Paradox in physics can be defined as an incompatibility between an interpretation of a physical phenomenon and the everyday experience. Ever since Einstein recognized that light has properties commonly associated with both waves and particles (the nature of waves and particles had previously been perceived and thought mutually exclusive), paradox has been increasingly accepted and even expected in theoretical physics. Einstein felt that the light paradox would someday, somehow be resolved, but with the advent of quantum theory, the strange and seemingly unnatural behavior of subatomic particles made acceptance of paradox a scientific norm.
It is in consequence no longer possible to dismiss a physical hypothesis because it seems unnatural or incompatible with accepted theory. And such high tolerance is not necessarily a good development. Gravitation theory is an excellent example: Gravity is treated as both a geometric warping of spacetime in the presence of mass and as a force, with little or no concern for the incompatibility of the two models; thus the tolerance of paradox has been extended to a tolerance of discrepancies between theories. Another example: “Dark energy” and “dark matter”, although unobserved and perhaps unobservable, are favored explanations for cosmological phenomena, despite a long-established scientific principle that ranks questioning theoretical models above accepting seemingly unnatural entities.
The so-called “twin paradox” suffers from the same sort of theoretical malaise. It arose from an implication of relativity theory, that acceleration will produce discrepancies between clocks – not relative differences as with uniform motion, but real differences that could result in a twin going to and from a distant star system and returning home significantly younger than the stay-at-home twin. This is not really a “paradox” if clock-speed is accepted as an attribute of each body’s state in spacetime, rather than a universal constant, and it has been confirmed by experiment. But there has been an enduring problem with explaining how arbitrary periods of time spent by the traveling twin in uniform motion would be resolved upon the twins’ reunion: When in uniform motion, each twin will regard the other’s clock to be moving with an identical relative discrepancy, but upon their reunion they will have to agree that those observations were only relative, and the buildup of the mutual effect must somehow vanish.
Not only has the conundrum (not a paradox) involved with the twins’ experience of a disappearing mutual discrepancy been tolerated, a proposed resolution has evoked almost no curiosity, and has even provoked outright dismissal. Only The European Journal of Science (EJS), an intrepid but relatively remote publication, has shown an interest in and appreciation for a resolution of the twin “paradox” (conundrum), and has published it in their January 2016 issue.
So do physicists love their paradoxes, discrepancies, and conundrums too much?
The paper can be found here:
https://www.researchgate.net/publication/293477077_The_Twin_Paradox_Resolved
Article The "Twin Paradox" Resolved
Note that the journal where the article is published is The European Scientific Journal, not the European Journal of Scientific Research.
> do physicists love their paradoxes, discrepancies, and conundrums too much?
I don't believe serious physicists with any connection to special relativity, however remote, think there is anything to resolve with the twin paradox. Except for pedagogic reasons, perhaps.
Evidently, your answer to my question is "yes." So perhaps your "serious physicists" aren't serious enough. I've indicated the problem of arbitrary periods of uniform motion, when each twin would observe the other's clock to be moving more slowly. Unless you have an explanation for how their clocks would agree on such periods at their reunion, your comment is flippant.
I repeat: There are no paradoxes, no discrepancies, no conundrums, really nothing to ponder about in connection with the twins travel.
Have you ever heard of the "triangle inequality paradox"? I mean why it is longer around the third corner of a triangle than the straight line between the other two. Never heard of it? How come? If one applies exactly the same logic of analysis to this case as is done for the twins travel (just replace simultaneity with the concept of equal forwardness) one arrives at the same paradoxes, discrepancies, conundrums...
If you're going to make dismissive and condescending comments you should first read my paper, or at least read the abstract with some care.
I'm familiar with the "it's not the acceleration" school, first put forward by Laue in 1913, and I've shown why it's false. Put simply, when neither twin is accelerating, both are in relative motion, neither has a privileged reference frame, and both are observing the other's clock to have the same discrepancy. Both clocks cannot have been slower or faster than the other at the twins' reunion.
