Frame of references in time dilation

In summary, the time dilation effect of traveling at high speeds is a result of the laws of special relativity. From the perspective of the captain on the space dock, the crew's time would appear to slow down as they move at .9c. However, from the perspective of the crew, the captain's time would also appear to slow down. This apparent contradiction is resolved by understanding that acceleration and non-inertial frames of reference play a role in the twin paradox, and that the laws of special relativity only apply in inertial frames.
  • #1
J Goodrich
17
0
Let's suppose that I am the Captain at a space dock sitting in interstellar space. My crew decides to go on a trip in our ship, so they board and set off at .9c.

t = t0 / sqrt( 1 - v^2/c^2 ), t0 = 1, v = .9c, therefore
t = 1 / sqrt( .19 ) = 2.3 (approximately)

So as they speed off, 1 second of the time that I experience corresponds to 2.3 seconds of the time that they experience, which suggests that if I log that they travel (assuming they say go in a big circle back to our dock, not stopping/altering their speed) a month they come back having experienced/aged 2.3 months.

I believe this is all correct.

Now here is my problem: since motion is relative, could the crew in the ship not have said that me, sitting in our dock, is instead in motion and that they were stationary? From their respective, shouldn't have I (and really the rest of the universe) have aged 2.3 seconds for their every second? What makes one perspective more correct than the other or how is this apparent contradiction otherwise solved?
 
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  • #2
J Goodrich said:
Let's suppose that I am the Captain at a space dock sitting in interstellar space. My crew decides to go on a trip in our ship, so they board and set off at .9c.

t = t0 / sqrt( 1 - v^2/c^2 ), t0 = 1, v = .9c, therefore
t = 1 / sqrt( .19 ) = 2.3 (approximately)

So as they speed off, 1 second of the time that I experience corresponds to 2.3 seconds of the time that they experience, which suggests that if I log that they travel (assuming they say go in a big circle back to our dock, not stopping/altering their speed) a month they come back having experienced/aged 2.3 months.
From who's point of view? From your point of view, time moves more slowly in the crews frame of reference- you experience 2.3 seconds to their one second. From their point of view, your time has slowed and they experience 2.3 seconds to your one second.

I believe this is all correct.

Now here is my problem: since motion is relative, could the crew in the ship not have said that me, sitting in our dock, is instead in motion and that they were stationary? From their respective, shouldn't have I (and really the rest of the universe) have aged 2.3 seconds for their every second? What makes one perspective more correct than the other or how is this apparent contradiction otherwise solved?
No, they were not in an inertial frame- first they had to accelerate to .9c, then move in a circle, which, even though speed is constant, velocity is not so they were accelerating, and finally declerate to 0 relative to you. While velocity is relative, acceleration is not. They would have felt forces you did not and so were not in an inertial frame of reference.

This is really just a restatement of the "twin paradox" which has been done many times on this forum. As long as two observers are both in "inertial" frames of reference, they are moving at constant speed relative to each other and each observes the other as aging more slowly. There is no "paradox" until they are both stationary relative to each other and that requires breaking the "inertial" frame of reference- and the usual formulas of special relativity no longer apply.
 
  • #3


The concept of frame of reference is crucial in understanding time dilation. In your scenario, you are correct in stating that from the perspective of the crew on the ship, they could consider themselves as stationary and you as moving. This is because motion is relative and there is no absolute frame of reference.

However, what makes your perspective more correct is the fact that you are the one who is not experiencing any acceleration or change in speed. In special relativity, it is the acceleration that affects time dilation, not just the speed. So while the crew on the ship may argue that you are also experiencing time dilation, it is negligible compared to the time dilation they are experiencing due to their high speed.

Moreover, time dilation is not just a matter of perspective, but it is a measurable phenomenon. It has been experimentally verified through various experiments, such as the famous Hafele-Keating experiment, where atomic clocks were flown around the world and showed a difference in time compared to stationary clocks on the ground.

In conclusion, while the crew on the ship may have a valid argument that you are also experiencing time dilation from their perspective, the fact that you are not undergoing any acceleration or change in speed makes your frame of reference more accurate. And the experimental evidence for time dilation further solidifies this understanding.
 

1. What is a frame of reference in time dilation?

A frame of reference in time dilation refers to a specific point of view or perspective from which time appears to be moving at a different rate compared to another frame of reference. This is a key concept in understanding time dilation, which is the phenomenon where time appears to pass slower or faster depending on the relative motion of two objects.

2. How does time dilation affect our perception of time?

Time dilation can affect our perception of time by making time appear to move slower or faster depending on the relative motion of two objects. This is because time is not absolute and can be influenced by factors such as velocity and gravity.

3. What are some real-life examples of time dilation?

One example of time dilation is the famous "twin paradox," where one twin travels at high speeds in space while the other twin stays on Earth. When the traveling twin returns, they will have aged less compared to their twin on Earth due to the effects of time dilation. Other examples include the time differences experienced by astronauts in space compared to those on Earth, and the time discrepancies between clocks on GPS satellites and those on Earth.

4. How does Einstein's theory of relativity explain time dilation?

Einstein's theory of relativity states that time and space are relative concepts and can be affected by factors such as gravity and velocity. This theory explains time dilation by showing how time can appear to move slower or faster depending on the relative motion of two objects. The theory also predicts that time will appear to move slower in stronger gravitational fields, which has been confirmed by experiments.

5. Can time dilation be observed on a daily basis?

Yes, time dilation can be observed on a daily basis, although the effects are usually very small. For example, due to the Earth's rotation and its orbit around the sun, clocks at different locations on Earth will have small differences in time. Also, the global positioning system (GPS) would not work accurately if the effects of time dilation were not taken into account.

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