This week's "Streams of Time" gives us a lot to think about. The first problem is to even think of a way to think about it. As a first step we all need to ask ourselves "what exactly do I understand by such phrases as 'the rate at which time passes', 'the rate of its flow', 'the passage of time proceeds faster', etc ?" Is there something else than time itself against which we can compare the 'passage of time' ? In the general context, I don't know. I can take the next step only in one special context of idealized physics, the context of two identical observers or "clocks" in uniform relative motion and/or acceleration, each comparing the rates of his own physical processes against those he sees in the moving replica. But even in that case, each sees the other as evolving slower, so how to say which "rate of time passage" is really greater or lesser??
As Dr. Scott so persuasively illustrates, the "time" that pervades physics is definitely more subtle than the concepts of it that we inherited from thinkers before 1905. For example, the pre-Einstein notion indispensably requires that the universe is like a movie reel in that some things going on in it can be unambiguously identified as "simultaneous", moment after moment, as though belonging to successive snapshots. We have to correct our observations of distance events to take account of delays involved in the propagation of information to us, but once that is done, every event can be assigned a unique time, and all events with the same time label belong the same frame of the movie. Time is measured along the movie reel.
Plausible as that may seem before you think about it logically, reality doesn't work this way. If it did then the speed of a television signal would look different to people moving at various speeds, e.g. almost equally fast alongside it or in the opposite direction. Maxwell's Equations for all forms of electromagnetic propagation show a speed uniquely determined independent of the observer's or the source's speed. Do the need to be generalized to take account of those variables? Well, the fact is, they work fine. In fact all the laws of nature seem to work the same regardless of the constant speed of the observer relative to any preferred "zero" of speed. It follows by simple logic that there is no unique time base available to everyone. Events A and B at different places that are simultaneous in my reckoning generally are not in yours: A may be distinctly before or after B. And neither of us is wrong. There just isn't any universal time base analogous to pre-1905 concepts that still pervade our culture.
Here is a puzzle you might enjoy pondering in order to check your grasp of 20th-century concepts of time. It arose as a "paradox" while I was checking my own in response to Presentation 4; its principal effect in my own case (how about yours?) was to remind me that I had lost (or never achieved, years before these recent decades of inattention to relativistic insights?) even such perfectly consistent and logical appreciation of "time" as has been available to everyone who can read since 1915. The scenario is as usual, the railway car of 1905 with a Traveler, observed by a Farmer in the field outside. To each the other seems zipping by at speed v: they agree on that much. The wheels go click-click from one rail to the next, and a little protrusion from the wheel's flange clicks on the rail junction each time the wheel rolls once around (squashing whatever bug may have alighted there since the preceding wheel passed). To ensure that this happens repeatedly at regular intervals we pick the wheel circumference equal to the rail length. Farmer, resting over his lunch, hears one click per heartbeat.(Let's suppose heartbeat intervals subjectively invariant: we are all the same and no one gets excited). With binoculars he observes Traveler, resting over his lunch. He notes that everything is happening half as fast in the train, on account of v being a goodly fraction of c. The wheel clicks are audible in the moving car, too, necessarily exactly as often as they radiate to the outside. So does Traveler hear one click per heartbeat or two? If two, how do you reconcile this with his agreement about speed v relative to Farmer? If you restate the problem with the wheel axles welded to the rails rather than to the coach car, does the answer change? The train wheels turn once per rail-length, and both persons agree about the relative speed of wheel and rail … but all processes in the moving car are slower, and that must include wheel- turns as part of the car, so doesn't Traveler's observation of less than a wheel turn in the time of Farmer's observation of a wheel turn mean that from one point of view the bug has been squashed and from the other it has not? If the bug alighted not on the rail but on the protrusion as it nears the rail, does he think he has been squashed or not? And further trouble: Suppose each person's heartbeats are visible, and each person's hearing a click (or inference that a click happened, after correcting for propagation delays) is also visibly evident (e.g., maybe his pupils dilate each time), and assume that each person's seeing a heartbeat or a click-perception through his binoculars is visible, too. Do each person's heartbeats and personal click-perceptions accumulate in lock-step at a faster pace than his observation of the other's, and doubly faster than his observation of the other's recording his own through binoculars?
Physics problems of this sort have perfectly consistent answers, implausible though that promissory note may seem before we adjust our concepts of time to reality. (I am at this writing still trying to work through this home-brew paradox to a consistent conclusion, but I do so in confidence that while I might not make it before Presentation 5, I will eventually. Unfortunately it seems to entail General Relativity's notions of curved space-time, which I never did fully master in school, but after uploading this I will try to pick of the thread again …)
Like this one, the simpler "twin paradox" seems at first to illustrate that some concepts of time just don't work. As usually presented, it purports to show that the 1905 concepts of special relativity don't work. But what it really shows is (a) that they don't work if the postulate corresponding to the adjective "special" is violated, and (b) that pre-1905 concepts don't work in context of real physics. In 1905 Einstein only worked out consistent concepts of space and time (actually, a consistent concept of space-time, in which all observers see the same space-time interval between events, but not necessarily the same interval of space or of time) for the special case that all observers are moving each at his own fixed speed and direction, experiencing no accelerations. But the "twin paradox" (like the rotating wheel paradox) entails accelerations, so if handling it within the framework of Special Relativity seems to lead to some paradox, that should be no great surprise, and should not be taken to prove anything.