Shall I say "you've heard of Special Relativity haven't you? Never heard of it? How come?" No, that would be both insulting and unnecessary, wouldn't it.
James @
Do you think it makes a fundamental difference for the triangle inequality whether the triangle has sharp or a little bit rounded corners? Or, if the triangle was actually defined to be the interior shape formed by three infinite straight lines crossing each other? Each line with its own notion of forwardness.
I.e., one can replace the twins by a triplet, all of which are in inertial motion well throughout the duration of the experiment.
And yes, I did download and look at your paper.
Kåre, your question about triangles begs the twin question: In standard relativity theory, either of two bodies in relative uniform motion can be considered at rest or in motion, and both will observe the other to have the same variant clock speed. Therefore, uniform motion cannot account for one twin to age more than the other.
Your opening statement invoked all serious physicists involved in relativity. But regardless of the merit of your argument, it is not relativistic.
> uniform motion cannot account for one twin to age more than the other
Of course not. Just like the fact that the length of a straight line increases proportionally with the ticks along a cartesian coordinate axis aligned with it, does not tell you anything about the triangle inequality.
If you can't see the relation between the triangle inequalities, for triangles in euclidean space or triangles of timelike intervals in Minkowski space, you have a much too narrow view of special relativity.
The analogy of triangles and coordinate systems takes the stay-at-home twin's reference to be absolute. It is not relativity.
Clock. Let it be pies. Twin eats a pie when she is hungry. Eating a pie is an event. In her own frame the interval is T. It is pure time. In the moving frame the interval is sqrt(T'^2 - X'^2). Interval is invariant. Obviously, T' > T. But in pies it is still 1 pie.
So, are pies clocks?
> takes the stay-at-home twin's reference to be absolute.
No. It is you who do that. I told you to apply the same reasoning to both cases.
Igor, the pie is akin to the timepiece, the device; the eating is the duration that can be measured (T). A pie is a poor timepiece, as unlike a typical clock, it cannot be re-eaten; it goes from one to zero!
Kåre, when I apply relativity to both twins I take each coordinate system, one at a time, and I see that each is observing the other's clock to be moving more slowly. Because uniform motion is relative, when the twins are re-united, the accelerations aside, since either one can be considered the one at rest or in motion, they will necessarily agree on the total time spent in uniform motion. My figure 2 in "The 'Twin Paradox' Resolved" shows this graphically, in accordance with the Lorentz transformation..
Relativistic effects are relative, hence there is no real time dilation when the twins are in uniform motion.
So, who eats more pies? Does it help if the pie is eaten every, say, 500,000,000,000 oscillations of the caesium-133 atom?
Einstein liked clocks and I always wondered why did he make life so difficult for himself?
What is a clock? A periodic device to measure non-periodic events?
Igor, your fondness for pies is amusing, but I'm not sure it's helpful for understanding relativity.
A clock is a device used to measure duration, just as a measuring rod is used to measure distance. Clocks are no more, no less essential in our world than they would be in a newtonian world of absolute time and space.
> Relativistic effects are relative.
Not everything is relative in SR; the special theory of relativity is more about finding the invariant results than the coordinate-dependent ones. Because only the first ones can have meaningful physical content. But to achieve that one must sometimes know how the coordinate dependent quantities transform under change of coordinates.
Well, certainly, the clock speeds of twins moving uniformly are relative according to SR.
I don't want to single out Kåre. This is not an isolated phenomenon. When I wrote, above, "tolerance of paradox has been extended to a tolerance of discrepancies between theories", there is no better example than the claim that the twin effect is due to their uniform motion, which can only be maintained in blatant disregard of its incompatibility with Special Relativity.
> certainly, the clock speeds of twins moving uniformly are relative according to SR.
No. They may look relative, due to the relativity of simultaneity.
> the claim that the twin effect is due to their uniform motion,
And who exactly is claiming that?
"They may look relative"
"How else might they be relative?"
> the claim that the twin effect is due to their uniform motion,
"And who exactly is claiming that?"
