Reports that scientists at CERN have found neutrinos to travel faster than light do not necessarily mean that special relativity is wrong.
First, the difference to the speed of light is apparently very small, so this could easily be the result of errors in setting up the experiment, measuring relevant variables, synchronizing clocks... The author of the report on the experiment has said himself that "we are not claiming things, we want just to be helped by the community in understanding our crazy result".
Second, there are already a number of known "faster-than-light" phenomena which are not deemed to contradict relativity, and this may turn out to be just another one of those.
Third, I note that the reported result of the neutrino speed experiment chimes rather well with two of my findings relating to special relativity developed in this blog so far:
1) Faster-than-light signals would not involve any reversal of cause and effect and would not enable time travel into the past, according to a proper understanding of special relativity which avoids the trap of the "simultaneity syndrome" in modern physics.
2) The acceleration of macroscopic objects may be constrained by the fact that they contain electrically charged particles, which cannot be accelerated beyond the speed of light because light itself can be regarded as outwardly propagating disturbances in the electric fields of charged particles, as mentioned in this post.
For example, let there be an electron surrounded by or made up of a spherically symmetrical electric field, which can be visualized as a series of concentric spheres around the electron. If the electron is briefly accelerated, the distance between neighbouring spheres is reduced in the direction of acceleration and increased in the opposite direction as the information about the acceleration travels outwards. The disturbance of the electric field - an electromagnetic signal - is located at the boundary between the spheres that have been accelerated and those that haven't.
The law of light propagation could quite simply be that electromagnetic radiation emanating from an accelerated electron always traverses the same number of spheres as defined above in the same period of time as measured by Einstein-adjusted clocks in the system of the electron prior to acceleration.
According to this model, accelerating objects that contain electric charges also produce outwardly propagating field disturbances and are surrounded by "spheres" that move ever closer to each other in the direction of acceleration. The inability to accelerate charged particles up to or beyond the speed of light could then be a consequence of the fact that those spheres cannot be compressed to infinite density or beyond.
Particles that do not carry any electric charge, on the other hand, would not be constrained in the same way, though there may be other constraints regarding their acceleration.
The sphere model is a line of thought I intend to develop later, once I've reached the appropriate point in my understanding of special relativity as developed in this blog.
Friday 23 September 2011
Friday 9 September 2011
Special relativity as a conservative enterprise
Five years after Leo Sartori's book Understanding Relativity was published, Wolfgang Rindler published his Relativity - Special, General, and Cosmological (2001). Like Sartori, Rindler says the emphasis throughout his book is on "understanding the concepts" underlying relativity. But does he give fuller answers than Sartori to the questions of
● how decision-making contributes to the principle of the constancy of the speed of light;
● why it may be useful or advisable to adjust clocks in line with Einstein's procedure;
● and whether or in what sense Einstein's clock adjustment procedure can be regarded as a synchronization procedure and whether, therefore, it leads to meaningful statements about one-way speeds, simultaneous existence and causality?
In a nutshell, he does, but it is not easy to distill answers to those questions from his presentation.
For a start, Rindler does not mention Einstein's clock adjustment procedure in the context of his explanation of the light speed principle. Instead, Rindler asserts that the existence of an invariant velocity follows from the relativity principle and the assumption of causal invariance. According to him, the only function of the light speed principle is thus "to fix the invariant velocity", and "Maxwell's theory and the ether-drift experiments clearly suggest that it should be c" (pp. 12, 15).
I'm going to examine the kind of empirical and theoretical arguments for the light speed principle put forward by Rindler and others in due course, in the months and years to come. Suffice it to say that Maxwell's theory and the idea that there is an invariant velocity both presuppose a concept of distant simultaneity, a fact which is acknowledged and addressed in Einstein's 1905 paper but not even mentioned in Rindler's book.
Curiously, however, Rindler's book contains a subsequent and quite disconnected section entitled "The coordinate lattice; Definitions of simultaneity" (pp. 41-43), which does discuss the issue of what constitutes a "satisfactory" clock synchronization procedure. It is this section which suggests some answers to my questions.
Rindler begins by making the same mistake as Sartori. He maintains that, in order to synchronize clocks, "it is sufficient to emit a single light signal from the origin, say at time t0: each lattice clock is set to read t0 + r/c as the signal passes it, where r is its distance from the origin". Rindler thus uses the one-way speed of light to synchronize clocks when in fact a clock synchronization procedure must already be in place for that speed to be well-defined, as recognized by Einstein in his 1905 paper.