For the most understandable thinking about the twin paradox within the framework of special relativity that I know of, see Leo Sartori's 1996 book, Understanding Relativity, Chapter 6: Paradoxes of Relativity.
But the cleanest way to think about it that I know starts from the central postulate that Einstein added to that of Special Relativity (viz., that the laws of nature should be the same for anybody in un- accelerated motion) to make "Special" into "General" Relativity (viz., that there is no difference between acceleration and gravity). If you buy that one too, then simple logic leads to the inescapable conclusion (which made Gen Rel so hard to swallow for decades) that all processes go slower on the floor and faster on the ceiling of a room in a uniform gravitational field or being accelerated upward in the absence of noteworthy gravitating masses. The difference in rates is proportional to the acceleration and to the altitude difference, i.e., to the gravitational potential energy difference between floor and ceiling. In four entirely different experiments that I know of, something equivalent to this is an observational fact, and quantitatively right on the money.
(Another riddle: In this room it might seem that a stack of initially synchronous pocket-watches, with second hands all lined up at the start, will eventually present to the photographer a helical column of hands, and that the helix gets more and more wound up. But I am not sure that is right. That would presume a common time base in which the photograph catches all places at a simultaneous instant. But can something equivalent can be constructed by inference from observations after correcting for propagation delays?)
Back to Presentation 4: What does this have to do with twins? Well, if they both leave earth in opposite directions, turn around, and return to earth, symmetry requires that they arrive at equal maturity. But if one stayed home and the other experienced accelerations first in leaving, then in turning around, and finally in braking to a stop upon return, then we need to ask how those accelerations pertinently break the symmetry, if they do. The first and third accelerations happen near home (the floor-ceiling distance is negligible) so there is hardly any differential rate between processes in the accelerating twin and the one staying home. But the turn-around at the far end if this excursion presents twice that duration of the same acceleration times an immense floor-ceiling distance, proportional to cruise speed and to the number of years of travel. That twin accordingly loses a lot of "time" during this process. Worked through quantitatively, it is exactly the amount expected under the half-baked Special Relativity calculation that ignored accelerations and then couldn't come up with a reason to apply the calculation to only one twin rather than equally to both of them. Specifically, on the un-accelerated legs of the trip each twin is moving at v/c of light speed relative to the other so each expects to find the other younger by the familiar factor sqrt(1- (v/c)^2), [which, for small v/c is close to 1- 0.5(v/c)^2 slower ageing, thus an age difference of 0.5(v/c)^2 ] times the duration 2T of the whole experience, so v^2/c^2. This much seems troublesomely asymmetric. But during the remote turn- around interval 2v/a, at acceleration or gravity "a" and floor-ceiling distance vT, the stay-at-home looks to have aged an additional 2v^2 /c^2. Summing these two separate contributions, Traveler arrives home expecting the stay-at-home to have aged less than herself by one amount plus more than herself by twice that amount, whereas the stay-at-home expects to see Traveler younger by that amount. It all fits together. End of ostensible paradox, according to Peacock's Cosmological Physics (1999). Once again, there are several experiments which depend on this logic and come out OK within acceptably small errors of measurement.
(Historical note on puzzle-solving: this slowing of everything in a high-gravity place relative to a lesser-gravity place has the entertaining consequence that the speed of light does not anymore look the same to all observers. The laws of nature are different in curved space-time, in violation of the postulate from which relativity was first obtained in the "Special" form.)
(And a puzzle: What if space-time is curved on a cosmic scale so that the twins can take off in opposite directions and can compare ages as they pass each other at the antipodes of the closed hyper-spherical universe, without ever needing to decelerate or turn around? Symmetry seems to require that they look the same age to each other despite the long interval of extreme relative speed. I don't know how to deal with this one.)
