You "heard" wrong. Time dilation is not significant for observers at non-relativistic velocities, but the relativity of simultaneity is calculated using Lorentz transformations, which necessarily includes even inappreciable time dilation. The relativity of simultaneity very much does assume the constant speed of light. This is the whole reason that time dilation and length contraction are evoked.
The relativity of simultaneity is a direct consequence of the two postulates of SR, and as such necessarily assumes the constant speed of light, seeing how that is one of the postulates. And who said anything about "different observers, measuring particles to be at different locations at the same time"?
You "heard" wrong. Time dilation is not significant for observers at non-relativistic velocities, but the relativity of simultaneity is calculated using Lorentz transformations, which necessarily includes even inappreciable time dilation. The relativity of simultaneity very much does assume the constant speed of light. This is the whole reason that time dilation and length contraction are evoked.
The relativity of simultaneity is a direct consequence of the two postulates of SR, and as such necessarily assumes the constant speed of light, seeing how that is one of the postulates. And who said anything about "different observers, measuring particles to be at different locations at the same time"?
Relativity of simultaneity video
It looks like from watching this video that the velocity of the train then changes the observed speed of light. It assumes that the trains movement then allows the flash from lightning in the front of the train to be seen before the flash behind the train because of the trains velocity.
The trains velocity should not change the measured speed of light!
If the speed of light was not measured to change for the observer on the train, then he would have to observe the flash of light in front of him to have traveled slower and the one behind him to have traveled faster than the observer would measure it to travel at the station in order for them to both measure it to travel at the same speed regardless of the difference in velocity.No.. Not like that. Observed speed of light didn't change at all. Speed of light is constant.Only thing is that train was hastening towards it.
If the speed of light was not measured to change for the observer on the train, then he would have to observe the flash of light in front of him to have traveled slower and the one behind him to have traveled faster than the observer would measure it to travel at the station in order for them to both measure it to travel at the same speed regardless of the difference in velocity.
The flashes are only depicted as being the same speed relative to the observer on the station in both cases. How could it then be seen to travel at the same speed for both observers then?
It just seems like there isn't any Galilean Invarience in the consistancy of the speed of light in the relativity of simultaneity. If the observer on the train assumed that he was at rest, then the flashes of light would reach him at the same time. It is as though the observer on the train cannot assume that he is at rest.Easy.. Length contraction and time dilation.. That is why!!!
If the speed of light was not measured to change for the observer on the train, then he would have to observe the flash of light in front of him to have traveled slower and the one behind him to have traveled faster than the observer would measure it to travel at the station in order for them to both measure it to travel at the same speed regardless of the difference in velocity.
The flashes are only depicted as being the same speed relative to the observer on the station in both cases. How could it then be seen to travel at the same speed for both observers then?
It just seems like there isn't any Galilean Invarience in the consistancy of the speed of light in the relativity of simultaneity. If the observer on the train assumed that he was at rest, then the flashes of light would reach him at the same time. It is as though the observer on the train cannot assume that he is at rest.
No.If train is moving in uniform velocity,then observer in the train would think that he is in rest. Actually,we assume it is uniform,so observer would think that he is in rest. Note: SR is according to Galilean system of Co-ordinates.
Because spacetime actually warps itself in order for all co-ordinate systems to measure the same speed of light?SR states that if relative to K,K' is a uniformly moving co-ordinate system devoid of rotation,then natural phenomena run their course with respect to K' according to exactly the same general laws as respect to K. So Imagine an observer in the train and an observer outside. A light is shot out in direction of the train. So an observer who is at rest outside would measure the constant speed of light. But observer in the train would measure a slower speed of light according to our old classical mechanics calculation. But this is in violation of SR. Do you know why?
This is what I don't understand about the relativity of simultaneity. The observer on the train should be able to assume that he is at rest and the flashes of light reach him at the same time, even a flash from an object with a relative velocity would NOT change his measured speed of light. But, the relativity of simultaneity says that the flashes of light would reach him at different times from his own frame of reference. It just doesn't add up, so you could only conclude that Einsteins mind experiment is not Galilean Invariant.
