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

[swansont]

The Apollo 13 astronauts were able to turn about and head back toward earth weightless the whole way.

 

Were they? They were not in a closed orbit, they were in (or nearly in) a free-return trajectory, meaning they were not in a gravitational bound state with respect to the moon. The gravitational force and centripetal force would not have been equal.

 

It took Apollo 13 ~ 77 hours to get to the moon, giving them a speed of about 3600 m/s. (Their occultation time was about 25 min, which agrees with this speed at an altitude of about 60 km ± 60 km or so). For an orbit at that speed, you would need a radius of about 375 km, which is well inside the moon's radius of 1737 km. Thus, they could not have been in free-fall, so they were not weightless. They should have been pulling about a third of a g of acceleration during that maneuver.

 

edit: Ignore this. The only force present is gravity (duh). I don't know what I was thinking when I was typing this up.

[Delta1212]

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.

 

Here's a difference between accelerated and inertial motion: acceleration is the result of the application of a non-zero net force to an object. While it may not be possible to determine which of two objects is accelerating based purely on the change in their relative velocities, only one will be experiencing a force and this is what creates the asymmetry.

 

What you're proposing is the equivalent of saying that when you throw a baseball, you aren't accelerating the ball at all, but rather pushing off from it and dragging the entire rest of the universe with you while the ball remains in place. That would mean you accelerated the entire universe instantaneously, which you not only didn't apply enough force to accomplish, but would require both action at a distance and for you to propagate information at superluminal speeds (specifically, again, instantaneously).

 

 

Even besides all that, it is possible to determine whether you are currently accelerating without relying on external points of reference, unlike with an inertial reference frame where speed can only be determined with respect to something else. If I'm on that spaceship for instance, and drop a ball, if the spaceship is accelerating, the ball will "fall" in the opposite direction. If the spaceship is not, the ball will float. Were you to actually find a way in which to accelerate everything in the universe except for the spaceship, conducting such a simple experiment would demonstrate that it was the universe that was accelerating and not you, regardless of the fact that you're less massive.

Edited February 28, 2012 by Delta1212

[D H]

... and also why the Newtonian concept of an inertial frame is incorrect.

Nonsense.

 

Hmmm. Then I guess this is nonsense, too.

 

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

 

And a bit later in the same post,

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.

[Iggy]

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.

It is not symmetrical. I said as much. One can, however, use the same physics (GR) in either coordinate system (where either twin is at rest throughout) and get the correct answer.

 

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

I'm not saying that acceleration relative to an inertial frame is relative. I'm saying acceleration is relative. Acceleration means change in velocity.

[DrRocket]

Hmmm. Then I guess this is nonsense, too.

 

 

 

And a bit later in the same post,

 

 

Once again you demonstrate a total lack of understanding of the basic concepts of physics.

 

A global inertial reference is indeed a convenient fiction. It is convenient in the sense that it allows one to use the convenient fiction of Newtonian mechanics for many applications and the convenient fiction of special relativity in other applications.

 

A convenient fiction indeed. But nevertheless a fiction.

 

In general relativity a local inertial reference frame, is nothing more and nothing less than a local reference frame attached to a body in free fall. Yep, that does exist. Where do you think that the "equivalence principle" came from ? It is basically just this simple idea.

 

I suspect that you do not understand manifold theory and hence do not understand what "local" means. But local reference frames do indeed exist and without them one does not have the mathematical theory of manifolds and differential geometry. General relativity is based on the theory of Lorentzian manifolds and gravitation is the result of curvature in that setting. Local coordinate systems are rather important, and in general relativity local Lorentzian frames are particularly important.

 

So, yes the post that I labeled as "nonsense" is indeed "nonsense". So is your reply. Nonsense on top of nonsense.

[D H]

I'm not saying that acceleration relative to an inertial frame is relative. I'm saying acceleration is relative. Acceleration means change in velocity.

It's the acceleration relative to an inertial frame (specifically, with respect to a co-moving local inertial frame) that makes the twin situation asymmetric. There's something quite special about this acceleration. It is measurable with an accelerometer. An accelerometer is a local device; there's no need to look outside the window to measure this acceleration.

[Iggy]

It's not relative. You can measure your acceleration as a purely local experiment.

In fact, that is precisely what cannot be done. If I'm in a windowless elevator it is impossible to tell if I am accelerating toward the surface of a planet or floating in deep space. I can tell if I'm in an inertial frame, but that doesn't automatically tell me that I'm "accelerating" in an absolute sense. In one coordinate system I may be accelerating while I'm at rest in another. The only way to make acceleration absolute is to declare all non-inertial coordinate systems invalid.

