What is causing time dilation: Speed or acceleration?

[SpiderET]

In case when we have accelerating spaceship without any influence of gravity, what is causing the time dilation? Is it primary caused by the speed of the spaceship or it is caused by acceleration leading to higher speed? What is the primary cause of time dilation?

 

[Nugatory]

In case when we have accelerating spaceship without any influence of gravity, what is causing the time dilation? Is it primary caused by the speed of the spaceship or it is caused by acceleration leading to higher speed? What is the primary cause of time dilation?

I'm not sure that there's a good answer to the question "what causes time dilation?", just as there's no really good answer to the question "What causes the sum of two sides of a triangle to always be longer than the third side". In both cases, it's just the way the geometry of the universe we live in works.
With that said... time dilation will be observed any time that different speeds are involved so we might say it's the speed that matters. But of course accelerations (by definition) cause changes in speed, so it's not surprising to observe time dilation effects along with accelerations. In this case, the spaceship is moving relative to some observer back on earth, so the earthbound observer will say that the spaceship clock is running slow - but of course from the spaceship observer's point of view, he is at rest and the Earth is moving away from him, so it's the Earth clock that is runnoing slow. They're both right, and the acceleration just makes the calculations harder to do.

Your best bet will be to start with the Lorentz transformations (google for it, and keep looking until you find an easy derivation - you can do it all with high school algebra), see how time dilation is calculated from these transformations.

 

[SpiderET]

I'm not sure that there's a good answer to the question "what causes time dilation?", just as there's no really good answer to the question "What causes the sum of two sides of a triangle to always be longer than the third side". In both cases, it's just the way the geometry of the universe we live in works.
With that said... time dilation will be observed any time that different speeds are involved so we might say it's the speed that matters. But of course accelerations (by definition) cause changes in speed, so it's not surprising to observe time dilation effects along with accelerations. In this case, the spaceship is moving relative to some observer back on earth, so the earthbound observer will say that the spaceship clock is running slow - but of course from the spaceship observer's point of view, he is at rest and the Earth is moving away from him, so it's the Earth clock that is runnoing slow. They're both right, and the acceleration just makes the calculations harder to do.

Your best bet will be to start with the Lorentz transformations (google for it, and keep looking until you find an easy derivation - you can do it all with high school algebra), see how time dilation is calculated from these transformations.

Im familiar with Lorentz transformations, but it is not clear from it, what is the primary cause. Because you have mass increasing as the speed increases, so you need bigger force to get acceleration and it is possible that the time dilation happens exactly in moment when this force is producing time dilation (and contraction). Or maybe is the time dilation happening in the moment when the speed is reached and then we could use the Lorentz transformation of time dilation based on speed?

It seems to me the the proper and short answer would be that there is no clear mainstream explanation why is speed of light constant and consequently we don't know exactly what is the primary cause for time dilation. We have equotations which describe how things change depending on speed, but we don't know why exactly is this happening. But maybe I am wrong and there is some explanation of primary cause.

 

[A.T.]

or it is caused by acceleration

The instantaneous clock rate doesn't depend on the instantaneous acceleration:
http://en.wikipedia.org/wiki/Clock_hypothesis
But the accumulated proper time between two events does depend on the acceleration profile.

By analogy, even if the amount of steering wouldn't affect the instantaneous speed of a car, it would still affect the total distance traveled between two points.

 

[Chestermiller]

As Nugatory implied, time dilation is in essence nothing more than a consequence of the unique non-Euclidean geometry of 4D spacetime. In other words, it's strictly geometric.

Chet

 

[pervect]

In case when we have accelerating spaceship without any influence of gravity, what is causing the time dilation? Is it primary caused by the speed of the spaceship or it is caused by acceleration leading to higher speed? What is the primary cause of time dilation?

In the inertial reference frames of special relativity, time dilation is dependent on speed, and not at all on acceleration. I would strongly recommend not worrying about accelerated frames of reference until you've mastered inertial frames , but I feel I do have to mention that the answer to your question does depend on your choice of reference frames. The answer would be different in an accelerating frame of reference, because the value you compute for time dilation depends on the procedure you use to compare distant clocks, your notion of simultaneity. And the notion of simultaneity depends on which frame of reference you use - hopefully you've heard about the relativity of simultaneity by now. If you haven't heard of the relativity of simultaneity before, I'd suggest reading https://www.physicsforums.com/threa...on-implies-relativity-of-simultaneity.805210/ which explains why symmetrical time dilation logically requires that simultaneity be relative.

