Wouldn’t time dilation govern a speed limit?

[ynot]

WARNING - written by a layman.

As well as time dilation slowing the rate that clocks run and things age etc, wouldn’t it also slow the rate of the very speed that was causing the time dilation? Isn’t time dilation effectively speed dilation? In other words, the faster you go the slower you go, and if you could ever reach the speed of light you would stop completely as time stops. As you were constantly increasing your speed to reach the speed of light however, wouldn’t time dilation reduce your ability to constantly increasing your speed, and at a certain point of speed/time dilation couldn’t you only travel at a constant speed? In other words, wouldn’t the maximum speed that a thing could travel be governed by the amount of time dilation that the speed creates? If so, could time dilation be what governs the speed of light?

 

[Fredrik]

As well as time dilation slowing the rate that clocks run and things age etc, wouldn’t it also slow the rate of the very speed that was causing the time dilation?

I'm having a hard time making sense of the question. Your speed isn't the cause of time dilation, it's just a number that describes how two coordinate systems are different.

Are you asking if your speed is different in different coordinate systems? That's probably not what you meant because the answer is too obvious. If your position is stated relative to a fixed point on the ground, then your speed is obviously going to be different than if your position is stated relative to a moving train.

 

[Gate2501]

I'm pretty sure that dilation is a measurement effect between two observers moving at different speeds *relative* to one another.

I don't think that it is some physical property that actually happens to *you* as you speed up. As far as you are concerned nothing is happening at all in terms of dilation unless you try to take a measurement of someone else moving differently than you.

Right?

 

[ynot]

I'm having a hard time making sense of the question. Your speed isn't the cause of time dilation, it's just a number that describes how two coordinate systems are different.

Are you asking if your speed is different in different coordinate systems? That's probably not what you meant because the answer is too obvious. If your position is stated relative to a fixed point on the ground, then your speed is obviously going to be different than if your position is stated relative to a moving train.

Isn’t it the case that if B travels away from A, B will become time dilated relative to A, and the degree of this dilation is related to the speed that B is travelling compared to A? The faster the speed the greater the dilation, and if B underwent a constantly increasing acceleration to reach the speed of light (compared to A), B’s time would stop compared to A’s, and B would therefore stop moving compared to A. Before this happened however, B would go through a process of slowing down compared to A, and at a particular point the slowing down would mean that B would be unable to sustain the increasing acceleration. This would mean that time dilation has governed the maximum speed that B is able to travel compared to A to a speed that is less than the speed of light.

 

[PixyMisa]

Isn’t it the case that if B travels away from A, B will become time dilated relative to A, and the degree of this dilation is related to the speed that B is travelling compared to A?

Yes.

The faster the speed the greater the dilation, and if B underwent a constantly increasing acceleration to reach the speed of light (compared to A), B’s time would stop compared to A’s

Well, B can't reach the speed of light, but it can approach it as closely as you want. So time on B would appear to be passing arbitrarily slowly.

and B would therefore stop moving compared to A.

Nope!

B is moving at close to the speed of light relative to A. That's stipulated.

From the point of view of A, B is moving at close to the speed of light, and experiencing drastically slower time.

From the point of view of B, B is moving much faster than the speed of light, and experiencing normal time.

If B is moving fast enough that time is dilated by a factor of 100 relative to A, B experiences this as moving 100 times faster than light.

Before this happened however, B would go through a process of slowing down compared to A, and at a particular point the slowing down would mean that B would be unable to sustain the increasing acceleration. This would mean that time dilation has governed the maximum speed that B is able to travel compared to A to a speed that is less than the speed of light.

Time dilation means that to B, the trip takes far less time than it appears to take to a stationary observer (A); to put it another way, to B it appears that they have exceeded the speed of light - but only as far as their trip time is concerned. The can still communicate with A using light, because relative to A they are still moving below light speed.

 

[Fredrik]

Isn’t it the case that if B travels away from A, B will become time dilated relative to A, and the degree of this dilation is related to the speed that B is travelling compared to A? The faster the speed the greater the dilation, and if B underwent a constantly increasing acceleration to reach the speed of light (compared to A), B’s time would stop compared to A’s, and B would therefore stop moving compared to A. Before this happened however, B would go through a process of slowing down compared to A, and at a particular point the slowing down would mean that B would be unable to sustain the increasing acceleration. This would mean that time dilation has governed the maximum speed that B is able to travel compared to A to a speed that is less than the speed of light.

Pixy Misa answered all your questions, so I'm just going to point out the flaw in your logic:

What you're saying is that since

"greater relative speed" = "more time dilation"​

and

"more time dilation" = "less relative speed" (which is definitely not true)​

we must have

"greater relative speed" = "less relative speed"​

Your conclusion contradicts itself. It seems to me that you're confusing the rate at which a clock is running with the speed with which it is moving. You start out by correctly treating the former as a function of the latter. Then you treat them as if they are the same thing, which they are not, and the result is nonsense.

 

[Fredrik]

From the point of view of B, B is moving much faster than the speed of light, and experiencing normal time.

Don't you mean "...B is not moving at all, and..."? You're always stationary in your own frame.

