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Problems with the Theory of Elementary Waves
conceptualism, realism and experimental reality
by Tom Radcliffe

Date: 2000-08-21
Forum: Enlightenment
Copyright: Tom Radcliffe

Lewis Little's essay on the Theory of Elementary Waves


I discuss Lewis Little's essay "The Theory of Elementary Waves" and point out many problems with it. As well as a number of technical issues with the paper, if the theory was true then no large-scale optical interference phenomenon such as gravitational lensing would occur. As such phenomena do occur, I conclude that as well as being obscure and sometimes contradictory, the theory of elementary waves is false. Further consideration shows that other phenomena, such as the emission of neutrinos from nuclear reactions, would be radically different from the way they actually are if the theory of elementary waves were true.

Debunking Theories

One of the least useful tasks a scientist can perform is to debunk theories that are obviously flawed. There are several reasons for this, the first of which is that even obviously flawed theories are often interesting and stimulate new thinking and better approaches to old problems. There's an old joke about a paper being rejected for publication with the comment, "There is a great deal here that is new, interesting and correct; however, that which is new is neither interesting nor correct." The really hurtful aspect of this dismal is that what's new isn't interesting, rather than that it isn't correct. Few scientists are silly enough to expect to be correct when proposing new, especially radically new, ideas. But we'd very much like them to be interesting, to not be flawed in ways that are so obvious as to be apparent even at a cursory reading.

This is the second reason why debunking is a less than useful task: it is too easy for the "debunkee" to claim that the debunker has simply not understood the theory being debunked. Some proponents of cold fusion, for instance, have shown an enormous plasticity in their claims, altering them at will to ward off the counter-argument-of-the-moment. Thus, whatever is being argued against by the debunker is never quite what is being argued for by the debunkee. Theories that are stated in non-standard mathematical language are particularly prone to this kind of mutual incomprehension, which frequently leads to suspicions -- or even accusations -- of willful dishonesty on both sides

Having said all this, I'm now going to take on the task, briefly, of stating what I think is wrong with Lewis Little's essay, "The Theory of Elementary Waves." I will include some philosophical background that I hope will explain some of my obvious distaste for the theory and the way it is presented. I believe the theory is trivially incorrect, but I'd be lying if I claimed that it's very existence didn't annoy me, in part because it requires that I write this note explaining why I think it's wrong, rather than doing work of more positive value.

Requirements for Good Theories

I am not a Popperian, and believe that Popper's hypothetico-deductive approach to science has been a major factor in hiding the importance of concept-formation in the sciences. Never-the-less, falsifiability is the minimal requirement that any theory meet. This is a very weak requirement, that is very nearly equivalent to "saying something clear and distinct about the world." If we do this, then we have a falsifiable theory because we can look carefully and see if the world is actually described by our clear and distinct statement under all circumstances. Sometimes it isn't at all clear how we would go about falsifying a theory -- Newtonian mechanics appeared so unfalsifiable to Kant that he raised it to the status of a necessary truth -- but if we state clearly what the world is like there is always the chance that it will fail to conform.

Good theories don't violate Ockham's razor, and in particular they don't violate it by hypothesizing entities that cannot be detected by any means whatsoever. Until 1905 aether theories were taken seriously and attempts to detect the effects of the aether were undertaken by the likes of Michealson and Morely. After 1905 it was clear that all of these attempts were doomed to failure, because the Lorentz transformations ensured that none of the hoped-for effects would exist. Given the impossibility of ever detecting the aether by any means at all, the physics community gently dropped it. "To exist" implies many things, and one of the things it implies is "to have an effect." It is ironic that many of those who object to quantum theory on the basis that it contains unknowable quantities are at the same time proponents of aether theories, despite the unknowability of the aether.

Good theories don't contradict themselves, and they also deal fairly with reliable experimental results. Not all experimental results are equally reliable, but neither do most experimental results stand alone. In many cases, for a single experiment to be wrong would imply that many other experiments would have to be wrong as well. A deep awareness of this web of inter-related results is one of the things that distinguishes a physicist from a layperson. What looks like a minor result to an outsider may be tied to many other results by one who knows where the connections lie.

