Is Einstein's Time Dilation and Length Contraction Real?

Hi Christopher, yep, I think I was a bit cryptic in that reply - sorry!

The underpinnings of "an inertial observer present at two events will always observe a shorter time interval between the two events than any inertial observer not present a both events" come from the Lorentz transform, but the simplest way to put is as follows.

The invariant spacetime interval is given by ds^2 = dt^2 - dx^2 for timelike intervals between two events. The observed (squared) time by any observer is hence: dt^2 = ds^2 + dx^2.

For an observer present at both events, dx = 0, so it is obvious that it gives the minimum value for dt (since ds is the same for all observers).

Hope this clears some of it, at least ;)

Regards,

Burt Jordaan (www.Relativity-4-Engineers.com)

Hi, Burt.

Last time I chose an unsuitable would-be “neutral observer”. I stipulated that he move so as to be halfway in spatial distance between the two test clocks; bad choice. Also my diagram had some glitches which you reported; thank you for that. Let me try again.

Let us look at a Minkowski diagram of the twin clocks scenario for the study of “Einstein’s time dilation”, drawn in the reference frame of the home-clock. The two clocks are identically constructed and simultaneously zeroed at home. The home-clock stays inertial. The away-clock moves out from the home event, O, and back again, travelling inertially at one and the same speed except at the turn-around event, T´, which in the reference frame of the home-clock is simultaneous with an event M´ at the home-clock. We compare the durations of time that these two test clocks register between their separation event, when the away-clock sets out, and their re-meeting event, when the away-clock arrives back. The scenario has two legs, outward and homeward. The total times can be found and compared by putting together the two leg times.

The outward-homeward symmetry about M´T´ means that we need look closely at just one leg, let it be the outward.

For the sake of a demonstration, we introduce a suitably chosen neutral observer. The neutral observer’s clock moves between the two test clocks, so that in his reference frame the two test clocks move at equal and opposite velocities, away from him in opposite senses; this is the desired demonstrative symmetry that makes the two test clocks run at equal rates and move at equal speeds.

In the next Minkowski diagram, the broken lines are world lines (dashed) and lines-of-simultaneity (dotted) for the home-clock (blue), the away-clock (red), and the neutral clock moving at equal and opposite velocities between them (green), plotted in the frame of reference of the home clock. The full lines are for the same, plotted in the frame of reference of the neutral clock. The diagram shows a transformation of reference frames that takes the broken lines into the full lines. Events labelled for the home-clock reference frame are primed, for example M´; for the neutral observer’s reference frame unprimed, for example M. The transformation takes the turning point T´ into T; it takes the "mid-time" event of the home-clock M´ into M; and it takes the "halftime" event of the outward leg of the home clock, H´, simultaneous with T´ as judged in the reference frame of the neutral observer, into H. c and -c mark the light cone of the origin O. x marks the distance and t the time axes.

In the reference frame of the home-clock: The turn-around events, M´ , P´ , and T´, though simultaneous, will occur not when the neutral observer is at half spatial distance between the two test clocks; but rather, when the neutral observer’s clock is spatially nearer to the away-clock than to the home-clock:
spatial distance M´P´ > spatial distance P´T´.

The two reference frames are related by a Lorentz transform. It requires that space be isotropic, that is to say, that if observer A moves inertially at velocity v with respect to observer B, then observer B must be travelling inertially at velocity –v with respect to observer A. The Lorentz transform preserves scale. Also it preserves collinearity. The events M, P and T are collinear in a line of simultaneity in the reference system of the neutral observer, because they are simultaneous for the home-clock’s reference system, at M´, P´, and T´.

The transformation diagram was drawn (with the aid of my textbook from schoolboy days) by elementary straightedge and compass methods known to Euclid, according to simple rules of Minkowski geometry. No numerical calculations here.

We will make our decisive comparison in the reference system of the neutral observer: The turn-around event T of the away-clock is simultaneous with an event H at the home clock that occurs before the turn-around event P of the neutral observer’s clock; T is also simultaneous with event L at the neutral observer’s clock; P in turn occurs before the midtime event M of the home-clock, which is simultaneous in this frame with event N at the neutral observer’s clock.

The comparison is made with respect to a single neutral reference clock. The two test clocks run at a common rate and travel in opposite respective directions at a common speed. Over one leg of the scenario, we just compare how far the test clocks travel and consequently how long they run for: it is obvious in the diagram that the home-clock moves a greater distance and takes a longer time to do so. In spatial distance measured in the neutral observer's reference system, the spatial excursion of the home-clock is greater than the spatial excursion of the away-clock:

spatial distance LT > spatial distance NM.

With the two test clocks' spatial excursions at equal speeds, the longer spatial excursion takes the longer time. The neutral reference clock registers that the extra time that the home-clock takes is from L to N.

The above argument is in terms of ‘simultaneity in a reference frame’. That is a rather theoretical argument in the sense that it supposes arrays of countless remotely stationed research assistants each with his own clock, all synchronised by the Einstein method. In many real situations, there are not so many actual research assistants, and the observer must be content to calculate what virtual research assistants would report, by use only of what he can see of the other clock faces with his telescope, and his own clock.

