Close to the speed of light relative to what?

[Tiago]

Hi,

We know that gravity affects time and the presence of big masses such as planets will cause big distortions in spacetime wich slows things down (if I'm floating in space, won't I be distorting spacetime for.. say.. an ant? Won't the ant gravitate towards me?).

Anyway. we know that velocity also affects time, and if I'm travelling very close to the speed of light, time would go slower for me than people on Earth. But only the speed of light is constant, everything else is relative to another frame of reference. So if I say the Earth is travelling at N km/h, that would have to be relative to something (perhaps the Sun). So, in order for me to be travelling at 99% of the speed of light, what reference frame am I using? Earth? I need to be going at the speed of the Earth, plus the 99% of the speed of light? And wich velocity of Earth? Relative to what?

Thanks

 

[ShayanJ]

Hi
The presence of any kind of any energy, by any amount, distorts spacetime. Its just that the amount you and an ant distort spacetime, is very very very very small so people just forget about it.
Uniform motion is relative. So if we consider the frame A to be at rest and frame B to be moving with speed v w.r.t. A, we can also consider B to be at rest and A to be moving with velocity -v w.r.t. B. Then A sees that B's time slows down and B sees that A's time slows down and both of them are right.

 

[phinds]

... if I'm travelling very close to the speed of light, time would go slower for me than people on Earth.

No, it would not. Time always passes locally at one second per second. What is observed by a remote observer is not what happens locally.

 

[Tiago]

Ok, but if I'm going close to the speed of light for 10 years, when I'd return to Earth, 20 years (or so) would have passed and I only aged 10. So time went slower for me than time of people on Earth. What's confusing me is at what speed should I go to do that. Einstein says it should be very close to the speed of light, but relative to what? To the velocity of the Earth?

 

[Dale]

Einstein says it should be very close to the speed of light, but relative to what? To the velocity of the Earth?

Relative to ANY inertial frame whatsoever (this is the first postulate of relativity). You can pick any inertial frame that you like, do that calculation, and come out with the same result. It doesn't have to be the inertial frame where the earth is at rest or anything.

 

[phinds]

Ok, but if I'm going close to the speed of light for 10 years, when I'd return to Earth, 20 years (or so) would have passed and I only aged 10. So time went slower for me than time of people on Earth.

No, time progressed for you at exactly the same rate as it did for the people on Earth, one second per second. The fact that you traveled along a different world line mean you AGED by a different amount while the time passed at the same rate. This is a confusing concept but it is the way it is.

 

[A.T.]

What is observed by a remote observer is not what happens locally.

Kinetic time dilation has nothing to do with local vs. remote, just with relative motion. A moving clock runs slower than a resting clock, even when they pass close to each other, and are observed locally.

 

[phinds]

Kinetic time dilation has nothing to do with local vs. remote, just with relative motion. A moving clock runs slower than a resting clock, even when they pass close to each other, and are observed locally.

DOH ! I knew that

 

[Nugatory]

We know that gravity affects time and the presence of big masses such as planets will cause big distortions in spacetime which slows things down (if I'm floating in space, won't I be distorting spacetime for.. say.. an ant? Won't the ant gravitate towards me?).

Yes, you and the ant will be drawn towards one another. You don't even need any general relativity; Newton's law of gravitation $F=Gm_1m_2/r^2$ and $F=ma$ is adequate for this job. It's a good exercise to try calculating the force between a 100 kg person and an ant weighing a few milligrams.

 

[nitsuj]

No, time progressed for you at exactly the same rate as it did for the people on Earth, one second per second. The fact that you traveled along a different world line mean you AGED by a different amount while the time passed at the same rate. This is a confusing concept but it is the way it is.

I am confused by this concept. It implies clocks don't measure time, but merely "age".

 

[Nugatory]

I am confused by this concept. It implies clocks don't measure time, but merely "age".

Clocks measure the amount of time that has passed between two events - the successive ticks of the clock. "Age" is just another word for the amount of time that has passed since two events (in the case of a human, birth and right now when you and the human in question are colocated). Thus, we can use a human body as a clock, although not an especially useful and well-calibrated one - the greyer the hair and the more wrinkled the skin, the more time has passed since the birth event.