A good theory therefore has at least the following properties:

The "theory of elementary waves" (TEW) violates most of these; the most telling of which is the final one. That is, the TEW is falsifiable, and it is not at all hard to show that it is in fact false. But before getting to the central point, I want to talk a bit about other features of the theory that annoy me.

Bad Features of TEW

Apart from being false, why does TEW annoy me? Particularly when I find so many other "alternative" theories stimulating and fun? I'm not here as defender of quantum orthodoxy, because I think there's more going on in quantum theory than meets the eye, but I am not at all happy with TEW in particular. Here are some of the reasons why:

It Looks Very Familiar

In the 1940's Feynman and Wheeler worked on a theory that looked a lot like TEW. In conventional quantum and electro-magnetic theory, there are two solutions to the wave equations, one for "retarded" and one for "advanced" waves. One solution propagates forward, the other backward, in time. Ordinarily, the backward solution is discarded as a mathematical artifact, but Feynman and Wheeler decided to see what happened if they took both as real, and came up with a theory where radiation was only emitted if there was something there to detect it. This sounds a lot like TEW. Unfortunately, the theory couldn't be made relativistically invariant, and so did not describe the actual universe we live in, which is relativistically invariant.

Now, looking similar to a previously failed theory isn't such a bad thing, but the curious thing is that there is no mention of this in the TEW paper. >From the perspective of good scholarship, this is annoying.

It's Presented as a Realist Theory

I'm a conceptualist, and in the words of Carolyn Ray, one of the leading conceptualist philosophers working today, to a conceptualist: "to know that x is a P is to show that it fits the criteria for being a P."

Now, the "elementary waves" of TEW are supposed to obey a wave equation that is a solution to the field equations of the theory, but for some reason these equations are never presented, despite the claim that, "the product looks exactly like a wave propagating according to the usual field equations." To a conceptualist, this means that they are waves. But the claim is made that despite this they are not really waves, but "much like a simple flux of material, with the material carrying a wave `implanted' in it".

This immediately implies that the creator of TEW is engaged in a very different enterprise from me. I'm concerned with creating concepts that describe reality without contradiction. This is very different from the enterprise of declaring -- on the basis of I know not what -- what is real, which is what TEW purports to do. From my perspective, if it obeys a wave equation, it's a wave.

It's Contradictory

The full paragraph from which the above quotes are taken reads:

	  Because the waves are not waves in a medium, they do not 
	  propagate according to the usual dynamics of waves. In 
	  fact, as will be described more fully later, the description 
	  of their propagation is much simpler than that of the 
	  usual waves. They actually propagate much like a simple 
	  flux of material, with the material carrying a wave `implanted' 
	  in it, so to speak. However, the product looks exactly like 
	  a wave propagating according to the usual field equations. 
Now, either something is described by a wave equation, or it is not. If it is, then it is a wave, and it propagates according to the usual dynamics of waves. So this paragraph, which says the waves do not propogate according to the ususal dynamics of waves but do obey the usual wave equation, is just contradictory.

Another instance of contradiction occurs between the claim: "this [the success of the theory] has been achieved with no additional variables" (emphasis in original) and the later admission: "Waves must carry parameters characteristic of the frame of reference of the particle which created the `organization' carried by that wave." As these parameters are nowhere represented in current theory, one might be forgiven for calling them "additional variables", in contradiction to the initial claim.