If B is moving fast enough that time is dilated by a factor of 100 relative to A, B experiences this as moving 100 times faster than light.

Ah, I see what you have in mind. The distance to any object in B's path is Lorentz contracted to 1/100 of what it is in A's frame. When they stop, they will be able to say that they traveled e.g. 100 light-years in 1 year of their own time, just as if they had traveled 100 times the speed of light.

 

[ynot]

It seems to me that you're confusing the rate at which a clock is running with the speed with which it is moving.

This is the crux of my question. I would have thought that if time dilation effects the relative speed that a clock runs at, it would also effect the relative speed at which it’s moving. How can it be that dilation effects the speed that a clock runs (which is the same as saying the speed that it moves), but it doesn’t affect the speed at which it’s moving?

ETA - This is all relative to a “stationary” observer of course.

 

[PixyMisa]

Don't you mean "...B is not moving at all, and..."? You're always stationary in your own frame.

Well, yeah, but they know that they've accelerated, so they know that they really are in motion even though the maths works out the same either way.

Ah, I see what you have in mind. The distance to any object in B's path is Lorentz contracted to 1/100 of what it is in A's frame. When they stop, they will be able to say that they traveled e.g. 100 light-years in 1 year of their own time, just as if they had traveled 100 times the speed of light.

Exactly. Of course, that's contradicted by the fact that they were able to stay in radio contact with A - albeit massively red-shifted.

 

[PixyMisa]

This is the crux of my question. I would have thought that if time dilation effects the relative speed that a clock runs at, it would also effect the relative speed at which it’s moving. How can it be that dilation effects the speed that a clock runs (which is the same as saying the speed that it moves), but it doesn’t affect the speed at which it’s moving?

ETA - This is all relative to a “stationary” observer of course.

Relative to a stationary observer, the clock on the spaceship slows down, and the speed is unaffected.

Relative to an observer on the spaceship, the clock is unaffected, and the speed increases. Not decreases, increases. Or to look at it another way, as Fredrik said, distances contract along the path of travel of the spaceship in the same proportion as time dilation.

Either way, you can (for example) cover 100 light-years of distance in 1 year of ship time.

Indeed, thanks to time dilation, you can cross the galaxy at 1G acceleration in a human lifetime.

 

[Fredrik]

This is the crux of my question. I would have thought that if time dilation effects the relative speed that a clock runs at, it would also effect the relative speed at which it’s moving. How can it be that dilation effects the speed that a clock runs (which is the same as saying the speed that it moves), but it doesn’t affect the speed at which it’s moving?

I wouldn't say that time dilation affects a clock's ticking rate. I would say that the speed of the clock relative to us affects it's ticking rate, and I would call that effect time dilation.

The formula that tells us the relationship between the clock's speed and its ticking rate is very simple. You just multiply its ticking rate at rest (1 tick per second) by sqrt(1-v²/c²) to get its ticking rate in motion (e.g. 0.8 ticks per second when v=0.6c).

What you're saying is that this formula implies the opposite of what it's actually saying. It's saying that the ticking rate is slower when the speed is faster. So how could it imply that a slower ticking rate leads to a slower speed?

 

[ynot]

Relative to a stationary observer, the clock on the spaceship slows down, and the speed is unaffected.

Can you explain why you say the speed is unaffected?

Here is my explanation of why I think it would be affected . . .

As an analogy - Comic character The Flash is running at half the speed of sound and as a result he is being time-dilated. This means his legs are moving slower and therefore he is running slower. The faster The Flash runs the more time dilated the action of his legs become and the slower he runs. IF The Flash could run at the speed of light, he would be 100% time dilated and his legs would stop moving altogether.

In the “real” world - A spaceship is being accelerated by the thrust of a rocket. Time dilation slows the rate of the thrust and the spaceship is therefore accelerated at a slower speed. The faster the spaceship accelerates, the more the thrust is being time dilated, and the slower the spaceship accelerates.

It seems to me that a consequence of time dilation would be that “the faster you go the slower you go“. Also, all motion in the universe would be slower than it would have been without time dilation.

 

[ynot]

I wouldn't say that time dilation affects a clock's ticking rate. I would say that the speed of the clock relative to us affects it's ticking rate, and I would call that effect time dilation.

The formula that tells us the relationship between the clock's speed and its ticking rate is very simple. You just multiply its ticking rate at rest (1 tick per second) by sqrt(1-v²/c²) to get its ticking rate in motion (e.g. 0.8 ticks per second when v=0.6c).

What you're saying is that this formula implies the opposite of what it's actually saying. It's saying that the ticking rate is slower when the speed is faster. So how could it imply that a slower ticking rate leads to a slower speed?

I’m merely trying to understand what the consequences of time dilation would be, regardless of how bizarre the outcome. Time dilation isn’t my idea. What would the outcome of the formula be if you apply it to the action of the clock moving instead of running?

 

[Gate2501]

As an analogy - Comic character The Flash is running at half the speed of sound and as a result he is being time-dilated. This means his legs are moving slower and therefore he is running slower. The faster The Flash runs the more time dilated the action of his legs become and the slower he runs. IF The Flash could run at the speed of light, he would be 100% time dilated and his legs would stop moving altogether.