But then Rindler asks what actually makes for a satisfactory clock synchronization procedure, and some of his answers are instructive. "In particular," Rindler says, "the time coordinate t can be chosen so that the mathematical expression of the physical laws reflects their inherent symmetries."
Rindler makes three important points in this key sentence: first, as far as physicists are concerned, time coordinates are a matter of choice; second, that choice should be guided by the effect it has on the mathematical form of physical laws, in other words: whether or not such time coordinates define a relationship of simultaneity is quite irrelevant; third, the desired effect is for the "inherent symmetries" of physical laws to be preserved.
Rindler doesn't elaborate much on the last point, but he suggests that a situation in which a gun shoots bullets faster in one direction than another because of the way we have chosen our time coordinates should be avoided. At first sight this requirement may seem plausible enough. Galileo and Newton would no doubt have agreed. But then, they didn't know about high-speed particle experiments which show that it becomes ever more difficult to accelerate particles as they approach the speed of light. Today we know that a bullet fired in the forward direction by a gun moving at close to c through the laboratory moves more slowly away from that gun than a bullet fired by the same gun in the backward direction - as seen from the laboratory using Einstein-adjusted clocks, that is.
So why should time coordinates in the system of the gun be adjusted such that in that system the bullets move away from the gun at equal speeds in every direction? Rindler doesn't say explicitly, but the idea seems to be that if we do so the laws of physics take on a particularly simple, symmetric form in all uniformly moving frames of reference, just as they do in Newton's theory and in the "ether" frame of Maxwell's theory. The result is that, in Rindler's words, in special relativity every uniformly moving frame of reference is "as good as absolute space" in Newton's theory and also "as good as Maxwell's ether frame".
In a sense then, special relativity is a conservative enterprise: it defines time coordinates, or adjusts clocks, in such a way that the laws of physics remain symmetrical in different directions just as in Newton's and Maxwell's theories of old - despite subsequent empirical findings suggesting that the phenomena themselves lack such symmetry.
The conservatism of special relativity is neatly encapsulated in a formula chosen by Rindler to describe how light propagates. "According to Einstein's second axiom, light in every inertial frame behaves like light in Maxwell's ether," Rindler says on p. 38 (his emphasis). It appears that the ether model has not been abandoned in modern physics, after all, but has been generalized to every inertial frame of reference!
There is nothing wrong with a conservative approach to physics as long as there are good reasons for it. Clearly, physicists have decided that they prefer to work with symmetrical laws, to which they have been used for centuries. Even if they were prepared to admit asymmetrical laws, there would still be the small matter of determining in which frames of reference, if any, bullets or light propagate in symmetrical conditions in every direction so that Einstein's clock adjustment procedure can be used to synchronize clocks in those frames, as discussed in a previous post.
But the conservatism of special relativity comes at a price. By clinging on to symmetrical laws through a suitable choice of time coordinates, special relativity dispenses with the requirement that clocks should be synchronized and thus throws concepts such as one-way speed, simultaneous existence and causality into disarray, as illustrated by the "simultaneity syndrome" in modern physics discussed in this post.
Rindler does not seem to be aware of this problem as he refers to a clock adjustment procedure based on the light speed principle as a way of "synchronizing clocks", without any qualification, and a few pages later he promptly falls victim to the "simultaneity syndrome". In summary, then, Rindler gives answers to the first two questions set out at the start of this post but not to the third.
In my next post I will examine whether a book wholly devoted to "the meaning of spacetime", Vesselin Petkov's Relativity and the Nature of Spacetime (2005), gives a more satisfactory explanation of clock adjustment and synchronization in special relativity.
● how decision-making contributes to the principle of the constancy of the speed of light;
● why it may be useful or advisable to adjust clocks in line with Einstein's procedure;
● and whether or in what sense Einstein's clock adjustment procedure can be regarded as a synchronization procedure and whether, therefore, it leads to meaningful statements about one-way speeds, simultaneous existence and causality?
In a nutshell, he does, but it is not easy to distill answers to those questions from his presentation.
For a start, Rindler does not mention Einstein's clock adjustment procedure in the context of his explanation of the light speed principle. Instead, Rindler asserts that the existence of an invariant velocity follows from the relativity principle and the assumption of causal invariance. According to him, the only function of the light speed principle is thus "to fix the invariant velocity", and "Maxwell's theory and the ether-drift experiments clearly suggest that it should be c" (pp. 12, 15).