You (and others) invoke triangles of world-lines to try to explain the Twin Effect. Unless they represent uniform motion, if they represent accelerations, 1) they should be curved lines, 2) acceleration makes "triangle inequalities" unnecessary for an explanation of the Twin Effect, and 3) I've shown in my paper (re: figure 3) that the "inequality" of the length of the traveling twin's world-line is due to the projection of the stay-at-home twin's measure of space on the other's motion.
James@ You are very fond of making strawmen to argue against; that is a bad strategy if you want to get your ideas across.
Kåre, a charge of "making strawmen" normally includes an identification of the strawmen.
Pies are important. They are events.
Some of us hold the following belief:
1. Events can be marked with 4 parameters: t, x, y, z. This does depend on the frame.
2. Events are ordered by the space-time interval: ds = \sqrt(c^2dt^2 - dx^2 - dy^2 - dz^2).
3. The space-time interval is invariant in all inertial frames.
4. If in one of the frame the spatial part of the interval increases then the time part has to increase as well. But the events are ordered just the same, because it is the interval that matters.
5. The need in relativity theory arose because Maxwell equations are Lorentz covariant. Einstein tried hard to give a simple explanation to the relativity and confused many. If somebody tries to correct Einstein they have to deal with the Maxwell equations. Musing does not go.
6. In the twin paradox the frame associated with one of the twins is not inertial. The space-time intervals have to be calculated as ds^2 = g_ik dx^i dx^k. But that is general relativity.
Too long. About muons in the next post.
Muons have lifetime about 2 mks. Moving even with the speed of light they would travel about 600 m.
Being undergraduates we had a simple lab - detect muons created in the upper layers of the atmosphere by cosmic rays. That's about 100 km. That is possible because in our frame the life of a muon is \tau/\sqrt(1- v^2/c^2).
Quite convincing.
The EM wave equation is \cos(\omega t - k x) or \cos(\omega( t - x/c)).
Theoretician would write \omega t - k x = k^ix_i and would be happy. This is invariant.
But one can do simple Lorentz transformations.
\omega t - k x = \omega (t' - v/c^2 x')/\sqrt(1 - v^2/c^2) - k(x' - v t')/\sqrt(1 - v^2/c^2).
One can see that this reduces to
\omega' (t' - x'/c) where
\omega' = \sqrt( (1 + v/c)/(1-v/c)).
Frequency is Doppler shifted but the speed of light propagation remains the same.
That's just one of the reasons why people do not even consider your theory, James.
Igor, my explanation involves only the uniform periods of the traveling twin's journey. I accept the generally agreed explanation for the time-discrepancy between the twins: the accelerations involved in going to and from the distant star-system.
Regarding the uniform periods, my explanation is entirely conventional, relying only on the Lorentz transformation and its derivative, the invariant interval (which is just the elapsed time according to the observed body). So I don't see your point.
Regarding the pie, we may be arguing semantics, but a pie is not an event; a pie is an object, an event would be something that happens to the pie at a time and place.
This question -- specifically as it applies to the Twin Paradox -- seems to be put to rest.
One of the objections raised here is interesting in that it highlights a common difficulty in relativity theory: consistently distinguishing an observer's coordinate system from that of the observed:
In considering the Twin Paradox, those who attribute the discrepancy between the twins' clocks to periods in relative uniform motion do so by failing to distinguish the stay-at-home twin's measure of spatial distance from that of the traveling twin. As I discussed in my paper "The Twin Paradox Resolved", the apparent discrepancy between the lengths of the twins' world-lines in periods of uniform motion (as in my figure 3) is due to the treatment of the stay-at-home's measure of the traveler's motion in space as absolute. (At a relative velocity of .8c the stay-at-home will measure the traveler's distance traveled as 4 light-years, but the traveler's measure will be of 2.4 light-years.)
The confusion of coordinate systems in the attribution of the twin affect to relative uniform motion is analogous to the confusion expressed in the conventional Minkowski diagram, which treats the observer's measure of time as absolute, as in the projection of a light ray as moving 1 second in space per 1 second of time (light moves at a relative 0 seconds in time).
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