Here is your problem.

His legs would never move slower due to dilation. Time would pass more slowly for them relative to an observer not traveling so fast.

So his legs don't go any slower, but they would technically age slower than his torso.

 

[ynot]

Here is your problem.

His legs would never move slower due to dilation. Time would pass more slowly for them relative to an observer not traveling so fast.

So his legs don't go any slower, but they would technically age slower than his torso.

And exactly how does “Time would pass more slowly for them” not also mean that they would move more slowly relative to an observer not travelling so fast? Slower time = slower movement. I have the problem?

 

[Gate2501]

Yes, you have the problem. Slower relative time measurements do not equal slower movement.

To help you understand, lets say that the flash is running near the speed of light passing a nice old lady on a bench. As far as the flash is concerned, the old woman is EXTREMELY time dilated. As far as she is concerned, HE is extremely dilated. Neither of them can really be *right* about whose time is really dilated (unless one of them accelerated during the observations), because it is a RELATIVE quality.

 

[sol invictus]

And exactly how does “Time would pass more slowly for them” not also mean that they would move more slowly relative to an observer not travelling so fast? Slower time = slower movement. I have the problem?

Your idea is basically correct, but you're making a simple mistake. It is impossible for time dilation to reduce the speed to zero, because at zero speed there is no time dilation. What can happen is that as the speed increases, time dilation gets stronger and stronger, causing the speed to asymptote to a maximum - the speed of light.

The Flash example is a little tricky, since even in his own restframe his legs need to be moving at relativistic speeds to make it interesting. The rocket example is better. A rocket that accelerates at a constant rate (according to an observer on the rocket) will indeed accelerate more slowly with time according to a stationary observer. But accelerating more slowly does not equal decelerating! It just means the rocket's speed will approach c, but never get there.

Yes, you can think of the speed of light limit as a consequence of time and space dilation, but it's usually better to think of things the other way around.

 

[Spud1k]

Another key thing that has to be remembered is that regardless of time dilation, velocity remains constant unless it is influenced by something else. Let's take the rocket travelling at half the speed of light; without its thrusters running will keep its speed. When it turns its thrusters on, it speeds up. From its perspective, it speeds up as normal. To a stationary observer, its speed accellerates slower than it would otherwise, because the rocket's time is travelling slower.

If the rocket was travelling close to the speed of light, its time would progress so slowly that from the persepective of the outside observer, it would never accellerate enough to reach the speed of light. So in a way, time dilation does impose the speed-of-light limit, but as sol said, I think it's wrong to think of it as the reason behind it. The cool thing about special relativity is there is a whole bunch of different manifestations that slot in nicely alongside each other.

 

[ynot]

My question is not how or why time dilation happens. What I’m simply asking is - Does time dilation created by relative movement apply to the relative movement that creates it? I think it does and have given examples of why I do.

I have never said that the speed of light or 100% time dilation COULD be achieved. I have simply speculated WHAT IF it could. (let’s pretend). The fact that they can’t is not important to my question. What’s important are the effects of time dilation.

Forget the Flash analogy. The accelerating rocket is better as it represents an actual example. I’m suggesting that if a spaceship that accelerates away from me becomes time dilated (relative to me), then the thing that gives it the energy to accelerate (the thrust of the rocket) becomes time dilated (relative to me). This means (to me) that the speed of the thrust is slowed (relative to me) and consequently the acceleration is slowed (relative to me). If anyone disagrees with this please explain why non-mathematically.

 

[Reality Check]

My question is not how or why time dilation happens. What I’m simply asking is - Does time dilation created by relative movement apply to the relative movement that creates it? I think it does and have given examples of why I do.

I have never said that the speed of light or 100% time dilation COULD be achieved. I have simply speculated WHAT IF it could. (let’s pretend). The fact that they can’t is not important to my question. What’s important are the effects of time dilation.

Forget the Flash analogy. The accelerating rocket is better as it represents an actual example. I’m suggesting that if a spaceship that accelerates away from me becomes time dilated (relative to me), then the thing that gives it the energy to accelerate (the thrust of the rocket) becomes time dilated (relative to me). This means (to me) that the speed of the thrust is slowed (relative to me) and consequently the acceleration is slowed (relative to me). If anyone disagrees with this please explain why non-mathematically.

If we were talking about Special Relativity then:
According to an outside observer (you) everything that happens in an accelerated frame of reference (the accelerated rocket) is time dilated.
According to the rocket there is nothing unusual happening in its own frame of reference (but if it had an observer they would see you as being time dilated).

But you have an accelerating frame of reference here so that is General Relativity which is not my area of expertise. I suspect that you will actually measure the same acceleration, e.g. the rocket thrust is measured in mass/second. So you measure the mass that is output by the rocket in a certain period of time to get the rocket's acceleration. Time dilation means that the time you measure goes up by the gamma factor. But the mass you measure also goes up by the gamma factor. Dividing the 2 means that the acceleration does not change from your point of view.