Regular readers will be aware that I’ve offered an explanation of the apparent superluminal neutrinos detected in the CERN-OPERA experiment. Things have moved on since my last post on the subject, and I submitted a paper with a more thorough explanation to ArXiv a week ago – more about that another time.

My argument boils down essentially to the point that I believe that light doesn’t travel at the same speed in every direction (relative to an observer on our moving planet, and according to our reckoning of time and distance) and the physics establishment does, for reasons that defy simple logic.

A couple of days ago I thought I’d see if I could find some books that shed some light (groan!) on the matter. What I was interested in was whether physicists are confused. I think it’s fair to say that they are.

I ended up tracking all the way back to Einstein’s seminal paper, *On the Electrodynamics of Moving Bodies* (1905). I found myself standing in Waterstones reading a translation in Hawking’s *On the Shoulders of Giants*, which basically consists of some reprints and a few pages of comment by the current Lucasian Professor. £22 (OK, £15 on Amazon) for a paperback. Nice work.

Anyway, it’s possible to find *On the Electrodynamics* kicking around on the internet (pdf), though not easily on the first page of Google’s results, which I guess tells you something straight away about the readership of the “most important scientific paper of the 20th century”.

Any reader of *On the Electrodynamics* can’t help being struck by the paper’s obvious shortcomings. Yes, shortcomings. Just because a paper includes brilliant, revolutionary ideas does not mean it is perfect in all respects. And *On the Electrodynamics* has two serious flaws which have perhaps contributed to today’s confusion:

**1. References or, rather, the lack of them – Einstein’s assumption of isotropy**

Einstein did not include any references in his paper. As a result, we simply do not know how carefully he’d studied certain works of the era. In particular, it makes it difficult to evaluate his opening arguments. My impression is that Einstein just wanted to focus on the crux of his argument.

Einstein first sets out his postulates, or assumptions:

“…the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities,

the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the ‘Principle of Relativity’) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, thatlight is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. [my stress]”

Maybe these postulates are only nearly true. The crux of my argument is that if the speed of light is *independent* of its source, then we *always* (except in one very special case) need to apply the same equations Einstein used (Lorentz transformations) to determine the speed of light relative to ourselves, the observer. We can’t just assume we’re the stationary observer! It’s a simple point.

Let’s read on a little more. Einstein is very particular about the need to reckon time in terms of synchronous clocks:

“If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an ‘A time’ and a ‘B time’. We have not defined a common ‘time’ for A and B, for the latter cannot be defined at all unless we establish by definition that the ‘time’ required by light to travel from A to B equals the ‘time’ it requires to travel from B to A. Let a ray of light start at the ‘A time’ tA from A towards B, let it at the ‘B time’ tB be reflected at B in the direction of A, and arrive again at A at the ‘A time’ t′A. In accordance with definition the two clocks synchronize if:

tB − tA = t′A − tB

We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:—

1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.

2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.

Thus with the help of certain imaginary physical experiments we have settled what is to be understood by synchronous stationary clocks located at different places, and have evidently obtained a definition of ‘simultaneous’, or ‘synchronous’, and of ‘time’. The ‘time’ of an event is that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.

In agreement with experience we further assume the quantity2AB/(t′A − tA) = c

to be a universal constant—the velocity of light in empty space.”

He’s going to go on, of course, to assume that the stationary clocks are in the “stationary” [sic] system, and show that the clocks will not appear synchronous to a moving observer.

But how do we know that light would travel at the same speed from A to B as from B to A? This need not affect the round-trip time.

One book I found in Ealing Central Library is devoted specifically to this issue of synchronising clocks. In *Einstein’s Clocks, Poincaré’s Maps* by Peter Galison, we find (p.217) that the French mathematician, well, polymath, really, Henri Poincaré, understood the problem of “true” and “local” time in 1904:

“‘[Lorentz’s] most ingenious idea was that of local time. Let us imagine two observers who want to set their watches by optical signals; they exchange their signals, but as they know that the transformation is not instantaneous, they take care to cross them. When the station B receives the signal of station A, its clock must not mark the same time as station A at the moment of the emission of the signal, but rather that time augmented by a constant representing the duration of the signal.’ [wrote Poincaré – so far so good]

At first, Poincaré considered the two clock-minders at A and B to be at rest – their observing stations were fixed with respect to the ether. But then, as he had since 1900, Poincaré proceeded to ask what happened when the observers are in a frame of reference moving through the ether. In that case ‘the duration of the transmission will not be the same in the two directions, because station A, for example, moves towards any optical perturbation sent by B, while the station B retreats from a perturbation by A. Their watches set in this manner will not mark therefore true time, they will mark what one can call

local time, in such a way that one of them will be offset with respect to the other.This is of little importance, because we don’t have any way to perceive it.‘ [my stress] True and local time differ. Butnothing, Poincaré insisted, would allow A to realize that his clock will be set back relative to B’s, because B’s will be set back by precisely the same amount.’All the phenomena that will be produced at A for example, will be set back in time, but they will all be set back by the same amount, and the observer will not be able to perceive it because his watch will be set back’[my stress]; thus, as theprinciple of relativitywould have it,there is no means of knowing if he is at rest or in absolute movement. [my stress]”

