## Relativity of Simultaneity

### Question

Will Observer A see the two flashes simulataneous - Yes or No

For the most recent modifications and additions to this page See Remarks and Objections part 2 and Literature

### Background

Different Observers observe the reality different when something has happened and where something has occured.
Relativity of Simultaneity means that one Observer can judge two events as simulataneous while a different Observer will disagree.
In order to explain this Einstein uses the Train Thougt Experiment
In the book "Introducing Einstein's Relativity" by Ray d'Inverno at page 23 in the chapter "Relativity of Simultaneity" He writes about this thought experiment: "From the configuration, it is clear that A will judge that the two events, when the light sources first switch on, occur simultaneously. " For your author this is not clear.

### The Train Thought Experiment

The Train Thought Experiment consists of a train and two Observers A and B. Observer A is on the ground, near the track and Observer B is on the train.
The following figure shows this.
```     LS1              B              LS2
FD1 <-------------------------> FD2   ---->v
O                     O
---------------------------------------------
A
```
The train contains at each side: a Firing Device FD and a lightsource LS (a lamp).
The Firing Device consists of two contacts: one contact on the ground and one contact on the train. The distance d between the two contacts on the ground and the two contacts on the train is identical, such that when the train (the train contacts) is above the ground contacts both lights are on (simultaneous) and when this is not the case both lamps off.
The observer A is equidistant from the two firing devices and from the two light sources. For Obsever B the same is true.
Now suppose the train starts left from the ground contacts and moves to the right. What will each observer see? First both lamps will be off, then the lamps will fire and again both lamps will be off.
What Observer A will see is described in the paragraph Background . This is the subject of the discussion.
Ofcourse when A sees the two lightflashes simultaneous, Observer B, who moves into the direction of FD2 and LS2 will not see the two lightflashes simultaneous (i.e. LS2 first)

### Remarks and Objections part 1

Relativity of Simultaneity starts from two postulates: "All inertial observers are equivalent" and "The velocity of light is the same for all inertial systems" and the definition of distance of an object which is simple "half the time between the sending and receiving of a lightsignal towards this object".

The paragraph "The relativity of Simultaneity" in the afore mentioned book, starts with the sentence:"Consider two events which take place at the same time, according to A, and also at two points equal but opposite distances away."
IMO two events can take place (happen) at the same time. IMO there exists a whole plane from where those two events can de observed simultaneous. You have to be at the right position and the right moment to actual observe (see) those two events simultaneous.
A establishes this by sending out one light signal, which will be reflected at the two points and which will received simultaneous by A. This is completely in agreement with the above definition of "distance of an object". However for me the big question is: did the reflection (the two events) actual happen simultaneous. I'am not sure about that.

IMO the whole idea behind the Train Thought Experiment is to start with two events which will happen simultaneous. But than the issue is: does A actual see those two events simultaneous.
You can also start from the opposite approach. A Observes something simultaneous. Issue: did what he saw actual happen simultaneous.

IMO the only way out is to actual perform this experiment. The Train Thought Experiment is not a very good yardstick to establish accurately how nature behaves i.e. to establish who sees something (that happened at the same time) simultaneous and who not.

### Remarks and Objections part 2

For a copy of the page in the book "Introducing Einstein's Relativity" See: Fig 2.13 Light signals emanating from the two sources

First I would like to make three remarks:

1. Your author does not challenge the mathematics behind the Special Relativity Theory. In casu the Lorentz Transformations.
2. Your author does not challenge the following sentence: IF Obsever A sees the two light signals simultaneous than Observer B can not see the two light signals simultaneous.
3. Your auther does not challenge the reverse stated above.

In fact there are two issues:

1. Does any of the Observers actually See the light going on simultaneous. Or to state this different: What does an Observer has to do in order to See the lights going on simultaneous.
2. Length Contraction

In order to answer those questions you have to perform the experiment under two conditions: 1) At a speed v almost zero (This is called calibration) 2) At a speed v = large.
Calibration consists of three different parts:

1. The train is above the firing devices at rest: Both lamps shouls be ON.
2. The train is not above the firing devices at rest: Both lamps should be OFF.
3. Initial position is Left of the Firing Devices. You start the train with the smallest possible speed v. v = zero. When the train hits the Firing Devices Observer A should See the the two lights going ON simultaneously (a little later). And so will Observer B. (For B the time difference will be extremely small. You can discuss this, but this is unimportant for the rest of the discussion).