On all paths through spacetime, you will age at one second per second. All clocks (and any time-dependent process can be used as a clock - human ageing, your wristwatch, sand in an hourglass, superbly accurate atomic clocks, the decay of a sample of radioactive material, ...) moving along that path will tick at that rate and therefore report the same amount of elapsed time between any two points on that path.

However, if I take two clocks, separate them, and then move them back together they will have followed different paths through spacetime between the first "they were together" event and the second. It is possible (and this is the essence of the twin paradox) that the amount of time elapsed on these two paths is different.

 

[nitsuj]

Clocks measure the amount of time that has passed between two events - the successive ticks of the clock. "Age" is just another word for the amount of time that has passed since two events (in the case of a human, birth and right now when you and the human in question are colocated). Thus, we can use a human body as a clock, although not an especially useful and well-calibrated one - the greyer the hair and the more wrinkled the skin, the more time has passed since the birth event.

On all paths through spacetime, you will age at one second per second. All clocks (and any time-dependent process can be used as a clock - human ageing, your wristwatch, sand in an hourglass, superbly accurate atomic clocks, the decay of a sample of radioactive material, ...) moving along that path will tick at that rate and therefore report the same amount of elapsed time between any two points on that path.

However, if I take two clocks, separate them, and then move them back together they will have followed different paths through spacetime between the first "they were together" event and the second. It is possible (and this is the essence of the twin paradox) that the amount of time elapsed on these two paths is different.

I agree; clocks measure time, and don't "age". In the case of a "clock" it is idealized to be a perfect measure of time.

 

[Dale]

I am confused by this concept. It implies clocks don't measure time, but merely "age".

I would say that clocks measure the derivative of age, also called proper time and usually denoted by $d\tau$. You can integrate proper time from "birth" to get age: $\tau = \int d\tau$. I don't know if there is an authoritative standard terminology, but that would be mine.

 

[nitsuj]

I would say that clocks measure the derivative of age, also called proper time and usually denoted by $d\tau$. You can integrate proper time from "birth" to get age: $\tau = \int d\tau$. I don't know if there is an authoritative standard terminology, but that would be mine.

I agree; clocks measure time, and don't "age". In the case of a "clock" it is idealized to be a perfect measure of time.

 

[ghwellsjr]

I would say that clocks measure the derivative of age, also called proper time and usually denoted by $d\tau$. You can integrate proper time from "birth" to get age: $\tau = \int d\tau$. I don't know if there is an authoritative standard terminology, but that would be mine.

I always thought $d\tau$ was a differential.

 

[nitsuj]

I agree; clocks measure time, and don't "age". In the case of a "clock" it is idealized to be a perfect measure of time.

I re-read an old thread where I thought thoroughly about time & age and more less came to the conclusion that "age" is sequenced accumulation of physical occurrence to a "body/object" (or the display on an imperfect clock), and time is a component of spacetime geometry. As phinds said "rate" is distinctly different from age.

In that case only an idealized perfect clock measures time, and for example my mechanical watch that gains 2 minutes per day ages, the hourglass ages, and the most consistent measures of the "rate" c (such as a light clock) is a measure of strictly time, not merely an accumulation of "change" but the rate.

If I understand the concepts right, I am saying a proper clock measures lightlike intervals. Our "biological" clock, hour glass ect can be a measure of proper time, timelike intervals, which of course different from coordinate time and the lightlike intervals of a perfect clock.

So with coordinate time I see the light clock in motion has the same rate of c, but the accumulation of "ticks" (different from rate) takes longer (different path).

 

[Dale]

I always thought $d\tau$ was a differential.

Oops, yes you are right. It is a differential line element on a timelike world line. I was sloppy above.

 

[Tiago]

So to go back to my initial question, Stephen Hawking says that a good way to travel to the future would be to go on a rocket and travel very close to the speed of light and come back to Earth in a few years (ok, so far so good). But when he says "travel very close to the speed of light", we'd be travelling at that speed relative to what frame? The Earth? So we'd need to picture the Earth at rest and the rocket at 99% of the speed of light? So that would mean, we'd traveling at the speed of the Earth plus 99% the speed of light?

