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Cleonis
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Take the following setup:
A series of pulses of radio signal is relayed around the world, along the equator. There is no "gap", it is a continuous loop along numerous relay stations build along the equator. The total number of pulses is fixed at 648,000 - I'll explain in a minute why that number. The spacing between the pulses is continuously monitored and if necessary adjusted, so that there is an even spacing.
To keep the numbers relatively simple I take a day of 86400 seconds (a solar day), I take the Earth circumference as 40,000,000 kilometer, and I take the speed of electromagnetic waves as 300,000 km/s
An electromagnetic wave travels around the equator in 0.1333333... seconds
During that 0.133333... second time interval the relay stations on the equator have traveled 61.7 meter, as they are co-rotating with the Earth. That 61.7 meter distance is 1/648,000th of the Earth's circumference.
Let two series of pulses be circumnavigating: one in the direction of the Earth's rotation, the other counter to it. If the Earth would be non-rotating then the two counterpropagating series will have the same spacing.
Since the Earth is rotating the co-propagating series of pulses will have a somewhat wider spacing 684,001/684,000 larger than in the non-rotating case. Similarly, the counter-propagating series will be spaced 683,999/684,000 smaller.
The above effect is an instance of the Sagnac effect. In particular, the above case is analogous to a Ring Laser Interferometer setup. The reason that the Sagnac effect occurs is the fact that electromagnetic waves propagate at a particular velocity. In a Sagnac setup the speed of light serves as a reference.
If you evaluate the loop as a whole then clearly the relay stations have a velocity relative to the reference created by the counterpropagating EM-waves. That's because the setup involves a closed loop.
Here is what I think is an interesting question:
If you evaluate just a section of the loop (in other words, if measurements are confined to a local frame) then what propagation speed of EM-waves relative to the relay stations will you find?
The answer:
- If you confine measurements to a local frame, then the clocks in that frame must be synchronized using emissions from within that local frame only. Given that clock synchronization you will find a lightspeed of c in both directions.
- The global frame, evaluating the loop as a whole, does not have the same clock synchronization as the local frame. For the global frame a global time applies. If you use that global clock synchronization you find that light does not have velocity c relative to the relay stations.
This is why I called this thread 'Local frames versus global frame'.
If the setup involves a loop, and information flowing along the loop is evaluated, then global clock synchronization is different from clock synchronization along sub-sections.
A series of pulses of radio signal is relayed around the world, along the equator. There is no "gap", it is a continuous loop along numerous relay stations build along the equator. The total number of pulses is fixed at 648,000 - I'll explain in a minute why that number. The spacing between the pulses is continuously monitored and if necessary adjusted, so that there is an even spacing.
To keep the numbers relatively simple I take a day of 86400 seconds (a solar day), I take the Earth circumference as 40,000,000 kilometer, and I take the speed of electromagnetic waves as 300,000 km/s
An electromagnetic wave travels around the equator in 0.1333333... seconds
During that 0.133333... second time interval the relay stations on the equator have traveled 61.7 meter, as they are co-rotating with the Earth. That 61.7 meter distance is 1/648,000th of the Earth's circumference.
Let two series of pulses be circumnavigating: one in the direction of the Earth's rotation, the other counter to it. If the Earth would be non-rotating then the two counterpropagating series will have the same spacing.
Since the Earth is rotating the co-propagating series of pulses will have a somewhat wider spacing 684,001/684,000 larger than in the non-rotating case. Similarly, the counter-propagating series will be spaced 683,999/684,000 smaller.
The above effect is an instance of the Sagnac effect. In particular, the above case is analogous to a Ring Laser Interferometer setup. The reason that the Sagnac effect occurs is the fact that electromagnetic waves propagate at a particular velocity. In a Sagnac setup the speed of light serves as a reference.
If you evaluate the loop as a whole then clearly the relay stations have a velocity relative to the reference created by the counterpropagating EM-waves. That's because the setup involves a closed loop.
Here is what I think is an interesting question:
If you evaluate just a section of the loop (in other words, if measurements are confined to a local frame) then what propagation speed of EM-waves relative to the relay stations will you find?
The answer:
- If you confine measurements to a local frame, then the clocks in that frame must be synchronized using emissions from within that local frame only. Given that clock synchronization you will find a lightspeed of c in both directions.
- The global frame, evaluating the loop as a whole, does not have the same clock synchronization as the local frame. For the global frame a global time applies. If you use that global clock synchronization you find that light does not have velocity c relative to the relay stations.
This is why I called this thread 'Local frames versus global frame'.
If the setup involves a loop, and information flowing along the loop is evaluated, then global clock synchronization is different from clock synchronization along sub-sections.