If there is no universal frame of reference then how can time dilation occur?

[davidaw]

Hi guys, I'm just a high schooler who was thinking about general relativity and couldn't quite get a grasp on one certain idea.. I asked my physics teacher this, but he wasn't really quite sure himself.

 

If you have empty space, and you have to objects, and one of them is "moving" at nearly the speed of light, and the other is "sitting still".. then according to Einstein (correct me if I'm wrong) the one with the higher speed would have a slower time frame (its "clock" would slow down) relative to the other object.. but if there is no absolute frame of reference then how can you distinguish which object is "moving", because really they are both moving relative to each other. If this is the case, how could you actually distinguish which one was on the "slower" time frame...?

 

Thanks again!! Just let me know if I didn't explain my question well enough..

Edited February 14, 2012 by davidaw

[Appolinaria]

Hi, I'm sure some members will respond, but meanwhile, I had slightly similar questions in another thread and Swansont provided a good link that may be useful to you.

 

http://www.scienceforums.net/topic/60289-n00b-questions/

[elfmotat]

Each object measures their own clock as running normally and the others' as running slow.

Edited February 14, 2012 by elfmotat

[davidaw]

Thanks for the link! I guess this is what I don't understand, "As long as there are no accelerations, the effect is symmetrical. With acceleration you still have the effects, but the one who accelerates will end up with a clock that has run slow." ~ Swansont.. Here he says that "the one who accelerates will end up with a clock that has run slow", but if movement is completely dependent on the frame of reference than how can you say that the guy who is accelerating will have a slower clock?.. because from different reference points you could say that they are both accelerating. It is hard to explain what I am talking about.. I'm sorry if I'm not being clear.

 

Edited February 14, 2012 by davidaw

[elfmotat]

Thanks for the link! I guess this is what I don't understand, "As long as there are no accelerations, the effect is symmetrical. With acceleration you still have the effects, but the one who accelerates will end up with a clock that has run slow." ~ Swansont.. Here he says that "the one who accelerates will end up with a clock that has run slow", but if movement is completely dependent on the frame of reference than how can you say that the guy who is accelerating will have a slower clock?.. because from different reference points you could say that they are both accelerating. It is hard to explain what I am talking about.. I'm sorry if I'm not being clear.

 

 

Only one person will actually feel an acceleration, while the other feels nothing. Acceleration is not relative in the same way that velocity is.

[swansont]

Only one person will actually feel an acceleration, while the other feels nothing. Acceleration is not relative in the same way that velocity is.

 

Bingo.

 

As long as the frames are inertial (constant velocity motion) the time dilation will be symmetric between the two frames — each will see the other's clocks as running slow. But as soon as one of them accelerates, this symmetry is broken. For them to get into the same inertial frame to compare clocks side-by-side requires an acceleration.

[DrRocket]

Hi guys, I'm just a high schooler who was thinking about general relativity and couldn't quite get a grasp on one certain idea.. I asked my physics teacher this, but he wasn't really quite sure himself.

 

If you have empty space, and you have to objects, and one of them is "moving" at nearly the speed of light, and the other is "sitting still".. then according to Einstein (correct me if I'm wrong) the one with the higher speed would have a slower time frame (its "clock" would slow down) relative to the other object.. but if there is no absolute frame of reference then how can you distinguish which object is "moving", because really they are both moving relative to each other. If this is the case, how could you actually distinguish which one was on the "slower" time frame...?

 

Thanks again!! Just let me know if I didn't explain my question well enough..

 

elmotat, unsurprisingly, hit the nail on the head.

 

One more thing, since you asked this in terms of general relativity.

 

The notion of reference frames applies to special relativity, not so much to general relativity. Special relativity is the local version of general relativity, and is a useful approximation so long as gravitation is not very important. It is in local coordinates that one can speak of comparison of time registered by clocks that are spatially removed from one another, hence of "time dilation".

 

In general relativity time and space are co-mingled. What clocks measure is called proper time, and that is connected to the world line (space and time history) of the clock. So different clocks that see a different position-time history will register different time intervals. This is where acceleration enters the picture.

 

A clock that is in free fall in a gravitational field has a world line that is what called a "geodesic". In general relativity geodesics are lines of maximal proper time. So, given two clocks that meet at two points in space and time, one moving in free fall and one subjected to forces other than gravity (and that is what is meant by accelerating in general relativity) the clock in free fall will always register the longest time interval between the points at which the clocks meet.

