Which would be delayed??

[Debhoro]

Hi,

 

I’m not a physicist but I’m very curious about relativity, I read and studied a little and I have one big issue I can’t understand.

 

Let’s make an example, it would be easier for me to explain my point as English is not my first language:

 

There are 2 old friends Mr.Green and Mr.Red who are in their own space-ships in the middle of the universe, at this moment the 2 spaceships are connected through a door and Mr.Green and Mr.Red can meet each other. From the windows they can’t see anything, it’s all dark and they don’t have any reference point. Moreover the 2 space ships are moving forward at a low constant speed (let’s say 50km/h) in a straight line.

The 2 friends decide to synchronize their watches and then each one return to his space ship, they close the connection door and separate the 2 space ships. Now Mr.Green is at the right side of Mr.Red and they are seeing each other through a little window.

While the space ship of Mr.Green keep the same speed and direction, the space ship of Mr.Red start to accelerate and turn to the left. However, both the acceleration and the change of direction occurs very slowly and it’s impossible for Mr.Red to perceive them.

The space ship of Mr.Red accelerate up to about the speed of light, executing a very big round of 360º to the left and returning to the initial point. Once there, it starts again to move in a straight line trying to reach Mr.Green and decelerating little by little. Again it’s impossible for Mr.Red to perceive the change of speed.

After a while the 2 space ships are side by side and connected through the door, the 2 friends open the door and they immediately check their watches: the clock of Mr.Red should be late compared to the clock of Mr.Green, as he travelled close to the speed of light (even if he doesn’t know it as it was impossible for him to perceive it), but accordingly to the theory of relativity Mr.Red has the right to say that he was stable and it was Mr.Green who moved.

 

The question is: the watch of which one is late compared to the other?

 

Thanks for your help

[swansont]

Mr. Red's clock will be slow, since he accelerated. The phrase "the acceleration and the change of direction occurs very slowly and it’s impossible for Mr.Red to perceive them" is moot; it's still an acceleration.

[Debhoro]

Thanks for your reply.

 

Then I’ll try to imagine a different example, without acceleration or deceleration:

Mr.Green is stable somewhere in the universe and Mr.Red is moving in circle around Mr.Green. As you can imagine the speed of the space ship of Mr.Red is almost the speed of light, there is no acceleration or deceleration, they are in that situation since always (pretty dumb scenario, I know…).

 

Which one will live longer? Mr.Red is the person travelling at high speed, but from his point of view he’s stable and Mr.Green is moving around him.

Would it be correct to say that both of them could state that they are going to live longer than the other person (even if they will never find it out)?

[Delta1212]

Velocity is a vector, which means a change in direction is acceleration. Circular motion requires constant acceleration.

[swansont]

The orbiting Mr. Red has the slower moving clock owing to the motion (assuming no gravity). We continually see this with GPS satellites and it's been observed with clocks-on-a-plane experiment(s) although for both of those gravity must also be taken into account.

[Debhoro]

The orbiting Mr. Red has the slower moving clock owing to the motion (assuming no gravity). We continually see this with GPS satellites and it's been observed with clocks-on-a-plane experiment(s) although for both of those gravity must also be taken into account.

 

Exactly!!

But what I wanted to know was (without considering gravity): why should we think GPS satellite are delayed? If we see it from the point of view of the GPS, they are stable and the Earth is moving, so the clock of the GPs is actually moving faster than clocks on Earth.

 

I guess the answer to this is:

 

Velocity is a vector, which means a change in direction is acceleration. Circular motion requires constant acceleration.

[swansont]

 

Exactly!!

But what I wanted to know was (without considering gravity): why should we think GPS satellite are delayed? If we see it from the point of view of the GPS, they are stable and the Earth is moving, so the clock of the GPs is actually moving faster than clocks on Earth.

 

I guess the answer to this is:

 

 

Yes. Acceleration is not relative — you can tell who is accelerating, and that's whose clocks are affected.

[Orodruin]

 

Yes. Acceleration is not relative — you can tell who is accelerating, and that's whose clocks are affected.

 

With the conclusion that GR is needed to get the correct result for GPS satellite clocks as they actually tick faster than clocks on Earth. On the other hand, someone standing on Earth is accelerating in the GR setting while the satellite is not ...

[`hýsøŕ]

 

With the conclusion that GR is needed to get the correct result for GPS satellite clocks as they actually tick faster than clocks on Earth. On the other hand, someone standing on Earth is accelerating in the GR setting while the satellite is not ...

both somebody on earth and the satellite are acceleration because they're moving in a circle.. change in direction of motion with time ->> acceleration

[Orodruin]

The GPS satellite is not accelerating. It is in a state of free fall and follows a geodesic in space-time. If you were sitting on the satellite you would not feel any acceleration.