 

[nitsuj]

So to go back to my initial question, Stephen Hawking says that a good way to travel to the future would be to go on a rocket and travel very close to the speed of light and come back to Earth in a few years (ok, so far so good). But when he says "travel very close to the speed of light", we'd be travelling at that speed relative to what frame? The Earth? So we'd need to picture the Earth at rest and the rocket at 99% of the speed of light? So that would mean, we'd traveling at the speed of the Earth plus 99% the speed of light?

Yes there would be a frame where it is observed that you were in motion prior to going (according to your frame) 0.99 of c relative to Earth.

However it is not a simple sum, according to the frame that observed Earth (and you the time traveler) in motion, your rulers and clocks were contracted/dilated prior to you deciding to go 0.99 of c relative to Earth. So to that observer you never reached 0.99 of c relative to Earth, but your measures/observations/calculations tell you you have, again this is because your rulers 'n clocks are not making the same measurements as the frame that observed Earth in motion.

So just as your rulers and clocks aren't making the same measurements (in turn calculation of velocities) we cannot simply add velocities as x+y.

The concept is more easily understood with a car and it's headlights. First the posit c is invariant; regardless of comparative motion every observer calculates light to have the velocity of c. So when a car is driving down the road with it's lights on, the driver calculates the light emitted from the headlights to be c, and the observer at rest to the road also calculates the light from the headlights to be c, not simply the car velocity + c. The "mechanics" is the car driver's rulers and clocks were contracted/dilated compared to yours (from your frame) to a point where he/she calculates the lights velocity to be c and not the car velocity + the headlight light velocity...note according to the driver he/she is at rest and your rulers and clocks are contracted/dilated.

 

[ghwellsjr]

So to go back to my initial question, Stephen Hawking says that a good way to travel to the future would be to go on a rocket and travel very close to the speed of light and come back to Earth in a few years (ok, so far so good). But when he says "travel very close to the speed of light", we'd be travelling at that speed relative to what frame? The Earth? So we'd need to picture the Earth at rest and the rocket at 99% of the speed of light? So that would mean, we'd traveling at the speed of the Earth plus 99% the speed of light?

Usually, when we say that something is traveling at a particular speed, we mean with reference to a particular Inertial Reference Frame (IRF). So you could say that in your chosen IRF, the earth is traveling at some speed, say, 10% of the speed of light (we'll call that 10%c) in some particular direction, and then you could say that the rocket is traveling at 99%c according to that same IRF in the same direction (or any other direction). Then the speed of the rocket relative to the earth will not be 99%c. It won't generally be a speed that you could easily calculate off the top of your head but it can be determined based on your specification of your scenario.

But we can also specify a scenario by saying that something is traveling at a particular speed with reference to some other object and then we don't care what the speed of that object is with reference to any other object or IRF. We just use that second object as the definition for an IRF in which it is at rest.

So in your example, if you just say that the rocket is traveling at 99%c with respect to the earth, it doesn't matter if the earth is also traveling at some particular speed with respect to the sun or any other object, as long as you aren't interested in determining anything that is happening on that other object or what observers on that other object see or determine that is happening on the earth or on the rocket.

So when Stephen Hawking says that we can travel into the future by taking a rocket at 99%c and returning, he is assuming the IRF in which the earth is at rest. At that speed, the Time Dilation Factor is 7.1 so if you say that the rocket is gone for 10 years, you have to tell us if you meant 10 years on earth or 10 years on the rocket. If you meant 10 years on earth, then you would have aged only 10/7.1 by the time you got back which is equal to 1.4 years so you would have traveled 8.6 years into the future of earth which isn't very much. If you meant 10 years of the rocket's time then the earth would have aged 10 times 7.1 or 71 years by the time you got back so you would have traveled 61 years into the future of earth and you would see a huge difference.

By the way, when considering speeds close to that of light, the Time Dilation due to gravity can generally be ignored since its contribution to the problem is so slight.

So the bottom line is that you get to set up your scenario any way you want and if all you care about is the relative aging between the people on earth and the people on the rocket, then you don't have to take into account any other objects or their relative speeds to either the earth or the rocket. The only thing that matters is the speed of the rocket relative to the earth.

Does that make sense to you?