 

[Nugatory]

Because you have mass increasing as the speed increases, so you need bigger force to get acceleration and it is possible that the time dilation happens exactly in moment when this force is producing time dilation (and contraction). Or maybe is the time dilation happening in the moment when the speed is reached and then we could use the Lorentz transformation of time dilation based on speed?

No, that's not how it works. If anything, relativistic mass increase is a consequence of time dilation and length contraction and not the other way around. However, the entire concept of relativistic mass has been largely abandoned because it's a very unsatisfactory base for building further understanding; we have an FAQ at https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-it-is-not-used-much.796527/

It seems to me the the proper and short answer would be that there is no clear mainstream explanation why is speed of light constant

If you want something clearer and more satisfying than "that's the way the universe we live in works", you're right. That's why Einstein chose to treat the constant speed of light as a postulate.
On the other hand, nature did give us a really big hint that it should be that way, because we can calculate the speed of light from Maxwell's equations of electricity and magnetism, and there's nothing in those equations about the speed of the observer. Thus the only way that the speed of light would not be the same for all observers regardless of their relative speed would be if the different observers had different laws of E&M (absurd, and also contradicted by centuries of experiments as the state of motion of earthbound physics labs changes with the seasons) or if some other physical phenomenon was also involved. Much of physics between 1861 (Maxwell) and 1905 (Special Relativity) was devoted to identifying that hypothetical other physical phenomenon, which went by the name "luminiferous ether", until Einstein showed that we didn't need it.

and consequently we don't know exactly what is the primary cause for time dilation.

And I think that's pretty much exactly what I said in the very first sentence of my last response

Physics is a lot better at explaining how the universe works then at explaining why it works that way. The answer to just about any "what causes" question leads to either another "but then what causes that?" question, and the regression terminates only when we get to something like conservation of momentum that we're all happy with, so will accept the "because that's the way the universe we live in works" non-answer.

 

[SpiderET]

The instantaneous clock rate doesn't depend on the instantaneous acceleration:
http://en.wikipedia.org/wiki/Clock_hypothesis
But the accumulated proper time between two events does depend on the acceleration profile.

By analogy, even if the amount of steering wouldn't affect the instantaneous speed of a car, it would still affect the total distance traveled between two points.

Thanks for good hint.
Citing from article regarding Clock hypothesis:
The clock postulate is not meant to be obvious, and it can't be proved. It's not merely some kind of trivial result obtained by writing special relativity using non-cartesian coordinates. Rather, it's a statement about the physical world. But we don't know if it's true; it's just a postulate. For instance, we can't magically verify it by noting that the Lorentz transform is only a function of speed, because the Lorentz transform is something that's built before the clock postulate enters the picture. Also, we cannot simply maintain that an acceleration can be treated as a sequence of constant velocities that each exist only for an infinitesimal time interval, for the simple reason that an accelerating body (away from gravity) feels a force, while a constant-velocity body does not. Although the clock postulate does speak in terms of constant velocities and infinitesimal time intervals, there's no a priori reason why that should be meaningful or correct. It's just a postulate!
End of citate.

It seems to me, that Clock hypothesis can't be proved. So if somebody says, no, its not about speed it is only accelaration, then this would be also something which can't be proved in current experiments. So all we have are some logical assumptions.

 

[wabbit]

Im familiar with Lorentz transformations, but it is not clear from it, what is the primary cause. Because you have mass increasing as the speed increases, so you need bigger force to get acceleration and it is possible that the time dilation happens exactly in moment when this force is producing time dilation (and contraction). Or maybe is the time dilation happening in the moment when the speed is reached and then we could use the Lorentz transformation of time dilation based on speed?

It seems to me the the proper and short answer would be that there is no clear mainstream explanation why is speed of light constant and consequently we don't know exactly what is the primary cause for time dilation. We have equotations which describe how things change depending on speed, but we don't know why exactly is this happening. But maybe I am wrong and there is some explanation of primary cause.

I don't think you'll find an answer in physics, for the reason that physics (or science) is not concerned with ultimate causes but with observable phenomena. Time dilation expresses consistency relations between different observers in relative motion measuring their respective clock rates in a world where signaling speed is limited. As such, as far as I can tell it doesn't require a "deeper" explanation.
We could say that "the finite speed of light causes time dilation", but that is just one perspective, useful perhaps if you want to compare this world to one with infinite light speed (where there is no time dilation) - it is not the identification of a "true" or "essential" cause.