Non-standard Language

There are few greater barriers to the acceptance -- or even the serious consideration -- of a new theory than presenting it in non-standard language. In the case at hand we have a theory whose author tells us, at least some of the time, that it could be stated in the ordinary language of field theory. There are a lot of people who are very good at analyzing novel field theories and seeing if they conform to reality. I have found even the areas of TEW where the description is not obviously contradictory difficult to understand, simply because it has not been stated in the ordinary language of field theory. My impulse upon first seeing the theory was to set out to build a simple computational simulation of the waves and to create computational "experiments" to see how the theory differed from ordinary quantum mechanics. But I rapidly realized that the nature of the description -- even the non-contradictory parts -- was not sufficient to do this. And in the absence of such a description, which must exist if the author's claims are true, it is extremely difficult to understand the detailed differences between TEW and ordinary QM.

Gravitational Lensing

This section describes an experiment that has already been done whose results demonstrate that TEW is false. The important claims made by TEW are as follows:

  1. Waves propagate from detector to source
  2. Detectors modulate or "organize" pre-existing waves to introduce coherence that produces observed interference effects
  3. Particles only propagate along a single path, determined by the waves
  4. Waves are just the waves of the standard theory with time reversed; in particular, they propagate with the same velocity as the waves of the standard theory
A weaker form of the last point is that the theory is local -- waves do not propagate with infinite velocity, nor indeed any velocity greater than that of light.

There is a simple form of the double-slit experiment that occurs on a very large scale -- that of gravitational lensing. In this phenomenon, light from a distant star passes close to a massive object whose gravity bends the light slightly. When the light reaches a detector many light-years distant on Earth, the light from the two paths interferes to produce a brightening due to the so-called "Einstein ring" of gravitationally refracted light around the star. This is a non-controversial phenomenon that has been used in various kinds of astronomical observation for many years, notably in the search for MACHO's (MAssive Compact Halo Object) that may constitute a significant fraction of the dark matter that makes up the bulk of the universe.

Lewis Little agrees with Feynman that the double slit experiment contains the essence of quantum theory. And gravitational lensing, despite some rather interesting mathematics dealing with the specific form of the lens, is nothing other than a simple interference experiment of the same kind. So if TEW can't account for it, then it can't account for the central mystery of quantum mechanics. And it's clear that TEW can't account for gravitational lensing, as follows.

A simple interference experiment contains three elements: the source, the detector, and the interference element. In the double slit experiment the interference element is the screen with the two slits in it. In gravitational lensing, it is the gravity of the object that the light passes nearby.

The situation as described by TEW is shown in the figure below. In fact, this description is being overly generous to TEW. It shows a photon, which according to TEW is a particle, being emitted on a perfectly deterministic trajectory from a distant star 300 million years ago. Immediately we see a difficulty, because photons aren't supposed to be emitted if there is nothing there to detect them, and the Earth at this point is very far away from where it will be when the photon reaches it. Let us press on regardless, although we'll revisit this problem in a bit.

Gravitational lensing

Half way between where the Earth will one day be and the star it came from, the photon passes by a massive object that distorts its path a little, although from a TEW perspective this is mysterious, because apparently particles don't carry physical properties like mass in TEW, only waves do:

	All of the dynamics of particles are determined by the
	waves.  The particle itself needn't carry any of the
	'classical' dynamical qualities generally attributed to
	particles:  mass, momentum, energy, etc.  All of these
	properties describe only the waves, with the particle
	then acting accordingly.
Still, we will press on, and note that as the photon gets very near to the Earth it will finally encounter the elementary waves that have been influenced by the telescope that will ultimately detect it. These waves cannot carry with them any effect of the massive object the photon passed by in it's travels 150 million years ago, because they won't reach that point for another 150 million years, by which time the massive object will have anyway long since drifted off to other regions.

At long last the photon gets detected, and a series of such detections will show a ring of brightness that in ordinary quantum theory gets explained by each wave-like photon traveling different paths to the telescope, and the wave components from each of those paths interfering with each other at the surface of the telescope's detector. In TEW, how this occurs is profoundly mysterious.

