Einstein's Errors: Part VII
Further Thoughts on the Meaning of Spacetime and the Validity of the Special Theory of Relativity (STR)
Outline of this series:
I. The Impetus for This Series
II. Special Relativity: The Standard Explanation
IV. A Further Look at Simultaneity
VII. Further Thoughts on the Meaning of Spacetime and the Validity of STR
VIII. Mettenheim on Einstein’s Relativity
Bibliography (appended to each part of the series)
What sets STR apart from the classical Galelei-Newton view of space and time? It’s the intertwining of space and time into four-dimensional spacetime. The four dimensions are the usual spatial dimensions represented by x, y, and z, and the time dimension, represented by t. One aspect of spacetime is the tradeoff between space (distance) and time discussed in “The Velocity Conundrum.” What is the physical meaning of that tradeoff? Is it real or illusory?
It is useful at this point to introduce another thought experiment. Consider a very fast train moving on a track in a long, straight tunnel. The tunnel (including the track) is a stationary frame of reference in relation to the train. That statement should lead you to wonder if the speed of the train is therefore accurately depicted as a fraction of c, the speed of light. It isn’t if the tunnel isn’t absolutely stationary (as it’s unlikely to be, as discussed in “Getting Light Right”), and the speed of the train is really its speed relative to the tunnel, not its absolute speed as a fraction of c.
For the purpose of the thought experiment, the tunnel must be considered absolutely stationary, so that the speed of the train is its speed as a fraction of c. Given that, the tunnel can be taken as a proxy for absolute spacetime, just as it should be in Einstein’s famous train-embankment thought experiment (see “A Fatal Flaw?”). But how can there be absolute spacetime if STR says there isn’t? I’ll get back to that.
In any event, the tunnel of this thought experiment is lined with sensors that detect and record the train’s passage at a velocity of 0.6c. The train’s position throughout its journey can therefore be described in terms of the space-time coordinates of the tunnel. Graphically:
The solid black line represents the progress of the train through the tunnel. From the standpoint of observers in the tunnel, the train takes 6 light-seconds to traverse the tunnel. (Note that a beam of light, represented by the dashed line, would reach from one end of the tunnel to the other end in 6 seconds, 4 seconds ahead of the train.) The gray area represents the space-time coordinates occupied by the tunnel during the 10 seconds of the train’s traversal. The gray area really consists of an infinite number of horizontal lines, each 0.6 light-seconds long, which is the constant length of the tunnel as it moves through time — but (theoretically) not through space.
In this version of the graph, the red dots mark the passage of each second of the train’s trip through the tunnel, as perceived by observers on the train:
Note that there are only 8 red dots along the train’s path, which means that observers on the train experience an 8-second trip through the tunnel, not a 10-second trip. According to STR, the time-dilation effect slows the clocks on the train, relative to clocks in the tunnel. When the train is moving at 0.6c, its clocks “tick” every 1.25 seconds for every 1 second that passes for observers in the tunnel, which means that the train’s clocks advance at 0.8 times the rate of clocks in the tunnel (1/1.25 = 0.8). Further, by the length-contraction effect, observers in the tunnel would perceive that the train has shrunk to 0.8 times its “real” length, that is, the length measured by observers on the train.
This leads to the question why a clock in a moving body (might) move more slowly the faster the body moves, and why a moving body would seem to have shrunk (according to observers in another frame of reference). Are these mathematical illusions or real phenomena? If the Lorentz relationships are symmetrical, as I understand them to be, they would seem to be mathematical illusions similar to the effect of distance on the perceived height of another person. When A and B are together, they can use a tape measure to agree on their heights. If they walk away from each other, they seem smaller to each other, but they know that this is an illusion that will vanish when they are standing next to each other.
Why is there a mathematical illusion? It arises from Einstein’s use of the Lorentz transformation to explain the non-simultaneity of events. (He calls it the relativity of simultaneity, but he means to say that events in different frames of reference can’t truly be simultaneous.) However — as I explain in “A Fatal Flaw?” — Einstein’s thought experiment doesn’t demonstrate non-simultaneity. In fact, as my thought experiment in that essay demonstrates, there is no such thing as non-simultaneity. Which is to say that simultaneity is alive and well.
