Measuring One-Way Speed of Light

[DrStupid]

Consider a cylinder rotating about the x-axis of some inertial frame. Suppose that it has a straight line painted on it parallel to the axis in this frame. Now consider the line in another inertial frame, a quick Lorentz transform will show that the line forms a helix in another frame.

Always use the rest frame of the assembly. Problem solved.

 

[ghwellsjr]

Are you going to answer my question:

Do you accept without question or exception all the tenets of Special Relativity, including the Lorentz Transformation?

 

[DrGreg]

How do you define "the time taken for light" if time is dependent on a position?

For the purpose of this thought experiment, you measure t using two Einstein-synchronised clocks at the two positions and use the equation T=t+\alpha x.

However, in a practical scenario where you are given two T-synchronised clocks but you don't know how they have been synchronised, you just read T from the two clocks.

 

[PeterDonis]

DrStupid, we have apparently been talking at cross purposes; I was assuming that you were measuring the sensor signal continuously as the angular velocity of the assembly was continuously changed, but it doesn't look like that's the case:

For example:

1. Start recording of the sensor signal.
2. Drink some coffee.
3. Start recording of the angular velocity.
4. Read a newspaper.
5. Stop recording of the angular velocity.
6. Get record and go to the sensor.
7. Stop recording of the sensor signal.
8. Check the records to make sure that there are no oscillations or other fluctuations.
9. If the values are not constant than return to 1.

In other words, you spin up the assembly to some angular velocity, and keep it constant while you measure the sensor signal. Then you spin the assembly up some more, and hold it constant again while you measure the sensor signal. Then you repeat until you have enough points for a graph. Correct?

Then you have the following problem: how do you correlate the different angular velocity measurements? A spin-up process intervenes between each one, and that process will change the spatial geometry of the assembly (because it will change the internal forces within the assembly, since those forces depend on angular velocity). That includes possible changes in the relative alignment of the slits; in other words, the equilibrium state of the assembly at different angular velocities may have different alignments of the slits.

Also, you are still either assuming that the entire assembly has a single "co-rotating rest frame" for each angular velocity measurement (so an angular velocity measurement at one point applies to the entire assembly), or assuming a clock synchronization between different parts of the assembly for each angular velocity measurement (if you take angular velocity measurements locally at different points of the assembly).

 

[Dale]

Always use the rest frame of the assembly. Problem solved.

Not if the problem is to measure the speed of light in different frames.

If you use the rest frame of the cylinder then you assume the synchronization of that frame. That will lead to anisotropic speed of light as was already described

 

[DrStupid]

In other words, you spin up the assembly to some angular velocity, and keep it constant while you measure the sensor signal. Then you spin the assembly up some more, and hold it constant again while you measure the sensor signal. Then you repeat until you have enough points for a graph. Correct?

Exactly.

Then you have the following problem: how do you correlate the different angular velocity measurements? A spin-up process intervenes between each one, and that process will change the spatial geometry of the assembly (because it will change the internal forces within the assembly, since those forces depend on angular velocity). That includes possible changes in the relative alignment of the slits; in other words, the equilibrium state of the assembly at different angular velocities may have different alignments of the slits.

In steady rotating state the change of spatial geometry is radial symmetric and would therefore not affect the relative alignment of the slits.

Also, you are still either assuming that the entire assembly has a single "co-rotating rest frame" for each angular velocity measurement

This is not just an assumption. There is always a frame of reference where the assembly has no angular momentum.

(so an angular velocity measurement at one point applies to the entire assembly)

This is given when any part of the assembly has a constant angular momentum in the common rest frame. Indeed I still assume that the assembly will always reach such a state of steady rotation if it is sufficiently balanced to remain radial symmetric.

 

[DrStupid]

Not if the problem is to measure the speed of light in different frames.

Just use a device that is at rest in the particular frame of reference. I do not see the problem.

If you use the rest frame of the cylinder then you assume the synchronization of that frame.

I avoid any assumptions about synchronization. I make assumptions about the shape of the assembly but these assumptions are justified by its mechanical properties. I currently see no reason for the assumption that rotation would necessarily lead to torsion.