I'm going to examine the kind of empirical and theoretical arguments for the light speed principle put forward by Rindler and others in due course, in the months and years to come. Suffice it to say that Maxwell's theory and the idea that there is an invariant velocity both presuppose a concept of distant simultaneity, a fact which is acknowledged and addressed in Einstein's 1905 paper but not even mentioned in Rindler's book.
Curiously, however, Rindler's book contains a subsequent and quite disconnected section entitled "The coordinate lattice; Definitions of simultaneity" (pp. 41-43), which does discuss the issue of what constitutes a "satisfactory" clock synchronization procedure. It is this section which suggests some answers to my questions.
Rindler begins by making the same mistake as Sartori. He maintains that, in order to synchronize clocks, "it is sufficient to emit a single light signal from the origin, say at time t0: each lattice clock is set to read t0 + r/c as the signal passes it, where r is its distance from the origin". Rindler thus uses the one-way speed of light to synchronize clocks when in fact a clock synchronization procedure must already be in place for that speed to be well-defined, as recognized by Einstein in his 1905 paper.
But then Rindler asks what actually makes for a satisfactory clock synchronization procedure, and some of his answers are instructive. "In particular," Rindler says, "the time coordinate t can be chosen so that the mathematical expression of the physical laws reflects their inherent symmetries."
Rindler makes three important points in this key sentence: first, as far as physicists are concerned, time coordinates are a matter of choice; second, that choice should be guided by the effect it has on the mathematical form of physical laws, in other words: whether or not such time coordinates define a relationship of simultaneity is quite irrelevant; third, the desired effect is for the "inherent symmetries" of physical laws to be preserved.
Rindler doesn't elaborate much on the last point, but he suggests that a situation in which a gun shoots bullets faster in one direction than another because of the way we have chosen our time coordinates should be avoided. At first sight this requirement may seem plausible enough. Galileo and Newton would no doubt have agreed. But then, they didn't know about high-speed particle experiments which show that it becomes ever more difficult to accelerate particles as they approach the speed of light. Today we know that a bullet fired in the forward direction by a gun moving at close to c through the laboratory moves more slowly away from that gun than a bullet fired by the same gun in the backward direction - as seen from the laboratory using Einstein-adjusted clocks, that is.
So why should time coordinates in the system of the gun be adjusted such that in that system the bullets move away from the gun at equal speeds in every direction? Rindler doesn't say explicitly, but the idea seems to be that if we do so the laws of physics take on a particularly simple, symmetric form in all uniformly moving frames of reference, just as they do in Newton's theory and in the "ether" frame of Maxwell's theory. The result is that, in Rindler's words, in special relativity every uniformly moving frame of reference is "as good as absolute space" in Newton's theory and also "as good as Maxwell's ether frame".
In a sense then, special relativity is a conservative enterprise: it defines time coordinates, or adjusts clocks, in such a way that the laws of physics remain symmetrical in different directions just as in Newton's and Maxwell's theories of old - despite subsequent empirical findings suggesting that the phenomena themselves lack such symmetry.
The conservatism of special relativity is neatly encapsulated in a formula chosen by Rindler to describe how light propagates. "According to Einstein's second axiom, light in every inertial frame behaves like light in Maxwell's ether," Rindler says on p. 38 (his emphasis). It appears that the ether model has not been abandoned in modern physics, after all, but has been generalized to every inertial frame of reference!
There is nothing wrong with a conservative approach to physics as long as there are good reasons for it. Clearly, physicists have decided that they prefer to work with symmetrical laws, to which they have been used for centuries. Even if they were prepared to admit asymmetrical laws, there would still be the small matter of determining in which frames of reference, if any, bullets or light propagate in symmetrical conditions in every direction so that Einstein's clock adjustment procedure can be used to synchronize clocks in those frames, as discussed in a previous post.
But the conservatism of special relativity comes at a price. By clinging on to symmetrical laws through a suitable choice of time coordinates, special relativity dispenses with the requirement that clocks should be synchronized and thus throws concepts such as one-way speed, simultaneous existence and causality into disarray, as illustrated by the "simultaneity syndrome" in modern physics discussed in this post.
Rindler does not seem to be aware of this problem as he refers to a clock adjustment procedure based on the light speed principle as a way of "synchronizing clocks", without any qualification, and a few pages later he promptly falls victim to the "simultaneity syndrome". In summary, then, Rindler gives answers to the first two questions set out at the start of this post but not to the third.
In my next post I will examine whether a book wholly devoted to "the meaning of spacetime", Vesselin Petkov's Relativity and the Nature of Spacetime (2005), gives a more satisfactory explanation of clock adjustment and synchronization in special relativity.
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