 

Accelerometers measure acceleration relative to a local inertial frame.

You could understand my confusion maybe when you say that acceleration isn't relative, but the explanations so far include descriptions only of "acceleration relative to..." an inertial frame or the bulk mass of the universe or some other thing. The argument seems somewhat circular to me.

 

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

In the same way that there is no preferred inertial frame in SR, there should be no preferred coordinate system in GR, so I think it is exactly relative in that sense. What I'm hearing is that the 'traveling' twin cannot consider himself at rest -- cannot use a coordinate system where he is at rest -- but I don't understand the physics to say that. I think he can.

 

While it may not be possible to determine which of two objects is accelerating based purely on the change in their relative velocities, only one will be experiencing a force and this is what creates the asymmetry.

I agree that inertial forces are absolute.

 

Were they? They were not in a closed orbit, they were in (or nearly in) a free-return trajectory, meaning they were not in a gravitational bound state with respect to the moon. The gravitational force and centripetal force would not have been equal.

Thank you for the correction. I didn't know that. In principle, however, I think the point stands. It could be accomplished.

 

It's the acceleration relative to an inertial frame (specifically, with respect to a co-moving local inertial frame) that makes the twin situation asymmetric. There's something quite special about this acceleration. It is measurable with an accelerometer. An accelerometer is a local device; there's no need to look outside the window to measure this acceleration.

I understand what you're saying, but give me some credit here.

 

If I'm in a spaceship in deep space and there are no windows and I find myself pushed against the rear of the craft I can use general relativity to declare two different, and equally true, scenarios:

 

I am accelerating relative to most everything else in the universe (all of that stuff being at rest) and I feel an inertial force as a result.

 

I am at rest and most everything else in the universe is accelerating (changing velocity). When mass accelerates there is an associated gravitational field. I would expect that field to push me against the back end of the craft since I'm at rest in the uniform gravitational field. Everything else is freefalling in the field so I'm the only thing feeling the inertial force.

 

Einstein himself gave this thought experiment (with a train that changed velocity relative to its surroundings as I recall) to make the point that both frames were valid and gave the correct answer. Neither is any more correct than the other -- one is just more cumbersome and unintuitive. But, that shouldn't be an argument against its validity.

 

The acceleration of the spaceship is a coordinate choice. That's how it makes sense to me, but like I say, I can never get anyone to agree.

[D H]

A global inertial reference is indeed a convenient fiction. It is convenient in the sense that it allows one to use the convenient fiction of Newtonian mechanics for many applications and the convenient fiction of special relativity in other applications.

Of course a Newtonian inertial frame is a convenient fiction. If there was no validity to the Newtonian concept of an inertial frame, the various space agencies around the world wouldn't use what is essentially a Newtonian inertial frame, the International Celestial Reference Frame, to plan, control, and analyze their space missions. Oftentimes they do this from a purely Newtonian perspective; no general relativity at all. The organizations such as the International Earth Rotation and Reference Systems Service (http://www.iers.org), the International Astronomical Union (http://www.iau.org), the U.S. Naval Observatory (http://www.usno.navy.mil/USNO) that develop this best guess at an inertial frame do consider relativistic effects, but as a small perturbation of an otherwise Newtonian universe.

 

 

A convenient fiction indeed. But nevertheless a fiction.

In other words, ultimately incorrect.

 

There's a huge difference between a scientific hypothesis that is experimentally shown to be completely false and one that is shown to have limited applicability. Observations starting in the latter decades of the 19th century showed that something was wrong with Newtonian mechanics. Special relativity, general relativity, and quantum mechanics collectively showed that Newtonian mechanics is not universally true. This lack of universality does not mean that Newtonian mechanics is utterly false. There's a huge difference between a scientific hypothesis that is experimentally shown to be completely false and one that is shown to have limited applicability.

 

IMO, this is where Popper got things a bit wrong with regard to falsification. Per Popper's naive falsification, we should be using quantum mechanics or general relativity to do all physics, almost all engineering. That isn't the case. Even though 20th century science showed that Newtonian mechanics is not the universal truth that physicists for the 200 years following Newton thought it was, Newtonian physics still remains a very useful concept precisely because the limited domain in which it is accurate is very important to us.

[Delta1212]

In fact, that is precisely what cannot be done. If I'm in a windowless elevator it is impossible to tell if I am accelerating toward the surface of a planet or floating in deep space. I can tell if I'm in an inertial frame, but that doesn't automatically tell me that I'm "accelerating" in an absolute sense. In one coordinate system I may be accelerating while I'm at rest in another. The only way to make acceleration absolute is to declare all non-inertial coordinate systems invalid.

