The Twin Paradox implies that the Universe as a whole is a special frame

[jamesadrian]

TL;DR Summary

Twin Paradox implies that the universe as a whole is a special frame of motion according to "Relativity Simply Explained" by Martin Gardner.

The Twin Paradox implies that the universe as a whole is a special frame of motion according to "Relativity Simply Explained" by Martin Gardner. I want to be sure than I haven't misunderstood something. I don't find the explanation completely clear. If the universe as a whole is a special and unique frame of motion (all speeds being averaged) then I think that any explanation of the twin paradox that attempts to explain WHY it is true (not just how it works) should begin with this fact and account for it. Any references that attempt this would be greatly appreciated.

Thank you for your help.

Jim Adrian

 

[Ibix]

I don't have that book, but I'd say you've misunderstood something. The twin paradox does not show any such thing. It just shows that careless attempts to treat non-inertial motion don't work.

 

[Dale]

Summary:: Twin Paradox implies that the universe as a whole is a special frame of motion according to "Relativity Simply Explained" by Martin Gardner.

This is not correct. I am unsure if you are misunderstanding Martin Gardner or if he is a bad source.

Could you please provide the exact quote that you are referring to?

 

[pervect]

I've read some of Martin Gardner's columns in Scientific American in ages past, but I'm not familiar with the one that you are reference.

However I would guess you most likely misunderstood something, as it is definitely possible to construct a universe with no preferred frame of reference. It's just the flat, simply-connected, space-time of special relativity.

In this SR universe, as has been discussed in many other threads, some quite recent, if two twins take different routes and meet up again, the one that undergoes inertial motion will have the longest elapsed time on their clock. This reading on the clocks that each twin carries with them is known as "proper time".

In fact, this can serve as a definition of inertial motion. Inertial motion is that motion that maximizes proper time in this simple case.

Things get slightly more complicated with a more realistic universe, but it would not be productive to go into these extra complexities at the moment.

A useful analogy of this space-time example can be made in space. If two drivers on a flat plane take different routes from from some common "start" city to some common "destination" city, then the driver that drives in a straight line will drive the shortest distance.

There is a sign difference in the space-time geometry that makes the analogy of "shortest distance" instead the "longest proper time", but the principle is the same.

A driver who makes a sharp turn anywhere along the route is NOT driving in a straight line. The driver who argues "I only made one 90 degree turn - why was my journey so much longer than my twin" is misguided. It doesn't work that way.

It's also rather unproductive to ask in this case "what mechanism happened during the turn to make the trip longer". It's not the turn that made the distance longer, it's the geometry. The space-time case is similar. It's the geometry that makes the twin who doesn't move inertially age less. But in this case, it's not the Euclidean geometry of space, but the Lorentzian geometry of space-time.

The equivalent of the driver making a turn in space-time is a change in velocity. This can most easily be seen by drawing a classic space-time diagram. More can be said about the topic, but I don't want to over-complicate things at this point.

Similar to the drivers, making "just one turn" may have drastic effects on the elapsed time if the turn is sharp enough. The analogy to a "sharp turn" in the space-time case is a large velocity change. If our driver makes only one turn, but it's a minor course correction, a small angle, he won't drive much further than if he'd taken a true straight-line course. For the space-time traveling twin, the "sharp turn" is analogous to a large velocity change, and the "minor course correction" is a small velocity change.

 

[mitochan]

Summary:: Twin Paradox implies that the universe as a whole is a special frame of motion according to "Relativity Simply Explained" by Martin Gardner.
The Twin Paradox implies that the universe as a whole is a special frame of motion according to "Relativity Simply Explained" by Martin Gardner.

Oppositely I would like to say relativity simply explained no matter how each parts of universe distributes and moves. GR says there exist local IF
Rs at every spacetime. Usually local IFR is large enough to include whole events happening in our twin paradox discussions, or gravity effects are small enough to be neglected.

If not, we should consider GR instead of SR. In Schwartzshild spacetime twin A stays at constant height $r=r_1$. Twin B is popped up from there, reach height maximum $r=r_2$, falls and meets twin A at $r=r_1$. Which twin is older then ? It is a more complicated example than the usual one.
ref. https://www.physicsforums.com/threads/twin-paradox-for-freely-falling-observers.991709/

 

[Ibix]

GR says there exist local IF
Rs at every spacetime.

This doesn't make any sense. Did you mean that local inertial frames of reference can be defined around every event in spacetime?