 

[A.T.]

Clock hypothesis can't be proved

Physical theories in general cannot be proved. They can only be disproved.

 

[SpiderET]

Physical theories in general cannot be proved. They can only be disproved.

So when we apply this to discussed topic, can we disprove, that time dilation is caused by acceleration?

 

[SpiderET]

No, that's not how it works. If anything, relativistic mass increase is a consequence of time dilation and length contraction and not the other way around. However, the entire concept of relativistic mass has been largely abandoned because it's a very unsatisfactory base for building further understanding; we have an FAQ at https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-it-is-not-used-much.796527/

I know what you mean, but I can rephrase it without using mass at all. So we have spaceship accelerating at steady rate for example one g. But at 0,8 c this ship needs less pushing force to keep the steady acceleration than at 0,9 c. So as speed increases, bigger force is need to keep the acceleration. So maybe as this bigger and bigger force is acting, maybe we have bigger and bigger time dilation. If this would be the case, then the time dilation would be linked to acceleration and not speed.

 

[1977ub]

So when we apply this to discussed topic, can we disprove, that time dilation is caused by acceleration?

For someone outside the accelerating frame, there is found no more dilation than one would calculate by integrating all of the infinitesimal dilations related to range of velocities.

Of course if one is accelerating, one finds no local time dilation.

 

[PeterDonis]

at 0,8 c this ship needs less pushing force to keep the steady acceleration than at 0,9 c

Not necessarily; it depends. A ship whose crew experiences constant proper acceleration requires only constant force relative to the ship. When you transform this force into a fixed inertial frame, yes, the transformed "force" increases; but if the ship is exerting its own force, no direct observable actually depends on the transformed "force"--everything depends only on the force relative to the ship, which is constant.

If, OTOH, the ship is being pushed by an external force--say, for example, it is being pushed by a huge laser which remains fixed at the point of origin--then the force that must be supplied by the external source does increase as the ship's speed increases (relative to the point of origin), if the force felt by the ship and its crew remains constant.

However, note that in both of the above cases, the time dilation of the ship relative to the point of origin is the same. So I'm not sure how you could link time dilation to force. And in any case, the time dilation of the ship in this scenario, relative to the point of origin, would be the same as the time dilation of a ship in free fall that was momentarily at rest relative to the accelerated ship; this could be verified by, for example, observing that the Doppler shift of light signals emitted from both ships at that instant was the same, and that they were both the same distance away at the instant the light was emitted, so the correction for light travel time (which is how you go from observer Doppler shift to calculated time dilation) is the same for both.

Finally, as far as experiments go, all experiments have shown that time dilation depends only on speed, not on acceleration. So trying to construct a theory in which time dilation would depend on acceleration seems pointless, since any such theory is already falsified by experiment.

 

[A.T.]

can we disprove, that time dilation is caused by acceleration?

This is not a physical theory. Physical theories are quantitative.

 

[PeterDonis]

it can't be proved.

I assume you are quoting from this Usenet Physics FAQ article:

http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

Note that, even though the article says the clock postulate "can't be proved", further on it talks about ways that it can be tested (and, as I noted in my previous post, every time it has been tested it has been found to hold). Repeated tests don't "prove" the postulate; but they do give us a very high level of confidence that it is correct, which is as good as it gets in science.

 

[SpiderET]

Thanks all for input, it seems to me, that with some reasonable probability we can assume, that time dilation is caused by speed, not by acceleration.

 

[ghwellsjr]

I know what you mean, but I can rephrase it without using mass at all. So we have spaceship accelerating at steady rate for example one g. But at 0,8 c this ship needs less pushing force to keep the steady acceleration than at 0,9 c. So as speed increases, bigger force is need to keep the acceleration. So maybe as this bigger and bigger force is acting, maybe we have bigger and bigger time dilation. If this would be the case, then the time dilation would be linked to acceleration and not speed.

In your scenario, the spaceship starts out with no Time Dilation (gamma equals 1) and ends up with a Time Dilation factor of 2.3.

But if you transform your scenario to one in which it starts out at -90% c (gamma equals 2.3) and ends up at rest (gamma equals 1), then your argument falls apart.

You can also transform to an IRF in which the spaceship starts out at some other negative speed and ends up at the same positive speed so that it has the same Time Dilation at the beginning and the end.

Or you can consider an acceleration that is applied in such a way that the body does not change speed but rather goes around in circles in which case the Time Dilation is constant.