 

 

You could understand my confusion maybe when you say that acceleration isn't relative, but the explanations so far include descriptions only of "acceleration relative to..." an inertial frame or the bulk mass of the universe or some other thing. The argument seems somewhat circular to me.

 

 

In the same way that there is no preferred inertial frame in SR, there should be no preferred coordinate system in GR, so I think it is exactly relative in that sense. What I'm hearing is that the 'traveling' twin cannot consider himself at rest -- cannot use a coordinate system where he is at rest -- but I don't understand the physics to say that. I think he can.

 

 

I agree that inertial forces are absolute.

 

 

Thank you for the correction. I didn't know that. In principle, however, I think the point stands. It could be accomplished.

 

 

I understand what you're saying, but give me some credit here.

 

If I'm in a spaceship in deep space and there are no windows and I find myself pushed against the rear of the craft I can use general relativity to declare two different, and equally true, scenarios:

 

I am accelerating relative to most everything else in the universe (all of that stuff being at rest) and I feel an inertial force as a result.

 

I am at rest and most everything else in the universe is accelerating (changing velocity). When mass accelerates there is an associated gravitational field. I would expect that field to push me against the back end of the craft since I'm at rest in the uniform gravitational field. Everything else is freefalling in the field so I'm the only thing feeling the inertial force.

 

Einstein himself gave this thought experiment (with a train that changed velocity relative to its surroundings as I recall) to make the point that both frames were valid and gave the correct answer. Neither is any more correct than the other -- one is just more cumbersome and unintuitive. But, that shouldn't be an argument against its validity.

 

The acceleration of the spaceship is a coordinate choice. That's how it makes sense to me, but like I say, I can never get anyone to agree.

I understand what you're trying to say, and can see why, but again, if acceleration is a relative property (it is equally valid to say that an object is accelerating or everything except that object is accelerating) then you still need to explain how throwing a ball causes the entire universe except for the ball to accelerate. I'm not a physicist, but unless I'm grossly misunderstanding some fundamentals, there's no mechanism by which this could be occurring in a way that would match the observed effects. You'd need to be transmitting the accelerating force at FTL speeds.

 

I'd welcome an explanation of why I'm wrong, though. That's largely why I'm here to begin with.

[DrRocket]

In other words, ultimately incorrect.

 

 

Wrong again.

 

The Newtonian theory of mechanics and special relativity are ultimately incorrect. The former was shown invalid by relativity and special relativity applies only in the complete absence of gravity.

 

But the subject was the concept of an inertial reference frame. A concept cannot be incorrect. It can be inapplicable or inappropriately applied, but a conceptual construct is not incorrect unless is inconsistent. The concept of an inertial reference frame is perfectly valid. The Newtonian theory of mechanics and the special theory of relativity are consistent -- they are just not correct in the final analysis.

 

BTW, virtually ALL existing physical theories are probably incorrect. General relativity and quantum field theories -- the current pillars of physical theory -- are incompatible with one another. They cannot all be correct, and it is quite likely that all of them will be revised in some future theory that will be more nearly correct. It is also quite possible that in the usual progress of physical theories as a series of successively better approximations that we may never have a theory that is "correct" in the purist sense that you seem to use the word.

 

You are missing the essence of the issue and the essence of the basic physical theories in your effort to prove yourself "correct". These distinctions are important and crucial to ever reaching a profound understanding of the subject.

 

In fact, that is precisely what cannot be done. If I'm in a windowless elevator it is impossible to tell if I am accelerating toward the surface of a planet or floating in deep space. I can tell if I'm in an inertial frame, but that doesn't automatically tell me that I'm "accelerating" in an absolute sense. In one coordinate system I may be accelerating while I'm at rest in another. The only way to make acceleration absolute is to declare all non-inertial coordinate systems invalid.

 

 

 

You are touching on the essence of general relativity.

 

But you cannot apply these ideas in the context of special relativity or of Newtonian mechanics.

 

It is important to recognize the fundamental differences among these theories and to use them only in situations in which they are applicable.

 

Newtonian mechanics and special relativity are both extremely useful theories. But they do not apply to every situation. You cannot force fit them where they do not fit.

 

In Newtonian mechanics and special relativity acceleration is absolute. There is a very simple reason for this. Suppose you have found an inertial reference frame (forget about the problem that they don't really exist in nature and accept the idealization). Then every other inertial reference frame in the universe is in uniform motion with respect to the one that you have in hand. Inertial reference frames are very special. They are so special that acceleration with respect one is acceleration with respect to all of the others -- velocity differences differ by a constant vector, acceleration is the same in all of them.

