Velocities - how relative are they really?

[antred]

Hello everyone! Something about speeds and how they're supposed to be relative has been bugging me for a while. I'm not particularly well-versed in physics, so if these questions make you cringe ... well, sorry about that. ;)

So here goes - it is said that speeds are relative, right? If you have an object A that is moving toward another object (B) at a certain rate, you could just as well look at it as object B moving toward object A. So far so good. But where it kind of gets a little confusing to me is the following scenario.

Picture a starship that starts from planet Earth and travels away from it in a straight line at half the speed of light for 4 Earth years. If I understand things correctly, there is some sort of time dilation that has the effect that while for everyone who stays behind on Earth, 4 years will have passed by the time our spaceship ends its journey, the occupants of the starship themselves will have aged a little less than that. Am I making sense thus far?

Ok, but if speeds are really relative, then couldn't I just as well think of it as the spaceship sitting still and planet Earth moving away from it at half the speed of light? And if so, shouldn't time dilation then have the exact opposite effect, i.e. those who stayed on Earth age more slowly than the crew of the spaceship?
Obviously it isn't so, and something's wrong with my line of thinking - but what?

 

[Drakkith]

I THINK the factor in your example that makes the difference is acceleration. The Earth definitely did not feel an acceleration while your spaceship did. ONCE the spaceship is traveling at whatever velocity, then it is ok to say that the Earth may be traveling at that velocity instead of the ship. But again, I only think that is correct, I'm not sure.

 

[D H]

Ok, but if speeds are really relative, then couldn't I just as well think of it as the spaceship sitting still and planet Earth moving away from it at half the speed of light? And if so, shouldn't time dilation then have the exact opposite effect, i.e. those who stayed on Earth age more slowly than the crew of the spaceship?
Obviously it isn't so, and something's wrong with my line of thinking - but what?

I presume that you are asking about the twin paradox. If the spaceship just continued going in the same direction indefinitely, then people on the spaceship would see people on the Earth aging slower than they themselves are aging AND people on the Earth would see people on the spaceship aging slower than they themselves are aging.

In the twin paradox, the spaceship does not continue going in the same direction indefinitely. It instead turns around. The Earth does not "turn around". This symmetry breaking is what results in the non-symmetric result when the spaceship eventually returns to the Earth.

 

[Drakkith]

In the twin paradox, the spaceship does not continue going in the same direction indefinitely. It instead turns around. The Earth does not "turn around". This symmetry breaking is what results in the non-symmetric result when the spaceship eventually returns to the Earth.

So what does the turning around of the ship do exactly? How does that make it different? When the ship turns around and accelerates again, does the crew still see the people on Earth aging slower or faster? I would guess faster since they are traveling toward earth, and should be running into the light at a quicker rate, but I don't know if that really is the reason.

 

[Rap]

A spaceship moving away from Earth will say that people on Earth are aging more slowly. The people on Earth will say the people on the spaceship are aging more slowly.

If the spaceship turns around, while it is turning around, it will say that people on Earth are aging very rapidly. Then, as it goes towards Earth, again both will be saying that the other is aging more slowly. When the spaceship reaches Earth, the net effect will be that the people on Earth have aged more than the people on the spaceship.

Of course, they won't "see" this happening this way, because the information about aging must travel at the speed of light to get from the Earth to the spaceship or vice versa. But after they receive the information, this is what they will conclude, after taking the speed of light into account.

 

[Drakkith]

While it is turning around means from the time it starts to deccelerate until the time it accelerates back up to full speed? Or just the decceleration to the zero velocity point? Also, why do the people on Earth speed up in the frame of the spaceship when it turns around?

 

[JesseM]

Picture a starship that starts from planet Earth and travels away from it in a straight line at half the speed of light for 4 Earth years. If I understand things correctly, there is some sort of time dilation that has the effect that while for everyone who stays behind on Earth, 4 years will have passed by the time our spaceship ends its journey, the occupants of the starship themselves will have aged a little less than that. Am I making sense thus far?

Ok, but if speeds are really relative, then couldn't I just as well think of it as the spaceship sitting still and planet Earth moving away from it at half the speed of light? And if so, shouldn't time dilation then have the exact opposite effect, i.e. those who stayed on Earth age more slowly than the crew of the spaceship?
Obviously it isn't so, and something's wrong with my line of thinking - but what?

You are probably unaware of the relativity of simultaneity, which says that different reference frames disagree about which pair of events at different locations happen at the "same time" (simultaneously). So for example say your ship travels at 0.6c in the Earth's frame, so after 4 years of time in the Earth frame, it reaches some space station which is at a distance of 0.6*4=2.4 light years away from Earth. Because of time dilation, the ship is only aging at 0.8 the normal rate in the Earth frame, so after 4 years of time in Earth's frame the ship has aged 3.2 years. So in the Earth frame, the event of the ship reaching the distant space station, with the ship's clock having elapsed 3.2 years, is simultaneous with the event of the Earth's clock having elapsed 4 years. But in the ship's frame, simultaneity is different--in the ship frame, the event of the ship reaching the station with the ship's clock reading 3.2 years is simultaneous with the Earth's clock having elapsed 2.56 years. So in this frame, the Earth has been aging slower (by the same factor of 0.8), not the ship.

 

[Rap]

While it is turning around means from the time it starts to deccelerate until the time it accelerates back up to full speed? Or just the decceleration to the zero velocity point? Also, why do the people on Earth speed up in the frame of the spaceship when it turns around?

During the entire acceleration phase - from the time it starts to turn around, until it completely turns around and is back to its full speed towards Earth.

