# Einstein simultaneity train thought

1. Aug 27, 2011

### rajeshmarndi

in einstein train thought experiment, if two bulbs were placed, in the front and rear of a moving train. And a person A with a single switch for the two bulbs stands in the middle of the train.

Near the lights are clocks which register current time, when the light glows.

would the person A see the lights simultaneously and the clock register same time?

Also if instead of lights, two balls (speed < c) were released towards him, would those ball hit him simultaneously?

Another person B outside the train in the ground, when the train has just passed him half of its length, if i'm right would notice the light/ball simultaneously from the front and rear of the train. How would he see the light and the ball hitting the person A?

2. Aug 27, 2011

### Staff: Mentor

OK.

Yes. The light bulbs will turn on at the same time (according to train clocks) and the light from each would arrive at the midpoint (person A) at the same time.

Yes.

He would observe the light/balls arriving at the midpoint simultaneously, but he would not agree that the bulbs were turned on or that the balls were released at the same time.

3. Aug 27, 2011

### rajeshmarndi

Doc Al - thanks for ur short and very brief reply. It helps understanding in a easy manner.
why not the other way, he might see the lights/ball at the same time and doesn't therefore see him hit simultaneously.

Also if the case would have been of lightning striking the ends of the train simultaneously to the outside observer. Would the clock at the ends of the train that could register striking of lightning inside the train, record different time of impact?

4. Aug 27, 2011

### Staff: Mentor

That would be an impossibility. If the lights/balls reach the same location (where A is) at the same time in any frame they must reach that point at the same time in every frame. (Things that happen at the same location at the same time are called 'spacetime coincidences'.)
Yes.

5. Aug 27, 2011

### rajeshmarndi

i'll come to it later, i would like to know other outcome of the above example.

what would have been if outside observer see the light/ball released at the same time inside the train, how would he see the man being hit by the light/ball?

6. Aug 27, 2011

### Staff: Mentor

If the light/balls are sent out at the same time according to an observer on the ground, then the light/ball from the front of the train will reach person A first. (Everyone will agree on that.)

7. Aug 27, 2011

### ghwellsjr

Person A will see the clocks register the same time if and only if the clocks had been previously set so that this will happen. There's no a priori reason why this should happen. This is the whole point of Special Relativity. Clocks remote to an observer and at rest with respect to him need to be previously set according to Einstein's synchronization convention in order for them to have the same time on them in a situation like this.
Again, unless the outside observer had previously synchronized the clocks that are at rest with respect to him according to Einstein's convention (which means they won't be synchronized with person A's clocks), then you cannot talk meaningfully about the "lightning striking the ends of the train simultaneously to the outside observer".
If we are using the outside observer's previously synchronized clocks to define what is meant by "at the same time", then they won't hit person A at the same time. But the outside observer won't necessarily see (with his eyes) the light/balls being released at the same time, unless he happens to be located midway between them at the time (according to his clocks) that the light/balls are released and even then, he won't be able to see the light/balls being released until some time later.

8. Aug 28, 2011

### rajeshmarndi

Doc all -

So is it that the lightning that strike in the front is actually simultaneously to both or there cannot be anything meaningful simultaneous between them since they are in different inertial frame.

could u put this in simple,in other way.

9. Aug 28, 2011

### ghwellsjr

Rajeshmarndi, do you understand that time runs at different rates for observers in relative motion? This means that the clocks that are at rest with respect to one can never be synchronized with the clocks that are at rest with respect to the other one. Synchronized means that they always display the same time on them.

Do you understand that when we say that two events located at different places are simultaneous in a given frame if synchronized clocks at those two locations have the same time on them when the events occurred?

This means that any two events that are simultaneous in one frame cannot be simultaneous in another frame moving with respect to the first one.

So when you ask "is it that the lightning that strike in the front is actually simultaneously to both" doesn't make any sense because you have asked about a single event. You need two separate events defined according to a single frame of reference located at different places to ask whether they are simultaneous or not. If they have the same time coordinate but different spacial coordinates, then they are simultaneous.

Then you ask for a simpler way to explain how it is that when "the lights/balls reach the same location at the same time" in one frame they do so in every frame. But remember, this is just one event. An event is a specific location at a specific time according to a given frame. So this is not an issue of simultaneity because it involves just one event. The coordinates of this one event can be different in two different frames-they can have different times and x, y, z values, but it's the same event described differently according to the definition of the two different frames.

10. Aug 28, 2011

### rajeshmarndi

will think about it one more time and come again.

11. Aug 28, 2011

### rajeshmarndi

couldn't get what is spacetime coincidence.

12. Aug 28, 2011

### Staff: Mentor

When two events occur at the same time and place it is called a spacetime coincidence. An example: Two spaceships collide. They arrived at the same place at the same time. Everyone will agree that the ships smashed into each other (they can see the dents in the ships).

When events happen at the same time and place, everyone will agree that they did. But when things happen at the same time but at different places (separated by some distance) then there will be disagreement between different frames as to whether the events occurred at the same time or not. Simultaneity of spatially separated events is frame dependent.

13. Aug 29, 2011

### rajeshmarndi

if different inertial frame observer see events differently. Isn't it then the outcome of an event would be different to them bcoz in one frame the lightnings are simultaneously and in the other frames the lightnings are not simultaneously.

14. Aug 29, 2011

### Staff: Mentor

The lightning strikes happen at different locations (the ends of the long train), so different frames will see them happening at different times. But the arrival of the light from those strikes at the midpoint of the train occurs at the same location (the midpoint of the train), so all observers will agree whether they arrived simultaneously or not.