Is Time Dilation Explained by Special Relativity, General Relativity, or Both?

[Edem]

Is time dilation defined by Special Relativity, General Relativity or both?

The topic of time dilation seems to come up often. So I thought I would pose a question, and give my summary and conclusions.
I've recently been struggling to understand time dilation. While researching this topic l became very confused and frustrated by the many different ways that this is explained.
The widely used twins paradox example and it's variations (as explained), are often overly complicated and sometimes contradictory.
It appears that even the experts are confused.
I've seen and read that to explain it; you only need SR, you only need GR, or that you need both.
I have made sense of it in the following way from what I've learned in hours of research and thought.
Please correct me if I'm wrong on any point.

To start with, I see time dilation as defined by SR as follows;

Two observers moving at any constant velocity (an inertial state, no acceleration/deceleration), will observe time dilation. It will be observed when moving at the same speed in different directions (any direction other than parallel), or different speeds in any direction. They will observe it in the same way (meaning the other has slowed or quickened). From their perspective both observers view the other as moving and their self as still.
This slowing/quickening will not be observationally agreed upon, which is a paradox.
Both frames of reference are equally valid under the principle of equivalence.
Both would see the others time as slowing if the distance between them is increasing, and see the others time as quickening if the distance is decreasing.
The amount is determined by their relative speed and direction of travel.
If they were parallel and moving in the same direction at the same speed, there would be no dilation. They would both appear to be still to each other.

My conclusion;
Time dilation in SR is an observational distortion and will always be reconciled when two observers meet (which could only happen in real life with a collision if no deceleration is used).

Now for time dilation in GR.
I hold the following to be true (again, inform me if I'm wrong);

For two observers moving in any reference frame, the one in the greater gravitational field will have their time slowed. This will be observationally agreed upon (barring any additional dilation due to SR). This is not paradoxical, and this difference will not be reconciled when they meet.
The degree of dilation is determined by the difference of gravitational force and duration of time.
Acceleration and deceleration create a gravitational force.
The force of acceleration/deceleration is equal to the force of gravity.

My conclusion;
That the slowing of time under GR is actual, it will not be reconciled when two observers meet.
In real life this slowing of time is felt as "g force" when accelerating or decelerating at more then one gravity (the Earth's inertial state, which is what our biological bodies are evolved to live in). It's not very pleasant to have your time slowed by more than a little. And deadly to have it slowed quickly.

My final conclusion;
While both are observationally relevant, only SR is a paradox, and only GR relates to actual physical change (any age difference). Hence, all the confusion in the twins paradox.
In the real world there couldn't be any parting or any meeting (except for a collision) without velocity change (acceleration/deceleration).
GR is the only thing that explains an age difference in the twins paradox. But this would only be possible to a noticeable degree if the traveler were in a much stronger gravitational field for a very long period of time (which wouldn't be good).

To sum up;
Time dilation in SR is observational and not actual.
Time dilation in GR is observational and actual.
It seems that few explain this distinction between the two.
Einstein apparently did so by addressing them in separate theories.

Once again, please advise where I'm in error. I must be wrong somewhere! Because I could've put a question mark after half of the above statements.

 

[Edem]

SR of course also applies to accelerated motion. As Newtonian mechanics it's not restricted to uniform motion. You don't need GR to understand time dilation.

Okay, but gravitational time dilation isn't, if I understand correctly.

 

[jbriggs444]

My conclusion;
Time dilation in SR is an observational distortion and will always be reconciled when two observers meet (which could only happen in real life with a collision if no deceleration is used).

Upon re-uniting, the pocket watches of the two twins in the twin paradox will have different readings. Both twins will correctly predict the reading of the other twin's pocket watch at the time and place of the reunion. Yes this means that all disagreements during the journey will be reconciled when they rejoin at its end.

The twins could compare watches as they whiz past one another. No need to stop.

 

[vanhees71]

Is time dilation defined by Special Relativity, General Relativity or both?