 

[DrStupid]

For the purpose of this thought experiment, you measure t using two Einstein-synchronised clocks at the two positions and use the equation T=t+\alpha x.

This works for the frame with Einstein-synchronized clocks but there is time not dependent on position. How do you do that without Einstein synchronization?

However, in a practical scenario where you are given two T-synchronised clocks but you don't know how they have been synchronised, you just read T from the two clocks.

What is the physical meaning of the "time" of different "clocks" at different locations that are not synchronized?

 

[WannabeNewton]

I would still like a journal reference for the supposed (it isn't, due to necessity of clock synchronization but you seem to keep denying it) one-way speed of light measurement you have proposed. It's forum policy that you provide such a reference.

 

[micromass]

I would still like a journal reference for the supposed (it isn't, due to necessity of clock synchronization but you seem to keep denying it) one-way speed of light measurement you have proposed. It's forum policy that you provide such a reference.

And while you answer that, could you also answer ghwellsjr?

Do you accept without question or exception all the tenets of Special Relativity, including the Lorentz Transformation?

 

[PeterDonis]

In steady rotating state the change of spatial geometry is radial symmetric

I think you mean "the change is only in the radial direction", i.e., the geometry is *rotationally* symmetric (doesn't change with angle about the axis of rotation). This is true in the idealized case that the geometry starts out that way; but that amounts to an assumption of perfect balance of the assembly.

There is always a frame of reference where the assembly has no angular momentum.

But there is no guarantee that every individual piece of the assembly is at rest in that frame (to guarantee that, you need perfect rigidity). There is not even a guarantee that the axis of rotation of the assembly is at rest in that frame (to guarantee that, you need perfect balance of the assembly).

This is given when any part of the assembly has a constant angular momentum in the common rest frame.

Which may not even exist. See above.

 

[Dale]

Just use a device that is at rest in the particular frame of reference. I do not see the problem.

And which frame do you choose if you happen to have two such devices in relative motion? According to the synchronization of each the other will be a helix.

I avoid any assumptions about synchronization. I make assumptions about the shape of the assembly

Such assumptions are completely equivalent to assumptions about synchronization. There are many threads on this forum about such structural means of measuring the one way speed of light. Whatever shape you assume is logically equivalent to assuming some synchronization because if you choose a different synchronization convention then you will get a different shape for your structure.

but these assumptions are justified by its mechanical properties.

Then, as requested by others please provide a suitable reference.

 

[Wes Tausend]

...

There is, perhaps, another simplistic way to look at DrStupids experiment to see that it will not work. I can offer an analogy.

If I were to sychronize my wristwatch with Big Ben while standing beneath the clock, I can set my hands to strike 12 at what seems like exactly the same time as Big Ben. If I then proceed in a direction away from Big Ben, I can stop after some miles, turn around and observe Big Ben's time from a great distance and notice a difference in the two times between my watch and the huge London clock. Big Ben will appear to be slower because it has taken the light information from Big Ben some real amount of extra time to get to me (as in it takes 8.3 minutes for sunlight to reach earth), while my watch is still very close (mere inches), exactly as it was when I set it. The conclusion is I can only observe the time reading of Big Ben in some ratio portion of it's history compared to my wrist watch because that delayed information conundrum probably includes any clock observed by any increment of distance.

So this means that even if a rigid bar locks the hands of my wristwatch to the hands of Big Ben, the two clocks cannot be observed to read simultaneously if separated by any distance at all. The same must hold true for DrStupids discs separated by any length of bar. So if one were to observe the rotating image DrStupid used from the laser end (which end seems to be shown)...

...the slot may appear vertical on the close disc, but must appear only approaching vertical on the far disc. This is identical to my watch reading 12 o'clock when Big Ben appears from a distance to read just about to strike 12. If the laser fires through the near vertical slot (12 o'clock) in the close disc, it will seem to pass through the far disc also at 12 o'clock because the far disc will just happen to finally be vertical when the light gets there. Light will appear to have an infinite speed if one still insists that the disc slots (clocks) are in synchrony. If one does not insist that the two obviously different times (angles) are synchronous, then one is left with the question of which clock (stopwatch) is correct and the experiment fails altogether.

