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3Physics as Geometry...of a Pretty Swampy Space
ByStephen E. Robbinson February 24, 2015
This book is an interesting mind trip. Maudlin starts us at the base problem - the problem of absolute space and absolute motion, Newton's affirmative position on this absoluteness - his spinning bucket proof, his two globes linked by a cable - his argument with Leibniz, Leibniz versus Clarke, Galilean relativity. Soon we are introduced to the general schema in which Maudlin's view is framed throughout (to be modified in its special relativistic version) - this is the stack of time slices of space-time. A point in the same position (same space coordinates), slice after slice, is a motionless point over time - it traces a straight line through the stack of slices. A point in linear motion (one space coordinate changing) traces a straight line at an angle relative to the former. A point accelerating (a force must be applied for this) traces a curve through the stack. Transforms take us from one time-slice to another - a topological transform preserves the continuity of the lines, an affine transform preserves the straight lines - though now the line of a static point might be angled (moving) and vice versa. There are no absolute motions, no absolute points in space. And thus we come to special relativity (STR), where we realize the ride is about to become rather strange, for Maudlin announces that all standard explanations are wrong, in fact, even Einstein misstated things, having presented the theory in terms of the equivalence of inertial frames and the constancy of the speed of light, leading to the Lorentz transformations which relate one set of coordinates to another - an approach Maudlin argues, that "has already run off the rails." This includes talk of "time slowing down" or "travelling near the speed of light," for (given the affine transform effect noted above), "..we must expunge all ideas of things having speeds, including light." We are going to be studying, perhaps better, Maudlin Relativity, where we will find a new partition of, 1) things STR explains and, 2) things that Maudlin's view of the geometry of space/time explains.
The traditional approaches, I will note here (for Maudlin, in his disdain for the standard accounts, does not give them much space), have largely been stuck on the twin paradox, and integrally associated with this, the very physical and real "time-effects" that it is believed STR explains - the longer living mesons (or muons) when travelling at high velocity, the Hafele-Keating experiment where the clock carried on the jet is retarded when arriving back at the airport when compared to another left sitting at the airport. These effects are taken to be ontological, that is, physically real - no one denies the retardation of the jet carried clock. The twin effect (first declared an implication of STR by Langevin in 1911), should one twin have a long beard and grey air, the other look like a young Brad Pitt, would indeed be physically real - ontological. The difficulty is that in STR, the Lorentz transformations are embedded in a system, namely within the reciprocal motions of two observers, where one can claim to be stationary, the other in motion, or vice versa (that little statement of 1905, after Einstein notes the foreshortened ellipse in the moving system: "It is clear that the same results hold good of bodies at rest in the `stationary' system, viewed from a system in uniform motion.") In these equations, space changes compensate for time changes and vice versa, and thus, since they are compensatory, both changes (space, time) must be of the same order - either non-ontological (i.e., measurement effects only) or ontological (real, physical). As the "stationary" observer claims these effects for the moving system - and vice versa - STR won its acceptance in physics precisely on the fact that its effects are measurement effects, i.e., non-ontological. Thus the Michelson-Morley result was not considered the effect of an actual, physical contraction of the apparatus arm that lay parallel to its motion in the ether. Lorentz, trying to save the Maxwell-Lorentz equations for electromagnetism and their requirement for an absolute motion in the ether, had a bit earlier offered a physical model of the arm-contraction (or of any body in motion, to include a reduction of frequency) based on electro-dynamic forces. It was a rejection of the relativity inherent in Newton's first law. Physics rejected Lorentz's offer; Einstein's new version of relativity, with its measurement effects-only solution, was accepted. But this (correct, consistent interpretation) destroys STR's ability to explain any of the very ontological time-related effects it is currently and mistakenly given credit for - to include the jet-carried clock, the long living meson, or the twin-effect (should it actually happen). To be consistent with its structure, all effects, whether of time or space, must indeed be taken as measurement effects, that is, non-ontological. What has happened is that roughly ever since Langevin, two incompatible solutions - that of Lorentz, that of Einstein - have been fused into an unholy mess.
Maudlin's effort is in steering through this (at best by him implicitly explained) thicket; what he presents is truly new (at least I, for one, have not encountered these arguments). What one finds, as one works through it (and it must be worked through), is that he posits two levels of time-related change, and two levels of space-related change. Thus, for time, he insists that the slower aging twin-effect is very real, physical (ontological), but the "slowing clocks" is simply a "coordinate effect" (in my terms, a measurement effect only). (He never explicitly discusses, or locates within his scheme, Hafele-Keating or the muons.) Equally, there is a real, physical Lorentz contraction, but there is also another Lorentz contraction that is only a measurement effect. Given this symmetry, he has saved the standard STR explanation of Michelson-Morley - the contraction of the apparatus arm involved/required is indeed only a measurement effect (i.e., it is not the actual, physical contraction Maudlin holds can also exist) - and he believes he can explain the twin effect as real, physical, i.e., ontological. But, unfortunately, he leaves so many questions abegging.
The twin effect is explained by Maudlin simply by means of geometry, by a Minkowski diagram (of sorts). The stationary twin is simply one of those straight lines through the time slices (such as time slices are (or are not) in the Minkowski version of space-time). The rocket-twin moves away at an angle, and then moves back again at an angle, meeting back up with the stationary earth-twin. By Minkowski's math, the stationary line of the earth-bound twin is 100 years long while the total of the two angled lines is 60 years. The rocket-twin has aged less (only 60 years). The geometry (the shortened space-time path) explains it all - it is a "real, physical, ontological effect" - and "explained" by the geometry alone! End of story.
