Thread: Question on relative motion...

Hi,

I have a question. If a spaceship traveled away from Earth at near light speed and then returned, those on the spaceship would experience less time and return to Earth younger. Right so far?

But wait, since all motion and speed are relative, from the spaceships point of view it is the Earth that is traveling away and returning at near light speed, yes?

So, is it…
a) The difference is when the spaceship turns and returns (and why), or
b) Is the difference because this motion is ultimately relative to the microwave background, or
c) Something else?

I hope you understand what I’m trying to ask.

Thanks,
Rusty

Originally Posted by rrw4rusty

But wait, since all motion and speed are relative, from the spaceships point of view it is the Earth that is traveling away and returning at near light speed, yes?

No, not all motion is relative. Velocity is relative, but acceleration is not relative. The spaceship accelerates when it turns around, the earth does not.

As a start I recommend that you read the sticky in the physics section called Special Relativity Primer.

Originally Posted by KJW

Originally Posted by rrw4rusty

But wait, since all motion and speed are relative, from the spaceships point of view it is the Earth that is traveling away and returning at near light speed, yes?

No, not all motion is relative. Velocity is relative, but acceleration is not relative. The spaceship accelerates when it turns around, the earth does not.

Could we say (or ask whether) that acceleration is a fundamental physical phenomenon whereas relative motion between bodies is somehow less so ? (derivative of acceleration even?)

Acceleration and relative motion seem intimately connected but I wonder if the relationship might be something of a "false friend"

I have a question. If a spaceship traveled away from Earth at near light speed and then returned, those on the spaceship would experience less time and return to Earth younger. Right so far?

Not really. You don't grow younger, the people in the spaceship aged less then people on Earth. You don't grow younger but you will have aged less on the space ship. But you have also gravitational time dilation and velocity/gravitational time dilation can have a combined effect. So it depends how the space ship travels.
https://en.wikipedia.org/wiki/Time_dilation

But wait, since all motion and speed are relative, from the spaceships point of view it is the Earth that is traveling away and returning at near light speed, yes?

You can say this since for people in the spaceship it looks like everything around them is moving for them the spaceship is stationary.

Originally Posted by rrw4rusty

Hi,

I have a question. If a spaceship traveled away from Earth at near light speed and then returned, those on the spaceship would experience less time and return to Earth younger. Right so far?

But wait, since all motion and speed are relative, from the spaceships point of view it is the Earth that is traveling away and returning at near light speed, yes?

So, is it…
a) The difference is when the spaceship turns and returns (and why), or
b) Is the difference because this motion is ultimately relative to the microwave background, or
c) Something else?

I hope you understand what I’m trying to ask.

Thanks,
Rusty

You can't examine this by using time dilation alone, you also have to include length contraction and the relativity of simultaneity.
So for example, let's say that our spaceship is traveling at 0.8c to a planet that, as measured by the Earth, is 8 light years away.
We also assume that the Earth and this planet have synchronized their clocks. (Meaning that if the ship leaves Earth at 12:00:00 on Jan 1, 2020, it will also be 12:00:00, Jan 1, 2020 at the planet)
We will also set the spaceship clock to the same time at its departure.
So as far as the Earth in concerned, the spaceship leaves Earth at 0.8 c, takes 10 years to reach the other planet while the spaceship clock only ticks off 6 yrs. So it will be Jan 1, 2030 on both the Earth and planet clocks when the ship arrives and only Jan 1, 2026 by the ship clock.
The ship turns around and comes back, taking another 10 years Earth time, and 6 years ship time, so that the Earth clock reads Jan 1, 2040 upon its return and the ship clock reads Jan 1, 2032.

