# Special relativity - loss of simultaneity

The loss of simultaneity in Special relativity - is that real or created due to the fact that light take time to travel. So even though 2 events are simultaneous but since light takes time to travel, they may not be simultaneous for two different people.

Below is an example generally given for loss simultaneity Set up -Moving room with outside and inside observers.

A light signal is emitted from center of room & we ask two men what they expect to observe

Inside observer say Simultaneous

The Outside observer says not Simultaneous. Explanation for it is One wall is moving towards light (back wall) and other wall is moving away from it (front wall). So light will hit back wall first and front wall later & hence outside observer will say they are not simultaneous.

• This is a common misconception. It is not due to light travel time. One can do a test with recording clocks which one never looks at. Commented Jan 11, 2018 at 20:27
• So it is real then. But the argument that I see in most books in below and that kinda of gives the impression that it is due to fact light takes time to travel Commented Jan 11, 2018 at 20:47
• I am adding that argument in question. Please have a look and if possible give your comment Commented Jan 11, 2018 at 20:48
• Two people facing each other disagree about whether the Empire State building is to the left or to the right. Is that disagreement real or created? I have no idea how to answer that question, because I don't know what "real" and "created" mean in this context. (And since when is "created" the opposite of "real", anyway? ) What I do know is that the answer to your question about simultaneity is the same as the answer to my question about the Empire State building, whatever that answer might be. Commented Jan 11, 2018 at 22:04
• @WillO, my argument is not whether the frame is "real" or "created" - it is that regardless, relativity is not an excuse for asymmetrical assertions of truth that are mutually contradictory. If simultaneity is truly lost between the parties, then they must still agree who has really moved ahead and who has moved behind - in the same way that two parties looking at a tall building from opposite sides must agree whether a building is on their left or their right. Commented Jan 12, 2018 at 1:11

is that real or created due to the fact that light take time to travel.

It's a consequence of the fact that clocks are synchronized such that the one-way speed of light is invariant. But clock synchronization is conventional and this particular convention is known as Einstein synchronization.

This implies that the one-way speed of light is conventional (though the two-way speed of light is genuinely invariant) and that there are alternative, non-standard synchronizations in which the one-way speed of light is not invariant and that are observationally equivalent to SR:

As demonstrated by Hans Reichenbach and Adolf Grünbaum, Einstein synchronization is only a special case of a more broader synchronization scheme, which leaves the two-way speed of light invariant, but allows for different one-way speeds. The formula for Einstein synchronization is modified by replacing $1/2$ with $\epsilon$:

$$t_2 = t_1 + ε ( t_3 − t_1 )$$

$\epsilon$ can have values between 0 and 1. It was shown that this scheme can be used for observationally equivalent reformulations of the Lorentz transformation.

In fact, there is a synchronization procedure in which simultaneity is absolute and there is a preferred frame in which light propagates isotropically.

While this may seem at odds with the principle of relativity in that it seems to define a frame of absolute rest, this actually isn't the case since any inertial frame can be chosen to be the one in which light propagates isotropically.

For further reading, see the article Conventionality of Simultaneity at the Stanford Encyclopedia of Philosophy

The relativity of simultaneity is a real effect. In your example, the lack of simultaneity in one frame happens because light propagates at speed $c$ for all inertial observers.

Your reasonig to justify the lack of simultaneity isn't correct, otherwise it would imply the same even for newtonian mechanics but of course this cannot be true. To see this, repeat your example considering Galileo's velocity addition rule and the motion of two balls (instead of light rays) that hit a wall and bounce back. Doing so you'll find both observers say the two events (ball hits wall) are simultaneous.

Well how do we say something is real? One way, most common and most efficient is to observe it via EM waves which travel at the speed of light.

Your now is in your locality and someone else's now (who is away but not moving wrt you, i.e. same frame of reference) is in their locality. When you try to communicate this "now" to another observer (or vice versa), the fastest communication happens at speed of light and your now will differ due to the time taken by that communication.

This is simplest case and obviously the loss of simultaneity arises due to finite speed of light. In this case, you will agree on simultaneity only if the event in question is mid way. The other way is to have synchronized clocks and checking on simultaneity after the effect via the clocks.

When the two observers are not in same frame of reference, then it is not this simple and the calculation of "time taken by the communication" will be different. This difference will also be due to the fact that speed of light is finite, and same for all observers.

So in overall, loss of simultaneity arises due to finite speed of communication and in addition is dependent upon the relative speed and relative location of the event wrt to two observers.

Time dilation impacts the rate of change of time in different frames of reference but simultaneity is "checking now", which is due to finite speed of light. Checking on clocks is always after the effect.

For example, two people sitting couple of meters away never seem to disagree on simultaneity even if the event is not equidistant from them. Why? Because the difference in time is negligible, may be immeasurable.