# Speed of light and time dilation

• ciprian

#### ciprian

So, according to my understanding, if we leave Earth and travel close to speed of light and then come back we may have time dilation (there will be one year for us, but 10 years for the people on Earth).
But how does this work as long as there is no frame of reference?
Why can't we consider the same scenario from a different perspective - can't we consider that actually the Earth moved away from us close to the speed of light? Why it's not 1 year for the people on Earth and 10 years on our spaceship when we finally meet again?

As you can probably imagine, this topic is addressed here with great regularity. Try a forum search.

The short answer is this: the spaceship had to accelerate to leave Earth and had to turn around (a second acceleration) - and that's what breaks the symmetry.

acceleration is the rate which something speeds up or slows down.
But without a frame of reference who's accelerating? We can say that the spaceship does. But what if we consider the spaceship as point A and Earth as point B? At some moment in time, the distance beween A and B increases at a specific speed (let's say 0.99*c). Which one is accelerating: A or B?

The short answer is this: the spaceship had to accelerate to leave Earth and had to turn around (a second acceleration) - and that's what breaks the symmetry.
Right, but if the velocity is less than the escape velocity the traveler may come back slightly older than the one staying on Earth.

This is called the twin paradox. There's a lot of explanations of it on this website, as well as on wikipedia and on the internet as a whole. Read the faq, it should be there too.

acceleration is the rate which something speeds up or slows down.
But without a frame of reference who's accelerating? We can say that the spaceship does. But what if we consider the spaceship as point A and Earth as point B? At some moment in time, the distance beween A and B increases at a specific speed (let's say 0.99*c). Which one is accelerating: A or B?

No. We know for a fact that the spaceship is the one accelerating. The occupants feel the accelerative force pushing on them. Those on Earth do not feel this force (assuming, for the sake of argument that Earth is stationary).

Those on Earth do not feel this force (assuming, for the sake of argument that Earth is stationary).
Those on Earth are most certainly accelerating, you and I certainly feel the force everyday.

Those on Earth are most certainly accelerating, you and I certainly feel the force everyday.

While true, for the sake of the thought experiment, it is irrelevant - and in fact, should be eliminated.
(The Op's question could be simplified to 2 spaceships, one floating inertially, the other accelerating away. Now no gravity but same experiment).

So let's keep on track with what we're trying to demonstrate, OK?

No. We know for a fact that the spaceship is the one accelerating. The occupants feel the accelerative force pushing on them. Those on Earth do not feel this force (assuming, for the sake of argument that Earth is stationary).

Interesting.
My problem is how we determine who's accelerating and who's deaccelerating. Without any gravitation involved, then any acceleration or deacceleration will be felt the same way (pushing toward the spaceships walls in one direction or another).

Intuitively the bigger objects are relative stationary to the small ones - Earth vs humans, Sun vs Earth, center of the galaxy vs our Solar System, probably the center of our galaxy supercluster vs Milky Way, etc. So, if I'm changing speed in the opposite direction of the rotation of our Solar System vs center of Milky Way, am I accelerating or deaccelerating?
I assume I'm accelerating vs Sun but deaccelerating vs center of the galaxy... But then how does time dilation apply to me in a theoretical similar scenario?

Interesting.
My problem is how we determine who's accelerating and who's deaccelerating.
Both are non-inertial. Both are the spaceship.

Deceleration is nothing more than acceleration in a negative direction.
Intuitively the bigger objects are relative stationary to the small ones - Earth vs humans, Sun vs Earth, center of the galaxy vs our Solar System, probably the center of our galaxy supercluster vs Milky Way, etc.

No. Acceleration is not relative. It is absolute. We know for a fact which one is accelerating.

Interesting.
My problem is how we determine who's accelerating and who's deaccelerating. Without any gravitation involved, then any acceleration or deacceleration will be felt the same way (pushing toward the spaceships walls in one direction or another).

Intuitively the bigger objects are relative stationary to the small ones - Earth vs humans, Sun vs Earth, center of the galaxy vs our Solar System, probably the center of our galaxy supercluster vs Milky Way, etc. So, if I'm changing speed in the opposite direction of the rotation of our Solar System vs center of Milky Way, am I accelerating or deaccelerating?
I assume I'm accelerating vs Sun but deaccelerating vs center of the galaxy... But then how does time dilation apply to me in a theoretical similar scenario?

What you seam to be referring to is simply a matter of perception. In order to see
something moving we compare it against something else.

Let's imagine for example that your spaceship is stationary in space, and that the Earth and
everything else in the universe would be the one accelerating. How much energy do you
think it would take you to do that, even for a little acceleration ? Take for example that it
currently take about the power of about a small town (7 TeV) to accelerate a proton
to near the speed of light 0.999999991 c. Now how you could even accelerate the
universe is a whole other story. Your only other alternative would be a negative
acceleration compare to the universe. Where would an object need to go in order to be
subject to negative acceleration from rest is beyond my current understanding of physic.

The problem I see, is even if our solar system is spinning, it doesn't necessarily has a
big acceleration either negative or positive, it doesn't even have that much speed either
when compared to the speed of light to be honest. Please be careful with speed and
acceleration.

For example, let's say a galaxy is spinning at the speed of 10k Km/h at it extremity. If you
decide to go 10k Km/h in the opposite direction at the extremity of this galaxy you should
be essentially subject to about the same time, since your speed is about the same just in
different direction. If you go even faster let's say 20k Km/h in the opposite direction that
would mean that you would be going 10k Km/h faster then the galaxy.

EDIT : Thanks for pointing that out ghwellsjr.