 

[mitochan]

Well, I would say we can take local IFR at any where and any time, or at/around any spacetime point. Is it better saying ?

 

[jamesadrian]

Gardner says that when one takes the point of view of the Earth moving away from the spaceship as having an equal standing, the problem is that the whole universe moves with the Earth. He then points out the Mossbauer effect (Scientific American, March 1960). He does not explain how it works, but says that experiments using the effect can tell that time is going slower on the first floor of a skyscraper than it is at the top floor. He points out the the proximity of a large mass slows down clocks.

I would like to understand how the slowing of clocks by large masses makes the universe a special frame of reference for the purpose of understanding the twin paradox. I have only a vague idea.

Thank you for your replies and your help.

Jim Adrian

 

[jbriggs444]

I would like to understand how the slowing of clocks by large masses makes the universe a special frame of reference for the purpose of understanding the twin paradox.

It does not.

if your aim is to understand the twin paradox, the presence of large masses and curved space time is an irrelevant complication -- a distraction from the understanding you seek. You want simplicity, not complexity.

 

[Vanadium 50]

Could you please provide the exact quote that you are referring to?

Why won't you do that?

 

[Ibix]

I would like to understand how the slowing of clocks by large masses makes the universe a special frame of reference for the purpose of understanding the twin paradox.

It doesn't. Either you have misunderstood Gardner or he has misunderstood whoever he learned from. Can you please provide the exact quote you are referring to? A photo of the page will do, as long as you do it in reasonably bright light.

 

[FactChecker]

The Twin Paradox implies that the universe as a whole is a special frame of motion according to "Relativity Simply Explained" by Martin Gardner.

I notice that the post says "special frame of motion", not "inertial frame of motion". But we always knew that one can feel acceleration when they do not stay on an inertial path. That knowledge does not require any study of the twin paradox. So there are definitely different types of "frames of motion". I would say that the inertial ones are more special than non-inertial ones.
But none of that makes any specific IRF more special than another IRF, and you can imagine the twin paradox where the twin who stays at home is in any IRF.

PS. Even without reference to feeling acceleration, there are other ways to distinguish between an IRF and others. Within the context of the twin paradox, @PeterDonis has given one way in this post.

 

[Vanadium 50]

I notice that it says "special frame of motion"

"it" meaning the post, not the book, right? I was unable to find that phrase anywhere in the book.

 

[FactChecker]

"it" meaning the post, not the book, right? I was unable to find that phrase anywhere in the book.

Yes. I will clarify my post. Thanks.

 

[jamesadrian]

I have been taking an online course through Coursera that is from Stanford University (free if you don't want college credit). I watched about 15 lectures yesterday to get finally to the twin paradox.

Understanding Einstein: The Special Theory of Relativity

https://www.coursera.org/learn/einstein-relativity

You can sign up in a minute and look at week seven where four video lectures are about the twin paradox.

It paints a very different picture from that made by Garner. I looked at his bio and he was a philosophy major and wrote 60 book on science, almost all without flaw. I now think he was completely wrong about the twin paradox.

The acceleration required for the rocket to turn around and head back can be a minuscule part of the whole deal, so it does not get out of the realm of special relativity; but the fact that there is a turn around changes the frame of reference of the rocket and the lines of simultaneity change when the rocket changes direction. The age asymmetry can be explained by the lack of simultaneity which can be neatly represented in space-time diagrams as I found them in the Stanford course.Jim Adrian

 

[Ibix]

The acceleration required for the rocket to turn around and head back can be a minuscule part of the whole deal, so it does not get out of the realm of special relativity; but the fact that there is a turn around changes the frame of reference of the rocket and the lines of simultaneity change when the rocket changes direction. The age asymmetry can be explained by the lack of simultaneity which can be neatly represented in space-time diagrams as I found them in the Stanford course.

Special relativity can handle acceleration perfectly well - it's just that you need to be good at calculus for anything but the very simplest of cases so it tends to get left out of introductory courses. You only need to go into general relativity when there is gravity. Other than that, yes, you seem to have a better understanding now, yes.

 

[PeterDonis]

I now think he was completely wrong about the twin paradox.

Since you have not provided an actual quote from his book (despite repeated requests), we have no data on which to base a judgment one way or the other.

 

[jamesadrian]

Since you have not provided an actual quote from his book (despite repeated requests), we have no data on which to base a judgment one way or the other.

The excerpt I gave was the best I could do because his argument is long-winded and spread all over his chapter entitled "The Twin Paradox." His argument relies on the universe as a whole being a special frame of reference and he adds gravity to the argument in a way that does not explain anything. Unless I am to quote about 30% of the chapter, the only alternative is to buy the book "Relativity Simply Explained" by Martin Gardner.