 

So, when you work in the context of Newtonian mechanics or special relativity, acceleration is indeed absolute.

 

As a practical matter there are frames that are very good, not perfect but very good, approximations to true inertial reference frames. They are good when used with appropriate understanding of their limitations. Don't push them too far. Too far depends on the context.

 

If you want to deviate from that you are left with an alternate theory. The most common alternate theory is general relativity. It has the advantage that it is supported by a lot of experimental evidence. One of the things that you give up in general relativity are global reference frames. You then have to contend with mathematics that is quite a bit more abstract than what you see in Newtonian mechanics or special relativity. Reference frames become local charts. Ordinary derivatives become covariant derivatives. Geometry is no longer Euclidean. The metric is not positive-definite, but rather Lorentzian.

Edited February 28, 2012 by DrRocket

[IM Egdall]

Another way to look at it is this: Stay-at-home Steve is on Earth. Arianna takes a rocket trip to a distant star and returns to the Earth. When they compare their watches at the end of the trip. they find Arianna's watch on the rocket has run slower than Steve's on Earth. This assymetry is due to the fact that Steve has stayed in a single inertial reference frame all along. But Arianna in the rocket has actually been in two inertial reference frames -- one going away from Earth, and the other returning to Earth. It is this asymmetry experienced by Arianna which results in her clock runnung slower than Steve's.

 

 

Now you may try to argue that to Arianna, Steve had moved away from the rocket, and then he has moved towards the rocket. But this is not so. Steve felt (measured) no change in speed or direction. (A simple accelerometer would verify this.) But Arianna had to change inertial frames, and in doing so, she did feel (and measure) a change in speed and direction.

 

In the simplest analogy, it is as though Arianna jumped from her outbound uniformly moving ship to an inbound uniformly moving ship. (This is of course a simplification.) Steve did not have to do anything of the sort. He remained in the same reference frame -- the Earth -- the whole time.

 

You can show the slowing of time occurs for the rocket observer and not for the Earth-bound observer using special relativity (time dilation) and the doppler shift. If you want to see the details, go to marksmodernphysics.com then click on ITs Relative, Archives, and The Twins Paradox

[D H]

Were they? They were not in a closed orbit, they were in (or nearly in) a free-return trajectory, meaning they were not in a gravitational bound state with respect to the moon. The gravitational force and centripetal force would not have been equal.

Apollo 13 was not in a free return trajectory at the time of the incident. Apollo 8, 10, and 11 used a free return trajectory that involved flying around the Moon and returning to Earth with no maneuver required (theoretically, at least). This severely limited the choice of landing sites on the Moon. Subsequent missions, including Apollo 13, did not use such a trajectory. Those later missions instead started their voyage to the Moon on a free return trajectory that would have had the vehicle fall far short of reaching the Moon should the vehicle undergo some massive failure.

 

The first midcourse correction took the vehicle off of this sublunar free return trajectory and onto a translunar trajectory. This translunar trajectory was not a free return trajectory. A massive failure (worse than Apollo 13) at this stage was a irrecoverable CRIT1 (loss of mission, loss of life) failure, one of the very few irrecoverable CRIT1 failure scenarios that were waived.

 

Thus, they could not have been in free-fall, so they were not weightless. They should have been pulling about a third of a g of acceleration during that maneuver.

There was no maneuver as Apollo 13 went around the Moon. It was in free fall. There was a trans-Earth injection burn, but that wasn't performed until two hours after perilune. The Apollo 13 astronauts watched the Moon underneath, weightless. A point mass in a free fall trajectory cannot feel gravity. The Apollo capsule is not a point mass, but the tidal forces (which can be felt) on the Apollo 13 astronauts would have been very small.

Edited February 28, 2012 by D H

[DrRocket]

Another way to look at it is this: Stay-at-home Steve is on Earth. Arianna takes a rocket trip to a distant star and returns to the Earth. When they compare their watches at the end of the trip. they find Arianna's watch on the rocket has run slower than Steve's on Earth. This assymetry is due to the fact that Steve has stayed in a single inertial reference frame all along. But Arianna in the rocket has actually been in two inertial reference frames -- one going away from Earth, and the other returning to Earth. It is this asymmetry experienced by Arianna which results in her clock runnung slower than Steve's.