 

Bottom line is that anything subject to any force other than gravity, i.e. not in free fall, is "accelerating" in general relativity. In special relativity, gravity is neglected, and "accelerating" is sensed in the usual manner, but then you have to be very careful about what is and is not an inertial reference frame -- special relativity applies only in inertial reference frames.

 

This is a bit stilted, as I am trying to explain ideas that require the mathematics of differential geometry without actually using differential geometry, but hopefully the main idea has survived.

[Mike-from-the-Bronx]

-- special relativity applies only in inertial reference frames.

 

Dr Rocket;

 

I've read many of your posts and I'm confused about your opinion with regards to SR and Acceleration. Which side of the fence are you on?

 

Some references:

 

From the book "Special Relativity" by A. P. French

 

Copyright 1966 Massachusetts Institute of Technology

 

Chapter 5, Relativistic Kinematics, page 153

 

"Because Einstein developed a whole new theory (his general theory of relativity, published in 1916) based upon dynamical equivalence of an accelerated laboratory and a laboratory in a gravitational field, it is sometimes stated or implied that special relativity is not competent to deal with accelerated motions. This is a misconception. We can meaningfully discuss a displacement and all its time derivatives within the context of the Lorentz transformations."

 

From the book "Basic Relativity" by Richard A Mould

 

Copyright 1994 Springer-Verlag

 

Chapter 8, Uniform Acceleration, page 221

 

"Until the relationship between mater and metric is explicitly stated, we cannot be said to have left the domain of special relativity, even when working with non-inertial frames of reference."

[Janus]

Thanks for the link! I guess this is what I don't understand, "As long as there are no accelerations, the effect is symmetrical. With acceleration you still have the effects, but the one who accelerates will end up with a clock that has run slow." ~ Swansont.. Here he says that "the one who accelerates will end up with a clock that has run slow", but if movement is completely dependent on the frame of reference than how can you say that the guy who is accelerating will have a slower clock?.. because from different reference points you could say that they are both accelerating. It is hard to explain what I am talking about.. I'm sorry if I'm not being clear.

 

Besides the fact that the one that accelerates will feel it, there is another observation that he'll make that determines who accelerated. This is a change in Doppler shift, and becomes important a the point of turn around. As he is moving away from the first observer, he will see the light from him as red-shifted. When he turns around, that light will be now blue shifted. Thus he sees Red shift for half the time and Blue shift for the other half.

 

The non-accelerating observer will see something different. He has to wait for the information that the other observer turned around to get to him before he sees the Red shift change to Blue. For example, if the two observers are 1 ly apart at turn around, he will not see the change from Red to Blue until 1 yr after it happens. Thus if the total trip takes 3 yrs by his clock, he would see 2.5 years of Red shift and only 0.5 years of Blue shift.

 

So to summarize, The accelerating observer will see an immediate change in Doppler shift no matter how far he is from the source, while the non-accelerating observer will not and has to wait for the light traverse the distance between to see the change.

[elfmotat]

Dr Rocket;

 

I've read many of your posts and I'm confused about your opinion with regards to SR and Acceleration. Which side of the fence are you on?

 

Some references:

 

From the book "Special Relativity" by A. P. French

 

Copyright 1966 Massachusetts Institute of Technology

 

Chapter 5, Relativistic Kinematics, page 153

 

"Because Einstein developed a whole new theory (his general theory of relativity, published in 1916) based upon dynamical equivalence of an accelerated laboratory and a laboratory in a gravitational field, it is sometimes stated or implied that special relativity is not competent to deal with accelerated motions. This is a misconception. We can meaningfully discuss a displacement and all its time derivatives within the context of the Lorentz transformations."

 

From the book "Basic Relativity" by Richard A Mould

 

Copyright 1994 Springer-Verlag

 

Chapter 8, Uniform Acceleration, page 221

 

"Until the relationship between mater and metric is explicitly stated, we cannot be said to have left the domain of special relativity, even when working with non-inertial frames of reference."

 

Special Relativity applies whenever the metric is Minkowskian (flat). This means that SR still works as long as there are no nearby sources of gravitation. Accelerated worldlines are easily handled, because they only need be analyzed from an inertial frame. Accelerated frames are trickier, but they can still be handled within the domain of SR.