I'm sorry that I can't do better.Jim Adrian

 

[vanhees71]

Well, nevertheless it's a good example for the fact that one should learn science from scientists, not philosophers.

 

[FactChecker]

I think that to say that acceleration is a small part of it may be misleading. If you consider acceleration to be the derivative of velocity, then the acceleration and the turnaround are just different names for the same things. The lines of simultaneity change because of this. The SR math takes this into account.

 

[PeterDonis]

The excerpt I gave

What excerpt? You've tried to describe in your own words what you think he said, but I haven't seen an actual quote anywhere.

 

[PeterDonis]

Unless I am to quote about 30% of the chapter, the only alternative is to buy the book "Relativity Simply Explained" by Martin Gardner.

I happen to have the book and I have now dug out my copy. Are you sure you can't come up with a couple of reasonably short quotes to illustrate what you are saying Gardner said? I can see at least one obvious one (on p. 114 of my copy).

 

[Sagittarius A-Star]

Well, nevertheless it's a good example for the fact that one should learn science from scientists, not philosophers.

Yes. Martin Gardner wrote good articles about mathematical games, but this book about relativity seems to be a bad source.

This accelerating universe generates a powerful gravitational field. As explained earlier, gravity has a slowing effect on clocks.

Source: via another forum (see posting from « July 23, 2019, 08:52:50 am »)

He argues with Mach's principle in the case of rectilinear acceleration - without mentioning, that such complete inertial frame dragging was never verified by a calculation for the universe. He mixes up pseudo-gravity with tidal gravity and explains gravitational time-dilation incorrectly.

 

[PeterDonis]

this book about relativity seems to be a bad source

I'm afraid I have to agree. I don't think Gardner meant to say quite what the OP interpreted him as saying, but I can see how what Gardner wrote could have been misunderstood that way, and even after that misunderstanding is corrected there are plenty of issues that remain with what Gardner wrote.

The quote on p. 114 of my copy that I was referring to in post #22 is this:

The stay-at-home does not move relative to the universe.

Emphasis in original.

Gardner never explains what he means by "relative to the universe", which is the first issue. But from other things he says, it is clear, at least to me, that what he means by "relative to the universe" is something like "relative to the average of all matter in the universe". If we wanted to sharpen this up to be more technical (which Gardner really should have done), we could say "relative to a comoving observer in the same spacetime region as the twins", and we could test that the stay-at-home twin was at rest relative to a comoving observer by confirming that, for example, the stay-at-home twin sees the CMBR as isotropic and the traveling twin does not.

It certainly seems on the surface like this is saying that "the universe" defines a preferred frame. But we have to be careful here. The laws of physics do not define any preferred frame. But particular solutions of the laws of physics can have symmetry properties that do pick out a particular frame as being "preferred" in the sense that the solution looks a lot simpler when described using that frame. For example, in FRW spacetime, standard "comoving" coordinates make the solution look simpler than any other frame, because those coordinates match up with the homogeneity and isotropy of the spacetime geometry.

So all Gardner is actually saying is that, in his version of the scenario (about which more below), the stay-at-home twin is the one who is "at rest" with respect to the symmetry properties of the particular spacetime geometry that describes the universe, i.e., of the particular solution of the laws of physics that describes the universe. He is not saying that the laws themselves define a preferred frame, as of course they don't.

However, this still leaves a number of issues that are worth pointing out.

Gardner's claimed explanation of the difference in aging, in the traveling twin's rest frame, as being due to a "gravitational field" caused by the traveling twin accelerating "relative to the universe", relies on the claim that accelerating relative to the average of all matter in the universe--or, more technically, relative to a comoving observer in your vicinity--brings into being a "gravitational field". However, that claim, as it stands, is problematic for two reasons.

The first reason, about which more below, is that we can't just assert without proof that accelerating relative to a comoving observer brings into being a "gravitational field"--or, taking account of the second objection I'm going to raise in a moment, that accelerating relative to a comoving observer causes differential aging between twins who separate and then come back together. We have to actually prove it. And proving it requires specifying what spacetime geometry you are using. Gardner is never actually clear about this, but of course the standard formulation of the twin paradox is in flat Minkowski spacetime--and in flat Minkowski spacetime, there is no matter in the universe. There is no such thing as "relative to the rest of the universe" or 'accelerating relative to the rest of the universe" or "accelerating relative to comoving observers" in Minkowski spacetime. So by bringing in "the rest of the universe" as though it actually plays a role in the scenario, Gardner is changing the scenario. He is not really talking about the standard twin paradox any more, but about some ad hoc, not well specified variation of it that takes place in some not well specified spacetime geometry where "the rest of the universe" is significant.