 

The equations of special relativity, particularly the "time dilation effect" of the Lorentz transformations apply only when used in an inertial reference frame. You can analyze acceleration in special relativity, but first you need find an inertial frame in which that acceleration is determined. In the twin paradox there is only one inertial frame in evidence -- that of Steve. It is pretty clear from simple considerations of special relativity that Steve sees a greater time elapse than does Ariana, at least in his reference frame. Since the same physics takes place in all reference frames Steve's perspective is valid, and relatively easily understood. You can take Arianna's perspective, but to do that you need to reference things back to some inertial reference frame and modify the transformation laws -- a real mess. If you do that you will get the same answer, plus a headache.

 

One can also use general relativity. First, put Steve in orbit around the Sun, neglecting the Earth. That is what is really intended by the stay-at-home epithet. Then Steve is in free fall and therefore his world line is a spacetime geodesic. Arianna on the other hand has a world line that is not a geodesic -- she is undergoing forces other than gravity. Now their world lines intersect at two points -- when Arianna leaves and when she returns. The length of their two world lines is (in units in which c=1) the proper time measured by their respective clocks. Because Steve's world line is a geodesic it is the longest spacetime path between those two points, hence Steve measure a greater elapsed time than does Arianna.

[swansont]

Apollo 13 was not in a free return trajectory at the time of the incident. Apollo 8, 10, and 11 used a free return trajectory that involved flying around the Moon and returning to Earth with no maneuver required (theoretically, at least). This severely limited the choice of landing sites on the Moon. Subsequent missions, including Apollo 13, did not use such a trajectory. Those later missions instead started their voyage to the Moon on a free return trajectory that would have had the vehicle fall far short of reaching the Moon should the vehicle undergo some massive failure.

 

The first midcourse correction took the vehicle off of this sublunar free return trajectory and onto a translunar trajectory. This translunar trajectory was not a free return trajectory. A massive failure (worse than Apollo 13) at this stage was a irrecoverable CRIT1 (loss of mission, loss of life) failure, one of the very few irrecoverable CRIT1 failure scenarios that were waived.

 

OK, then I misunderstood what I had read about this.

 

There was no maneuver as Apollo 13 went around the Moon. It was in free fall. There was a trans-Earth injection burn, but that wasn't performed until two hours after perilune. The Apollo 13 astronauts watched the Moon underneath, weightless. A point mass in a free fall trajectory cannot feel gravity. The Apollo capsule is not a point mass, but the tidal forces (which can be felt) on the Apollo 13 astronauts would have been very small.

 

My confusion stems from the acceleration they must have undergone not being anywhere close to the local gravitational acceleration, which, now that I think about it, doesn't make sense.

[Iggy]

You are touching on the essence of general relativity.

I have discussed nothing but general relativity.

 

In Newtonian mechanics and special relativity acceleration is absolute.

 

Special relativity is the special case of uniform motion and in it uniform motion is special. That's fantastic, but I don't think it quite addresses my argument.

 

Another way to look at it is this: Stay-at-home Steve is on Earth. Arianna takes a rocket trip to a distant star and returns to the Earth. When they compare their watches at the end of the trip. they find Arianna's watch on the rocket has run slower than Steve's on Earth. This assymetry is due to the fact that Steve has stayed in a single inertial reference frame all along. But Arianna in the rocket has actually been in two inertial reference frames -- one going away from Earth, and the other returning to Earth. It is this asymmetry experienced by Arianna which results in her clock runnung slower than Steve's.

Everyone is a priori equating inertial forces with acceleration. This is the premise against which I'm arguing and it is the premise which GR overthrows. Why does Ariana feel an inertial force? This is the question. Either she is stationary in a gravitational field or she is accelerating. It depends on how you look at it. It's relative. The fact that she does feel an inertial force doesn't prove that she is accelerating in an absolute sense.

 

Now you may try to argue that to Arianna, Steve had moved away from the rocket, and then he has moved towards the rocket.

That is a fact which cannot be denied.

 

Perhaps I'm explaining this horrifically. Einstein belabors the point here: Dialog about...

[DrRocket]

I have discussed nothing but general relativity.

 

In which case the notion of a "reference frame" is purely local.

 

 

Special relativity is the special case of uniform motion and in it uniform motion is special. That's fantastic, but I don't think it quite addresses my argument.

 

Not really. Special relativity is general relativity in a flat spacetime in which the spatial part is Euclidean. In that unique case there is a single Lorentzian chart that covers the entire spacetime manifold. However, in any spacetime that has mass and therefore gravity (our universe for instance) this condition is not met.

 

It is quite possible to handle acceleration in special relativity. But to do it you ultimately refer everything to some inertial reference frame.

 

It does address your argument if you think about it. You are attempting to shift among reference frames that are not in uniform motion with respect to one another. It is impossible for both of them to be inertial and universal.