After all, if there were no such thing as simultaneity, the Lorentz transformation wouldn’t work; that is, there would be no way to translate between frames of reference. But the Lorentz transformation acts, in effect, like an omniscient observer who is able to calibrate events in frames of reference that are moving with respect to each other. And the ability to calibrate implies that there is an absolute standard of space and time. Different clock rates and different length measurements are incidental features. As Buenker (2016) puts it,
Galileo’s Relativity Principle needs to be amended to read: The laws of physics are the same in all inertial systems but the units in which their results are expressed can and do vary from one rest frame to another [emphasis in original].
The real issue is whether different frames of reference have different spacetime coordinates. Do clocks in frames of reference that are moving relative to each other really move at different rates due to their relative velocities (as opposed to their gravitational or energy states)? Does this mean, for example, that a very precise clock stationed at the center of the universe (if there were such a thing) would move faster than every identical clock elsewhere in the universe — all of which are moving at some speed relative to the (hypothetical) center? Does this mean that a clock placed at the edge of the universe — which is constantly expanding outward — would run far, far, far more slowly than the clock at the center of the universe?
If this is so, what is the physical mechanism that causes it? This, I think, is the question that baffles people who struggle to understand Einsteinian special relativity. If STR is true, there must be a physical explanation that can be described in a fairly simple way. But, as far as I am aware, STR is never explained in physical terms. Readers and viewers are simply told that time slows and length contracts as a body goes faster. They are shown equations, graphs, drawings, cartoons, and animations that are consistent with the assertions that time slows and length contracts. But they aren’t given a physical explanation for such phenomena.
Here’s an explanation that I’ve read: Because spacetime is a compound of space and time, a body that moves only in time “uses” no space, other than the space that it occupies. A body that moves in space because it has a velocity “uses” more time the faster it goes (it takes longer for it to reach a given age), and must therefore sacrifice some space. It’s a zero-sum view of spacetime, which accords with this explanation of spacetime:
that measurements of distance and time between events differ among observers, [but] the spacetime interval is independent of the inertial frame of reference in which they are recorded.
Absolute space and absolute time have been replaced with … absolute spacetime. Conceptually, at least. But there’s still a crying need for a deep explanation of spacetime, something beyond its (supposed) mathematical properties.
What is the physical (material) mechanism at work when the “use” of time reduces the availability of space, and vice versa? Time is open-ended. Space is open-ended on a cosmological scale (assuming an ever-expanding universe).
According to general relativity, spacetime is curved; that is, both time and space are curved. Not that they can really be separated, but physicists have developed a dodge. There are time-like objects, whose journey through spacetime can be described in terms of time values. There are space-like objects, whose journey through spacetime can be describe in terms of spatial values. But unless there is an object that truly moves only through time — an object at the non-existent center of the universe — this is a meaningless distinction. To put it another way, if there is spacetime rather than space and time, there can’t be a separate thing called time, curved or not.
But there is a separate thing called time. A stationary human being knows that time is passing because he knows that he has consecutive thoughts. He also knows that he is continuing to breath, that his heart is continuing to beat, and so on. But the sum of these events, when reviewed in the observer’s mind, don’t reveal a curvature of time, merely its continuation, or — more to the point — the continuation of the observer and the objects around him. Time doesn’t curve, go in straight lines, or do loop-the-loops. It just flows. The idea of curved time is a patently nonsensical mathematical abstraction.
Phipps (2006,2012) argues at length — and with seeming authority — that STR is fundamentally flawed because it is based on Maxwell’s equations rather than what Phipps calls a neo-Hertzian alternative. This alternative is based on the field equations of Heinrich Hertz. I begin with Phipps (1993):
In the last chapter of [Electric Waves], which appeared in 1892, [Hertz] treated the “electrodynamics of moving bodies” by an original set of equations comprising what we would call today an “invariant covering theory” of Maxwell’s equations for vacuum electrodynamics. The new equations differed from Maxwell’s through the inclusion of an extra velocity-dimensioned parameter, the components of which Hertz designated (α, ß, γ). The presence of this extra velocity parameter spoiled the space- time symmetry of Maxwell’s equations, but caused them to become rigorously invariant under the Galilean transformation of coordinates….