Length Contraction becomes an issue for any speed. That means that for any speed v (Except is v is very small) the length of the train changes and observer A does not see the two light signals simultaneous. In order to see them simultaneous you have to change the distance between the two Firing Devices.
If the length of the train is l0 than this distance is l0 - l0 * SQR(1-v^2/c^2).

The best way to challenge the idea that Observer A sees the two ligt signals simultaneous (During Calibration part 3) is by making a complete copy of the experiment or set up, with the only difference that you place this set up on a moving platform, which has a speed v. This copy includes the track, Firing divies and an Observer A near the track, at the centre between the two firing devices.
This is called Experiment 2 compared with Experiment 1 previous discussed i.e. the rest frame experiment.

The question is what does Observer A on the moving platform see, when you perform the calibration step part 3. i.e. that the train has a very small speed relative to the track on the moving platform.

1. Both lights are simultaneous. The same as Observer A in Experiment 1.
2. Both lights are not simulataneous. This is infact the opinion of Observer A in Experiment 1 based on what he sees i.e. two simultaneous light signals.
3. Neither Observer A in experiment 1 nor Observer A in experiment 2 in general will see the light signals simultaneous. There is however a small chance that one will see them simultaneous.
Answer 2 follows the same reasoning as what Observer B sees in experiment 1. In that case Observer A sees in Experiment 1 the two signals simultaneous and so are the events that caused those signals. In experiment 2 the events are also simultaneous and identical (1) as in experiment 1, resulting that the moving Observer A in experiment 2 can not see them simultaneous.
This is logical all correct IF Observer A in experiment sees them simultaneous. But why should there be a preference for Observer A in experiment 1 to see something simultaneous compared to Observer A in experiment 2. Both are the same experiments. Why ?

IMO Answer 3 is the correct answer, implying that the description of experiment 1 is wrong.

(1) There is one major difference between the two experiments: in experiment 2 length contraction is involved. This involves the whole experiment setup. Not only the train (Such as in experiment 1) but also the distance between the 2 firing devices.
The consequences are that it is not possible to perform the two experiments in such a way that all the 2 events of each experiment (i.e. all four) are occuring simultaneous.
To bypass this offset you have to make the train on the moving platform longer. When you do that in the correct way and you perform the calibration test then from the point of view of Observer A the two tests are identical (He sees simultaneous light signals in the 2 experiments and the 4 events are all simulataneous). For Observer A in experiment 2 this modification does not make any difference: he sees the light signals not simultaneous.

### Simulateity of Relativity Literature.

The following documents discuss Simultaneity of Relativity together with Length Contraction on the Internet.
1. One of the most interesting documents on the internet is the following: " Space Interferometry Mission as a Test of Lorentz Length Contraction" by Curt Renshaw
This document raises four issues:
1. At Figure 3 "Train and Track Mounted Contacts" Length contraction of a physical moving object is discussed. The Observer is at rest. That is the same as in figure 2.13 discussed in the above paragraph.
2. Above figure 3 is written: "In the figure, the same train, stationary on the track, subtends a larger angle in the distant observer’s field of view. The moving length-contracted train fires a different set of contacts, and the angle subtended between these contacts from the observer’s position is smaller."
That means if you want to see two simultaneous events simultaneous, you have to change the difference between the contacts or firing devices in order to offset the length contraction.
That reasoning is completely in agreement as discussed in the above paragraph.
3. In Figure 1 and in Figure 5 length contraction between the distance of a fixed objects (telephone poles and stars) and a moving Observer (on a train and on earth) is discussed. This is different from length contraction of a physical object. The first type does nor reflect a physical change. The second one does. Length Contraction of a fixed object is discussed above.
4. At page 144 "Subtle is the Lord" by Abraham Pais is written: "The question whether the Lorentz contraction does or does not exist is confusing. It does not "really" exist in so far as it does not exist for an observer who moves with the rod; it "really" exists, however, in the sense, that it can as a matter of principle be demonstrated by a resting observer". IMO in the SIM experiment this is not the case.
3. For a little older document See: "Stellar Aberration and Einstein's Relativity" by Paul Marmet
4. Also see the book: "Reflections On Relativity" and specific chapter 2.5: 2.5 Stellar Aberration
5. See Also: "The State of Experimental Evidence for Length Contraction, 2002" by Delbert J. Larson