Galison goes on (p.257ff) to speculate as to how familiar Einstein was in 1905 with Poincaré’s discussion of the idea of obtaining local time by the synchronisation of clocks. Regardless, when Einstein swept away the ideas of “local time” and “true time”, he took no account of the little difficulty highlighted by Poincaré. We can only speculate as to what Einstein thought and what he didn’t, but it would clearly have been more difficult to move away from the idea of the ether to that of relativity had it also been necessary to assume a “preferred” or isotropic reference frame relative to which the Earth is moving. That doesn’t mean it doesn’t exist, though. And, for my money, relativity includes a logical inconsistency. You simply can’t assume the light moves independent of its source and then perform transformations to show that the view of a moving observer of the reference frame in which the light is emitted perceives the light *not* to be moving at equal velocities in all directions relative to objects in the emitting frame, whilst those in the emitting frame magically *do* see equal velocities.

**2. Unclear use of symbols**

There’s one way to “rescue” Special Relativity. Let’s imagine you’re a confused young physics student. You might imagine that the Lorentz transformations retain equal light speed in all directions despite diagrams to the contrary, that is, you might pay particular attention to the qualification “length contraction not depicted” in representations of Einstein’s train thought-experiment.

You might define a thought-experiment (flashes when light from the centre reaches the ends of a moving train) and write something like:

“In fact [from the point of view of an observer on the platform] it [the moving train] is shorter in the same proportion as the second flash is later than the rear one.”

as Adam Hart-Davis does on p.231 of *The Book of Time*.

Hart-Davis appears to assume time-dilation and the relativity of simultaneity are the same thing. His calculations are then totally confusing (even if we ignore the fact that he presents calculations based on the length of the train before he’s told us how long it actually is and later says km/h when he means km/s!). The formula for calculating the time delay between flashes at the rear and front of the train as perceived by the observer on the platform is:

t = (1/√(1 – v^2/c^2))(τ – vx/c^2)

where:

- τ is the time difference as seen by the observer on the train
- t is the time difference as seen by the observer on the platform
- √ is supposed to be a square root sign – I’ve used ^2 for squared (can’t see how to get a superscipt on here)
- v is the velocity of the train (according to the observer on the train)
- c is the speed of light
- x is the length of the train (according to the observer on the train)

The term 1/√(1 – v^2/c^2) is known as γ (gamma) and can be ignored when v is small compared to c, as Hart-Davis does when calculating for a train moving at 22m/s. The curious thing is, he also ignores γ when calculating the delay when the train is running at 200,000,000m/s and gets a 44ns delay. He doesn’t explain this.

Hart-Davis then uses γ correctly to show the train looks only ~15m long (he implies this is exact – it isn’t) rather than 20m.

Presumably what Hart-Davis has done is assume that the length contraction of the train (a factor of ~0.75) cancels out with the time dilation factor (also ~0.75), the proportion by which time on the train runs slower than on the train. Is this correct? I guess so, though I’m not claiming to be 100% sure!

Nevertheless, the length contraction doesn’t cancel out the relativity of simultaneity – the signal still appears to take longer to travel to the front of the train from the perspective of the observer on the platform than from that of the observer on the train. The light simply has further to travel from the p.o.v. of the observer on the platform, as the front of the train is receding relative to the observer on the platform, but stationary relative to the observer on the train. The statement: “In fact [from the point of view of an observer on the platform] it [the moving train] is shorter in the same proportion as the second flash is later than the rear one”, is either totally confusing or simply incorrect.

You’d think they’d make a lot of effort to ensure accuracy in a book intended to inform, so maybe they’re confused.

And maybe it’s Albert’s fault. If you take a look at *On the Electrodynamics* you might notice that Einstein uses “t” and “τ” (Greek letter small tau) to derive the *difference* (the formula above) between times observed by stationary and moving observers. He then, breathlessly, one might imagine, rushes on to derive the time dilation factor (γ) in the *rates* of the clocks of the moving and stationary observers, using the same “t” and “τ”. What he really meant to relate in the second case were, of course, “δt” and “δτ”.

Naughty Albert! It’s like Peter Crouch pulling the hair of the Trinidad defender to score in 2006. He scored a goal, so we’ll ignore that little detail.

Or maybe Einstein was being deliberately obscure just to see if people really understood!