Its not right to say they speed up. They speed up according to the person in the spaceship. To the people on Earth, time goes by at the usual rate.

 

[Drakkith]

During the entire acceleration phase - from the time it starts to turn around, until it completely turns around and is back to its full speed towards Earth.

Its not right to say they speed up. They speed up according to the person in the spaceship. To the people on Earth, time goes by at the usual rate.

Of course, that is what I meant. Why does this happen?

 

[JesseM]

Of course, that is what I meant. Why does this happen?

It doesn't happen in any objective frame-independent sense, it just depends on what coordinate system the accelerating observer uses, different non-inertial coordinate systems have different opinions about simultaneity and thus different opinions about what clocks on Earth are doing "at the same time" that the traveler is accelerating. If you choose to use a non-inertial frame whose definition of simultaneity at each point on the traveler's worldline matches up with the definition in their instantaneous inertial rest frame at that point, then Earth clocks do move forward quickly during the acceleration, as seen in this diagram from the last section of the twin paradox page:

However, there is no rule that says the accelerating observer must use a non-inertial frame with this property.

 

[Drakkith]

It doesn't happen in any objective frame-independent sense, it just depends on what coordinate system the accelerating observer uses, different non-inertial coordinate systems have different opinions about simultaneity and thus different opinions about what clocks on Earth are doing "at the same time" that the traveler is accelerating.

I don't know what you just said here lol.

Do the people on Earth start to age quicker because events start to "catch up" to the spaceship as it deccelerates and then accelerates back towards earth? IE if light is emitted when the ship is 1 light year from earth, does it reach the ship in 1 year, or greater than 1 year because the ship is moving?

Edit: Looking at the stuff you added into your post now.

 

[Rap]

Of course, that is what I meant. Why does this happen?

I'm not sure I know what you mean by "why". I could answer "because that's what the theory of relativity says" and the theory of relativity has not been found to be incorrect.

Or, I could explain how this effect occurs, using relativistic arguments. Would this answer "why"? JesseM's explanation is a good one, it shows how the spaceship sees things as it turns around. As it turns around, its "lines of simultaneity" sweep past the worldline of the Earth.

Or, does "why" mean "why does relativity give a good description of what different observers measure"? This would be a question beyond me.

 

[JesseM]

I don't know what you just said here lol.

Well, which parts don't you understand? Do you know what an "inertial frame" is, and therefore what a "non-inertial" coordinate system would be? Do you understand the "relativity of simultaneity", that different coordinate systems disagree about which pairs of events are simultaneous? If not these are some of the most basic concepts of special relativity, I'd suggest reading some kind of basic intro to SR like the ones listed on this thread.

Do the people on Earth start to age quicker because events start to "catch up" to the spaceship as it deccelerates and then accelerates back towards earth?

No, the way a coordinate system defines simultaneity need not have anything to do with when the light from events reaches a given observer.

IE if light is emitted when the ship is 1 light year from earth, does it reach the ship in 1 year, or greater than 1 year because the ship is moving?

"1 light year" and "1 year" in what coordinate system? Distance always depends on your coordinate system in relativity, and time usually does unless you are talking about the proper time along some specific worldline.

 

[JesseM]

I'm not sure I know what you mean by "why". I could answer "because that's what the theory of relativity says" and the theory of relativity has not been found to be incorrect.

But it doesn't say that this happens objectively, only in a particular type of coordinate system.

Or, I could explain how this effect occurs, using relativistic arguments. Would this answer "why"? JesseM's explanation is a good one, it shows how the spaceship sees things as it turns around. As it turns around, its "lines of simultaneity" sweep past the worldline of the Earth.

The lines of simultaneity only behave this way in a non-inertial coordinate system with the particular property I described. There is no single "correct" way to design a non-inertial coordinate system, you could easily design one where the Earth's clocks were ticking slower during the traveler's acceleration phase, not faster, and it would be every bit as valid as the one shown in the diagram.

 

[Drakkith]

I'm not sure I know what you mean by "why". I could answer "because that's what the theory of relativity says" and the theory of relativity has not been found to be incorrect.

Lol, I guess I mean "What causes that?". Let me look up some more info on all this and I'll get back to you all if I have more questions.

 

[ghwellsjr]

A spaceship moving away from Earth will say that people on Earth are aging more slowly. The people on Earth will say the people on the spaceship are aging more slowly.

If the spaceship turns around, while it is turning around, it will say that people on Earth are aging very rapidly. Then, as it goes towards Earth, again both will be saying that the other is aging more slowly. When the spaceship reaches Earth, the net effect will be that the people on Earth have aged more than the people on the spaceship.

Of course, they won't "see" this happening this way, because the information about aging must travel at the speed of light to get from the Earth to the spaceship or vice versa. But after they receive the information, this is what they will conclude, after taking the speed of light into account.

During the entire acceleration phase - from the time it starts to turn around, until it completely turns around and is back to its full speed towards Earth.

Its not right to say they speed up. They speed up according to the person in the spaceship. To the people on Earth, time goes by at the usual rate.

Hey, Rap, I have a question for you. Suppose after the spaceship turns around and the people on the spaceship say that the people on the Earth are now very much older than they are, the spaceship decides to turn around again and resume their original velocity, will the people on the spaceship say that the people on the Earth quickly got younger?

 

[Rap]

Hey, Rap, I have a question for you. Suppose after the spaceship turns around and the people on the spaceship say that the people on the Earth are now very much older than they are, the spaceship decides to turn around again and resume their original velocity, will the people on the spaceship say that the people on the Earth quickly got younger?

Ha - good question. The answer is yes.

As per our previous conversation, this is not what they would see, but what they would calculate to have happened after the information reached them.