The above accounts for only the outward leg. It seems reasonable. We will rely on symmetry for the homeward leg.

The above argument does not try to say what immediate directly observed data, from his own clock and two oppositely directed telescopes, the neutral observer will record in his log book. Let us look at the latter, with the aid of the next Minkowski diagram, showing both legs in the reference frame of the home-clock. The neutral observer will record in his log the outset at O. Then, after a time, he will record his turn-around event P. Then, after a time of progress on his return leg, he will record seeing with his telescope the event H in the home-clock. Then, after a time, he will record seeing with his telescope the midtime event M of the home-clock. Then, after a time, he will record seeing in one of his two telescopes the turn-around event T of the away-clock, simultaneously with his seeing in his oppositely pointed telescope the homeward counterpart of the event H in the home-clock. Next on his log record will be his arrival at the final home meeting.

In contrast to the foregoing, as Burt has previously pointed out, when it is described in the time system of the neutral observer, the whole adventure will seem paradoxical or unintuitive, or one might even say apparently nonsensical. This is because the neutral observer’s reference frame has a jolt that for him is simultaneous with his turn-around event; at that event, his reference frame suffers an impulsive acceleration. His remotely stationed research assistants instantaneously move respective finite distances.

Let us see what this accelerated reference frame will report for the particular example scenario described in this diagram. The time axes of the two legs of the neutral observer’s reference frame are joined at the event P and its symmetrical partner. Some time after the outset of the travelling clocks from home, a second version of the home-clock appears from nowhere, and the home-clock begins to be present twice simultaneously moving at two different spatial places in the reference system of the neutral observer, one instance moving towards him, the other away from him. This is not at all physically mysterious or strange. It is simply that the reference system is an artefact, with artificial adventures due to the accelerated reference frame. Shortly after that duplicate appearance, the away-clock, at the event T simultaneous with the event L, disappears from this reference system, vanishing into nowhere. Again, this disappearance into nowhere is a mere artefact, not physically strange. Then, after some time, simultaneously with the turn-around event of the neutral observer, the two different records of the moving home-clocks cross each other instantaneously in the same event. The home-clock then continues to be simultaneously twice present moving at two different places in this reference system. After a time the away-clock reappears from nowhere in this reference system. Shortly after that, the home-clock that is moving away from the neutral observer disappears at event M into nowhere. Again these ‘events’ are just artefact. At a time after that reappearance, the three clocks meet in the final event of the scenario.

Accelerated reference frames do not preserve causality. The previous paragraph describes an example of an accelerated reference frame that, if mistakenly interpreted as physical, would seem to violate causality. The physicist knows from experience that it is the peculiarity of the accelerated reference frame that is the reason for the nonsensical appearance, and that nature does not violate causality. Real physical clocks do not appear from nowhere, nor do they disappear into nowhere, nor do they occur in two separate places simultaneously. That is why the physicist uses Minkowski spacetime and inertial reference frames, which preserve causality. Alfred Arthur Robb in 1913 showed the tight connection between causality and Minkowski spacetime by an argument based on causal ordering.

The foregoing demonstration is in terms of a fixed scale for the diagram, but this is not necessary. The Lorentz transformation is a Minkowski isometry, but any of a more general class of transformation of frames would have served the purpose of the demonstration. The scale of the transformed figure does not matter for the demonstration, and is therefore arbitrary for this purpose. Only the shape, defined by the angles, of the transformed figure matters; any similarity transform would do. All that matters for the present purpose is that the transformation preserve causality, that it be a member of the causality group, which is the Poincaré group composed with the group of dilations, (changes of scale, the same for every dimension). The Lorentz transform requires a little extra geometrical construction work, beyond what would be needed for a causality-preserving transform that does not preserve scale, less work to construct but still enough to demonstrate the point of concern here.

Now to the first part of the question at the head of this blog, “Is Einstein’s time dilation real?”

Judged by the neutral observer, the two test clock rates are the same; their speeds of movement are the same; they are not accelerated during the outward leg. The difference in total time registered is therefore not due to difference in the test clocks’ rates, nor in their speeds, nor in their accelerations. It is because one is inertial and the other is not; they have different adventures. Since the home-clock’s adventures are all inertial at home, and the comparison is made at home, it registers most time there. Just by being there. The local eyewitness has the most experience of the locale. The famous imaginary rider on the light pulse has no experience anywhere, and his clock registers no time at all. That just confirms that he is only imaginary; no ponderable matter can be accelerated to light speed.

Here we see that the simple claim that clocks are slowed by travelling fast is sheer nonsense, neither true nor false, just physically and conceptually meaningless.

But it is true that identically constructed and identically working clocks can disagree on the time lapse between two events (at which respectively they are present to register together) if they have different adventures on the way between.