[DrRocket]

Dr Rocket;

 

I've read many of your posts and I'm confused about your opinion with regards to SR and Acceleration. Which side of the fence are you on?

 

Some references:

 

From the book "Special Relativity" by A. P. French

 

Copyright 1966 Massachusetts Institute of Technology

 

Chapter 5, Relativistic Kinematics, page 153

 

"Because Einstein developed a whole new theory (his general theory of relativity, published in 1916) based upon dynamical equivalence of an accelerated laboratory and a laboratory in a gravitational field, it is sometimes stated or implied that special relativity is not competent to deal with accelerated motions. This is a misconception. We can meaningfully discuss a displacement and all its time derivatives within the context of the Lorentz transformations."

 

From the book "Basic Relativity" by Richard A Mould

 

Copyright 1994 Springer-Verlag

 

Chapter 8, Uniform Acceleration, page 221

 

"Until the relationship between mater and metric is explicitly stated, we cannot be said to have left the domain of special relativity, even when working with non-inertial frames of reference."

 

That depends on where you think the fence is. I'm not sure that there is one. On the other hand, there might be a wall, and that wall might divide two limited or equally erroneous views. It is a bit difficult to judge from excerpts alone.

 

I have no idea what that quote from Mould is supposed to mean.

 

I am a bit puzzle by French as well.

the sentence "We can meaningfully discuss a displacement and all its time derivatives within the context of the Lorentz transformations" is mysterious -- basically I don''t know what he means by "within the context of" . If he means that one cannot handle accelerations by reference back to inertial frames and Lorentz transformations in analogy with the handling of accelerating frames in Newtonian mechanics, then his statement is patently wrong. If he means that when you do that what pops out does not look like the expressions one sees in elementary treatments of relativity, then his statement is obvious.

 

But here is how I look at it:

 

Special relativity works only in the context of an inertial reference frame. Exactly the same statement applies to Newtonian mechanics.

 

But in Newtonian mechanics one an handle acceleration and accelerating reference frames, simply by referring back to some inertial frame. This results in pseudo-forces, such as the Coriolis force.

 

One can handle acceleration relative to an inertial frame within the context of special relativity. That is done quite regularly -- see for instance Introduction to Special Relativity by Wolfgang Rindler, or perhaps the sources that you reference with which I am not familiar. Just as with Newtonian mechanics and pseudo-forces, the form of transformations between non-inertial frames will be different in appearance from that anticipated by those familiar with Lorentz transforms. No surprise.

 

In either case what you see is the natural distortion that comes from trying to express well-understood principles in coordinate systems that are not naturally suited for that expression, though they may be convenient for some particular special purpose.

 

The big difference between the relativistic case and the Newtonian analogy is that Newtonian mechanics, in all forms, applies to a single global reference frame. The underlying assumption is that spacetime is flat, spatially Euclidean and time is universal. Relativity is fundamentally different. General relativity makes no such assumption. Spacetime in general relativity is a 4-dimensional Lorentzian manifold of topology and geometry that are determined by the distribution of mass/energy. There need be no single chart that covers the manifold, space and time are local notions only, and special relativity is only a local approximation -- i.e. special relativity applies on the tangent space, not on the spacetime manifold. One does not pass from special relativity to general relativity by some bizarre coordinate choice (only locally could this be done) and therein lies the fundamental distinction between the special and general theories.

 

One can say that Newtonian mechanics approximates special relativity in the sense that the equations give similar predictions at low velocities.

 

One can say that special relativity approximates general relativity for small gravitational fields.

 

But the two notion of approximation are fundamentally different. The relationship between Newtonian mechanics and special relativity is in some sense just happenstance. The equations differ by virtue of terms that are small under certain assumptions. The relationship between the special and general theories on the other hand is of a fundamentally geometric nature -- the difference between a manifold itself and the local approximation near a point by its tangent space ("all manifolds are locally flat').

 

 

The special and general theories are not two different theories but rather are part of a single geometric picture. So, yes one can approximate the physics as closely as one one would like using the special theory and the piece those local approximations together to produce a more global picture -- but that is nothing but a description of manifold theory. When you do that you are really just using general relativity.