(Gardner does eventually, on p. 116, raise the question of what would happen in a hypothetical universe that contained nothing but the two twins and their spaceships--which is to say, in the actual standard twin paradox in its standard formulation. More on that below. But he certainly does nothing to inform the reader that this hypothetical version he talks about almost as an afterthought is actually the standard version that everyone else discusses.)

The second reason the "gravitational field" claim is problematic as it stands is that "gravitational fields" are frame-dependent, and one of the key tenets of relativity is that no actual physical observable--which the difference in aging of the twins is--can be explained by something that is frame-dependent. That is not to say that we can't construct a non-inertial frame in which the traveling twin is at rest, or that in that frame, there will not be something that can be termed a "gravitational field", or that calculating the stay-at-home twin's elapsed time in this frame will bear some useful similarities to calculations done in an ordinary gravitational field, the kind generated by a planet like the Earth. All of those things are true. But that doesn't change the fact that the "gravitational field" present in such a non-inertial frame is a frame-dependent thing, and will not really bear the weight of explanation that Gardner wants to put on it.

As noted above, on p. 116 (of my copy), Gardner discusses the case (which, as noted, he treats as an afterthought, but which is actually the standard twin paradox in flat Minkowski spacetime) of a "universe" that contains nothing but the two spaceships, and asks what the result would be in such a case. Here is what he says:

The answer [to the question of whether there would be differential aging between the twins] depends on whether you adopt Eddington's view on inertia or the Machian view of Dennis Sciama. In Eddington's view the answer is yes. Ship A accelerates with respect to the metric spacetime structure of the cosmos; ship B does not. The situation remains unsymmetrical and the usual difference in aging results. From Sciama's point of view the answer is no. Acceleration is meaningless except with respect to other material bodies. In this case, the only material bodies are the two spaceships. The situation is perfectly symmetrical. In fact, there are no inertial frames to speak of because there is no inertia (except an extremely feeble, negligible inertia resulting from the presence of the two ships). In a cosmos without inertia it is hard to predict what would happen if a ship turned on its rocket motors! As Sciama says, with British understatement, "Life would be quite different in such a universe".

As @Sagittarius A-Star notes, Gardner fails to mention that, while the Eddington viewpoint he refers to is in fact just standard relativity theory using flat Minkowski spacetime, which is a perfectly valid solution to the Einstein Field Equation, the Sciama viewpoint he described was purely speculative, based on a purely hypothetical future theory that never actually got developed at all. (Sciama published one paper on it but AFAIK never followed up with anything more, and the one paper, while interesting, contains nothing that could be described as a complete theory, even a simple one, and AFAIK no one else has followed it up either.) The underlying contradiction is evident in Gardner's quote: he notes that "it is hard to predict what would happen" in such a model, but only after giving a definite prediction as to what would happen: there would be no difference in aging between the twins.

The "Machian" issue that Sciama was trying to come to grips with is one that a number of physicists have commented on. The simplest way to describe it is to note that the Einstein Field Equation of GR allows solutions--a number of which are heavily used in physics--in which "inertia", i.e., the spacetime geometry, is not completely determined by the distribution of matter and energy. One obvious example is that there are multiple vacuum solutions to the EFE, i.e., specifying that there is no matter or energy anywhere does not completely specify the spacetime geometry! To know which vacuum solution you are dealing with, you have to add other specifications. This means GR contains solutions which are not "Machian", if you think "Machian" means that the spacetime geometry should be completely determined by the distribution of matter and energy.

 

[jamesadrian]

Special relativity can handle acceleration perfectly well - it's just that you need to be good at calculus for anything but the very simplest of cases so it tends to get left out of introductory courses. You only need to go into general relativity when there is gravity. Other than that, yes, you seem to have a better understanding now, yes.

Ibix,

Thank you for this message. I have a lot of calculus, but the course I'm taking does not use anything but simple algebra. If there is an online course that does not spare the math in explaining special relativity, I would like to know about it. I have seen a general relativity course that dives into the math under the presumption that the student has a firm grasp on all of the features of special relativity. I would rather be prepared by a really thorough course in special relativity before going into general relativity. Of course, I might not be the best judge of that. I don't know general relativity.