[Hertz’s] theory did not become physics, because physics is never equations alone but equations plus physical interpretation. As often as not, and certainly in this case, interpretation proves the stumbling block. On the side of interpretation Hertz made a fatally bad guess….
… Maxwell, Hertz, and most other late nineteenth- century physicists were fixated on ether… so, when Hertz saw a new velocity parameter unavoidably emerging from his invariant mathematics, he automatically identified it with ether velocity….
… [I]t was not Hertz’s mathematics that was empirically discredited, but the combination of that and an obviously (in the modem view) unsound physical interpretation. An identical interpretational mistake (of staking all the physics on an ether mechanism) was made by Maxwell.
History, ever the joker, forgave Maxwell’s errant physics and preserved – indeed, virtually sanctified – his mathematics (a noninvariant special case of the Hertz equations … hence in formal terms a comparatively degraded breed of mathematics)….
Phipps (2006, 2012) concludes that time-dilation is a fact. But it is related to the energy state of a body, and it is asymmetrical (i.e., absolute); it is not the symmetrical time-dilation of STR. Further, he concludes that length-contraction is not a fact; length is invariant with frame of reference.
BIBLIOGRAPHY
Online courses in special relativity
Lecture 1 of “Special Relativity”, Stanford University
All lectures of “Special Relativity”, Khan Academy
All lectures of “Understanding Einstein: The Special Theory of Relativity”, Standford University
Selected books, articles, and posts about special relativity
Barnett, Lincoln. The Universe and Dr. Einstein. New York: Time Incorporated, 1962.
Bondi, Hermann. Relativity and Common Sense: A New Approach to Einstein. New York: Doubleday & Company, 1946.
Buenker, Robert J. “Commentary on the Work of Thomas E. Phipps, Jr. (1925-2016)”. 2016.
Einstein, Albert. “On the Electrodynamics of Moving Bodies”. Annalen der Physik, 322 (10), 891–921 (1905).
———. Relativity: The Special and General Theory. New York: Henry Holt, 1920.
Epstein, Lewis Carroll. Relativity Visualized. San Francisco: Insight Press, 2000.
Hall, A.D. “Lensing by Refraction…Not Gravity?“. The Daily Plasma, December 23, 2015.
Marrett, Doug. “The Sagnac Effect: Does It Contradict Relativity?“. Conspiracy of Light, 2012.
———. “Did the Hafele and Keating Experiment Prove Einstein Wrong?“. Conspiracy of Light, 2013.
von Mettenheim, Christoph. Popper versus Einstein. Heidelberg: Mohr Siebeck, 1998.
———. Einstein, Popper and the Crisis of Theoretical Physics (Introduction: The Issue at Stake). Hamburg: Tredition GmhH, 2015.
Noyes, H. Pierre. “Preface to Heretical Verities [by Thomas E. Phipps Jr.]”. Stanford: Stanford Linear Accelerator Center, Stanford University, June 1986.
Phipps, Thomas E. Jr. “On Hertz’s Invariant Form of Maxwell’s Equations”. Physics Essays, Vol. 6, No. 2 (1993).
———. Old Physics for New: A Worldview Alternative to Einstein’s Relativity Theory. Montreal: Apeiron, first edition, 2006.
———. Old Physics for New: A Worldview Alternative to Einstein’s Relativity Theory. Montreal: Apeiron, second edition, 2012 (The late Dr. Phipps — Ph.D. in nuclear physics, Harvard University, 1950 — styled himself a dissident from STR, for reasons that he spells out carefully and exhaustively in the book.)
Rudolf v. B. Rucker. Geometry, Relativity, and the Fourth Dimension. New York: Dover Publications, 1977.