Does Using a Sound Clock Affect Lorentz Transformations in Relativity?

[covers]

There's one thing I cannot get straight so I hope someone can help me out here.

Often the 'lightclock' example is used to explain certain aspects of special relativity. With this example its possible to understand the Lorentztransformation to some degree. Now my problem is, that I always think that if I would take a sound-clock instead of a lightclock the whole Lorentztransformation would change (the motion of sound is, as light, also independent of the source). Consider this, for a resting observer the light within the clock (the clock is in motion inside a spaceship) makes a zigzag path. Whereas the zigzag path of the light can at most form a 45 degree angle (when the spaceship moves with the speed of light). So the light takes longer from the viewpoint of a resting observer then from the viewpoint of an obeserver inside the spaceship. Now if we make the same experiment with a 'soundclock', the zigzag path of the sound is much more extrem, thus can form an angle which is much more then 45 degrees. When I think about this, that time dilation must therefore be much more extrem then with light, because from the viewpoint of the resting observer, the distance which the sound travels is much more stretched then the distance in the example of the lightclock.

Can someone help me out here? This really bugs me, and I am not able to find the error in this line of reasoning.

 

[actionintegral]

(the motion of sound is, as light, also independent of the source).

This may be true, I don't know. But I do know that the speed of sound is NOT independent of the speed of the OBSERVER. Light is.

The way I explain it to my daughter is as follows: Light is like a rainbow. No matter how fast you run to catch up with it, it is always moving away from you just as fast.

 

[bernhard.rothenstein]

There's one thing I cannot get straight so I hope someone can help me out here.

Often the 'lightclock' example is used to explain certain aspects of special relativity. With this example its possible to understand the Lorentztransformation to some degree. Now my problem is, that I always think that if I would take a sound-clock instead of a lightclock the whole Lorentztransformation would change (the motion of sound is, as light, also independent of the source). Consider this, for a resting observer the light within the clock (the clock is in motion inside a spaceship) makes a zigzag path. Whereas the zigzag path of the light can at most form a 45 degree angle (when the spaceship moves with the speed of light). So the light takes longer from the viewpoint of a resting observer then from the viewpoint of an obeserver inside the spaceship. Now if we make the same experiment with a 'soundclock', the zigzag path of the sound is much more extrem, thus can form an angle which is much more then 45 degrees. When I think about this, that time dilation must therefore be much more extrem then with light, because from the viewpoint of the resting observer, the distance which the sound travels is much more stretched then the distance in the example of the lightclock.

Can someone help me out here? This really bugs me, and I am not able to find the error in this line of reasoning.

I think that the light clock leads to the time dilation formula and not to the Lorentz-Einstein transformations. As Asher Peres has shown the time dilation formula leads to the addition law of relativistic velocities which at its turn could lead to all the transformation equations of special relativity. (See the link below).
The acoustic clock is not so easy to treat but it will shurelly not lead to other transformation equations. Have a look please at
Physics, abstract
physics/0607048 (arXiv)
sine ira et studio

 

[Doc Al]

Now my problem is, that I always think that if I would take a sound-clock instead of a lightclock the whole Lorentztransformation would change (the motion of sound is, as light, also independent of the source).

The key feature of a light clock that allows you to draw some interesting conclusions (time dilation, etc.) is that light has the unique property that its speed is the same as measured in any inertial frame. Sound does not have that property!

Oops: Looks like actionintegral already said the same thing.

 

[covers]

No matter how fast you run to catch up with it, it is always moving away from you just as fast.

You can catch up with sound, but not with light. That seems to make sense.
But what does this mean for the sound-clock? Does it mean the sound inside the clock (inside the moving spaceship) does not go straight? Does it bounce against the wall of the clock? Cannot be, as we could measure the speed of the spaceship that way! What doese it mean then? Maybe sound travels faster when it moves? Does not make much sense either... hmm

(See the link below)

Sorry, but I could not find that link...

light has the unique property that its speed is the same as measured in any inertial frame. Sound does not have that property!

But if sound moves at different speeds in different inertial systems, couldn't I calculate the speed of the inertial system itself from that property?

 

[robphy]

I think that the light clock leads to the time dilation formula and not to the Lorentz-Einstein transformations. As Asher Peres has shown the time dilation formula leads to the addition law of relativistic velocities which at its turn could lead to all the transformation equations of special relativity.

Once time-dilation is established for a light-clock (so that you know the ticks on any inertial worldline), you can do radar experiments... from which the Lorentz Transformations follow immediately.

Here's a geometric argument: if you draw a "longitudinal light clock", you will find that the area enclosed by one tick (i.e. the triangle with a future-timelike leg and two future-null legs) is a spacetime invariant. Upon comparison of the corresponding ticks from two lightclocks, the scaling behavior of the null legs yields the Lorentz Transformation in light-cone coordinates. By translating into rectangular coordinates (via radar methods), you get the standard 1+1 Lorentz Transformations.

See http://arxiv.org/abs/physics/0505134

 

[Doc Al]

But if sound moves at different speeds in different inertial systems, couldn't I calculate the speed of the inertial system itself from that property?

The speed of sound with respect to the observer depends on the inertial frame that is doing the observing. Depending upon the setup, you could use that to measure the relative speed of the sound medium (air) with respect to the observing frame. So? (What you couldn't do is perform an experiment with sound inside your spaceship lab and use the results to deduce the speed of your spaceship.)

The problem with the "sound clock" idea is that to properly deduce the speed of the sound with respect to various observers requires the use of the relativistic velocity addition formulas. The "light clock" is much simpler to analyze.

 

[bernhard.rothenstein]

Once time-dilation is established for a light-clock (so that you know the ticks on any inertial worldline), you can do radar experiments... from which the Lorentz Transformations follow immediately.

I think that the radar detec tion experiments are associated with Doppler which is a consequence of the time dilation
Sine ira et studio

 

[Office_Shredder]

But if sound moves at different speeds in different inertial systems, couldn't I calculate the speed of the inertial system itself from that property?

Yes. If you're traveling at Mach 1, and see you're going as fast as a sound wave, you know you're travellign at the speed of sound relative to the medium.

However, you don't know how fast the medium is travelling