore the height of the box is 0, no? So that would mean that the clock is constantly ticking, correct?

It is hard to make any sense of measurements from the point of view of a photon as the answers usually involve 0/0. (Indeterminate). However, you could ponder the point of view of a ball in the Stellar ball clock ;)

 

[peter0302]

Of course, the speed of a photon isn't constant :P It's just constant in a vacuum, and that is given as c

Sorry, this always irks me. :) The speed of a photon IS always constant. The reason light appears to slow down in a given medium is a consequence of the time it takes an electron to absorb a photon and emit a new one. The photon going in is not the same photon as the one going out.

 

[rbj]

Sorry, this always irks me. :) The speed of a photon IS always constant. The reason light appears to slow down in a given medium is a consequence of the time it takes an electron to absorb a photon and emit a new one. The photon going in is not the same photon as the one going out.

well, guess what might irk some other folks (but not me, i don't really care)? it's this "photon is absorbed and re-emitted" explanation for why the apparent SOL is slower in transparent materials. i think this: http://en.wikipedia.org/wiki/Refractive_index#The_speed_of_light outlines what i mean. it says

At the microscale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the permittivity of the medium. The charges will, in general, oscillate slightly out of phase with respect to the driving electric field. The charges thus radiate their own electromagnetic wave that is at the same frequency but with a phase delay. The macroscopic sum of all such contributions in the material is a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions (see scattering).

 

[pervect]

One might also want to take a look at ZapperZ's physics forum FAQ on this topic at https://www.physicsforums.com/showpost.php?p=899393&postcount=4 .

The photon is emitted and absorbed, but the absorption can be regarded as an absorption by the lattice to create a phonon.

I've seen explanations similar to the Wiki one posted above in Feynman's popularizations (i.e. QED).

 

[peter0302]

well, guess what might irk some other folks (but not me, i don't really care)? it's this "photon is absorbed and re-emitted" explanation for why the apparent SOL is slower in transparent materials. i think this: http://en.wikipedia.org/wiki/Refractive_index#The_speed_of_light outlines what i mean. it says

I think that's saying the same thing. The bottom line is that the photon going in is not the same photon as the one going out. The only reason for the apparent delay is due to the interaction with the atoms in the media. But inbetween atoms the speed is always c. And as soon as the light leaves the medium, its speed is likewise c. No?

 

[NtroPunDfeetd]

Does the photon actually travel at light speed? When your on a flatbed truck traveling down the highway at 70mph with a photon clock in hand, does the photon for you on the truck still travel at the speed of light and count your seconds accurately? To an observer on the ground does the photon look as if it's going slower? Has this ever been tested and proven?

Please answer my questions shortly and staying on track completely with what I'm asking; do not diverge from my question into other explanations.

 

[Doc Al]

Does the photon actually travel at light speed?

Yes. According to everyone.

When your on a flatbed truck traveling down the highway at 70mph with a photon clock in hand, does the photon for you on the truck still travel at the speed of light and count your seconds accurately?

Sure.

To an observer on the ground does the photon look as if it's going slower?

No. The photon travels at light speed. The clock ticks slower, since for the ground observer the photon travels a greater distance.

Has this ever been tested and proven?

No one has ever done experiments with photon clocks, but the effect it illustrates--time dilation--has been tested.

 

[Austin0]

Doc Al is Offline:
Posts: 23,346
Blog Entries: 1 Re: Time dilation and the photon clock

--------------------------------------------------------------------------------

Originally Posted by NtroPunDfeetd
Does the photon actually travel at light speed?

Yes. According to everyone.

.

To an observer on the ground does the photon look as if it's going slower?

No. The photon travels at light speed. The clock ticks slower, since for the ground observer the photon travels a greater distance.

What is the interpretation in the case of a photon clock at a location of low gravitational potential?
Is it traveling slower or traveling a greater distance due to the geometry at a small Scwarzschild radius?
Thanks

 

[yuiop]

What is the interpretation in the case of a photon clock at a location of low gravitational potential?
Is it traveling slower or traveling a greater distance due to the geometry at a small Scwarzschild radius?
Thanks

To keep it simple take the case of a short horizontal light clock. (Horizontal rulers are not length contracted by gravity.) To an observer higher up, the clock lower down is running slow and the speed of light lower down is slower than the speed of light higher up. These two effects conspire in such a way, that to a local observer co-located with the light clock at a small Schwarzschild radius, the speed of light appears normal. This slowing down of clocks and light, deep in a gravitational well is not an optical illusion, because by lowering a clock down and bringing it back up again, it can be demonstrated that the lowered clock really does run slower than a clock that remained higher up.

It follows that if the clock lower down is really running slower than the clock higher up, then the speed of light lower down must really be slower than the speed of light higher up, in order for a local observer lower down to measure the local speed of light as c.

 

[Austin0]

To keep it simple take the case of a short horizontal light clock. (Horizontal rulers are not length contracted by gravity.) To an observer higher up, the clock lower down is running slow and the speed of light lower down is slower than the speed of light higher up. These two effects conspire in such a way, that to a local observer co-located with the light clock at a small Schwarzschild radius, the speed of light appears normal. This slowing down of clocks and light, deep in a gravitational well is not an optical illusion, because by lowering a clock down and bringing it back up again, it can be demonstrated that the lowered clock really does run slower than a clock that remained higher up.

It follows that if the clock lower down is really running slower than the clock higher up, then the speed of light lower down must really be slower than the speed of light higher up, in order for a local observer lower down to measure the local speed of light as c.

Thanks for your very clear explanation. It was pretty much what my own logic arrived at but I no longer have the implicit faith in "logic" I once had.