Time Dilation is a coordinate effect of a particular IRF. Transforming to a different IRF changes the Time Dilation without changing the Proper Acceleration of the object. In fact, in the example where the object is accelerated in a circle, we can transform to an IRF in which the Time Dilation factor fluctuates from 1 to a maximum value and then back to 1 but there is no corresponding fluctuation in the Proper Acceleration.

And if that isn't enough to persuade you, consider an object at rest in an IRF where it has no Time Dilation (gamma equals 1) and then transform to an IRF that is moving at 90% c in some direction. Now the Time Dilation factor is 2.3 and there was no acceleration applied at all.

 

[ghwellsjr]

Thanks all for input, it seems to me, that with some reasonable probability we can assume, that time dilation is caused by speed, not by acceleration.

That's not even a good way to say it. If you start with an clock at rest in an IRF and then transform to an IRF where the clock has some speed, would you say that there was a "cause" of the speed? It's just a mathematical exercise having no physical "cause" at all. And if the speed has no physical "cause" then the Time Dilation doesn't either. It's just a mathematical exercise. The best you can do is say that the Principle of Relativity (the first of Einstein's postulates) is the "cause" because it asserts that there is no physical difference between inertial clocks and that combined with his second postulate leads to the mathematical concept of Time Dilation.

 

[Dale]

The clock postulate is not meant to be obvious, and it can't be proved. It's not merely some kind of trivial result obtained by writing special relativity using non-cartesian coordinates. Rather, it's a statement about the physical world. But we don't know if it's true; it's just a postulate.

We know that it is "true" as much as we can know anything in science. It has been experimentally verified for accelerations up to approximately 10^19 m/s^2.

 

[nitsuj]

Thanks all for input, it seems to me, that with some reasonable probability we can assume, that time dilation is caused by speed, not by acceleration.

What about gravitational time dilation?

Maybe stick with Chestermiller's reply... "...It's strictly geometric."

 

[stevendaryl]

What about gravitational time dilation?

Maybe stick with Chestermiller's reply... "...It's strictly geometric."

Some people find the geometric view kind of mysterious, but most of the apparent paradoxes of relativity are trivialities in the geometric view. Or at least, not that surprising.

If you ask about time dilation in terms of what causes it, it seems pretty mysterious: Alice sitting on Earth aged 20 years between 2015 and 2035. Bob traveling at relativistic speed from Earth to Alpha Centauri (or wherever) and back aged only 10 years. What made him age slower? Was it gravitational time dilation, velocity, or what?

But in the geometric view, both Alice and Bob travel from point A (Earth at the year 2015--a point in spacetime, not just in space) to point B (Earth at the year 2035). Because they took different routes to get between A and B, they took different amounts of time (proper time, the time shown on their watches) to make the trip. This is no more mysterious in the geometric view than the fact that two different people traveled from New York City to Chicago, and one took 10 hours while the other took 15 hours.

The physically meaningful notion of time in SR is proper time (often denoted by \tau). That's the time that is relevant for how much you age, how many times a clock ticks, etc. There is another notion of time, coordinate time, (often denoted by t) which serves as just a label for points in spacetime. Rather than thinking of the ratio

\frac{\delta \tau}{\delta t} < 1

as an indication that a clock has somehow been slowed down, you flip it over:

\frac{\delta t}{\delta \tau} > 1

to get a "velocity" measured relative to coordinate time, in the same way that \frac{\delta x}{\delta \tau} is a velocity measured relative to the x-coordinate. That different travelers have different t-components to their velocities is no more surprising than that different travelers have different x-components to their velocities.

 

[nitsuj]

Because they took different routes to get between A and B, they took different amounts of time (proper time, the time shown on their watches) to make the trip.

This is no more mysterious in the geometric view than the fact that two different people traveled from New York City to Chicago, and one took 10 hours while the other took 15 hours.

I like the "path distance" explanation, visually it's the easy to grasp and graphically is the literal interpretation. Also the analogy to point of view (such as rotating of a pencil changes it's length) is a good one.

