Can Jensen Receive Same-Time Signals from Sensors?

[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 separated 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?

Henrik

 

[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?

 

[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?

 

[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.

 

[sardar]

,

Thank you for your question. In principle, it is possible for Jensen to receive same-time signals from sensors 1 and 2. However, there are a few important factors to consider.

Firstly, the concept of simultaneity is relative in the theory of relativity. This means that different observers can have different perceptions of when two events occur at the same time. In this case, Jensen's perception of the two signals being received at the same time may be different from another observer's perception.

Secondly, the speed of light is a universal constant and is the maximum speed at which any signal can travel. This means that even if Jensen perceives the two signals as being received at the same time, they may have actually been received at slightly different times due to the finite speed of light.

Lastly, the effects of time dilation and length contraction must also be taken into account in this scenario. As the spaceship approaches the speed of light, time will appear to slow down for Jensen and the length of the spaceship will appear to contract. This means that Jensen's perception of the distance between the sensors may differ from the actual distance.

In conclusion, while it is possible for Jensen to receive same-time signals from sensors 1 and 2, his perception may differ from other observers and the actual timing of the signals may be slightly different due to the effects of relativity.