# Is the following possible in principle

1. Nov 11, 2014

### Hernik

Hi! Question: Is the following possible in principle or am I missing some important rules in relativity which makes it impossible?

Imagine a spaceship which can travel at relativistic velocity. It is 10 kilometers long and equipped with two sensors, 1 and 2, placed in each end of the ship. Right in the middle is an office from where Mr Jensen registers and records the signals from the two sensors. Wiring to and from the sensors is identical. So a signal from sensor 1 reaches the office in exactly the same amount of time as a signal from sensor 2.

Also consider two stars, A and B, that orbit each other in such a way that they always are seperated by 10 million kilometers.

Now the spaceship takes off in direction of A and B in order to pass the two stars almost at the speed of light. Jensen is on board attending his duties. Coincidently the dining room is in the front end of the spaceship whereas the toilet is in the back. This means Jensen has to walk back and forth every day. When doing so, he always measures the distance between the front and the back end of the ship...which is of course always 10 km, no matter how much the spaceship is accelerated.

The space journey is timed in such a way, that when the ship passes the two stars up close they are aligned parallel to the direction of the spaceship. As sensor 1 passes star A it sends off a signal to the office, and as sensor 2 passes star B it sends of a signal to the office.

But here comes the part where I do not feel so sure: If the velocity is right, is it possible that Jensen registers the two signals exactly at the same time?

Best regards, Henrik

2. Nov 11, 2014

### marcus

Henrik, how about making the speed (as a fraction of c) be equal to
β = 1 - 10-12/2
I think that would just about do it.

Decimal notation for something that close to one is hard to read but it would look like twelve 9s followed by a 5,
namely β = 0.9999999999995

The square of that is essentially β2 = 1 - 10-12

So the square root of 1 - β2 would turn out to be 10-6.

that speed would shrink lengths down by a factor of a million. So that 10 million km would contract to 10 km. Isn't that the speed you wanted?

Last edited: Nov 11, 2014
3. Nov 11, 2014

### Hernik

Thanks. I am not into the math.But if the spaceship passes with that velocity then there is an instant of time in Jensens life where each end of the 10 kilometer long spaceship are exactly next to each of the two stars?

4. Nov 11, 2014

### marcus

Simultaneity depends on the observer. I live on a star B planet and I see two separate events involving the Nose N and the Tail T of the spaceship.
I see N passing next to A
and I see T passing next to B
but I do not see those events happening simultaneously.

All of us observers agree that the two events occurred. But we don't all agree that they happened at the same time. Because we all have our separate "times". We all slice the spacetime up into "simultaneous" slices differently according to our different motions.

So I do not agree with what you said. I do not agree that there is a single "moment in Jensen's life" when those two events both happened.

According to me, who was watching from the star B, the event with star A must have happened about 100/3 seconds (33 seconds) AFTER the tail whizzed by my star.
It must have, because I only saw it occur (got news of it, so to speak) another 33 seconds after that. So I see it happen 66 seconds (a little over a minute) after the ship goes past me and I can deduce it happened 33 seconds after true ship went past.

So as I see Jensen, as a physical object, he participates in these two events about half a minute apart.
And as HE sees it, he participated in the two events simultaneously.

Last edited: Nov 11, 2014