The topic of time dilation seems to come up often. So I thought I would pose a question, and give my summary and conclusions.
I've recently been struggling to understand time dilation. While researching this topic l became very confused and frustrated by the many different ways that this is explained.
The widely used twins paradox example and it's variations (as explained), are often overly complicated and sometimes contradictory.
It appears that even the experts are confused.
I've seen and read that to explain it; you only need SR, you only need GR, or that you need both.
I have made sense of it in the following way from what I've learned in hours of research and thought.
Please correct me if I'm wrong on any point.

To start with, I see time dilation as defined by SR as follows;

Two observers moving at any constant velocity (an inertial state, no acceleration/deceleration), will observe time dilation. It will be observed when moving at the same speed in different directions (any direction other than parallel), or different speeds in any direction. They will observe it in the same way (meaning the other has slowed or quickened). From their perspective both observers view the other as moving and their self as still.
This slowing/quickening will not be observationally agreed upon, which is a paradox.
Both frames of reference are equally valid under the principle of equivalence.
Both would see the others time as slowing if the distance between them is increasing, and see the others time as quickening if the distance is decreasing.
The amount is determined by their relative speed and direction of travel.
If they were parallel and moving in the same direction at the same speed, there would be no dilation. They would both appear to be still to each other.

My conclusion;
Time dilation in SR is an observational distortion and will always be reconciled when two observers meet (which could only happen in real life with a collision if no deceleration is used).

Now for time dilation in GR.
I hold the following to be true (again, inform me if I'm wrong);

For two observers moving in any reference frame, the one in the greater gravitational field will have their time slowed. This will be observationally agreed upon (barring any additional dilation due to SR). This is not paradoxical, and this difference will not be reconciled when they meet.
The degree of dilation is determined by the difference of gravitational force and duration of time.
Acceleration and deceleration create a gravitational force.
The force of acceleration/deceleration is equal to the force of gravity.

My conclusion;
That the slowing of time under GR is actual, it will not be reconciled when two observers meet.
In real life this slowing of time is felt as "g force" when accelerating or decelerating at more then one gravity (the Earth's inertial state, which is what our biological bodies are evolved to live in). It's not very pleasant to have your time slowed by more than a little. And deadly to have it slowed quickly.

My final conclusion;
While both are observationally relevant, only SR is a paradox, and only GR relates to actual physical change (any age difference). Hence, all the confusion in the twins paradox.
In the real world there couldn't be any parting or any meeting (except for a collision) without velocity change (acceleration/deceleration).
GR is the only thing that explains an age difference in the twins paradox. But this would only be possible to a noticeable degree if the traveler were in a much stronger gravitational field for a very long period of time (which wouldn't be good).

To sum up;
Time dilation in SR is observational and not actual.
Time dilation in GR is observational and actual.
It seems that few explain this distinction between the two.
Einstein apparently did so by addressing them in separate theories.

Once again, please advise where I'm in error. I must be wrong somewhere! Because I could've put a question mark after half of the above statements.

I also don't know, why "experts" tend to teach introductory relativity as a collection of paradoxes, instead of introducing the adequate math right away. It seems as if they think it makes the subject more attractive to students, if they have to struggle with apparent (but completely absent!) paradoxes. Although amusing, they are not helping the beginner. What's unclear with my posting #8? That's all you need to understand the different aging of the twins in the socalled twin paradox. It's not a paradox at all; it's a well established empirical fact if you accept muons or other unstable particles as substitutes for twins. One has measured that muons or unstable nuclei running at high speeds in an accelerator are indeed living longer by a Lorentz factor $\gamma$ than when they are at rest.

See also my introduction to SR:

https://th.physik.uni-frankfurt.de/~hees/pf-faq/srt.pdf

 

[vanhees71]

Okay, but gravitational time dilation isn't, if I understand correctly.

Sure, everything related with gravity is described by GR. SR is GR in absence of gravitation!

 

[Edem]

Upon re-uniting, the pocket watches of the two twins in the twin paradox will have different readings. Both twins will correctly predict the reading of the other twin's pocket watch at the time and place of the reunion. Yes this means that all disagreements during the journey will be reconciled when they rejoin at its end.

The twins could compare watches as they whiz past one another. No need to stop.

I'm not sure I understand. Are you agreeing with me?