For waves that propagate from the detector to the source to cause interference, they must have the opportunity to interact with interference element, which in this case is the massive object the photons pass near on their way to Earth. If the waves control the dynamics, and they never get near it, the interference element could not possibly have any effect. But this is obviously not the case for gravitational lensing -- the interference element is typically millions of light years away, so waves that have been "organized" by a telescope on Earth can't possibly be influence by it for millions of years. Yet we observe interference -- in the form of gravitational lensing -- from light that interacted with the interference element while passing by it millions of years ago, when the telescope on Earth didn't even exist! Therefore, the cause of interference cannot be due to any influence passing from the detector to the source. Ergo, TEW is false.

Do The Stars Shine?

If photons are only emitted when there is a detector ready to see them, how is it that we see that stars at all? If I look out the window at the Moon, my eye serves as a detector for light that left the Sun eight minutes ago and then bounced off the lunar surface. How did it know my eye would be there to receive it? The claim might be made that if my eye didn't receive it, something was bound to, and that allows the light to be emitted. But this won't do, and I don't even have to invent a thought experiment to show why.

As well as visible light, stars emit a weakly interacting type of particle called neutrinos. Neutrinos have zero charge and (nearly) zero mass, and they interact with matter with a strength that is more than ten to the fortieth times smaller than light does. It is safe to say that the average neutrino leaving the average star won't ever be detected by or interact with anything.

This immediately raises a deep problem for TEW, for if the particles are never detected, where do the waves come from that they are emitted into? TEW tells us:

	If no detector is present at a point along the path of
	the particles, then no reverse waves are emitted at that
	point.  Rather, the waves originate from another detector
	or object further 'downstream' -- downstream, that is,
	from the point of view of the particles.
But in the case of neutrinos, there won't be any detector downstream most of the time, because the particle will never interact with anything again. So on this basis, we would expect stars, nuclear reactors and the like to emit far fewer neutrinos than they actually do. But we know from the energy balance of nuclear processes that there are neutrinos being emitted, and in exactly the numbers we expect. We can even, with dint of great ingenuity, detect some of them, and again with a single exception (there are fewer than expected coming from the sun, which is know as the Solar Neutrino Problem and which has solutions far simpler than TEW) we see the number we expect. How can this be? Where are the elementary waves coming from when the particles won't ever be detected?

There is even a case where neutrinos have been detected from a distant source -- supernova 1987A. This stellar explosion occurred in the Large Magellanic Cloud, a nearby galaxy at about 12 million light years distance. So the neutrinos were emitted about the time our ancestors were starting to think that coming down from the trees might be an interesting option. But they were detected -- 11 of them in all -- by the Kamiokande II neutrino detector in Japan. And if they hadn't been, we can be utterly certain that they would have continued to travel on through space, forever. The claim that they never would have been emitted if Kamiokande II had not existed seems fairly farfetched, for a theory that purports to be causal. One wonders how the neutrinos knew that the detector would be there to receive them, 12 million years before it was constructed.


The world is full of interesting theories. Some years ago a friend gave a talk on a very strange theory of nuclear structure, that pointed out that you could account for the "magic numbers" of the nuclear shell model by assuming that nuclei were constructed on a face-centered cubic lattice. It really is an odd fact, but as an audience member pointed out, the theory probably fails quite badly when you apply it to properties that depend intimately on nuclear shape, like dipole moments! This is a valid observation, and it means that there are common contexts where such a theory can't be used to describe reality; contexts so common that it really isn't a good candidate for a theory of nuclear structure. But it's still interesting and curious that there should be this odd numerological association between crystal structure and the shell model, which aren't otherwise obviously related.

The TEW doesn't even quite fall into this twilight-zone of "interesting but wrong." Indeed, it comes close to that lowest of categories, "Not even wrong." It reverses the direction of causality from source to detector in a way that is just too easy to detect, if it actually occurred. The case of gravitational lensing is but one among many similar experiments, and if need be one could create a purpose-built experiment to show that there is no casual influence that propagates from the detector to the source to create interference. But given we have the case of gravitational lensing and similar astronomical phenomena at hand, performing another experiment of this kind doesn't seem worth while.