# Thought experiment of Special relativity

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1. Aug 8, 2014

### ta66505477

I have a little bit confuse on the Simultaneity

I know if there are 2 coordinates. One coordinate S' is moving V relative to S. We all in inertial reference frame. like the following graph.

According to special relativity, we know that the person in S' agrees the light which hits A, B in same time.
The person in S disagrees with S' because the light does not hit A B in same time.

But, If I say, A and B are some kinds of the light sensors. Once A and B detect the light in same time, the car will explode. The guy in S' will die.

In S coordinate, the light does not touch the A B in same time because the train is moving. So the car is not going to explode since the light does not reach A B in same time.

I cannot understand how can someone be alive in S but is dead in S'

2. Aug 8, 2014

### A.T.

Same time in which frame of reference?

3. Aug 8, 2014

### Orodruin

Staff Emeritus
I remember the exact same discussion a while back (but with a lamp lighting up rather than a car exploding). The point is that, as AT says, you have to be more specific when you say that it blows up when A and B are hit at the same time. You have to specify in what inertial system they should be hit at the same time. Any device you may construct to compare the times when A and B are hit is also going to follow the rules of relativity and its construction is going to single out a particular frame in which the car explodes if A and B are hit at the same time. In other frames, it is going to explode if A and B are hit with a particular non-zero time difference. This time difference can be computed based on the frame and its relation to the particular frame.

4. Aug 9, 2014

### ta66505477

Suppose all the things are on the train including devices, time detector and the explosion system. So all device should "agree" the light came from same time because all the devices follow S' coordinate.

Space and time we cannot touch. We cannot hold it on hand so we can easily accept simultaneous time depending on different coordinate. But if we use the concept of simultaneity for applying in the real things, that could be something tricky ( or I am misunderstanding something)

I re-post the image
http://postimg.org/image/qrxdigm5b/

Last edited: Aug 9, 2014
5. Aug 9, 2014

### ghwellsjr

You didn't draw in the time detector and the explosion system but if they all agree that the light came from the same time, then we can assume that one way to implement them is to connect the detectors by equal length wires to the time detector and place it and the explosive system in the center of the train car, correct?

It isn't really tricky, as long as you understand that in the frame of the train, just like the light signals that travel in equal times to the detectors, you have to set up the wiring so that the electrical signals travel from the detectors to the time detector in equal times.

I have made a spacetime diagram to illustrate your scenario in the frame of the train car:

The thick blue line represents the light source, the time detector and the explosion system in the center of the train car. At the Coordinate Time of zero, the light source emits two signals, shown as thin blue lines, in opposite directions that travel at 1 foot per nanosecond (the speed of light) and hit the two detectors shown as the thick black and red lines, each four feet away from the light source. The detectors each send an electrical signal shown as thin lines in their respective colors which, for simplicity we will assume also travel at the speed of light, back to the time detector. As you can see, they arrive at the thick blue line at the same time and the explosion occurs.

Now to see what this scenario looks like in a frame such that the train is traveling at a speed of 0.6 feet per seconds, we use the Lorentz Transformation process to obtain a new set of coordinates for each of the events (dots) and connect the lines appropriately:

As you can see, the two electrical signals arrive at the time detector at the same time and so the explosion occurs.

Does this make perfect sense to you? Any questions?

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6. Aug 9, 2014

### ta66505477

I understood now.
What I have overlooked is the wire

Your graph makes perfect to me. I can think it intuitively by your graph. Like Path A takes less time but the light has to use more time to chase back in Path B. Path C initially takes more time to detector but quickly goes back to center because the train is going toward.

Thank you very much!

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7. Aug 9, 2014

### ghwellsjr

You're very welcome. Glad it makes sense now.