 

[Edem]

Apparently in the above quoted paragraph, Einstein is addressing GR in SR. The motion described is not an inertial state.

If this had read; Apparently in the quoted paragraph, Einstein is addressing the time dilation of GR in SR. This would be correct?

 

[russ_watters]

I'm not sure I understand. Are you agreeing with me?

Probably not. You weren't very specific, but you seemed to imply that with SR alone, the twins' watches would show the same elapsed time upon their later meeting. This isn't correct: their watches show different elapsed times.

 

[Edem]

I also don't know, why "experts" tend to teach introductory relativity as a collection of paradoxes, instead of introducing the adequate math right away. It seems as if they think it makes the subject more attractive to students, if they have to struggle with apparent (but completely absent!) paradoxes. Although amusing, they are not helping the beginner. What's unclear with my posting #8? That's all you need to understand the different aging of the twins in the socalled twin paradox. It's not a paradox at all; it's a well established empirical fact if you accept muons or other unstable particles as substitutes for twins. One has measured that muons or unstable nuclei running at high speeds in an accelerator are indeed living longer by a Lorentz factor $\gamma$ than when they are at rest.

See also my introduction to SR:

https://th.physik.uni-frankfurt.de/~hees/pf-faq/srt.pdf

Sorry, but I don't know the math and can't follow it. So, at this point I'm trying only to understand the concept, not the mathematical formulas used to derive precise predictable quantities.
The muons in above example are accelerating (exposed to g force). So their dilation is due to time dilation as described by GR.

 

[PeroK]

Please correct me if I'm wrong on any point.

Once again, please advise where I'm in error. I must be wrong somewhere! Because I could've put a question mark after half of the above statements.

Much of what you say is either wrong or misses the point.

My advice to you is to learn SR from a single, reputable source. The picking and choosing from all different sources has led to your confusion. The sources probably agree on more than you realize, but there are so many different ways to present a subject that you've ended up picking up on the differences, rather than on the core facts of SR (and GR).

 

[Edem]

Probably not. You weren't very specific, but you seemed to imply that with SR alone, the twins' watches would show the same elapsed time upon their later meeting. This isn't correct: their watches show different elapsed times.

Can you explain simply how this can be without using gravity (acceleration/deceleration). If both are at a constant velocity (inertial state) than their watches should agree when they meet.

 

[russ_watters]

Can you explain simply how this can be without using gravity (acceleration/deceleration). If both are at a constant velocity (inertial state) than their watches should agree when they meet.

No, it can't be explained without acceleration/deceleration because they can't separate or meet again without acceleration/deceleration.

 

[Edem]

Much of what you say is either wrong or misses the point.

My advice to you is to learn SR from a single, reputable source. The picking and choosing from all different sources has led to your confusion. The sources probably agree on more than you realize, but there are so many different ways to present a subject that you've ended up picking up on the differences, rather than on the core facts of SR (and GR).

The advice is appreciated, but the point to me is the actual physical change and not the illusionary observational distortion.

 

[PeroK]

The advice is appreciated, but the point to me is the actual physical change and not the illusionary observational distortion.

It's all physical. Time dilation has nothing to do with "illusionary observational distortion". It has to do with the nature of time itself.

 

[Edem]

It's all physical. Time dilation has nothing to do with "illusionary observational distortion". It has to do with the nature of time itself.

It's only observationally physical. You can't physically touch it.
Something you observe as shortened will not be shortened when it comes to rest.

 

[russ_watters]

It's only observationally physical. You can't physically touch it.

That's meaningless.

Something you observe as shortened will not be shortened when it comes to rest.

That's false and/or irrelevant. What you suggest is like taking a different route home from work and expecting the odometer reading not to show a different distance traveled.

Do you really want to learn or do you already understand and just choose not to accept?

 

[Edem]

That's meaningless.

That's false and/or irrelevant. What you suggest is like taking a different route home from work and expecting the odometer reading not to show a different distance traveled.

Do you really want to learn or do you already understand and just choose not to accept?