 

I think that this may illustrate why excess reliance on the "equivalence principle" can lead to difficulties in seeing the larger picture. As I said elsewhere, that principle was of great utility in helping Einstein to discover general relativity, but it is not particularly essential to a more modern and cleaner development of the theory. Einstein's genius comes through in the actual discovery of general relativity. But his path was, understandably, a bit tortured and characterized by fits and starts. Once discovered, there is much to be said for more modern, abstract, and elegant approaches to its development. Einstein was not very well schooled in geometry and relied on Marcel Gross to help him -- not a criticism. But is does suggest that there may be more elegant paths by which one could build upon the work of Riemann (on whose work that of Einstein in certainly based) to arrive at the same end point, but perhaps with an alternate perspective that brings greater clarity to some aspects of the theory.

[D H]

Dr Rocket;

 

I've read many of your posts and I'm confused about your opinion with regards to SR and Acceleration. Which side of the fence are you on?

 

What fence are you talking about?

 

Special relativity can handle non-inertial frames, in much the same manner as does Newtonian mechanics. The equations of motions just get a bit messier. Note very well: There's still an inertial frame with infinite extent lurking in the background somewhere. It is this global inertial frame lurking in the background to which Dr Rocket was referring he said "Special relativity works only in the context of an inertial reference frame."

 

There are two ways to find an inertial frame in Newtonian mechanics. One is to compare to Newton's concept of Absolute Space (aka God's frame; Newton was a deeply religious man). An inertial frame is a frame of reference whose origin is not accelerating and whose axes are not rotating with respect to this absolute inertial frame. There's a problem with this notion: That absolute frame is unknowable. It is metaphysical concept. rather Newton goes into this in detail in his first scholium.

 

Another approach is to use Newton's first law to test for the inertial nature of a frame. This removes the need for Newton's notion of absolute space and absolute time. One can do this with local experiments. Imagine a spacecraft far removed from any gravitational bodies outfitted with an inertial measurement unit (IMU) comprising an accelerometer and an inertial gyroscope. A frame based on that spacecraft is an inertial frame if those instruments register zero acceleration and zero rotational velocity. Constructing an inertial frame is no problem should those instruments yield non-zero readings.

 

This IMU-based concept of an inertial frame carries over into general relativity. Nonetheless, there's a huge difference between the concept inertial frames in general relativity versus those in Newtonian mechanics and special relativity. Inertial frames of reference are local in general relativity but global in Newtonian mechanics.

 

The concepts of frames of reference and coordinate systems are more or less synonymous in Newtonian mechanics. They are very distinct concepts in general relativity. Frames of reference are a physical concept. Coordinate systems are a mathematical concept. Just because inertial frames of reference are local in general relativity does not mean that one cannot attach space-time coordinates to some remote event in general relativity. You can.

[Mike-from-the-Bronx]

What fence are you talking about?

 

Well, since my post was addressed to Dr Rocket and you are not Dr Rocket I would not expect you to know.

[elfmotat]

Well, since my post was addressed to Dr Rocket and you are not Dr Rocket I would not expect you to know.

 

That's a pretty terrible attitude. Why do you assume he is the only person who can answer your question?

[DrRocket]

Just because inertial frames of reference are local in general relativity does not mean that one cannot attach space-time coordinates to some remote event in general relativity. You can.

 

This statement is pretty much self-contradictory. Maybe you ought to read up on what "local" means in mathematics and, by proxy in the case of general relativity, physics.

 

There is no reason to believe that a local coordinate system is valid as anything beyond an approximation at any location other than the single pointat which it is based. There will be some neighborhood in which a coordinate patch can be used to approximate the spacetime manifold, but there is absolutely no a priori reason to thing that it applied at some remote point on the manifold.

 

In regions in which the curvature is small the extent of the region in which the coordinates are a good approximation may be quite large. One can also create curvilinear coordinate systems that apply to somewhat large areas even in the presence of significant curvature. But you can also be badly misled -- as with the initial belief from Schwarzschild coordinates that the event horizon of a black hole is singular (it is not).