Strictly speaking, this violates Newton’s theory of absolute time, but in some respects reduces to it if the clocks’ adventures are only slightly different. Newton’s theory of time was flawed in its ignoring a finite speed of propagation of causal agency. The latter is needed for true causality, to provide for the distinction between action and reaction, Aristotle’s categories of agency and patience. Master of the methods of Euclid, and probably familiar with Aristotle’s categories, Archimedes had the tools for the “special” theory of relativity, but he missed it; so did Galileo and Newton. It waited perhaps unnecessarily for Larmor, Lorentz, Poincaré, Einstein, Minkowski, von Ignatowski, and Robb.

It is customary to say that it is velocity, not acceleration, that affects the speed of clocks, but this is misleading, unhelpful, or meaningless. Experiments that purport to prove it are done not on clocks, but on particles that have no zero setting facilities to be tested. Inertial reference frames allow arbitrary zero re-settings of clocks, while accelerated reference frames do not; this is a big difference. A clock that cannot be arbitrarily re-set to zero has serious drawbacks for practical purposes. The term ‘synchronisation’ means coordinated re-setting of zeros of several clocks. It usually does not refer to clock rates.

Time is not an event, nor a process, and so it cannot be caused, nor can it be a cause. It does not make sense to say that velocity or acceleration alter time, because such a statement seems to imply that time can be subject to, or patient of, causal agency. Time is in a sense part of the abstract theoretical receptacle that encompasses events and processes, which are causes and effects.

Regards,

Christopher

P.S. If the transform diagram does not display clearly on your browser, you may wish to download a .pdf file of it that will likely display clearly, from http://www.bellstheorem.com/docs/Lorentzonly1.pdf. The diagram of the transformation needs a clear display. Christopher

Hi Christopher. To clarify what I meant by my statement about relativistic subtraction, if the speed of your green clock is 0.4c and the coordinate speed of the your red clock is 0.8c (as it appears to be on the diagram), then the relative speed between the red and green clock is v_rg = (v_r - v_g)/(1 - v_r v_g) = 0.588c.

So, I do not think the projections that you made are correct. You cannot just rotate the worldlines around the origin by the same angle. The transformed red worldline is at the wrong angle.

Regards,

Burt Jordaan (www.Relativity-4-Engineers.com)

PS: Oops! I replied directly to your post and probably blocked you from editing it. The problem with the new look Blog is that it is frustrating to work at the very bottom of the long web page and losing sight of the thing you are replying to...

(1) Verification is a red herring. We can postulate standard instruments and honest people.

(2) You don't have to wait until the end to compare or compute results theoretically. With frames of reference studded with mile-markers and clocks, there can be a steady stream of data from each one's frame of reference saying, "The other just passed this marker number n, and our clock readings are Jill t₁ and Jack t₂." Since we are assuming the theory is sound, those readings would be exactly what we would compute. Thus, when they finally get together, they each have a full record of both sets of measurements, and neither is surprised.

BTW, I'm having fun with Bonk: The Curious Coupling of Science and Sex, although it is not as laugh-out-loud hilarious as the same author's Stiff: The Curious Lives of Human Cadavers. I just finished the chapter on sex machines, including the author's failed attempt to see the raw data or the apparatus of Masters and Johnson's camera in a simulated penis to get details of the female orgasm.

Stay tuned!

Fred Bortz -- Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)

Fred:

Unfortunately, you appear to have misunderstood Burt. The set of A-synchronized clocks "everywhere" is really just a way of making the time portion of A's coordinate system (within A's reference frame) "physical". So the readings on A's clocks, that B will observe, are simply a realization of A's coordinate time. Just think of a Minkowski spacetime diagram where A is stationary (in the diagram).

This is most certainly not the same as asking what time intervals a set of B referenced/synchronized observers will "see" when observing A's wristwatch. Instead it's really like asking what proper time interval has passed for B when traveling a velocity v relative to A's reference frame: B is comparing his "wristwatch" time to A's coordinate time.

(Δτ_B)2 = (Δt_B)2 - (Δx_B/c)2 = (Δt_B)2 - (Δt_Bv/c)2 = (Δt_B)2 (1-v2/c2)

where Δτ_B is the change in B's proper time, and Δt_B is the change in coordinate time B has passed, in A's reference frame. So Δτ_B < Δt_B (A's set of clocks will always be running ahead-of/faster-than B's "wristwatch" time).

What I believe you, Fred, are trying to get at is a set of B synchronized clocks/observers: One set for B's journey away from A, and another for B's journey back toward A. Your speeding up and such of B's observations of A's "wristwatch" time, via such B synchronized clocks/observers, is due to the "shifting" of such synchronizations, if one were to attempt such a thing. (The problem is, unless we use three observers, all in inertial frames—A, Bo for B's outgoing journey, and Bi for B's incoming journey—then there is no physical way to accomplish the resynchronization you envision. Of course, if we do use the three observers, each in different inertial frames, we get a discontinuity in the observation of A's "wristwatch" time at the pylon.)

Unfortunately, Fred, this leads to you misrepresenting what will be read off the pylon's clock, as B changes direction. There is no physical way, even under such high g-forces, for the pylon clock to change its reading as B turns around. (Although it appears from your EDIT that you recognized your mistake.)

David