Now what the ship would measure.
While moving at 0.8c relative to the Earth and planet, not only would the ship measure those clocks running slow, but he would measure a length contraction of both planets and the distance between them, and according to him the Earth and planet clock would no longer be in sync.* The distance between planet and Earth would only be 4.8 light years and the planet clock, instead of being Jan 1, 2020, it would already 6.4 years later, or May 26, 2026.
It would take 4.6/ 0.8 = 6 years to cross the distance between Earth and planet, during which time both planet and Earth clocks would advance by 3.6 years. Upon arrival to the planet the ship clock will read Jan 1, 2026, the planet clock reads Jan 1, 2030, and the Earth clock reads Aug 8, 2023.
The ship does an instant reversal of direction. Its time still reads Jan 1, 2026 and the planet time is still Jan 1, 2026, but now, since the ship has changed the direction of the relative velocity between the ship and Earth, The clock on Earth now reads 6.4 years ahead of the planet clock, putting it May 26, 2036 on Earth. During the return leg, the ship clock advances another 6 years while both planet and Earth clocks advance 3.6 years, and we end up with Jan 1, 2040 on Earth and Jan 1 2032 on the ship when they reunite.

One thing to keep in mind is that when I used the word "Measure" above, I did not mean what was directly observed. So for instance at the start both the Earth and the ship would directly see a reading of Jan1, 2012 on the Planet clock. The difference is that accroding to the Earth, this light left from a distance 8 light years away and took 8 years to reach Earth, during which time the planet clock ticked off 8 years. So the Earth concludes that it is Jan 1, 2020 at the planet when it sees that reading of Jan 1, 2012. It is the Jan 2020 time that I am referring to as " measured" time.
For the ship moving at 0.8 c relative to the Earth, while it directly sees the same Jan, 2012 time on the planet clock while it is next to the Earth, it "measures" a different time as being on the planet clock at that moment. The planet at that moment is not 8 light years away. The distance has not been constant ( the planet was further away when the light left than it is when the light arrives). The planet clock is ticking at a slower rate. All these factors combined cause the Ship to conclude that, in the time between the light leaving the planet and it arriving at the ship, Not 8, but 14.4 years have tick off on the planet clock, putting the "measured" time on the planet as being being in May of 2026.

* it is also true that the Earth would measure length contraction and relativity of simultaneity effects in the spaceship as well, But this would have no bearing on the results. The length of the ship doesn't effect how long it takes to cross the distance, and while relativity of simultaneity would cause a difference between clocks in the front and tail of the Ship, in this situation we are only dealing with one ship clock and not two separated ones.

Originally Posted by rrw4rusty

Hi,

I have a question. If a spaceship traveled away from Earth at near light speed and then returned, those on the spaceship would experience less time and return to Earth younger. Right so far?

But wait, since all motion and speed are relative, from the spaceships point of view it is the Earth that is traveling away and returning at near light speed, yes?

So, is it…
a) The difference is when the spaceship turns and returns (and why), or
b) Is the difference because this motion is ultimately relative to the microwave background, or
c) Something else?

I hope you understand what I’m trying to ask.

Thanks,
Rusty

You can't examine this by using time dilation alone, you also have to include length contraction and the relativity of simultaneity.
So for example, let's say that our spaceship is traveling at 0.8c to a planet that, as measured by the Earth, is 8 light years away.
We also assume that the Earth and this planet have synchronized their clocks. (Meaning that if the ship leaves Earth at 12:00:00 on Jan 1, 2020, it will also be 12:00:00, Jan 1, 2020 at the planet)
We will also set the spaceship clock to the same time at its departure.
So as far as the Earth in concerned, the spaceship leaves Earth at 0.8 c, takes 10 years to reach the other planet while the spaceship clock only ticks off 6 yrs. So it will be Jan 1, 2030 on both the Earth and planet clocks when the ship arrives and only Jan 1, 2026 by the ship clock.
The ship turns around and comes back, taking another 10 years Earth time, and 6 years ship time, so that the Earth clock reads Jan 1, 2040 upon its return and the ship clock reads Jan 1, 2032.