 

[Tiago]

Usually, when we say that something is traveling at a particular speed, we mean with reference to a particular Inertial Reference Frame (IRF). So you could say that in your chosen IRF, the earth is traveling at some speed, say, 10% of the speed of light (we'll call that 10%c) in some particular direction, and then you could say that the rocket is traveling at 99%c according to that same IRF in the same direction (or any other direction). Then the speed of the rocket relative to the earth will not be 99%c. It won't generally be a speed that you could easily calculate off the top of your head but it can be determined based on your specification of your scenario.

But we can also specify a scenario by saying that something is traveling at a particular speed with reference to some other object and then we don't care what the speed of that object is with reference to any other object or IRF. We just use that second object as the definition for an IRF in which it is at rest.

So in your example, if you just say that the rocket is traveling at 99%c with respect to the earth, it doesn't matter if the earth is also traveling at some particular speed with respect to the sun or any other object, as long as you aren't interested in determining anything that is happening on that other object or what observers on that other object see or determine that is happening on the earth or on the rocket.

So when Stephen Hawking says that we can travel into the future by taking a rocket at 99%c and returning, he is assuming the IRF in which the earth is at rest. At that speed, the Time Dilation Factor is 7.1 so if you say that the rocket is gone for 10 years, you have to tell us if you meant 10 years on earth or 10 years on the rocket. If you meant 10 years on earth, then you would have aged only 10/7.1 by the time you got back which is equal to 1.4 years so you would have traveled 8.6 years into the future of earth which isn't very much. If you meant 10 years of the rocket's time then the earth would have aged 10 times 7.1 or 71 years by the time you got back so you would have traveled 61 years into the future of earth and you would see a huge difference.

By the way, when considering speeds close to that of light, the Time Dilation due to gravity can generally be ignored since its contribution to the problem is so slight.

So the bottom line is that you get to set up your scenario any way you want and if all you care about is the relative aging between the people on earth and the people on the rocket, then you don't have to take into account any other objects or their relative speeds to either the earth or the rocket. The only thing that matters is the speed of the rocket relative to the earth.

Does that make sense to you?

So, from what I understand, all it matters is what speed everything "else" is travelling relative to light. If Earth is travelling (for example) at 10% the speed of light and the Sun is travelling at (again, an example) at 15% the speed of light, there is a ratio here that we can mathematically solve that would translate how time goes slower on the Sun than on Earth. And a rocket at 99% the speed of light would have a ratio (as you said) of 7.1. And so on. So everything is measured against the speed of light, no matter wich reference frame. The point is that the rocket would have a different ratio of time relative to the Earth and the Sun or any other star or planet.

 

[ghwellsjr]

So, from what I understand, all it matters is what speed everything "else" is travelling relative to light.

When we say that something is traveling at 10%c or 99%c we don't mean that it is traveling relative to light. We can't do that because light is never at rest and we need to specify speeds relative to something that we consider to be at rest and light is never at rest. But then we say that light is traveling at c relative to that something that we consider to be at rest.

If Earth is travelling (for example) at 10% the speed of light and the Sun is travelling at (again, an example) at 15% the speed of light, there is a ratio here that we can mathematically solve that would translate how time goes slower on the Sun than on Earth. And a rocket at 99% the speed of light would have a ratio (as you said) of 7.1.

You can do this as long as you are saying that these speeds are relative to some assumed Inertial Reference Frame. Then the ratios are relative to that IRF, not relative to the other objects. So if you say in your IRF that the earth is traveling at 10%c and the rocket is traveling at 99%c, then you can't apply the ratio of 7.1 between the rocket and the earth. You're just making the problem more complicated when you do it this way. There's nothing wrong with doing it this way, I'm just wondering why you want to make things more complicated than they need to be.

And so on. So everything is measured against the speed of light, no matter wich reference frame. The point is that the rocket would have a different ratio of time relative to the Earth and the Sun or any other star or planet.

To repeat, the speed of everything is measured (or specified) against the IRF that you select when you specify your problem and in that IRF, light travels at c. And the ratios of time are relative to the IRF, not the different objects that are traveling at different speeds according to that IRF.

 

[Tiago]

To repeat, the speed of everything is measured (or specified) against the IRF that you select when you specify your problem and in that IRF, light travels at c. And the ratios of time are relative to the IRF, not the different objects that are traveling at different speeds according to that IRF.