The odometer analogy doesn't work for me, it introduces a measurement of distance not time.
I'm trying to understand. My conclusions are recent and not carved in stone.
I'm now trying to understand how constant speed (no gravity) can effect time without violating the principles of equivalency I've recently learned.

 

[PeroK]

The odometer analogy doesn't work for me, it introduces a measurement of distance not time.

Ah, but time is distance. That's the fundamental point about spacetime, rather than space and time.

A clock, in fact, measures the distance it travels through spacetime. And that is at least one definition of time: "proper time".

Also, in GR, you can measure mass as a distance. The Sun's mass, for example, can be given as 1.5 km. See, for example:

https://en.wikipedia.org/wiki/Geometrized_unit_system

 

[russ_watters]

The odometer analogy doesn't work for me, it introduces a measurement of distance not time.

Length [contraction] *is* distance!

I'm trying to understand. My conclusions are recent and not carved in stone.

Carved in stone or not, you shouldn't enter a learning exercise already having conclusions.

I'm now trying to understand how constant speed (no gravity) can effect time without violating the principles of equivalency I've recently learned.

What principle of equivalence? You mean symmetry? I'm afraid you can't reconcile this. You are demanding symmetry exist where it doesn't.

 

[SiennaTheGr8]

@Edem

1) SR can handle accelerated motion just fine. You don't need GR for that.

2) Time dilation in SR happens regardless of whether the travelers whose times are mutually dilated ever meet up to compare wristwatch-readings (which would require one or both travelers to accelerate).

3) The "relativistic effects" of SR (time dilation, length contraction, the relativity of simultaneity) are every bit as real as the gravitational effects of GR (e.g., gravitational time dilation). They are not optical illusions.

In fact, length contraction is in some sense the very opposite of an optical illusion: If something were approaching you at 90% the speed of light and you took a photograph of it before it reached you, it would NOT appear length-contracted in the picture. To the contrary, its length in the picture would be GREATER than it would be if you took a picture of it at the same distance while it was at rest! Length contraction is measurable, but what you actually see (or photograph) depends on the behavior of light, and that's a different question altogether. See: https://en.wikipedia.org/wiki/Terrell_rotation

 

[PeterDonis]

gravity (acceleration/deceleration)

These are not the same. You can have acceleration/deceleration in the absence of gravity. Also, in relativity, the proper definition of "acceleration" (and deceleration, which is just a form of acceleration) has nothing to do with gravity: it is proper acceleration, i.e., acceleration that is felt, and can be measured directly by an accelerometer.

 

[Edem]

These are not the same. You can have acceleration/deceleration in the absence of gravity. Also, in relativity, the proper definition of "acceleration" (and deceleration, which is just a form of acceleration) has nothing to do with gravity: it is proper acceleration, i.e., acceleration that is felt, and can be measured directly by an accelerometer.

I thought that I read that Einstein wrote in SR that (and I paraphrase); the force of acceleration is equal to the force of gravity, no distinction can be made.

 

[PeterDonis]

I thought that I read

Where? Please give a reference.

Einstein wrote in SR that (and I paraphrase); the force of acceleration is equal to the force of gravity

Einstein certainly didn't say any such thing "in SR", because SR does not take gravity into account at all.

You might be misremembering or misunderstanding one of Einstein's statements of the equivalence principle; but unless you give a source for where you are getting this from, there's no way to tell for sure.

 

[Ibix]

I thought that I read that Einstein wrote in SR that (and I paraphrase); the force of acceleration is equal to the force of gravity, no distinction can be made.

The words SR and gravity do not go together. If you want gravity you need GR.

The point about the equivalence principle is that the "natural" state of things in GR is free-fall. If you're standing on a surface and feeling weight you are being pushed out of your "natural" path by something. You cannot tell (by purely local measurements) if you are "trying" to free-fall to the centre of the Earth and being pushed out of that state by the floor being in the way, or if you are "trying" to move in a straight line in deep space and being pushed out of that state by a rocket hidden under the floor.

This does not say "gravity and acceleration are the same thing". It says "free-fall is free-fall whether you are near a planet or not", and "not being in free-fall is not being in free-fall, whatever the reason you are not in free-fall".