Now what the ship would measure.
While moving at 0.8c relative to the Earth and planet, not only would the ship measure those clocks running slow, but he would measure a length contraction of both planets and the distance between them, and according to him the Earth and planet clock would no longer be in sync.* The distance between planet and Earth would only be 4.8 light years and the planet clock, instead of being Jan 1, 2020, it would already 6.4 years later, or May 26, 2026.
It would take 4.6/ 0.8 = 6 years to cross the distance between Earth and planet, during which time both planet and Earth clocks would advance by 3.6 years. Upon arrival to the planet the ship clock will read Jan 1, 2026, the planet clock reads Jan 1, 2030, and the Earth clock reads Aug 8, 2023.
The ship does an instant reversal of direction. Its time still reads Jan 1, 2026 and the planet time is still Jan 1, 2026, but now, since the ship has changed the direction of the relative velocity between the ship and Earth, The clock on Earth now reads 6.4 years ahead of the planet clock, putting it May 26, 2036 on Earth. During the return leg, the ship clock advances another 6 years while both planet and Earth clocks advance 3.6 years, and we end up with Jan 1, 2040 on Earth and Jan 1 2032 on the ship when they reunite.

One thing to keep in mind is that when I used the word "Measure" above, I did not mean what was directly observed. So for instance at the start both the Earth and the ship would directly see a reading of Jan1, 2012 on the Planet clock. The difference is that accroding to the Earth, this light left from a distance 8 light years away and took 8 years to reach Earth, during which time the planet clock ticked off 8 years. So the Earth concludes that it is Jan 1, 2020 at the planet when it sees that reading of Jan 1, 2012. It is the Jan 2020 time that I am referring to as " measured" time.
For the ship moving at 0.8 c relative to the Earth, while it directly sees the same Jan, 2012 time on the planet clock while it is next to the Earth, it "measures" a different time as being on the planet clock at that moment. The planet at that moment is not 8 light years away. The distance has not been constant ( the planet was further away when the light left than it is when the light arrives). The planet clock is ticking at a slower rate. All these factors combined cause the Ship to conclude that, in the time between the light leaving the planet and it arriving at the ship, Not 8, but 14.4 years have tick off on the planet clock, putting the "measured" time on the planet as being being in May of 2026.

* it is also true that the Earth would measure length contraction and relativity of simultaneity effects in the spaceship as well, But this would have no bearing on the results. The length of the ship doesn't effect how long it takes to cross the distance, and while relativity of simultaneity would cause a difference between clocks in the front and tail of the Ship, in this situation we are only dealing with one ship clock and not two separated ones.

Originally Posted by geordief

Originally Posted by KJW

Originally Posted by rrw4rusty

But wait, since all motion and speed are relative, from the spaceships point of view it is the Earth that is traveling away and returning at near light speed, yes?

No, not all motion is relative. Velocity is relative, but acceleration is not relative. The spaceship accelerates when it turns around, the earth does not.

Could we say (or ask whether) that acceleration is a fundamental physical phenomenon whereas relative motion between bodies is somehow less so ? (derivative of acceleration even?)

Acceleration and relative motion seem intimately connected but I wonder if the relationship might be something of a "false friend"

There is a mathematical basis for the distinction between velocity and acceleration with regards to relative motion. Lorentz transformations transform inertial motion to inertial motion, and the Minkowskian metric is invariant to Lorentz transformations. Thus, all inertial motion is equivalent, which implies the non-existence of absolute rest and that velocity is relative only. By contrast, no Lorentz transformation can transform between inertial and non-inertial motion. Thus, any transformation between inertial and non-inertial motion is not a Lorentz transformation, and the Minkowskian metric will not be invariant under such a transformation. Therefore, inertial and non-inertial motion are not equivalent. In other words, there is absolute zero acceleration and this is inertial motion, and any acceleration relative to inertial motion is non-relative acceleration.

Thank you, Janus, for your detailed explanation! You put a lot of time into that and actually, I knew all this, I think. I’ve been reading about relativity for decades. My question is what says the spaceship is moving and not the Earth? The sun? The star the ship is headed to? Or is it because we know the ship had accelerated away or, is it because the ship is traveling through the gravitational field?

Bottom line, if two objects are traveling away from each other at a constant speed, what says one that one is stationary (to what?) and one is moving? For all my reading, I’m not clear on this.

Rusty

Edit: I apologize if you answered this and it just didn't take in my brain, lol.

