The Facts Behind Fizeau's Experiment

For those interested in the maths

[Posts are sequential, to be read/heard in date order - opposite to the order they’re generally displayed in. Paid-for posts have technical content.]

This post provides the technical background to the post: “Relativity: unwrapping a mystery”. It shows very clearly how a totally conventional scientific process gives results that mimic a formula proposed by Einstein - without any causal connection with the relativistic effect attributed to it by him. This, at a stroke, invalidates one of the two key reasons cited by Einstein for formulation of his Theory of Relativity.

Just to recap briefly:
In 1851 Hippolyte Fizeau and his collegues were puzzled by a strange observation: when light was passed through water travelling in the same direction, the speed of that light was less than the speed of the water added to the speed of light in still water. Shortly after 1900 Albert Einstein, applying his Theory of Relativity, devised a formula giving the speed of a man walking along inside a moving train (among other such situations) as slightly less than the man’s walking speed added to the speed of the train. Einstein saw Fizeau’s practical results as strong support for his his theoretical formula; this became one of the two mainstays confirming for him the reality of his Theory of Relativity.

We now know that the speed of light in water is the result of light being slowed by its interaction with the atoms of the water itself. [In passing, it’s strange that Einstein didn’t figure this for himself, given that he’s the one who identified Brownian Motion, the random motion of dust motes in water, as being the result of collisions with the invisible atoms of hydrogen and oxygen in the water.]

A very simple first analysis, just assuming that the degree of impedance of light by atoms is proportional to the frequency with which light encounters those atoms, leads directly to a speed for light in moving water that is indeed a little less than the sum of the two speeds - the issue that puzzled Fizeau and his colleagues.

Figure A1 shows light entering a translucent medium.  If that medium is static then the light will encounter the atoms in it, and their electrons, with a certain (average) frequency.  If it’s moving in the same direction as the light then that frequency of encounters will decrease, since the atoms are effectively ‘running away’ from the light.  If on the other hand it’s moving in the opposite direction (i.e. towards the light), then that frequency of encounters will of course increase.

It’s this frequency of encounters, and how it changes in a moving medium, that in turn changes the degree to which the passage of light through the medium is delayed – and so determines the speed of light through the medium. This tells us the speed-of-light-in-water scenario is very different from how Einstein envisaged it.

This confirms that the simple interaction of water with atoms gives a speed of light through moving water that’s between speed of light through static water and that plus the speed of the water. Just from this observation it’s immediately apparent that the ‘light moving through water’ scenario is radically different from the ‘man through train’ scenario.  In the latter the man is being carried along by the train and is adding his walking speed to the speed of the train; in the former the light is being impeded by the water rather than carried by it, but impeded to a lesser extent the faster the water moves.

The idea that this scenario could be regarded as being due to relativistic addition of velocities is, with our present knowledge of the factors involved, totally fanciful.  Similarity of Einstein’s formula to the true relationship between these speeds is a matter of perception rather than causation, as we’ll see. But the formula we’ve just derived doesn’t accurately fit the experimental results, nor does it fully match either Einstein’s or Fizeau’s formulae. We need to look a little closer into exactly what’s going on.

We now know that the electromagnetic fields of light travelling through water (or any other translucent medium) interact with the electrons of the atoms in that medium, inducing a state of motion in those electrically-charged particles.  That motion of charged particles in turn creates its own electromagnetic wave which interacts with the light wave to form a new wave that travels more slowly than the usual speed of light.  This effect of course ceases when the light exits from that medium, so the light returns to its own unimpeded speed and direction. [See Fermilab video - Fermilab is the US National Accelerator Laboratory, comparable to the Large Hadron Collider].

The delay factor and the residual delayed energy flow through the medium are effectively components which together equate to the total energy flow giving rise to them both – the original electromagnetic waveform that is the light travelling through the translucent medium.  Those two components can be viewed mathematically as acting orthogonally – at right angles to each other – and so can be combined as two sides of a right-angled triangle to give the resultant total energy flow of the light passing through the medium.  [N.B. This is similar to the Relativistic energy-momentum relation, in which the rest energy of an object and the effective energy inherent in its linear momentum combine orthogonally to give the overall energy of the moving object.]

Simple analysis of this relationship leads to a very interesting result.

Those components combine mathematically as shown in the diagrams below. 
Let’s look first at the situation where light passes through static water.
[Note that these diagrams represents magnitudes of those components, not directions.]

Interestingly, the result for this analysis sits squarely between the formulae proposed by Fizeau and Einstein respectively:

To give some perspective, this gives a result that matches the results from both Einstein’s and Fizeau’s formulae to 10-digit accuracy for the extreme case of light passing through water flowing at 10,000 miles an hour.  In other words this proposed explanation matches all available experimental results to an accuracy well beyond the practical limits for any such experiment.

Of course, if water and light are moving in opposite directions then the light-flow will encounter electrons in the translucent medium correspondingly more frequently and light will be slowed to a correspondingly greater degree; this result is given in all three of these formulae (Einstein’s, Fizeau’s, this analysis) by replacing v with –v.

The conclusion from this analysis is that the results of Fizeau’s investigation (and all subsequent studies of the speed of light through moving water), which Einstein saw as such compelling evidence for his theory of Relativity, are fully explained without any reference to that theory.  In fact this scenario has nothing whatsoever to do with Relativity, apart from that close similarity of formulae.  And so one of Einstein’s two declared mainstays for his theory disappears into the scientific history books, as have numerous other misinterpretations of scientific phenomena.

Or should.  It’s interesting, though, to note that in all the references one can find in scientific texts to Fizeau’s experiment and its key role in the foundation of Relativity, almost nowhere do we find any reference to the fact that the speed of light through water is now well known to be subject to totally different effects from those envisaged by Einstein.  None of those scientific authors see fit to record that a result which Einstein regarded as of seminal importance to his theory was actually utterly irrelevant to that theory in practice, in terms of its claimed effects.

It seems that, from the standard scientific perspective, Relativity is a done deal.  Never mind where it came from, how it came about, how it happens; experimental observations consistently fit the theory, and that’s what important.

But that’s far from being the only thing that’s important.  A theory that puts constraints on significant aspects of possible human endeavour and future research, that proposes scenarios (none of which have been demonstrated in practice) which run strongly counter to what might be seen as ‘just plain common sense’, that’s founded largely on a premise which has since been shown to be erroneous – such a theory surely begs the question: “But how can that be so?”.

The purpose of this series of articles is to demonstrate clearly, concisely and above all scientifically, how that can be so – and how it may be so in a way that differs significantly from the widely held view, a way that opens the door to a whole range of possibilities not apparent from that widely held viewpoint.  Yes, measured outcomes are exactly as predicted by the theory – but for rather different reasons from those assumed by most advocates of that theory.  The back-story behind effects of Relativity is one that opens doors, scientifically speaking, rather than closing them.

So be sure to tune in for the next article, in which we’ll have a close look at those clocks which behave in such a puzzling manner.  We’ll follow that by a look at how a beam of light that passes a static observer at three hundred thousand kilometres a second can also be passing a spacecraft clocking up two hundred thousand kilometres a second at exactly the same relative speed – without having to invoke any special rule for either the speed of light or the nature of the cosmos.

We’ll get to E=mc squared, totally from this new perspective, a little further down the line. In the meantime, be sure to check out the wealth of resources, many of them free, here.