 

 

Another approach is to use Newton's first law to test for the inertial nature of a frame. This removes the need for Newton's notion of absolute space and absolute time. One can do this with local experiments. Imagine a spacecraft far removed from any gravitational bodies outfitted with an inertial measurement unit (IMU) comprising an accelerometer and an inertial gyroscope. A frame based on that spacecraft is an inertial frame if those instruments register zero acceleration and zero rotational velocity. Constructing an inertial frame is no problem should those instruments yield non-zero readings.

 

 

This works as a local approximation. which is the best that you can do.

 

But any IMU in free fall will produced the measurements that you describe, whether or not it is near a "gravitational body". So your test is no different from the test used in general relativity to identify a local Lorentzian reference frame.

 

The real problem with the inertial frame of Newtonian mechanics and of special relativity, is that it does not exist. It is an excellent local approximation and extremely useful for most engineering applications. But there is really no such thing as a true global inertial reference frame.

 

First you need to have a global coordinate system, but suppose that you have found one of those (good luck). A reference frame is just a global coordinate system attached to some physical feature (the observer). It is pretty easy to see that any two inertial reference frames are uniform motion with respect to one another. So, once you have one inertial reference frame you have a test to determine if any other frame is inertial.

 

The wrinkle is that you can't find the first one, which must of course be inertial to an arbitrarily strict level of precision. How about one attached to the Earth ? -- nope the Earth revolves around the sun. How about one attached to the sun ? -- nope the sund revolves about the center of the galaxy. How about one attached to the center of the galaxy ? --- nope the galaxy is a complicated dance within the local group. Etc, etc, etc.

 

So the idea of a global inertial reference frame is just a convenient fiction.

 

 

 

This IMU-based concept of an inertial frame carries over into general relativity. Nonetheless, there's a huge difference between the concept inertial frames in general relativity versus those in Newtonian mechanics and special relativity. Inertial frames of reference are local in general relativity but global in Newtonian mechanics.

 

It is only because they are local that inertial frames work in general relativity. And in general relativity a local reference frame is one attached to a body in free fall -- it is locally Lorentzian. Note also that gravity does not make an appearance in the local Lorentzian frame of general relativity -- a rather huge difference with the case of Newtonian mechanics in which the gravitational law is expressed in such a frame.

 

The big difference between the concepts of a local inertial frame in general relativity and the global frames of special relativity and Newtonian mechanics is that the former can be found to exist.

 

That's a pretty terrible attitude. Why do you assume he is the only person who can answer your question?

 

I agree. There are several people who could answer the question. It is a good idea to see responses from more than one such person, as the variation in perspective among those who can give adequate answers to such questions can lead to a deeper understanding than one can get by relying on just one good source.

 

Unfortunately, DH is not one of them.

[pantheory]

 

If there is no universal frame of reference then how can time dilation occur?

 

 

 

Time dilation has many faces. In Special Relativity which is based upon relative motion, each observer will have a different time frame and perspective of time dilation concerning the other time frame. On the other hand in General Relativity, the center of a gravitational field is a preferred reference frame concerning the comparison of two reference frames moving relative to the center of gravity. The frame moving faster relative to the same gravitational field will be more time dilated as measured by an observer near the center of the gravitational field, such as at the Earth's surface for instance.

 

Another face of time dilation concerning General Relativity, concerns distance from the center of gravity. An object that is not in motion relative to the center of gravity, will be more time dilated than an object further away from that center of gravity from that gravitational reference frame such as the Earth's surface.

 

 

 

[D H]

This statement is pretty much self-contradictory. Maybe you ought to read up on what "local" means in mathematics and, by proxy in the case of general relativity, physics.

Maybe you ought to read up on modern astronomy. Despite the fact that the inertial nature of space in the vicinity of the Earth is highly localized (a little 10 meter ball 10 meters with reasonably accurate equipment), general relativity did not suddenly say that the star catalogs astronomers have built over the century are worthless. Astronomers have continued to build these catalogs for the almost 100 years since Einstein developed general relativity. The only change is that they now account for relativistic effects in these catalogs.

 

You apparently read way too much into what I wrote. You appear to have read that I meant some globally true coordinates. Of course the exact validity of those coordinates are localized.