[Iggy]

DrRocket, you're not addressing what I'm saying at all. I'm not claiming that inertial frames are universal. I'm not saying that measurements can be taken from non-inertial frames in SR. I'm not saying that both frames are inertial in the twin paradox.

 

The following link was translated from german, so it is somewhat cumbersome to read, but it was written by Einstein and expresses the same thing I'm saying. If read, I think it would get us on the same page. Dialog about...

[DrRocket]

DrRocket, you're not addressing what I'm saying at all. I'm not claiming that inertial frames are universal. I'm not saying that measurements can be taken from non-inertial frames in SR. I'm not saying that both frames are inertial in the twin paradox.

 

 

You are the who is not listening. I am indeed addressing what you are saying, even if you do not recognize that fact.

 

Any two global inertial reference frames must be in uniform motion with respect to one another. It is impossible for both of the frames in the twin paradox to be inertial.

The term inertial reference frame in special relativity refers to a global inertial reference frame.

 

I have explained to you how the twin paradox is addressed in general relativity. The mathematics of general relativity is quite different and more involved than the simple mathemtics of special relativity. You are trying to mix the two in a way that cannot be done.

Edited February 29, 2012 by DrRocket

[Iggy]

I'm not saying that both frames are inertial in the twin paradox.

It is impossible for both of the frames in the twin paradox to be inertial.

Please, slow down and read what I'm saying.

 

I have explained to you how the twin paradox is addressed in general relativity...

 

You are trying to mix the two in a way that cannot be done.

You might be mixing me up with another member. That would explain things.

 

You mentioned special relativity, not I. I don't know why you keep referring to it. I'm the bloke that asserted that acceleration is relative. SR asserts only the equivalence of inertial frames. It is obviously ill equipped to even deal with the subject. I don't know why you brought it up in post 23 and I don't know why you continue to talk about it.

 

I'm going to quote the relevant bits of the link I posted in hopes it can illuminate where I'm coming from.

 

It is certainly correct that from the point of view of the general theory of relativity we can just as well use coordinate system K' as coordinate system K...

 

 

It should be kept in mind that in the left and in the right section exactly the same proceedings are described, it is just that the description on the left relates to the coordinate system K, the description on the right relates to the coordinate system K'. According to both descriptions the clock U2 is running a certain amount behind clock U1 at the end of the observed process.

 

When relating to the coordinate system K' the behaviour explains itself as follows: During the partial processes 2 and 4 the clock U1, going at a velocity v, runs indeed at a slower pace than the resting clock U2. However, this is more than compensated by a faster pace of U1 during partial process 3. According to the general theory of relativity, a clock will go faster the higher the gravitational potential of the location where it is located, and during partial process 3 U2 happens to be located at a higher gravitational potential than U1. The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 and 4. This consideration completely clears up the paradox that you brought up [that each clock would be running behind the other at the end]...

 

You declared the fields that were called for in the clock example also as merely fictitious, only because the field lines of actual gravitational fields are necessarily brought forth by mass; in the discussed examples no mass that could bring forth those fields was present. This can be elaborated upon in two ways. Firstly, it is not an a priori necessity that the particular concept of the Newtonian theory, according to which every gravitational field is conceived as being brought forth by mass, should be retained in the general theory of relativity. This question is interconnected with the circumstance pointed out previously, that the meaning of the field components is much less directly defined as in the Newtonian theory. Secondly, it cannot be maintained that there are no masses present, that can be attributed with bringing forth the fields. To be sure, the accelerated coordinate systems cannot be called upon as real causes for the field, an opinion that a jocular critic saw fit to attribute to me on one occasion. But all the stars that are in the universe, can be conceived as taking part in bringing forth the gravitational field; because during the accelerated phases of the coordinate system K' they are accelerated relative to the latter and thereby can induce a gravitational field, similar to how electric charges in accelerated motion can induce an electric field. Approximate integration of the gravitational equations has in fact yielded the result that induction effects must occur when masses are in accelerated motion. This consideration makes it clear that a complete clarification of the questions you have raised can only be attained if one envisions for the geometric-mechanical constitution of the Universe a representation that complies with the theory. I have attempted to do so last year, and I have reached a conception that - to my mind - is completely satisfactory; going into this would however take us too far...

 

There are several reasons that compel us to willingly accept the complications that the theory leads us to. In the first place, it means for a man who maintains consistency of thought a great satisfaction to see that the concept of absolute motion, to which kinematically no meaning can be attributed, does not have to enter physics; it cannot be denied that by avoiding this concept the foundation of physics has gained in consistency...