 

[Edem]

Length [contraction] *is* distance!

Carved in stone or not, you shouldn't enter a learning exercise already having conclusions.

I approached this topic as a mental exercise, hoping to come away with some understanding of the causes of time dilation. I was hoping that someone could explain it in a simple way that would make sense to me after all the confusioning, contradictory things that I've seen about it. I tried to make it clear in my initial post that my conclusions are tenuous. They are based on what I gleaned from trying to sort out the confusion. It seems that I've learned little, and that mental acrobatics are needed to explain it.

What principle of equivalence? You mean symmetry? I'm afraid you can't reconcile this. You are demanding symmetry exist where it doesn't.

Sorry, I guess it's symmetry. I thought it was a equivalency principal.
I thought that in an inertial state all frames of reference are equally valid.

 

[Edem]

Where? Please give a reference.

I can't recall, I've read too much on it in the last several days.

Einstein certainly didn't say any such thing "in SR", because SR does not take gravity into account at all.

My mistake, I actually meant to say GR.

You might be misremembering or misunderstanding one of Einstein's statements of the equivalence principle; but unless you give a source for where you are getting this from, there's no way to tell for sure.

I will try to find one.

 

[laymanB]

@Edem

I am still in the learning phase of SR and trying to get a grasp on it myself. Most of the math is still rather esoteric to me but hopefully not someday. Here is how I understand it today using a thought experiment.

There is one person on the surface of the Earth and another traveling in a spaceship near the speed of light at a constant velocity. When the spaceship traveler is perpendicular to the surface of the Earth where the other observer is, they synchronize their clocks and agree on the coordinate system they are going to use. Both of their clocks consist of two mirrors separated by 1/2 a light second in the Y direction (it is a large spaceship). The clocks send a light pulse from the bottom mirror to the top mirror where it is reflected and returns to the bottom mirror where a detector measures the incoming light pulse. This constitutes one second for each observer with their own clocks.

The spaceship is traveling with a velocity near the speed of light in the X direction relative to the Earth observer.

As the spaceship and the Earth are receding from each other let's say they have the ability to look at each other's clocks for a brief moment. From the perspective of each observer it appears that the other's clock is running slowly because each light pulse appears to take a longer path before it returns to the bottom mirror because the mirrors themselves appear to be moving along the X axis of relative motion.

So as each observer looks at the light clock of the other, they both come to the conclusion that the clocks of the other observer are running slowly. But in each of their own references frames, they will see their light clocks operating normally and counting off seconds.

For this thought experiment, let's assume that the size of the universe is small and has periodic boundaries so that the spaceship does not have to accelerate at all and comes back "around" to once again be perpendicular to the observer on the Earth after 10 light days, as measured by the spaceship. They compare their clocks again at the same point in space-time as before, and the clock in the spaceship has indeed recorded much less time than the observer on Earth. How is that possible?

The way I am (hopefully) seeing it, like the experts have posted, is that time is just another dimension. Like the spatial dimensions x,y, and z of familiar Cartesian coordinates we all know and love. Time can be measured in units of length by multiplying c (the speed of lights) by time. The Earth observer's change of position through space (orbiting around the Sun, the solar system orbiting around the galaxy) is negligible compared to the spaceship observer's change of position through space because the velocity of the spaceship dwarfs that of the Earth-solar system velocity. Here (I think) is the crux of the situation. Everyone is moving through space-time at the speed of light. The Earth observer is using most of his velocity to travel along the time axis and very little of the component velocity to travel through x, y, and z. So the Earth observer is moving very nearly to the speed of light along the time axis. The spaceship observer is traveling near the speed of light in the X direction so very little of his component velocity in traveling along the time axis. All the axis components of the velocity must add to c (the speed of light). So, you can either stay relativity still and travel through time quickly for your position in space-time, or you can travel about at velocities near the speed of light and come back to that same location in space-time without much time passing on your (spaceship) clock. You will be younger than the observer on Earth.

Hopefully that's close.

 

[Edem]

Thank you for the example laymanB. It does help some, I need to give it more thought.