(physics measures observables, never have I seen it as an axiom, but physical causes preceed effects. We live in a continuum. When these observations of physical happenings are made the casual structure of physics remains intact, spacetime doesn't "mess" with this ordering, that perspective makes sense to me and answers the "why" question for time dilation and the equivelant length contraction)

 

[wabbit]

@stevendaryl, Nice explanation. Simple and deep at the same time (no pun intended)

 

[maline]

To rephrase what stevendaryl said: clocks never really run slower. They accurately measure the proper time between events they are at, which is anyway the only physically meaningful (i.e. frame invariant) type of time. In the twin paradox scenario, the traveling twin is younger because he has "taken a shortcut" through spacetime- there truly is less (proper) time along his path. So "time dilation" may be a misleading term.
That said, suppose we do choose to discuss coordinate time, which is what you need in order to say "my friend is thinking of me right now". To do this, you must choose a frame that labels events with numbers for position & time. The simplest frames are those in which coordinate velocity is constant for objects with no forces acting on them, in regions where there is no gravity. "Time dilation" means that a frame that labels a clock as "moving" will also label the ticks of that clock as more than one second apart. In that sense, time dilation can be called "an effect of the clock's motion". Acceleration plays no role here.
The reason acceleration comes up is that it answers the question "Why can't we discuss a frame in which the traveler is never moving, which will label times to agree with the traveler's clock, and using such a frame, predict that the Earth twin should experience less time?" The answer is that to make such a prediction we need to assume our frame is inertial, but it's not: the Earth changed its "velocity" in this frame without any force acting on it. What happens according to such frames follows different, more complicated, rules.
Another reason to mention acceleration is that it provides a good rule of thumb: since the longest possible (timelike proper) path between two spacetime points is a straight line, therefore if one twin turned on rocket engines and the other didn't, the one who did is also taking the shorter path.

 

[PeterDonis]

Another reason to mention acceleration is that it provides a good rule of thumb

For flat spacetime, yes. But this rule of thumb does not generalize well to curved spacetime. For example, an object "hovering" a hundred miles above the Earth's surface is accelerated, while an object in a circular orbit at the same altitude is in free fall; but the second object has a shorter path through spacetime (less elapsed proper time) between two successive events where they meet.

 

[maline]

As for "why is the speed of light the same in all frames?", one answer is that light can only move at that speed, because light is made of electric & magnetic fields that produce each other as specified by Maxwell's equations. This was, I think, how Einstein originally thought of it. However, this now seems a bit backwards: the way electric &magnetic fields interact is "determined" by the need for Lorentz invariance, so the result that EM waves move on null paths should not surprise anyone.

 

[harrylin]

[..]
It seems to me, that Clock hypothesis can't be proved. So if somebody says, no, its not about speed it is only accelaration, then this would be also something which can't be proved in current experiments. So all we have are some logical assumptions.

The clock hypothesis is not a postulate at all, and is easy to disprove by means of rotation experiments with different radii: you can test the effect of the same speed but much higher acceleration, and compare the results with each other and with predictions. Experiments with certain atomic clocks showed that those are not sensitive to acceleration. Some mechanical clocks will certainly be sensitive to acceleration, and that has nothing to do with relativity in particular. The clock hypothesis merely assumes that clocks are used that are insensitive to acceleration forces.

 

[maline]

The clock hypothesis is not a postulate at all, and is easy to disprove by means of rotation experiments with different radii: you can test the effect of the same speed but much higher acceleration, and compare the results with each other and with predictions. Experiments with certain atomic clocks showed that those are not sensitive to acceleration. Some mechanical clocks will certainly be sensitive to acceleration, and that has nothing to do with relativity in particular. The clock hypothesis merely assumes that clocks are used that are insensitive to acceleration forces.

Not so fast!
http://iopscience.iop.org/1402-4896/85/6/065702/article
They are testing a hypothesis that for very high accelerations, there is an additional time-dilation effect. Friedman claims (at a speech I attended) to have some positive results, but nothing conclusive as of yet.
Of course, this demonstrates your point that the clock hypothesis is testable. Even if Friedman is right, it is clear that any acceleration within "normal" range has no detectable effect.

 

[harrylin]

Not so fast!
http://iopscience.iop.org/1402-4896/85/6/065702/article
They are testing a hypothesis that for very high accelerations, there is an additional time-dilation effect. Friedman claims (at a speech I attended) to have some positive results, but nothing conclusive as of yet.
Of course, this demonstrates your point that the clock hypothesis is testable. Even if Friedman is right, it is clear that any acceleration within "normal" range has no detectable effect.

Yes in my earlier comment I was thinking of mechanical clocks, and similarly atomic clocks could suffer from radiation effects or other established effects from strong acceleration. Already the usual derivation of the accelerated electron therefore specifies slow acceleration. Such effects are distinguishable from the Lorentz time dilation and may be predictable with classical physics.