Accelerating spaceship paradox

In summary, the conversation discussed the concept of time dilation and how it is perceived from different perspectives. It was mentioned that there is no maximum value for the ship clock as seen from Earth, and a formula for calculating the ship clock value as seen from Earth was provided using the parameters of time on Earth, ship time, and acceleration.
  • #1
yeknod71
2
0
Hi,

Please consider:

At time zero a spaceship takes off from Earth and keeps traveling under constant acceleration.

From Earth's perspective, the spaceship's speed keeps increasing but never reaches c. Also from Earth's perspective, the clock on the spaceship keeps slowing down and asymtotes a certain time value (let's call tMax).

However, from spaceship's perspective, their clock has not slowed down and passes tMax. They can take a photograph of their clock showing greater values than tMax, and return to earth. It can be arranged that in the background of this photograph there is evidence that it was taken before the spaceship turned around. How will observers on Earth explain this photograph?

Thanks in advance.
 
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  • #2
yeknod71 said:
Hi,

Please consider:

At time zero a spaceship takes off from Earth and keeps traveling under constant acceleration.

From Earth's perspective, the spaceship's speed keeps increasing but never reaches c. Also from Earth's perspective, the clock on the spaceship keeps slowing down and asymtotes a certain time value (let's call tMax).
No such value as tMax exists. From Earth, the ship clock does slow down as it approaches c, but so does the rate at which the ship approaches c. There is no maximum value that the ship clock can read as seen from Earth.
However, from spaceship's perspective, their clock has not slowed down and passes tMax. They can take a photograph of their clock showing greater values than tMax, and return to earth. It can be arranged that in the background of this photograph there is evidence that it was taken before the spaceship turned around. How will observers on Earth explain this photograph?

Thanks in advance.
 
  • #3
Janus said:
No such value as tMax exists. From Earth, the ship clock does slow down as it approaches c, but so does the rate at which the ship approaches c. There is no maximum value that the ship clock can read as seen from Earth.

Thanks, so that was my misunderstanding. If not too much trouble, what would be the formula to calculate ship clock value as seen from Earth, as a function of Earth clock value as seen on Earth, assuming a constant acceleration?
 
  • #4
That would be:

[tex]t = \frac{c}{a}\sinh^{-1} \left( \frac{aT}{c} \right )
[/tex]

Where t is the shiptime
T is the time on Earth
and a is the acceleration.
sinh-1 is the inverse hyperbolic sin.
 

What is the "Accelerating spaceship paradox"?

The "Accelerating spaceship paradox" is a thought experiment that explores the concept of time dilation, where time moves slower for objects that are moving at high speeds.

How does the paradox work?

The paradox involves two identical spaceships that are traveling in opposite directions at close to the speed of light. According to Einstein's theory of relativity, time will appear to move slower for the spaceship that is moving faster. This means that when the two spaceships meet again, the faster one will have experienced less time, leading to a paradox where one spaceship has aged less than the other.

Why is this paradox important?

This paradox is important because it helps us understand the effects of traveling at high speeds on time. It also highlights the concept of relativity and the fact that time is not constant, but rather is relative to the observer's frame of reference.

Is there a solution to the paradox?

While the paradox may seem impossible to resolve, it can be explained by the theory of relativity. The paradox arises due to the fact that time is not an absolute concept, but rather depends on the observer's frame of reference. Both spaceships experience time differently and there is no objective way to determine which one has "aged" more.

Are there any real-life examples of this paradox?

Yes, there are several real-life examples of this paradox, such as the effect of time dilation on astronauts in space or the time difference experienced by GPS satellites due to their high speeds. These examples further demonstrate the validity of Einstein's theory of relativity.

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