# Simultaneity; is it valid to deduce that events occur at the same time?

• MalachiK
In summary, the discussion revolves around the concept of simultaneity in different reference frames, and how it is affected by the finite speed of light. The scenario of lightning strikes and synchronized clocks on a moving train is used as an example to illustrate this concept. It is concluded that while events may not be simultaneous in different frames, the observers will always agree on what frame the events are simultaneous in. This has implications in the understanding of relativity and quantum mechanics.
MalachiK
Ok folks, this is my first post to this forum and I’m afraid that I might be asking an embarrassingly simple question!

I’m reading Einstein’s book on SR and GR and I’ve reached a discussion of simultaneity that involves an observer attempting to decide if lighting strikes that occur ahead and behind of a moving train happen at the same time. This is how I understand the argument so far; due to the finite speed of light that has the same value in all reference frames, the information about the event that takes place ahead of the train will reach the observer in a shorter time that the information about the event that happens behind the train. As a result of this, it is not possible to reason that the simultaneous arrival of light from both events corresponds to both events happening at the same time in the rest frame of the train track. This idea is then developed to illustrate that events that are simultaneous in one intertial frame are not simultaneous in another. This all makes sense to me.

As part of his exposition, Einstein asks the reader to think about how they could determine the simultaneity of such lightning strike events, and given the constand speed of light it is made clear that this cannot be done simply by reference to the light that arrives from the events.

However, what if there were clocks placed as the sites of the lightning strikes? These clocks could be synchronised in the rest frame of the track. Wouldn’t the light / information from the lightning strike then arrive at the observer along with information about the state of the clock at the instance that the strike happened? Wouldn’t this then allow the moving observer to determine the simultaneity (or lack there of) in the rest frame of the track?

I suspect that I’m missing something profound about relativity here, and maybe I’m thinking about measuring the wrong time or something. I was sure that this sort of question must come up all the time, but I can’t find a satisfying answer.

Thanks for any replies.

MalachiK said:
However, what if there were clocks placed as the sites of the lightning strikes? These clocks could be synchronised in the rest frame of the track.

But they are then out of sync in the train's rest frame. Similarly, if two clocks are placed on the train, at the ends, and synchronized in the train's rest frame, they are out of sync in the rest frame of the track.

However, what if there were clocks placed as the sites of the lightning strikes? These clocks could be synchronised in the rest frame of the track. Wouldn’t the light / information from the lightning strike then arrive at the observer along with information about the state of the clock at the instance that the strike happened? Wouldn’t this then allow the moving observer to determine the simultaneity (or lack there of) in the rest frame of the track?
Yep! Although the events are not simultaneous in different frames, the different observers will always agree on what frame the events are simultaneous in. So the guy on the ground can observe the events to be simultaneous and the guy on the train can observe them not to be, but the guy on the train could calculate (or observe in your example) that the events are simultaneous in the ground's frame. Notice in your example that if the clocks are synchronized in the ground's frame then they are of course not synchronized in the train frame. The guy on the train observes the events to happen at different times (according to his wristwatch), but the clocks on the ground will read the same time according to him. Hopefully I just re-explained what you were thinking - you seem to have a good grasp on this.

As part of his exposition, Einstein asks the reader to think about how they could determine the simultaneity of such lightning strike events, and given the constand speed of light it is made clear that this cannot be done simply by reference to the light that arrives from the events.
My guess is that Einstein is talking about absolute simultaneity (which of course doesn't exist in SR). There is no disagreement between the observers as to who sees the events as simultaneous.

I think that somewhere in here there is an answer to my long-standing confusion about entanglement (QM). A cause at one particle is said to have an "instantaneous" effect on the other. This means that a change happens to both particles simoultaneously, and I've always wondered (aside from the sloppy description of the Quantum Mechanicle event being sited), "simoultaneously to whom?"

Note also that there are lots of other threads about this specific scenario. You'll find a few of them if you do a search. (I haven't tried it, but I'm guessing that you'll have lots of hits if your search includes at least two of the words einstein, train and simultaneous).

Jaunty said:
Yep! Although the events are not simultaneous in different frames, the different observers will always agree on what frame the events are simultaneous in. So the guy on the ground can observe the events to be simultaneous and the guy on the train can observe them not to be, but the guy on the train could calculate (or observe in your example) that the events are simultaneous in the ground's frame.

Ah ha! This is very much what I was thinking. In fact, my second question was going to be about how we could just do away with the clocks and calculate the times at which the events occurred in the rest frame by using our knowledge of the speed of light. It seems that the observer in the train can arrive at the rest frame timings but upon comparing these to his own clock finds that his times / sequence of events are different. I think I made the mistake of somehow thinking that an observer in the rest frame and the observer on the train are required to never agree on what's going on, when in fact (as you've stated) they can easily agree on the frame in which the events are simultanious.

Thanks for all the replies and giving me a chance to think this one through!

You don't need extra clocks to find the order of events.Before the motion of the train you can synchronize one clock on the train with one clock on the tracks. You don't even have to assume that the speed of light is constant in the train's reference frame. You just need to assume that the speed is constant in the track's frame. From your velocity and the red shift between the lightning A and B, you can calculate the time and therefore order of the lightning events.I don't see the point of this chapter as it is just regular galilean relativity.

Hello Emreth

This thought experiment is a used as a helpful illustration to teach the relativity of simultaneity. It works very well. Of course any better ideas that serve the same purpose i am sure would be very welcome.

Matheinste

## 1. How do we define simultaneity?

Simultaneity is the concept that two or more events occur at the same time. In physics, it is often defined as the events happening at the same instant in time when observed from a specific reference frame.

## 2. Is it possible for events to occur at the same time in different reference frames?

Yes, it is possible for events to occur at the same time in different reference frames. This is because simultaneity is relative and can be different depending on the observer's perspective and reference frame. This is known as the theory of relativity.

## 3. Can we accurately measure simultaneity?

The concept of simultaneity is difficult to measure accurately because it is relative and depends on the observer's reference frame. Additionally, the speed of light is finite and can affect the perception of simultaneity. However, precise measurements of simultaneity can be made using specialized equipment and techniques.

## 4. What is the role of time dilation in simultaneity?

Time dilation is a consequence of the theory of relativity and states that time moves slower for objects moving at high speeds. This can affect the perception of simultaneity because the time difference between events can vary depending on the observer's reference frame and relative speed.

## 5. Can we ever be certain that events truly occur at the same time?

Due to the relative nature of simultaneity, it is impossible to be certain that events truly occur at the same time. However, using precise measurements and understanding the effects of relativity, we can determine the degree of simultaneity between events and make predictions and calculations based on this understanding.

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