The Mysterious Synchronization of Clocks in Special Relativity

[shlosmem]

Let's say we have a clock that work like this , districts beam of lights are sent in constant time gaps (created by a crystal or some other radioactive process) to a sensor. the sensor is connected to a counter that counts the number of beams, and here we have our clock.
Now if we put 2 clocks such this in a room they will remain more or less synchronized regardless to the position we put them.
But if we think on a train traveling very fast, and we put 2 of the clocks in the train one is sending the lights to the driving direction and one to the opposite direction, according to an observer standing outside the train the clocks cannot remain synchronized because relative to the observer the lights meets the sensor more frequently on the second clock. But as we know a traveler inside the train will see synchronized clocks.
How this inconsistency in the state of world is explained in special relativity? (if the clocks transmitting the counting numbers what the outside observer will receive)

 

[PAllen]

The outside observer will readily understand that both clocks 'tick' mutually consistently. For the one firing in the direction of train's motion, the emitter's motion means the spacing between pulses is compressed, while the receiver moving away perceives expansion relative to emitter. These effects exactly cancel. For the clock firing the other direction, the emitter's pulses appear (to outside observer) to have expanded gap, but then receiver moving towards emission point, sees compression. The effects cancel. Thus, both outside observer and train observer see both clocks running at the same rate. There is no need for relativity at all in this analysis. Relativity only enters to note that both train clocks are slow as observed by outside observer, compared to their own. That is, the fact that both clocks agree for both observers is fully explained by Galilean relativity. Only the time dilation of both clocks as observed by outside observer is a relativistic effect.

 

[shlosmem]

For the one firing in the direction of train's motion, the emitter's motion means the spacing between pulses is compressed, ... For the clock firing the other direction, the emitter's pulses appear (to outside observer) to have expanded gap, ... .

Thanks PAllen,
But I am not sure I fully understand. Why the observer will see emitters who are identical but creating the light beams in a different rates?

 

[Gaz]

I have thought about this one to surly the clocks will appear to slow down in one direction and speed up in the opposite direction as they traveling towards and away from the standing observer unlike the vertical clocks that appear to just slow down.
They would not be unsynchronized though as they both will of course slow and speed up the same amount still meaning one tick (backward and forth motion of the clocks) would take the same amount of time by both clocks. And as the light would spend more time traveling away from the observer than traveling towards the over all amount no doubt if you calculated it will agree with a vertical clock on the same train.

 

[harrylin]

Let's say we have a clock that work like this , districts beam of lights are sent in constant time gaps (created by a crystal or some other radioactive process) to a sensor. the sensor is connected to a counter that counts the number of beams, and here we have our clock.
Now if we put 2 clocks such this in a room they will remain more or less synchronized regardless to the position we put them.
But if we think on a train traveling very fast, and we put 2 of the clocks in the train one is sending the lights to the driving direction and one to the opposite direction, according to an observer standing outside the train the clocks cannot remain synchronized because relative to the observer the lights meets the sensor more frequently on the second clock. But as we know a traveler inside the train will see synchronized clocks.
How this inconsistency in the state of world is explained in special relativity? (if the clocks transmitting the counting numbers what the outside observer will receive)

First it may be useful to make two corrections.
1. A train that "is traveling fast" suggests constant speed. Then according to the outside observer, the light meets the sensor just as frequently on the rear clock because the distance is constant (conservation of cycles!). However, during the preceding acceleration phase, indeed the light meets the sensor more frequently on the rear clock.
2. The traveler inside the train will interpret the clocks as having gone out of sync if this traveler does an "Einstein synchronization" inside the train for its new state of motion.

 

[shlosmem]

"Then according to the outside observer, the light meets the sensor just as frequently on the rear clock because the distance is constant (conservation of cycles!)."

harrylin - This is exactly what I'm trying to understand her. I thought of 3 facts the outside observer will say.
1. The two light emitters are working on the same rate.
2. The speed of the light is equal for every direction.
3. The distance the light making (from the source to the sensor) is different for every clock.
The conclusion for all this 3 that clocks can’t be synchronized for the observer, so one of them must be wrong. Now PAllen Claim that the first fact is wrong, but I’m still not sure how it can be, If according to rules of physics the 2 emitters should have the same rate.

 

[shlosmem]

Now I think that we can make this question even harder! This 2 clocks also are not showing the same number they are working with the same rate. But let's make a third clock, that work with a single beam of light moving between mirrors and placing a sensor and counter on one of the mirrors. We can make the distance between the mirrors in such a way that according to someone on the train all the 3 clocks will be synchronized. But according to observer outside the train, the third clock will be completely out of sync with the first 2 clocks, in a way that this clock will be much slower! (This will be like a swimmer swimming one way with the river stream and one way against the river stream).

 

[harrylin]

"Then according to the outside observer, the light meets the sensor just as frequently on the rear clock because the distance is constant (conservation of cycles!)."

harrylin - This is exactly what I'm trying to understand her. I thought of 3 facts the outside observer will say.
1. The two light emitters are working on the same rate.
2. The speed of the light is equal for every direction.
3. The distance the light making (from the source to the sensor) is different for every clock.
The conclusion for all this 3 that clocks can’t be synchronized for the observer, so one of them must be wrong. Now PAllen Claim that the first fact is wrong, but I’m still not sure how it can be, If according to rules of physics the 2 emitters should have the same rate.

Please read it again: according to PAllen (and myself), for a train at constant speed: "both outside observer and train observer see both clocks running at the same rate."
That means that (1.) The two light emitters are working on the same rate. The consequence of the train analysis is what is often called "relativity of simultaneity". For a primer, see: https://en.wikipedia.org/wiki/Relativity_of_simultaneity#The_train-and-platform_thought_experiment