Thank you for your help.

Jim Adrian

 

[vanhees71]

There is no way to communicate adequately about physics without math, including calculus.

 

[eltodesukane]

I would not rely on Martin Gardner to learn about relativity.

 

[thetrellan]

I've read some of Martin Gardner's columns in Scientific American in ages past, but I'm not familiar with the one that you are reference.

However I would guess you most likely misunderstood something, as it is definitely possible to construct a universe with no preferred frame of reference. It's just the flat, simply-connected, space-time of special relativity.

In this SR universe, as has been discussed in many other threads, some quite recent, if two twins take different routes and meet up again, the one that undergoes inertial motion will have the longest elapsed time on their clock. This reading on the clocks that each twin carries with them is known as "proper time".

In fact, this can serve as a definition of inertial motion. Inertial motion is that motion that maximizes proper time in this simple case.

Things get slightly more complicated with a more realistic universe, but it would not be productive to go into these extra complexities at the moment.

A useful analogy of this space-time example can be made in space. If two drivers on a flat plane take different routes from from some common "start" city to some common "destination" city, then the driver that drives in a straight line will drive the shortest distance.

There is a sign difference in the space-time geometry that makes the analogy of "shortest distance" instead the "longest proper time", but the principle is the same.

A driver who makes a sharp turn anywhere along the route is NOT driving in a straight line. The driver who argues "I only made one 90 degree turn - why was my journey so much longer than my twin" is misguided. It doesn't work that way.

It's also rather unproductive to ask in this case "what mechanism happened during the turn to make the trip longer". It's not the turn that made the distance longer, it's the geometry. The space-time case is similar. It's the geometry that makes the twin who doesn't move inertially age less. But in this case, it's not the Euclidean geometry of space, but the Lorentzian geometry of space-time.

The equivalent of the driver making a turn in space-time is a change in velocity. This can most easily be seen by drawing a classic space-time diagram. More can be said about the topic, but I don't want to over-complicate things at this point.

Similar to the drivers, making "just one turn" may have drastic effects on the elapsed time if the turn is sharp enough. The analogy to a "sharp turn" in the space-time case is a large velocity change. If our driver makes only one turn, but it's a minor course correction, a small angle, he won't drive much further than if he'd taken a true straight-line course. For the space-time traveling twin, the "sharp turn" is analogous to a large velocity change, and the "minor course correction" is a small velocity change.

I'm confused. I've been seeing discussion over the past month or so on the twin paradox saying that more time has passed for the traveling twin. But as I understand it https://en.wikipedia.org/wiki/Twin_paradox the traveling twin is supposed to have aged less. Shouldn't he, therefore, have experienced less passage of time, not more? What is this layman's understanding missing?

 

[PeterDonis]

I've been seeing discussion over the past month or so on the twin paradox saying that more time has passed for the traveling twin.

Where have you been seeing that?

 

[Ibix]

I'm confused. I've been seeing discussion over the past month or so on the twin paradox saying that more time has passed for the traveling twin. But as I understand it https://en.wikipedia.org/wiki/Twin_paradox the traveling twin is supposed to have aged less.

Your understanding is correct. The post by @pervect that you quote is making an analogy between Euclidean geometry where two sides of a triangle are longer than the third, and Minkowski geometry where two sides of a triangle are shorter than the third. Thus the non-inertial car driver travels further, but the non-inertial twin experiences less elapsed time.

The analogy is a good answer to people demanding to know "what happens to the non-inertial clock that makes it experience less time". You counter by asking what answer they would accept to "what happens to the car's odometer that makes it experience more distance". There are also very good analogies with the relativity of simultaneity, a topic that seems to confuse people a lot.

However, I suspect the distance/proper time analogy has confused you. In Minkowski spacetime, a straight line is the longest route between two events.

 

[thetrellan]

Where have you been seeing that?

uh, right here? For one.

 

[Ibix]

uh, right here? For one.

Pervect isn't saying what you are saying, though - in fact he explicitly says "the one that undergoes inertial motion will have the longest elapsed time on their clock". Am I correct in my interpretation above, that you are reading his Euclidean length analogy as saying the traveller should be older? Because that's a difference between Euclidean and Minkowski geometry.

 

[PeterDonis]

uh, right here? For one.

@pervect says exactly the opposite:

if two twins take different routes and meet up again, the one that undergoes inertial motion will have the longest elapsed time on their clock

The one that undergoes inertial motion is the stay-at-home twin, not the traveling twin.