Ok, but what do we mean when we say that Earth is travelling at 10% the speed of light? How do we even measure that? Earth is travelling at different speeds according to different IRF's, right?

 

[ghwellsjr]

Ok, but what do we mean when we say that Earth is travelling at 10% the speed of light? How do we even measure that? Earth is travelling at different speeds according to different IRF's, right?

The speed of light is just a number. It used to be measured but now it has a defined value. When you say that something is traveling at 10%c, you just mean 10% of that defined value.

If you want to say that the earth is traveling at 10%c according to some IRF, you don't have to measure anything. You are setting up a scenario any way you want.

And yes, you can have the earth traveling at any speed (short of c) in different IRF's. The easiest way to do this is start with an IRF in which earth is at rest and then use the Lorentz Transformation to get to another IRF in which the earth is traveling at some other speed.

 

[pervect]

Ok, but what do we mean when we say that Earth is travelling at 10% the speed of light? How do we even measure that? Earth is travelling at different speeds according to different IRF's, right?

The whole point is that it doesn't mean anything to say "the Earth is travelling at 10% of the speed of light". You keep asking the question, as if you thought it had meaning, or might have meaning.

It would be meaningful to say "The Earth is travelling at 10% of the speed of light relative to some specified object or frame". But you need to specify the object or frame you are measuring the speed relative to for the speed to have any meaning.

You keep asking the same question again, and we keep trying to give the same answers in different ways. Apparently there is some issue, because you keep asking the question over and over again, but I don't know what the issue is :(. I can only hope that this time you read the answer and feel satisfied with it.

 

[Tiago]

The whole point is that it doesn't mean anything to say "the Earth is travelling at 10% of the speed of light". You keep asking the question, as if you thought it had meaning, or might have meaning.

It would be meaningful to say "The Earth is travelling at 10% of the speed of light relative to some specified object or frame". But you need to specify the object or frame you are measuring the speed relative to for the speed to have any meaning.

You keep asking the same question again, and we keep trying to give the same answers in different ways. Apparently there is some issue, because you keep asking the question over and over again, but I don't know what the issue is :(. I can only hope that this time you read the answer and feel satisfied with it.

Don't worry, it's probably me that's not explaining myself in the best way. My point was, if the Earth is travelling at different speeds according to different IRF's, it also means that it's travelling at different % of c. According to the Sun it might be travelling at 10% the speed of light, according to jupiter it might be at 12%c, and so on. So when we say that our rocket is travelling at 99%c, it also means that it can travel at 99%c according to the Earth, but according to the Sun it might travelling at 80%c. And this should mean that we're "travelling in time" according to Earth, but not according to the Sun, right? (cause 80% is not significant) Hope I got this right, but please don't worry if I didn't :) I really thank everyone's effort in sharing their knowledge to educate people like me who don't have the proper basics in physics but love the area and are fascinated by it. Wish I could go back and take a course in physics, cause there are things that are easier to learn with teachers than just reading from wiki articles :)

 

[Dale]

So when we say that our rocket is travelling at 99%c, it also means that it can travel at 99%c according to the Earth, but according to the Sun it might travelling at 80%c. And this should mean that we're "travelling in time" according to Earth, but not according to the Sun, right?

Essentially this is correct. Time dilation is not an absolute thing where we say that clock A is time dilated and clock B is not. Time dilation is relative so clock A is time dilated in clock B's frame and clock B is time dilated in clock A's frame, and there are other frames where both are time dilated to greater or lesser degrees.

However, despite that, if A and B meet at some event and start their clocks, then separate and later reunite to compare their clocks, then every reference frame will agree on the numbers obtained at the final comparison.

 

[ghwellsjr]

Don't worry, it's probably me that's not explaining myself in the best way. My point was, if the Earth is travelling at different speeds according to different IRF's, it also means that it's travelling at different % of c.

Yes, that's true but the fact that you are stating this makes me wonder if you really understand what it means. Specifying a speed as a percentage of c does not imply anything about an IRF. It's just a conversion factor. We could have also specified 10%c as 29979.2458 kilometers per second which has no reference to the speed of light.

According to the Sun it might be travelling at 10% the speed of light, according to jupiter it might be at 12%c, and so on.

