Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chris on 27/04/2017 17:43:07
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Kris has written to say:
I think you can (at least theoretically) synchronize the distant clocks:
Let’s have two light sources at points A and B separated by distance d and sending constantly (perpendicular to AB) signals to clocks at A’ and B’
Let’s have an opaque rigid rod of the length d traveling with constant speed v (non relativistic) parallel (and very close to) the line AB from B towards A . Initially the light from B to B’ will be blocked and the light from A to A’ will be allowed to be transmitted . When front end of the rod will start cutting off the light from A to A’ the light from B will start to be transmitted to B’ . At this moment we will have both clock at A’ and B’ synchronized.
A' <- v B'
| <-------------------------d-------------------------------
| |
| ----------------------------d---------------------------- |
A B
Of course it won't be easy to synchronize the clocks with high accuracy allowing for precise measurement one way speed of light. It will depend how precisely can we measure the distance d (however this can be done on stationary rod A'B" and lasers AB and then the rod can be moved out and moved in with constant speed v. (The requirement for the v to be constant is not actually that important; the rod should move with the constant speed to minimize the stress and vibrations). The accuracy of one way speed of light would depend also on the length d; however the bigger the d the more difficult it will be to maintain rigidity of the rod.
Is my reasoning incorrect?
Can you help?
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speed v (non relativistic)
This is the key assumption; it is quite easy to synchronise two clocks that are in the same place and with zero relative velocity.
It is harder (but still possible) to synchronize clocks that are in different places but with zero relative velocities (or non-relativistic velocities, which are "close to" zero).
It's when you get to relativistic velocities (or very different gravitational potentials) that it becomes effectively impossible to provide an unambiguous clock synchronization.
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speed v (non relativistic)
This is the key assumption; it is quite easy to synchronise two clocks that are in the same place and with zero relative velocity.
It is harder (but still possible) to synchronize clocks that are in different places but with zero relative velocities (or non-relativistic velocities, which are "close to" zero).
It's when you get to relativistic velocities (or very different gravitational potentials) that it becomes effectively impossible to provide an unambiguous clock synchronization.
Not necessarily. The OP said that the length of the moving rod is d'. If he meant this literally then it has length d' as it would be measured in the frame of reference in which the light sources are both at rest.
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Kris has written to say:
I think you can (at least theoretically) synchronize the distant clocks:
Let’s have two light sources at points A and B separated by distance d and sending constantly (perpendicular to AB) signals to clocks at A’ and B’
Let’s have an opaque rigid rod of the length d traveling with constant speed v (non relativistic) parallel (and very close to) the line AB from B towards A . Initially the light from B to B’ will be blocked and the light from A to A’ will be allowed to be transmitted . When front end of the rod will start cutting off the light from A to A’ the light from B will start to be transmitted to B’ . At this moment we will have both clock at A’ and B’ synchronized.
A' <- v B'
| <-------------------------d-------------------------------
| |
| ----------------------------d---------------------------- |
A B
Of course it won't be easy to synchronize the clocks with high accuracy allowing for precise measurement one way speed of light. It will depend how precisely can we measure the distance d (however this can be done on stationary rod A'B" and lasers AB and then the rod can be moved out and moved in with constant speed v. (The requirement for the v to be constant is not actually that important; the rod should move with the constant speed to minimize the stress and vibrations). The accuracy of one way speed of light would depend also on the length d; however the bigger the d the more difficult it will be to maintain rigidity of the rod.
Is my reasoning incorrect?
Can you help?
The problem with this method of synchronization is its dependence on the notion of simultaneity, i.e. that the ends of the rods will be at A and B simultaneously.
Do you know if the OP is aware of how clocks are synchronized in relativity, i.e. how Einstein defined the concept of simultaneous events to define synchronization?
Does the Op
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I think you can (at least theoretically) synchronize the distant clocks:
Let’s have two light sources at points A and B separated by distance d and sending constantly (perpendicular to AB) signals to clocks at A’ and B’
Let’s have an opaque rigid rod of the length d traveling with constant speed v (non relativistic) parallel (and very close to) the line AB from B towards A . Initially the light from B to B’ will be blocked and the light from A to A’ will be allowed to be transmitted . When front end of the rod will start cutting off the light from A to A’ the light from B will start to be transmitted to B’ . At this moment we will have both clock at A’ and B’ synchronized.
A' <- v B'
| <-------------------------d--------------------------------------------------
| |
| ----------------------------d-------------------------------------- |
A B
Of course it won't be easy to synchronize the clocks with high accuracy allowing for precise measurement one way speed of light. It will depend how precisely can we measure the distance d (however this can be done on stationary rod A'B" and lasers AB and then the rod can be moved out and moved in with constant speed v. (The requirement for the v to be constant is not actually that important; the rod should move with the constant speed to minimize the stress and vibrations). The accuracy of one way speed of light would depend also on the length d; however the bigger the d the more difficult it will be to maintain rigidity of the rod.