I believe the speed of light is different than slower speeds in that both clocks are actually correct. My wristwatch gives the correct time for my position and Big Ben gives the correct time for the folks loitering right beneath it. It is this non-intuitive "time" quality that makes Special Relativity special. Or at least, that is the way now I see it unless corrected.

I thought DaleSpam's straight longitudinal paint-striped cylinder with the stripe "helixed" during rotation (post #29) to say the same thing as I claim above.

Wes
...

 

[ghwellsjr]

...
So this means that even if a rigid bar locks the hands of my wristwatch to the hands of Big Ben, the two clocks cannot be observed to read simultaneously if separated by any distance at all.

I think you have misunderstood the problem. In your analogy, the two clocks shouldn't be observed to read the same time. It's the difference in their observed times that is claimed to be how long it took the light to propagate from Big Ben to your wristwatch. So if you observed Big Ben to strike 12 when your wristwatch read one microsecond after 12 o'clock, then if you measured your distance to be 1000 feet, you would conclude that light traveled 1 foot per nanosecond.

But there are other ways for you to observe the same thing. The rod could be twisted so that your wristwatch was actually 1/2 microsecond behind Big Ben. Then if it took only 500 nanoseconds for the light to traverse 1000 feet you would see the same thing as before but the light really would have traveled 2 feet per nanosecond and you'd never know the difference, you'd still conclude that it was traveling only 1 foot per nanosecond.

The same must hold true for DrStupids discs separated by any length of bar. So if one were to observe the rotating image DrStupid used from the laser end (which end seems to be shown)...the slot may appear vertical on the close disc, but must appear only approaching vertical on the far disc.

Of course each slot has to be exactly vertical when the light passes through it but the shaft is supposed to make one complete revolution between the time a segment of light makes it through the first slot and then later through the second slot. But the same problem happens if the shaft is twisted as in your Big Ben analogy. You measure the speed of light by assuming that the spin interval of the shaft for exactly one revolution is actually how long it took for the light to traverse the distance. If the shaft is twisted, you will make a wrong measurement.

But even if you assume that the shaft is not twisted in its rest frame, then when you use the Lorentz Transformation to establish what happens in a moving frame, the light does not take the same amount of time to traverse between the two slots and the only way that can happen is if the shaft is twisted. So you could just as easily assume that the shaft was not twisted in the moving frame which means it would be twisted in its rest frame. The point is that you cannot tell if it is twisted but you can still assume that it is not twisted but it's just an assumption which is tantamount to Einstein's convention.

 

[DrStupid]

I would still like a journal reference for the supposed (it isn't, due to necessity of clock synchronization but you seem to keep denying it) one-way speed of light measurement you have proposed. It's forum policy that you provide such a reference.

I'm not aware of such a reference.

 

[micromass]

I'm not aware of such a reference.

Then the discussion is over. The rules clearly state that everything you claim on this forum must be backed up by suitable references when they are demanded. If you cannot supply such a reference, then your posts are not suitable for this forum.

So I ask you to stop posting in this thread. You can resume if you do eventually find that reference. Any further posts (without suitable reference) will be infracted.

 

[DrStupid]

Here is a corresponding reference: http://arxiv.org/pdf/1103.6086.pdf

 

[Dale]

The posted reference does not meet PF guidelines. ArXiv is not a peer reviewed professional journal, it is an archiving system. The paper was archived four years ago and still has not been published, that is generally an indication of very low quality.

 

[harrylin]

Here is a corresponding reference: http://arxiv.org/pdf/1103.6086.pdf

Based on such papers I intended to do such an experiment many years ago (I found that it would have been a HUGE undertaking to do it well enough), until I found a much better reference by Ives in J.O.S.A. of 1939, Theory of the Double Fizeau Toothed Wheel (I easily found a free link to the paper but maybe it's still officially copyrighted so I do not copy the link here). The paper explains clearly that we should expect a null result, as the required twist of the axle is exactly provided for by length contraction.

Thus it explains "the reason for the assumption that rotation would necessarily lead to torsion", that you asked for.