If the earth is traveling at 10%c according to the sun, then the sun is traveling at 10%c in the opposite direction according to the earth, correct? I still don't know why you want to include the sun or Jupiter in a scenario that is fundamentally about a rocket taking a trip at some speed with respect to the earth.

So when we say that our rocket is travelling at 99%c, it also means that it can travel at 99%c according to the Earth,

No, it doesn't mean that unless you specifically say so. When you set up a scenario, it is your responsibility to specify all the details. If you want the rocket to travel at 99%c with respect to the earth, then you have to say so. You can't just say that it is traveling at 99%c and leave it up to us to guess that you meant with respect to the earth.

but according to the Sun it might travelling at 80%c.

Even if you meant that the rocket is traveling at 99%c with respect to the earth and the sun is traveling at 10%c with respect to the earth, you can't just say that the rocket is traveling at 80%c (or some other speed) according to the sun. The problem is that since the rocket spends the first part of its time traveling away from the sun (and the earth) and the last part of its time traveling back towards the sun (and the earth), there has to be at least two different speeds that the rocket is traveling according to the sun. The first speed will be slightly less than 99%c and the last speed will be slightly more than 99%c. You have to use the velocity addition formula to determine what these speeds are. I'll show you how to do that later.

And this should mean that we're "travelling in time" according to Earth, but not according to the Sun, right?

No, that's not right. In fact, the difference between the amount of aging that goes on during the trip for the earth and the sun is only 10%. I'll show that later also.

(cause 80% is not significant) Hope I got this right, but please don't worry if I didn't :) I really thank everyone's effort in sharing their knowledge to educate people like me who don't have the proper basics in physics but love the area and are fascinated by it. Wish I could go back and take a course in physics, cause there are things that are easier to learn with teachers than just reading from wiki articles :)

Let me show you some spacetime diagrams to illustrate the concepts that you have been raising in this thread. We'll start with the rest frame of the earth and with the sun traveling at 10%c. The rocket travels at 99%c for 5 years, then turns around for another 5 years to get back to earth. The dots mark off one-year increments of time for each object:

As you can see, the earth has aged 71 years compared to 10 years on the rocket when they meet. But the sun has aged 64 years by the time it meets up with the rocket which is not the huge difference you expected. Note that the Time Dilation of the rocket is the same during both halves of its trip according to the IRF in which the earth is at rest.

Now we can use the Lorentz Transformation process to see what this scenario looks like in the rest frame of the sun:

Although the Lorentz Transformation automatically determines all the details of all the objects, it might be a little hard to see the actual speeds of the rocket during both parts of its trip. We can use the velocity addition formula for this purpose. For velocities that are fractions of the speed of light where c=1, it looks like this:

s = (v+u)/(1+vu)

For the situation where the rocket is traveling in the same direction as the sun, we have to set v = 0.99 and u = -0.1:

s = (v+u)/(1+vu) = (0.99-0.1)/(1+(0.99)(-0.1)) = (0.89)/(1-0.099) = (0.89)/(0.901) = 0.98779

And for the return part of the trip, we set v = 0.99 and u = 0.1:

s = (v+u)/(1+vu) = (0.99+0.1)/(1+(0.99)(0.1)) = (1.09)/(1+0.099) = (1.09)/(1.099) = 0.99181

As you can see, in the IRF of the sun, there is very little difference between the speeds of the rocket in the two directions. It may be difficult to see the difference in their Time Dilations but it is just enough to make the Proper Times as marked by the dots come out the same in this IRF as it did in the original IRF, that is, the respective agings of the objects when they meet are identical.

Just for the fun of it, I have made another pair of diagrams for a different scenario where instead of the sun traveling at 10%c with respect to the earth, I'm having Saturn travel at 66%c with respect to the earth to make the differences between the red object and the other objects more apparent:

The relationships between the rocket and the earth are the same as in your scenario but there is a big difference between Saturn and the sun. Saturn ages by only 32 years when it meets up with the rocket. Note that a big part of this difference is due to the larger Time Dilation of Saturn compared to the sun. Remember, Time Dilation increases with speed.

But now we can transform to the IRF of Saturn:

Now you can easily see a difference in the Time Dilations of the rocket during each part of its trip.

Any questions?