Is my reasoning incorrect?
-
I think you can (at least theoretically) synchronize the distant clocks:
Let’s have two light sources at points A and B separated by distance d and sending constantly (perpendicular to AB) signals to clocks at A’ and B’
Let’s have an opaque rigid rod of the length d traveling with constant speed v (non relativistic) parallel (and very close to) the line AB from B towards A . Initially the light from B to B’ will be blocked and the light from A to A’ will be allowed to be transmitted . When front end of the rod will start cutting off the light from A to A’ the light from B will start to be transmitted to B’ . At this moment we will have both clock at A’ and B’ synchronized.
A' <- v B'
| <-------------------------d--------------------------------------------------
| |
| ----------------------------d-------------------------------------- |
A B
Of course it won't be easy to synchronize the clocks with high accuracy allowing for precise measurement one way speed of light. It will depend how precisely can we measure the distance d (however this can be done on stationary rod A'B" and lasers AB and then the rod can be moved out and moved in with constant speed v. (The requirement for the v to be constant is not actually that important; the rod should move with the constant speed to minimize the stress and vibrations). The accuracy of one way speed of light would depend also on the length d; however the bigger the d the more difficult it will be to maintain rigidity of the rod.
Is my reasoning incorrect?
This is simply a repeat of the opening post. It's much easier to synchronize distant clocks by using the method defined by Einstein in his first paper on relativity. In an inertial frame of reference let there be two clocks, equipped with light detectors, at rest and which start ticking when they detect a flash of light. In the midpoint between them let a flash of light be emitted in all directions. When the clocks detect the flash of light from this midpoint source they are, by definition, synchronized.
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"This is simply a repeat of the opening post. It's much easier to synchronize distant clocks by using the method defined by Einstein in his first paper on relativity. In an inertial frame of reference let there be two clocks, equipped with light detectors, at rest and which start ticking when they detect a flash of light. In the midpoint between them let a flash of light be emitted in all directions. When the clocks detect the flash of light from this midpoint source they are, by definition, synchronized."
Yes, the clocks will be synchronized, providing the speed of light is isotropic (which I believe is the case), but if it isn't?
If the speed of light is infinite in one direction and 0.5c the other direction? How can you tell?
The Wikipedia sais :
"Although the average speed over a two-way path can be measured, the one-way speed in one direction or the other is undefined (and not simply unknown), unless one can define what is "the same time" in two different locations. To measure the time that the light has taken to travel from one place to another it is necessary to know the start and finish times as measured on the same time scale. This requires either two synchronized clocks, one at the start and one at the finish, or some means of sending a signal instantaneously from the start to the finish. No instantaneous means of transmitting information is known. Thus the measured value of the average one-way speed is dependent on the method used to synchronize the start and finish clocks. This is a matter of convention. The Lorentz transformation is defined such that the one-way speed of light will be measured to be independent of the inertial frame chosen."
The one way speed of light may well be c (which has been widely accepted), but to prove it so far has been unsuccessful.
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Yes, the clocks will be synchronized, providing the speed of light is isotropic (which I believe is the case), but if it isn't?
If the speed of light is infinite in one direction and 0.5c the other direction? How can you tell?
If that were the case then relativity would be wrong. Note that in your method you assume that the length of the moving rod is identical to distance between the clocks. How do you propose to determine that? Even the slightest length contraction would mean a non-synchronization of the clocks.
A method to synchronize clocks by using clock transport is simple and therefore the one way speed of light can be determined with clocks synchronized in such a manner. The Wikipedia article is just plain wrong. Observations using Very Long Baseline Interferometry (VLBI) has confirmed the one way speed of light.
See Special Relativity: A Modern Introduction by Hans C. Ohanian, (2001), page 32
See also: http://www.espenhaug.com/OneWaySpeedOfLight.html
Especially this one: https://www.technologyreview.com/s/421603/the-one-way-speed-of-light-conundrum/
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"If that were the case then relativity would be wrong. Note that in your method you assume that the length of the moving rod is identical to distance between the clocks. How do you propose to determine that? Even the slightest length contraction would mean a non-synchronization of the clocks."
The length contraction will be d' =d(1-v^2/c^2), which will be way below our ability to measure the distance.
If d=10m, v=100m/s the length contraction will be in order of (10^-12)m. If we can determine the position of the laser and the ends of the rod to 1nm (10^-9)m , the length contraction will be 1000x smaller than our uncertainity in aligning lasers with the rod (while all being stationary). Error of 1nm will cause uncertainity in clocks synchronization (if the rod is travelling with the speed v=100m/s) to be (10^-9)/100m/s=(10^-11)s . To cover the distance d=10m the light will need 10m/(3x10^8)m/s ~ 3x(10^-8)s. So our measurement of one way speed of light should be still quite good (within 0.3% of uncertainity)