 

[Edem]

After doing a little research on points of error in my understanding, revealed by others in this thread. It is clear to me that I lack a basic understanding of some of the terms and words I was throwing around. My apologies.

I joined and posted here hoping to resolve my confusion on this topic (and others).
My initial post on this thread was meant to put out what I thought was right about the topic, mostly so that what was wrong would be pointed out.

I plan on more study of time dilation and related topics. If I learn more, I will be back to discuss. Thanks to all for your "time" and input.

 

[laymanB]

Thank you for the example laymanB. It does help some, I need to give it more thought.

You're welcome. Just don't go using my example in any doctoral dissertation, I'm sure it is full of loose language and probably errors. It could also be flat wrong, we will let the experts weigh in.

I think the first place to start is learning Galilean invariance. You talked several times about being in an inertial state. I'm not sure what that is but I am assuming you mean an inertial frame of reference. An inertial frame of reference is a frame of reference in which Newton's laws are true. This means someplace where you can do an activity like juggling and everything will feel "normal" to your everyday experience like on the surface of the Earth, even though the surface of the Earth is not technically an inertial frame, it is close enough. Once you pick an inertial frame of reference, then any other frame moving with constant velocity relative to that frame is also inertial. Here is a good YouTube video from 1960.


This should give you a good idea of why the light path looks different in the clock example above. If you already understand this fairly well, then disregard it. Once you understand that the Einstein's second postulate states that the speed of light will be measured with the same speed in any reference frame, you can begin to work out the implications how people will disagree about time and distance measurements in their frames of reference and neither is more correct. I'm still learning too.

 

[vanhees71]

Sorry, but I don't know the math and can't follow it. So, at this point I'm trying only to understand the concept, not the mathematical formulas used to derive precise predictable quantities.
The muons in above example are accelerating (exposed to g force). So their dilation is due to time dilation as described by GR.

That's the wrong approach. You have to learn the math first. You cannot even talk about physics without this math. Of course, muons are accelerated due to gravity of the Earth, but you can safely neglect the effects of gravity of the Earth in HEP physics. It's way too weak to have an important impact on the particles.

Of course, there are exceptions to this rule, as the beautiful example of the measurement of the energy levels of neutrons in the gravitational potential of the Earth (note that this is in the Newtonian approximation) above a reflecting surface, but that's of course physics of ultra-low energetic neutrons. Here is a diploma thesis on the subject:

http://www.pi.uni-hd.de/Publications/dipl_krantz.pdf

 

[Dale]

The odometer analogy doesn't work for me, it introduces a measurement of distance not time.

That is precisely the point. A measurement of time is a measurement of a kind of distance in spacetime, called the spacetime interval. Distance in normal Euclidean space is $ds^2=dx^2+dy^2+dz^2$ and the spacetime interval is $ds^2=-dt^2+dx^2+dy^2+dz^2$ so it is a distance in a spacetime with one timelike dimension and three spacelike dimensions.

The odometer analogy is intended to help you understand geometry in spacetime using mental experiences that you already have with geometry in space. You do yourself a great disservice by skipping it. It is one of the most powerful mental tools you have available.

 

[Dale]

assume that the size of the universe is small and has periodic boundaries

Note that this assumption violates the principle of relativity. The geometry is called a four-torus. A four-torus may be locally flat, but there exists a preferred reference frame globally.

 

[1977ub]

No, it can't be explained without acceleration/deceleration because they can't separate or meet again without acceleration/deceleration.

If a twin can be understood to be an AI and its history can be transferred electronically between closely passing ships, then the outgoing twin has his history transferred to an incoming ship without deceleration per se. Then when the incoming ship returns home, his history is transferred to a computer at home without deceleration per se.

 

[PeroK]

If a twin can be understood to be an AI and its history can be transferred electronically between closely passing ships, then the outgoing twin has his history transferred to an incoming ship without deceleration per se. Then when the incoming ship returns home, his history is transferred to a computer at home without deceleration per se.

That's a neat idea. Slightly less fancifully you could transfer the clock reading to an identical clock moving in the opposite direction and thus measure the proper time of the out and return journeys without a physical turn around.