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Let's imagine for example that your spaceship is stationary in space, and that the Earth and
everything else in the universe would be the one accelerating. How much energy do you
think it would take you to do that, even for a little acceleration ? Take for example that it
currently take about the power of about a small town (7 TeV) to accelerate a photon
to near the speed of light 0.999999991 c. Now how you could even accelerate the
universe is a whole other story. Your only other alternative would be a negative
acceleration compare to the universe. Where would an object need to go in order to be
subject to negative acceleration from rest is beyond my current understanding of physic.
Let us eliminate the issue of the mass of the Earth and eliminate the issue of the accelerative motion of the Earth and eliminate the issue of the gravity of the Earth all in one fell swoop.

Let us replace the Earth with a second spaceship. Make it a large one of you want.

One mothership sits in inertial motion in space (we'll call it stationary but there is no such thing). The other scoutship takes off for parts unknown, turns around and comes back.

We know for a fact - from the point of view of both reference frames - which one did the accelerating and which one did not. The one that did the accerelating is the one that experienced accelerative forces. It is this one that has the younger twin upon return.

Let us replace the Earth with a second spaceship. Make it a large one of you want.

One mothership sits in inertial motion in space (we'll call it stationary but there is no such thing). The other scoutship takes off for parts unknown, turns around and comes back.

We know for a fact - from the point of view of both reference frames - which one did the accelerating and which one did not. The one that did the accerelating is the one that experienced accelerative forces. It is this one that has the younger twin upon return.

Ciprian this is the best way of thinking about it. Read and think about it carefully; a person on the mothership would observe themselves floating but if they look at the scoutship they will see everyone stuck to the floor by acceleration. Everyone on the scoutship would see themselves stuck to the floor feeling the acceleration whilst observing everyone on the mothership just floating.

Ciprian this is the best way of thinking about it. Read and think about it carefully; a person on the mothership would observe themselves floating but if they look at the scoutship they will see everyone stuck to the floor by acceleration. Everyone on the scoutship would see themselves stuck to the floor feeling the acceleration whilst observing everyone on the mothership just floating.

Yes, let's assume that the mothership is A and the scoutship is B.
Now, if A and B are stationary, B will eventually have 2 accelerations: a positive and a negative one. And we said that due to those 2 accelerations, time on B will go slower.

But what if we have now a point of reference (C - a planet or something else), and initially A and B are moving at 0.9c relative to C? They are still stationary one relative to each other. But if B gets 2 accelerations (and get to 0 relative to C which is 0.9c relative to B, and then back to 0 relative to B) - is not this similar to scenario 1? Will time on B (relative to C) go slower or faster relative to A?

Yes, let's assume that the mothership is A and the scoutship is B.
Now, if A and B are stationary, B will eventually have 2 accelerations: a positive and a negative one. And we said that due to those 2 accelerations, time on B will go slower.

But what if we have now a point of reference (C - a planet or something else), and initially A and B are moving at 0.9c relative to C? They are still stationary one relative to each other. But if B gets 2 accelerations (and get to 0 relative to C which is 0.9c relative to B, and then back to 0 relative to B) - is not this similar to scenario 1? Will time on B (relative to C) go slower or faster relative to A?
In all cases you mentioned, B is the one doing the acceleration, therefore it is the one that experiences the time dilation.

It is true that any two observers moving relative to each other will see the other aging slower (if they could see that far) - but - if they ever wish to return to the same point (and same reference frame), it is because one of them turned around and came back. That one will have aged slower.

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let's say at different intervals (as measured on C):
tC = 0, tA, tB and tC are 0 (A and B are at over 0.9c relative to C)
tC = 10, tA, tB are 1 due to time dilation (A and B are still at over 0.9c relative to C)
tC = 20 (A is at over 0.9c relative to B and C) tA = 2, tB = 11?
tC = 30 (A and B are at over 0.9c relative to C) tA = 3, tB = 12?
so B is older than A, despite it had 2 accelerations. Where's my mistake?

They will each see the other moving at the same speed but they will each see the other one aging slower.

If you fix this quick, I'll delete this post.
Good catch! Fixed.

Yes, let's assume that the mothership is A and the scoutship is B.
Now, if A and B are stationary, B will eventually have 2 accelerations: a positive and a negative one. And we said that due to those 2 accelerations, time on B will go slower.

But what if we have now a point of reference (C - a planet or something else), and initially A and B are moving at 0.9c relative to C? They are still stationary one relative to each other. But if B gets 2 accelerations (and get to 0 relative to C which is 0.9c relative to B, and then back to 0 relative to B) - is not this similar to scenario 1? Will time on B (relative to C) go slower or faster relative to A?
let's say at different intervals (as measured on C):
tC = 0, tA, tB and tC are 0 (A and B are at over 0.9c relative to C)
tC = 10, tA, tB are 1 due to time dilation (A and B are still at over 0.9c relative to C)
tC = 20 (A is at over 0.9c relative to B and C) tA = 2, tB = 11?
tC = 30 (A and B are at over 0.9c relative to C) tA = 3, tB = 12?
so B is older than A, despite it had 2 accelerations. Where's my mistake?
You haven't made any mistakes in your timing numbers, your mistake is you haven't brought A and B back together. As long as they are separated, their age difference is frame dependent, as you are demonstrating. It takes at least three accelerations to have the twins start out together and end up together and the middle acceleration has to be twice as big or last twice as long to get the traveling twin back home.

So if you give him a third acceleration equal to his second one, he will now be going even faster than he was when he was at rest with respect to A and he will have even more time dilation than he had on the first half of his trip. Then he needs a fourth acceleration when he gets to A so they will be at rest with respect to each other. At this point, C's frame will agree that the age difference between the two twins is exactly the same as what A and B both experience.