Originally Posted by KJW

There is a mathematical basis for ...

Actually, there is a satisfaction achieved when one provides a mathematical basis for some physical notion. For example, dark energy that is based on a cosmological constant will look like empty space. This is because a spacetime whose only curvature is due to a cosmological constant is invariant to Lorentz transformations. That is, such a spacetime looks the same regardless of how fast one is travelling. In other words, one can't determine one's velocity relative to the dark energy, giving the dark energy the appearance of empty space (relative to which one also can't determine one's velocity).

[Although this thread is not about dark energy, it is about relative velocity, so the above is not entirely off-topic.]

Originally Posted by rrw4rusty

My question is what says the spaceship is moving and not the Earth? The sun? The star the ship is headed to? Or is it because we know the ship had accelerated away or, is it because the ship is traveling through the gravitational field?

It's the one thing you didn't mention... the turnaround. Only the spaceship actually turns around. The earth doesn't.

Originally Posted by KJW

Originally Posted by rrw4rusty

My question is what says the spaceship is moving and not the Earth? The sun? The star the ship is headed to? Or is it because we know the ship had accelerated away or, is it because the ship is traveling through the gravitational field?

It's the one thing you didn't mention... the turnaround. Only the spaceship actually turns around. The earth doesn't.

And this makes a difference how? Up to this point no time compression takes place? What if the Earth were also a ship called Earth instead and instead of the spaceship turning around the ship 'Earth' accelerated and caught the spaceship...who then would experience less time?

Sorry if I sound stupid.

Rusty

Originally Posted by Robbedoes

But wait, since all motion and speed are relative, from the spaceships point of view it is the Earth that is traveling away and returning at near light speed, yes?

You can say this since for people in the spaceship it looks like everything around them is moving for them the spaceship is stationary.

No, there is a difference between what the spaceship sees of the earth and what the earth sees of the spaceship. When the spaceship turns around, they see earth move towards them (Doppler blueshift) immediately, whereas the earth only sees the spaceship move towards them (also Doppler blueshift) after the delay of the time it takes the light from the spaceship turnaround to reach the earth. This difference in the point of view of the earth and spaceship with regards to the Doppler effect is enough to account for the time difference between the two clocks.

Originally Posted by rrw4rusty

What if the Earth were also a ship called Earth instead and instead of the spaceship turning around the ship 'Earth' accelerated and caught the spaceship...who then would experience less time?

Whoever does the accelerating experiences less time than the one who is inertial. And one knows one is accelerating without looking out the window by the weight they experience.

Originally Posted by KJW

Originally Posted by rrw4rusty

What if the Earth were also a ship called Earth instead and instead of the spaceship turning around the ship 'Earth' accelerated and caught the spaceship...who then would experience less time?

Whoever does the accelerating experiences less time than the one who is inertial. And one knows one is accelerating without looking out the window by the weight they experience.

So, if in the middle of a void, two ships were traveling away from each other at constant speed, which ever one turns around and accelerates back to the other ship will experience less time?

Rusty

Originally Posted by rrw4rusty

Originally Posted by KJW

Originally Posted by rrw4rusty

What if the Earth were also a ship called Earth instead and instead of the spaceship turning around the ship 'Earth' accelerated and caught the spaceship...who then would experience less time?

Whoever does the accelerating experiences less time than the one who is inertial. And one knows one is accelerating without looking out the window by the weight they experience.

So, if in the middle of a void, two ships were traveling away from each other at constant speed, which ever one turns around and accelerates back to the other ship will experience less time?

Rusty

Correct. And if they both accelerate, then it's the one with the greater acceleration who will experience less time.

One of the problems with using an earthbound clock as the stay-at-home twin is that such a clock is actually accelerating upward at 9.8ms^–2 due to gravity and not inertial as is usually assumed. So one should really consider the stay-at-home twin as being in deep space with truly inertial motion.

Originally Posted by Janus

The ship does an instant reversal of direction. Its time still reads Jan 1, 2026 and the planet time is still Jan 1, 2026,

It should be: the planet time is still Jan 1, 2030,

Regards,

Zlatan