 

That does not mean things beyond the tiny little ball over which space appears to be locally inertial cannot be given some meaningful coordinates. Those modern catalogs include pulsars, which are orders and orders of magnitude outside that little tiny local ball where space is locally inertial. It does not even mean that these coordinates can only be used inside that tiny little ball. That modern catalogs are specified in ICRF coordinates means that they are not exactly correct for an observer on or near the Earth. Aim a modern telescope with milliarcsecond pointing accuracy at the exact spot specified for some object and you won't see the desired object. You'll have to make some adjustments to those coordinates. Those solar system barycentric coordinates are still valid. They just aren't globally true.

 

Astronomers have dealt with relativistic effects for almost 200 years before Einstein; they just didn't know that that is what they were doing. The classical explanation of stellar aberration is very close to the relativistic explanation given the small velocity at which the Earth orbits the Sun. And unlike what you said in an earlier post, it's not happenstance.

 

The relationship between Newtonian mechanics and special relativity is in some sense just happenstance.

This is nonsense. Of of Einstein's key goals in formulating general relativity was to ensure that it yielded Newtonian mechanics in the Newtonian limit. This was essential. He had no choice but to do this. Some future theory that unifies general relativity and quantum mechanics will similarly have to show that this new theory yields general relativity and quantum mechanics when looked at under the right conditions. Any new scientific theory must agree with existing science in the regimes where that existing science agrees well with observation. Failing to do that would immediately falsify this new theory.

 

 

But any IMU in free fall will produced the measurements that you describe, whether or not it is near a "gravitational body". So your test is no different from the test used in general relativity to identify a local Lorentzian reference frame.

Of course. Why do you think I introduced the concept of an IMU? They are at the heart of the difference between the concept of a locally inertial frame in general relativity and the concept inertial frames in Newtonian mechanics and of special relativity.

 

The real problem with the inertial frame of Newtonian mechanics and of special relativity, is that it does not exist. It is an excellent local approximation and extremely useful for most engineering applications. But there is really no such thing as a true global inertial reference frame. ... So the idea of a global inertial reference frame is just a convenient fiction.

Once again, of course. What is it that makes you think I think otherwise, particularly when I said the exact same thing you did?

 

There are several people who could answer the question. Unfortunately, DH is not one of them.

My, my. You have quite an atrocious and quite repugnant attitude.

[DrRocket]

Maybe you ought to read up on modern astronomy. Despite the fact that the inertial nature of space in the vicinity of the Earth is highly localized (a little 10 meter ball 10 meters with reasonably accurate equipment), general relativity did not suddenly say that the star catalogs astronomers have built over the century are worthless. Astronomers have continued to build these catalogs for the almost 100 years since Einstein developed general relativity. The only change is that they now account for relativistic effects in these catalogs.

 

You apparently read way too much into what I wrote. You appear to have read that I meant some globally true coordinates. Of course the exact validity of those coordinates are localized.

 

Maybe you ought to read what you wrote.

 

You very clearly addrressed coordinates "in general relativity".

 

Your statement was just plain wrong.

 

 

 

Once again, of course. What is it that makes you think I think otherwise, particularly when I said the exact same thing you did?

 

No, you didn't.

 

I guess we are back to that reading thing.

 

 

My, my. You have quite an atrocious and quite repugnant attitude.

 

Not really. I do have limited patience with incompetent "experts", requiring time and effort to clean up the resulting mess that would confuse neophytes.

[Cap'n Refsmmat]

Not really. I do have limited patience with incompetent "experts", requiring time and effort to clean up the resulting mess that would confuse neophytes.

Yes, really. There is a difference between correcting minor errors and assuming that perceived minor errors are a sign of total incompetence. There is a difference between helping neophytes better understand physics and convincing them that we're all unapproachable academic snobs.

 

I say this as the foremost expert on attitudes appropriate for SFN.

 

Please choose tact in the future.

[DrRocket]

Yes, really. There is a difference between correcting minor errors and assuming that perceived minor errors are a sign of total incompetence. There is a difference between helping neophytes better understand physics and convincing them that we're all unapproachable academic snobs.

 

I say this as the foremost expert on attitudes appropriate for SFN.

 

Please choose tact in the future.

 

The error was not minor and it was repeated and reinforced. I can recognize incompetence even when you cannot or chosoe not to.

 

 

My, my. You have quite an atrocious and quite repugnant attitude.

 

Try working on your so-called "expert".

 

...convincing them that we're all unapproachable academic snobs

 

You migh consider practicing what you preach.