 

In asserting the equality of coordinate systems as a matter of principle it is not said that every coordinate system is equally convenient for examining a certain physical system; we see this in classical mechanics also. For example, strictly speaking one cannot say that the Earth moves in an ellipse around the Sun, because that statement presupposes a coordinate system in which the Sun is at rest, while classical mechanics also allows systems relative to which the Sun rectilinearly and uniformly moves...

 

In Mister Lenard's example the situation is similar. In terms of the theory of relativity the case may not be construed in such a way that possibly it is after all the surroundings (of the train) that experienced the change in velocity. We are not dealing here with two different, mutually exclusive hypotheses about the seat of the motion, rather with two ways, equally valid in principle, of representing the same factual situation...

 

Einstein 1918

 

Now, please, understand: my claim is not founded in special relativity. I'm saying that the twin who we normally think of as "accelerating" has just as much right to consider himself at rest in his coordinate system... which is only natural. I am always at the center of my coordinate system. I should have the right to say that it is the other twin who is changing velocity. Does GR not give me the freedom to say that?

Edited February 29, 2012 by Iggy

[DrRocket]

Does GR not give me the freedom to say that?

 

no

[JohnStu]

Man is this post derailed.

 

There is a universal frame of reference just that they don't have an accurate one yet.

 

 

[Iggy]

What you're proposing is the equivalent of saying that when you throw a baseball, you aren't accelerating the ball at all, but rather pushing off from it and dragging the entire rest of the universe with you while the ball remains in place. That would mean you accelerated the entire universe instantaneously, which you not only didn't apply enough force to accomplish, but would require both action at a distance and for you to propagate information at superluminal speeds (specifically, again, instantaneously).

I apologize -- I missed responding to a lot of good points.

 

Clearly, throwing a baseball doesn't cause the universe to accelerate.

 

Different coordinate systems have different properties. Specifically, in terms of general relativity, the gravitational field looks different in each. I don't think switching coordinate systems necessarily means causing a change in those properties in the way you're thinking.

 

As an analogy, the kinetic energy of the umpire is zero from the pitcher's perspective, but it is much larger from the baseball's perspective. Throwing the baseball doesn't really "cause" the kinetic energy of the umpire to change as if the baseball had to push him. In the same way... I don't think that igniting thrusters on a spacecraft causes a uniform gravitational field to appear throughout the universe, nor does it cause everything in the universe to accelerate in freefall in that field. The coordinate system changes.

 

Even besides all that, it is possible to determine whether you are currently accelerating without relying on external points of reference, unlike with an inertial reference frame where speed can only be determined with respect to something else. If I'm on that spaceship for instance, and drop a ball, if the spaceship is accelerating, the ball will "fall" in the opposite direction. If the spaceship is not, the ball will float.

But, you are assuming that feeling a pseudo-force necessarily means that you are accelerating (you are changing velocity). That is a presumption that general relativity does not make. You can be "at rest" (not changing velocity) in general relativity and yet feel an inertial force.

 

For example, if you used an accelerometer right now it would tell you that you're accelerating. But, general relativity would let you use a coordinate system where you're at rest right now on the surface of a planet. Likewise, in a spaceship in deep space if there is a uniform gravitational field throughout the universe against which you are holding yourself motionless with thrusters then you could describe yourself as stationary -- not accelerating -- but feeling an inertial pseudo-force.

 

If that coordinate choice is valid in general relativity then acceleration is not an absolute thing. It depends on perspective. The spaceship accelerates relative to earth and the rest of the cosmos, while earth and the cosmos accelerates relative to the spaceship.

 

Were you to actually find a way in which to accelerate everything in the universe except for the spaceship, conducting such a simple experiment would demonstrate that it was the universe that was accelerating and not you, regardless of the fact that you're less massive.

But, in GR the gravitational field of accelerating mass has a component that acts to drag things in the direction of acceleration. If everything out there is accelerating in one direction, while you're in a spaceship, you would expect to have to hold yourself motionless against that gravitational field by firing thrusters. As a result, you would feel an inertial force even though you are at rest -- just like sitting on the surface of a planet.

 

It is also the uniform gravitational field that resolves the asymmetrical time dilation from the perspective of the younger twin.

 

If GR is correct that the coordinate systems are equally valid then it isn't that "the spaceship is absolutely accelerating" and it isn't that "the universe is absolutely accelerating", but that they are accelerating relative to one another. It is a matter of perspective. I find that idea intuitive and agreeable. Like Einstein said, "it means for a man who maintains consistency of thought a great satisfaction to see that the concept of absolute motion, to which kinematically no meaning can be attributed, does not have to enter physics"

 

Does GR not give me the freedom to say that?

no

Enlightening. Thank you.