[Debhoro]

Wait, if I understood it right, on Earth we are accelerating even if we don’t feel it.

What’s different with GPS satellites? They are orbiting the Earth so they are accelerating

 

Am I wrong?

[Orodruin]

We do feel it. It is the fact that the Earth has to keep pushing us up. This is how gravity is working in GR, there is no gravitational force and objects follow the closest thing you can get to straight lines (known as geodesics) in curved space-time unless accelerated. The curvature of space-time at Earth's surface is such that you would start approaching the center if not accelerated by the ground.

 

The satellite on the other hand is not being acted upon by any force and is therefore not feeling any acceleration. It is orbiting Earth because space-time is curved in such a way that this geodesic becomes an orbit.

[Debhoro]

ummm….let’s see….the satellite orbit around Earth and doesn’t get lost in space because geodesics lines keep it there, isn’t it?

So the geodesics are changing the direction of the satellite, thus are applying a force, and that means it’s accelerating.

 

Also, doesn’t circular motion require a constant acceleration (as stated by Delta1212 above)??

 

I’m getting confused…

[Delta1212]

ummm.lets see.the satellite orbit around Earth and doesnt get lost in space because geodesics lines keep it there, isnt it?

So the geodesics are changing the direction of the satellite, thus are applying a force, and that means its accelerating.

 

Also, doesnt circular motion require a constant acceleration (as stated by Delta1212 above)??

 

Im getting confused

When you get into General Relativity, the rules are a bit different because gravity isn't treated as a force so much as a change in the geometry of space. That new geometry means that an object that is "standing still" may be accelerating, and an inertial path can take you in a circle.

 

That said, you can no longer calculate time dilation just using relative speed at that point. You have to take into account gravitational effects as well, which changes the result. So you still can't set up a system the way you had described and obtain the result you were asking about.

[Debhoro]

OK! Maybe (just maybe) I got it.

So you’re saying that the satellite is actually following the geodesics like any object would do, it’s just that the geodesics is circular and not straight because of the gravity of Earth.

 

Correct?

[MigL]

If I may elaborate...

 

The satellite is, in effect, falling. A fall with no horizontal component, such that it falls through the centre of the earth, is in orbit, If it has enough horizontal component, it goes right around the earth, still in an orbit. This is simple Newtonian gravity.

What GR adds is that an object in free fall, such as an orbit, has and feels no forces on itself.

If it has no forces acting on it, it experiences no acceleration !

 

And Orodruin is absolutely right, your weight, i.e. the force you feel, is not due to gravity pulling you down, but from the ground pushing you up.

[Rahul08]

The satellite actually move in horizontal direction.But according to general relativity, the gravity of the earth just curves the space time fabric. the satellite then falls ito this circular curve and revolves around the earth.

To understand this, we can use an example:

Hold a rubber sheet. Place a ball on the cetre of the sheet. Now the ball curves the sheet around it. If we let another small ball in any direction, the ball will automatically revolve around the earlier ball.

This path is called its orbit.

 

To my knowledge, Acceleration is change in velocity with time, but not change in direction.

 

I think this image will give you a better idea.

 

Please correct me if i am wrong.

[xyzt]

 

To my knowledge, Acceleration is change in velocity with time, but not change in direction.

 

I think this image will give you a better idea.

 

Please correct me if i am wrong.

You are wrong, acceleration is change in velocity. This includes change in direction.

[Rahul08]

Oh yes, Thank you for correcting me. I forgot for a moment tht velocity is a vector quantity.

Thanks xyzt.

[phyti]

ummm….let’s see….the satellite orbit around Earth and doesn’t get lost in space because geodesics lines keep it there, isn’t it?

So the geodesics are changing the direction of the satellite, thus are applying a force, and that means it’s accelerating.

 

Also, doesn’t circular motion require a constant acceleration (as stated by Delta1212 above)??

 

I’m getting confused…

An object in free fall receives a uniform acceleration for all it's components, thus there is no sensation of acceleration. Think of astronauts experiencing weightlessness in a plane flying a parabolic arc.

The person on the ground experiences acceleration, which you can verify by standing on a scale.

Gravity is always on.

[xyzt]

Oh yes, Thank you for correcting me. I forgot for a moment tht velocity is a vector quantity.

Thanks xyzt.

You are welcome.