It is said that he didn't base his theories on the M&M experiment, in the M&M experiment it assumes that it is under acceleration and in motion and that beams of light traveling in different directions would then arrive at the same location at the same time, regardless of the differences in the relative velocity. Most text then explain the M&M experiment as one of the foundational experiments of the Special Theory of Relativity!
Because spacetime actually warps itself in order for all co-ordinate systems to measure the same speed of light?
OK. What is this M&M experiment and what is Galilean Invariant?? I have read the full book relativity written by Albert Einstein and i haven't heard the word Galilean Invariant. Only Galilean System of Co-ordinates and Non-Galilean System of Co-ordinates. OK. Observer in the train would think that he is in rest.But he is actually "moving".. So his velocity would necessarily play a part.
Oh!! Galilean System of Co-ordinates same as Galilean Invariance!!!Michelson-Morley Experiment This is the experiment that disproved aether, and is commonly used to explain that changes in the motion of Earth doesn't alter the speed of light. In the direction of motion, and perpendiclar to the direction of motion do not have an effect on the speed of light. This is done by splitting a beam of light in a half-silvered mirror. It is then sent in different directions, and then a detector measures if the frequency is the same when they enter it.
Galilean Invariance All laws of physics are the same at any degree of constant motion. There is no absolute frame that is a true rest, you can only measure your velocity relative to something else.
It isn't a violation of the theory of relativity, the theory of relativity as we know it is Galilean Invariant. It is only the mind experiment that explains the relativity of simultaneity that isn't Galilean Invariant. Both observers cannot say that they both can receive a flash of light at the same time that is the same distance away from them. All that means is that different frames then have different outcomes for things that should be the same in both frames. In other books, I think it mentions that Einstein didn't base his theories on the M&M experiment because of this. He just didn't know about the experiment that was not in agreement with this mind experiment.No. Space-time doesn't warp up.. SR is euclidean continnuum. I asked why different measured speed of light is in direct violation of theory of relativity??
Michelson-Morley Experiment This is the experiment that disproved aether, and is commonly used to explain that changes in the motion of Earth doesn't alter the speed of light. In the direction of motion, and perpendiclar to the direction of motion do not have an effect on the speed of light. This is done by splitting a beam of light in a half-silvered mirror. It is then sent in different directions, and then a detector measures if the frequency is the same when they enter it.
Galilean Invariance All laws of physics are the same at any degree of constant motion. There is no absolute frame that is a true rest, you can only measure your velocity relative to something else.
It isn't a violation of the theory of relativity, the theory of relativity as we know it is Galilean Invariant. It is only the mind experiment that explains the relativity of simultaneity that isn't Galilean Invariant. Both observers cannot say that they both can receive a flash of light at the same time that is the same distance away from them. All that means is that different frames then have different outcomes for things that should be the same in both frames. In other books, I think it mentions that Einstein didn't base his theories on the M&M experiment because of this. He just didn't know about the experiment that was not in agreement with this mind experiment.
It can, and it has but I don't think it is completely accurate. I think it is an attempt to explain how the beam in front of the train and the beam behind the train could still be measured to be the same speed of light, because only length contraction and time dilation alone couldn't have opposite effects on both beams.I think both,M&M experiment and Einstein's Thought Experiment can describe SR.
I misread your post, it was worded kind of strangely. Your right speed of light is constant in all frames.Different measured speed of light is direct violation of Special theory of relativity. That Law is Speed Of light is Constant. There is nothing like "space".Every description of event is based on co-ordinate system attached to a rigid body. Since Light is an event, The Law is Speed of light is constant in all Co-ordinate system. And who said Relativity of simultaneity is not Galilean Invariant?? It is Galilean Invariant. Train is in uniform motion. I already explained SR