[D H]

Man is this post derailed.

 

There is a universal frame of reference just that they don't have an accurate one yet.

No, there isn't. The Newtonian concept of an inertial frames is a fiction. A very useful fiction, but a fiction nonetheless.

 

 

But, you are assuming that feeling a pseudo-force necessarily means that you are accelerating (you are changing velocity). That is a presumption that general relativity does not make. You can be "at rest" (not changing velocity) in general relativity and yet feel an inertial force.

You can not feel inertial forces. Inertial forces, like the Newtonian concept of an inertial frame, are fictions. Very useful fictions, but fictions nonetheless. Another word for inertial force is fictitious force.

 

Imagine you are standing still on the ground, watching someone on a merry-go-round. From that person's perspective, you are moving, and also accelerating. In addition to the vertical normal force and vertical gravitational force, you apparently are also subject to a horizontal centrifugal force and a horizontal coriolis force. Do you feel those horizontal forces? Of course not. They aren't quite real. From your perspective, you are subject to just the normal force (which you can feel) and gravitation (which you can't). From the perspective of a falling apple, the only force acting on you is the upward normal force. That gravitational force you think is pulling you Earthward is a fictitious force. You can't feel it precisely because it is an inertial force.

[Iggy]

You can not feel inertial forces.

I'm not sure how to respond. When I say "feel an inertial force" I mean "detect the fact that one is not in an inertial frame". I mean when mass has weight.

 

Your response, when asked if acceleration was relative, was to say "you can measure your acceleration as a purely local experiment". That's the thing I'm responding to. It isn't true. How would you propose it be done? You're in a box with no windows and an accelerometer measures 9.8 m/s^2 -- are you accelerating?

 

Of course, it's easy to say that you are "accelerating relative to an inertial frame", but I'm the one saying that acceleration is relative. Telling me that you can detect acceleration relative to something isn't a refutation.

 

Imagine you are standing still on the ground, watching someone on a merry-go-round. From that person's perspective, you are moving, and also accelerating. In addition to the vertical normal force and vertical gravitational force, you apparently are also subject to a horizontal centrifugal force and a horizontal coriolis force.

From that person's perspective the entire universe is rotating. You would have to assert, using general relativity, that rotating a universe about someone subjects everything in that universe to a centrifugal force. Very good arguments have been made that it does not.

 

Do you feel those horizontal forces? Of course not. They aren't quite real. From your perspective, you are subject to just the normal force (which you can feel) and gravitation (which you can't).

Pseudo forces are coordinate system dependent. When I say that they can be felt, I obviously mean that they can be felt in the coordinate system in which they exist.

 

It's like proper time. You may not experience someone else's proper time, but that doesn't mean it doesn't exist. Everyone, in whatever coordinate system they are in, needs to agree on a person's proper time -- just like they all need to agree on the magnitude of inertial force (i.e. the extra weight) that the girl on the merry-go-round feels... even if they themselves don't feel it.

Edited March 1, 2012 by Iggy

[D H]

Your response, when asked if acceleration was relative, was to say "you can measure your acceleration as a purely local experiment". That's the thing I'm responding to. It isn't true. How would you propose it be done? You're in a box with no windows and an accelerometer measures 9.8 m/s^2 -- are you accelerating?

Yes.

 

Of course, it's easy to say that you are "accelerating relative to an inertial frame", but I'm the one saying that acceleration is relative. Telling me that you can detect acceleration relative to something isn't a refutation.

Well, to be blunt, you're wrong.

 

Theories in physics have to follow three simple metarules.

1. The theory has to have some logically consistent underpinning. This can range from a simple ad hoc equation whose only logically consistent underpinning is that the equation is a mathematically well-formed formula to a much deeper set of precepts from which one can derive mathematical predictions.
   
2. More important: It has to describe some testable behavior. No matter how internally consistent it might be, a "just-so" story that is not testable is not a physical theory.
   
3. Most important: It has to agree with observable reality.

 

Your concept is wrong for the simple reason that it does not agree with observable reality. The Hafele–Keating experiment, for example.

 

You appear to be misconstruing the concept of covariance in general relativity, which says that all reference frames are equally valid, to say something contrary to relativity theory. You are ignoring that no matter which explanation one uses / which point of view one takes in the twin paradox, the answers are always the same. The traveling twin ages less.

 

To argue against general relativity you need to construct some experiment and show how relativity fails that test. General relativity, at least so far, is consistent with every experiment constructed to test it.