## Simultaniety

### question 1:

What means simultaneous

### question 2:

How do you know that two events happened simultaneous

### Purpose

Simultaneous means that two events happen now, at the same moment (time).
For example: At the same time when you read this text I can turn on a light

The second question is much more difficult for two reasons:

1. When we observe two events at the same time, they did not necessarilly happen at the same time.
2. When we observe two events not at the same time, they could have happend at the same time.
The all influencing factors are: the distance involved, our own speed and the accuracy of clocks involved.

### An experiment to decide when a certain event happened

This experiment involves one event, a certain distance away from an observer.
The purpose of this experiment is to calculate when this event happened.
The experiment involves a fixed distance, some clocks and some simple mathematics.

Consider the following:

```  (Observer) O                 X       M (Mirror)    OM = c
A     v = .5c  ----->
```
I have an Observer at O, a mirror M at distance c, and an Astronaut A who will travel the same distance (at speed .5c). The point X see later.

The experiment involves the following

1. To calculate the speed of light.
2. To calculate by O the speed of A and the time t1 of the Event.
3. To calculate by A the speed of A and the time t2 of the Event.
If the two times are equal you can repeat the experiment. O knows now when the event will happen and indicate if this is simultaneous with a different (similar) event.

First observer will transmit a light pulse to M, the refection comes back after 2 seconds. Conclusion the speed of light is c.

In order to calculate the speed of the Astronaut by O you need two clocks. When the trip begins you again transmit a light pulse and you start two clocks. When the lightpuls comes back you stop clock 1 and when the Astronaut comes back you stop clock 2. When the number of counts on clock 2 (4sec) is twice of clock 1 (2sec) than the Astronaut has travelled at .5c

In order to measure the speed of A by the Astronaut you give A two identical clocks. A will stop his first clock when he receives the light pulse (reflected via the Mirror) at point X and the second clock after returning back to base.
The Observer does the same (and after some simple calculations) and will say:

Distance OX = 2/3c. Distance XM = 1/3c.
Predicted time that A reaches X is OX/.5c = 2/3c/.5c = 4/3sec

I will not make any claim if the number of counts of clock 2 of both O and A are identical (both were stopped at the same moment.) When the Astronaut comes back he will compare his two clocks and the relation will be (in my opinion) 4/3 versus 4, (or 4 versus 12) which is in agreement with the predicted value of O. If that is the case the Astronaut will also conclude that during the time that he has travelled a distance "4" light has travelled a distance "8", or that his speed was 0.5c.

Personal I have no objections if one astronaut moves at 0.7c in one direction and a second astronaut at 0.7c in the opposite direction, to claim that, the relative speed of the other is 1.4c

### Reflection

The reader might comment that the distance between Observer O and Mirror is not constant.
This is a valid point
To take this into account, repeat the speed of light test after the Astronaut has returned. The difference in time represents the increase (or decrease) in the distance of the Mirror. For the distance that the Astronaut has travelled half of this distance has to be taken into account.

None