But this cannot be the end of the story. There is that reciprocity of systems that cannot be erased from Einstein's approach, despite Maudlin's disdain. Minkowski's geometric generalization simply extends the space-time interval invariance, already intrinsic in the Lorentz transformations, to all possible coordinate axes. It does not remove Einstein's embedding of Lorentz's equations within his (Einstein's) reciprocity. The rocket-twin has equal right to claim HE is stationary. We now need a new Minkowski diagram with a new origin for the coordinates. When we create a Minkowski diagram, we necessarily fix on one observer - all the rest are set (depicted) in motion with respect to him. There is but one real, actual observer in Minkowski space-time - the rest, moving at various speeds, are virtual - imaginary - with their proportions of space and "time" now adjusting ("time" being now a purely mathematical treatment of the 4th coordinate) relative to the one real, stationary observer. With the new diagram, with the rocket-twin stationary, the situation is reversed. Now the rocket-twin ages more. This was a point of Bergson (Duration and Simultaneity, 1922), and so too by M.I.T. physicist A.P. French (Special Relativity, 1968), who stated categorically that STR cannot be used to explain the longer living meson (or muon) speeding towards earth - that in fact, we would need two Minkowski space-time diagrams, one for each case - the observer on earth, a hypothetical observer on the meson. Each can claim he is stationary, the other in motion. In other words, he argued, in STR the meson's "extended life" can only be treated (just as the "length change" of M-M's apparatus arm) as a measurement effect, and STR is used illegitimately (i.e., a different theory is needed, like, er, Lorentz) in explaining the phenomenon as a real, ontological effect - though ontological the effect most certainly is.
The reciprocity problem, Maudlin dismisses with both a strawman and questionable reasoning, totally ignoring even Einstein, even his own affine transformations (which take a stationary object to a moving object - and vice versa) as "Confusion 1" re STR. Yet "1" is precisely why there exists his "Confusion 2," where folks are desperately trying to escape the reciprocity implications by appealing to accelerations (as did French) to explain the twins, the clocks, the mesons. Hence Maudlin becomes very murky. Is not the longer living meson a real effect? Would Maudlin explain this too like the rocket-twin - by ignoring reciprocity? And the Hafele-Keating clock? Obviously a real effect. Explained similarly? The explanation of these effects is obscure in Maudlin. Note, we could we give the earth-twin a clock with markers for 100 years, and put a similar 100-year clock on the rocket. The rocket-clock, on return, would necessarily point to 60, while the earth-twin's clock points to 100. Is this not one of those "clock slowings?" Yet clock slowings are only a "coordinate effect" (not real) per Maudlin. Slower aging of the rocket-twin real, his clock-slowing not real? Hafele-Keating - not real? Murky. In truth, there is even a physical contradiction lurking. Maudlin's treatment is abstract, with no real velocity numbers given. In his purely geometric analysis of the rocket-twin's path, 40 years were knocked off. Let us suppose the rocket is moving at 99.8% the speed of light. At least 40 years will again be knocked off. The earth-twin, sitting in his kitchen, can send out a light ray at the same time the rocket leaves, bouncing it off a mirror placed where the rocket turns back and it returns. The light velocity is invariant, it is unaffected by the Minkowski (Lorentz) math applied to the rocket twin, it has nothing lopped off its path. Travelling always just barely faster than the rocket, it returns (much, 40+ years) later?
In general, Maudlin is well aware that geometry alone is insufficient. For real, physical effects we must have explanations involving real forces. His twin-effect model however rests solely on geometry. This reliance on geometry alone is echoed elsewhere - the line between geometrical explanation and actual physics is throughout very vague. The speed of light is explained simply by the "light-cone" in Minkowski space-time. Yet, for Newton, the maximum velocity in a medium is given as v = sqrt(L/D), where L is the elasticity, D the density of the medium. Flick a chunk of jello - the wave velocity passing through the jello is determined by this ratio. Were we to assume that Lorentz's "ether" is still lurking around, perhaps now disguised as the "quantum vacuum," this medium should have an L and a D, therefore determining a maximum velocity within it. This would be a physical explanation. Just saying - as an example. Or the flow of time itself - in his Galilean exposition, time is simply the topological/affine transforms taking us from one time-slice of space to the next. What does this abstraction have to do with the dynamic evolution of the physical, universal field over time, i.e., the actual, physical transition from one time-slice of space to the next? Would there not have to be some real, phsyical,continuous process “generating” each time-slice of (all of) space? The "forces" creating curved lines - what are they other than ghostly creatures inhabiting this geometric space? And of course, in the Minkowski version, there is that famous space-time block where supposedly there is no flow of time - with all the attendant problems this generates (e.g., how do we account for the "illusion" of the flow of events) - unexplored by Maudlin.
The book is indeed a good mind trip, if only as a meditation on the struggles our current, very mathematical physics faces re what is actual "explanation." It is also an interesting demonstration of how far STR (or better, the Lorentz-STR fusion) actually is from being "settled" (many seem to think the shooting is all over). There are many interesting things however in the book. I have picked on a few salient things here - out of some possible areas of critique. How, to note one more, can Maudlin say that "we cannot compare speeds"? He has just done so in the twin paradox, while the light cone itself inherently compares speeds relative to everything moving slower than light. Yes, I know he is thinking of that affine transformation that takes straight-through lines (stationary object) to angled (i.e., moving object) lines. But he has just fixed the earth-twin as stock still in space, and set the rocket twin moving (prohibiting the latter from any say as to whether he happens to consider himself stationary), and then, yes, compared. Yet we cannot compare. A little too Zen koan-like for me. Just things that make the book less then satisfying as a treatment of the issues. For escape from this swamp, for a deeper, more coherent view, imo, we have to return to Bergson (1922) and his "Duration and Simultaneity," though for the equation-hating reviewers here, I must warn that Bergson breaks Einstein and the Lorentz equations down in detail to view the concrete meaning of Einstein's system.