[Cap'n Refsmmat]

The error was not minor and it was repeated and reinforced. I can recognize incompetence even when you cannot or chosoe not to.

This does not erase the distinction between tact and intellectual snobbery. It merely demonstrates your responsibility to choose words carefully.

 

If you'd really care to argue over this, I suggest you take it up via private message; let's keep this discussion on-topic. And civil.

[Iggy]

Only one person will actually feel an acceleration, while the other feels nothing. Acceleration is not relative in the same way that velocity is.

Bingo.

 

As long as the frames are inertial (constant velocity motion) the time dilation will be symmetric between the two frames — each will see the other's clocks as running slow. But as soon as one of them accelerates, this symmetry is broken.

I've had trouble with this and would appreciate any perspective.

 

Acceleration, to me, seems self-evidently relative. If the velocity between two twins is changing then either can consider himself at rest and consider the other to be accelerating. It would be a coordinate choice. Newton's apple accelerates relative to the earth, and the earth accelerates relative to the apple.

 

Only by equating inertial motion with constant velocity does acceleration break symmetry, but I wouldn't understand insisting on that type of equivalence because there are counterexamples. A person could even implement a twin paradox experiment where neither twin feels inertial forces. The Apollo 13 astronauts were able to turn about and head back toward earth weightless the whole way.

 

It makes more sense to me to allow a sort of reciprocity principle between relatively accelerating frames -- that is to say, it is not that one frame is at rest and the other changes velocity. But rather, the different amounts of mass in the two different coordinate systems makes it asymmetrical. In one frame a spaceship is at rest while most of the mass of the universe is changing velocity and in the other most everything is at rest while just a small spaceship changes velocity.

 

It seems so clear to me that's the thing that makes the situation asymmetrical, but I can never get anyone to agree with me.

[DrRocket]

I've had trouble with this and would appreciate any perspective.

 

Acceleration, to me, seems self-evidently relative. If the velocity between two twins is changing then either can consider himself at rest and consider the other to be accelerating. It would be a coordinate choice. Newton's apple accelerates relative to the earth, and the earth accelerates relative to the apple.

 

It seems so clear to me that's the thing that makes the situation asymmetrical, but I can never get anyone to agree with me.

 

The hypothesis of the twin paradox is symmetrical from a purely kinematical point of view. But it is distinctly not symmetrical from an overall physical point of view. Acceleration relative to an inertial frame is readily sensed and that distinguishes uniform motion relative to an inertial frame from uniform motion relative to any other frame -- when a car accelerates you can feel yourself pushed back into the seat even though you are at rest relative to the car.

 

Special relativity and the Lorentz transformations apply only between inertial reference frames. It is rather like applying a mathematical theorem -- before you can correctly use the conclusion you must first verify that the conditions of the hypothesis are satisfied. In special relativity that means starting with an inertial reference frame.

[D H]

Acceleration, to me, seems self-evidently relative.

It's not relative. You can measure your acceleration as a purely local experiment. Spacecraft, machinery that are subject to vibrations, hand controllers for some video games, and even cellphones are equipped with such a device. Accelerometers measure acceleration relative to a local inertial frame. (Or relative to "the fabric of space-time", a term I don't quite like.)

 

Einstein used the equivalence principle as a guiding principle in his formation of general relativity. Note that it is not an axiom of relativity. (It can't be; it doesn't work for describing how gravitation causes light to curve.) Nonetheless, it was an important guiding principle in the development of general relativity and remains an important concept in the understanding and testing of general relativity. The equivalence principle says quite a bit about why acceleration is something special, and also why the Newtonian concept of an inertial frame is incorrect.

 

Acceleration is not relative in the sense that velocity is relative.

[DrRocket]

.....the Newtonian concept of an inertial frame is incorrect.

 

Nonsense.

 

The Newtonian concept of an inertial frame is the same concept as an inertial frame in special relativity. The kinematical equations describing transformations among inertial frames are different, but the concept of the frames themselves is identical.

 

The concept is valid and very useful. It can hardly be called "incorrect". Witness the success of special relativity and of Newtonian mechanics as an approximation that is quite adequate in a great many situations.

 

What must be recognized is that an inertial reference frame is an idealization, whether one is working with special relativity or with Newtonian mechanics. And to effectively use that idealization one must check the specific circumstances of the situation under consideration.