So far as I am aware, a century of efforts have disclosed no inconsistency in Einstein's reckoning of space-time, nor any quantitative disagreement with observation. But the concept of "time" used in 20th century mechanics still has the problem that, like all the rest of fundamental physics, it makes no distinction between past and future … while we intuitively want to make such a distinction and a lot of non-"fundamental" physics actually does. There are five major classes of such phenomena, according to H. Dieter Zeh's book (3rd revision, 1999) The Physical Basis of the Direction of Time. I read every word of it two weeks ago while trying to address Dr. Scott's challenges, but I still don't understand very much. The five classes, anyhow, are:
1) things about radiation going out from an event, like the luminescence of a squeezed crystal: we never see corresponding radiation converging from afar to be absorbed in the crystal and make it jerk, because this would require perfect coordination of remote sources;
2) things about statistical mechanics and thermodynamics: ice-cubes melt in a glass of warm water, but we never see cool water segregate itself into an ice-cube surrounded by warm liquid; Zeh (and I) believe that the time-orientation of subjective psychology belongs under this theme, and that, as Ludwig Boltzmann argued a century ago, it is a relatively straight-forward matter of how we classify groups of possible states of composite substances made of many independent particles; the mystery that we remember the past but not the future belongs under this heading;
3) things about quantum-mechanical wave-functions collapsing to irreversibly choose one among latent possible positions, energies, etc; this is a fantasy, but so are all the other interpretations of QM, so it may be a while before anyone can convincingly explicate what "time" means in the first-order non-Lorentz-invariant Schroedinger equation (where time is accordingly asymmetric, like our intuitive tastes in time, but this maybe be only a cosmetic pandering to our taste, inasmuch as it can be compensated complex conjugation of the wave function, which has no effect on anything observable);
4) things about black holes and the big-bang that seem to have put the universe on a 1-way course in time; this topic seems unlikely ever to graduate from self-consistent "mere talk" (challenge enough!) to experimental demonstrations that one line of such talk is incorrect while the other must be accepted;
5) things about quantization of gravity and of time that don't seem to fit well with any, even very exotic, concept of time, and have the same problem of verification in experience.
In all five cases it seems important to distinguish whether we are talking of the "direction OF time" or the direction of processes IN time", as a first step. But since my own concept of "time" is now so muddled, I can't even take that first step today.
The only thing that emerges absolutely clearly to me from observing others thinking carefully about time seems well captured in Siddhartha's comment to Govinda: "Time is not real, Govinda" (Hermann Hesse, 1951). I have it from the Buddha that he meant it in this sense, that the arrow of time as we experience it, i.e., our present inconsistent jumble of concepts of time, are surely not real or do not all contribute to the same "reality," and so don't work. 2500 years later it seems that no other concept of "time" works, either, at least not broadly enough to cover all the cases of interest. But the concepts that physicists worked through to quantitative consistency and to exact agreement with such few observations as we have so far do work well for the phenomena of moving macroscopic bodies. That accordingly seems to me the best basis to start from in trying to generalize. Since Isaac Newton's creation of this problem it has remained endlessly fascinating that, right through Einstein's further clarification, this basis has no "arrow of time."
However ---- The ongoing CP-LEAR experiment at CERN seems to have turned up the first direct evidence of time-reversal NON-invariance in the decay of the neutral kaon (published at the end on 1998, too late for Zeh's book). If confirmed, this would seem to overturn the prejudice proffered just above, that there is no "arrow" in elementary processes, whatever theory and all other evidence may say. See a recent summary and the CPLEAR website that alludes to it.
About the puzzle engaged above in terms of heartbeats per wheel click:
It seems to me that if all processes in constant relative motion look slower, all in the same proportion, in ratio 1/sqrt(1-(v/c)^2) as we learned in undergrad physics of special relativity, and letting that factor be 2 for simplicity in the present example (i.e., v is 86% of light speed), then Farmer feels two heartbeats for each one he sees in his binoculars, and similarly hears two clicks for each heartbeat he sees in his binoculars. Symmetrically, if Traveler has binoculars, he has the same experience: Farmer looks slow, doing only one heartbeat to Traveler's two. Each also witnesses the other responding to each wheel- click in synchrony with his (the other's) heartbeats. And each witnesses the other recording his opposite's observation of his own heartbeats and click-perceptions on an even more dragged-out time scale, and so on and on. This is not intuitive, but is it inconsistent?
What about the wheel squashing a bug at each rail junction? Surely both observers must be in agreement about that (and in agreement with the bug), i.e. all agree about the wheel perimeter equaling the rail length and the wheel not slipping along the track. But does Traveler hear one or two "click-squash" events per heartbeat, while Farmer hears only one? If two, then don't they disagree about speed? Nope: because they disagree about both wheel and rail length. To Traveler, the rails are only half as long as they are to Farmer. So is the wheel perimeter, due to a curious consequence of General Relativity: the wheel rim is subject to immense and uniform acceleration v^2 * radius, which makes it shorter than the 2pi*radius expected in Euclidean space: space is curved in a gravitational field! With this understanding, everything about "space" does in fact fit together, leaving no contradiction whereby to discard the relativistic concept of time.
If the axles were welded to the rails on Farmer's land, they would spin in just the same way against the moving carriage-bottom, and the carriage is fore-shortened by half due to its motion in Farmer's frame.
From within the carriage car, wheels attached to the rail (and from Farmer's viewpoint, wheels normally attached to the moving car) look to have a funny shape on account of their lack of foreshortening where touching the carriage (or the rail) (0 relative speed) and their super- foreshortening on the opposite side where moving at double speed. I don't know how this enters into estimation of wheel perimeter, but I think it doesn't matter because we need to do that only for the frame to which the axles are welded, whichever that may be.
I am not at all sure I got this right, but I think the solution is something like this, and as an item of religious dogma I believe that if I had the patience to plumb these Mysteries a little deeper, or knew an aficionado of Relativity with the patience to help me sort out school- boyish riddles one by one, it would all come clear to me. I leave that further exercise to the faithful student and perhaps her Physics professor.