In Search of Continuity: Thoughts of an Epistemic Empiricist by Ian Durham

Since Ian came to my defence on an earlier occasion, I'd like to say something here.

Albert: you claim that "Einstein's Relativity is a continuous theory and actually the most successful of all times. General Relativity converges to classical Newton's Laws at the weak field limit. I do not see this theory and its continuity as a myth".

Neither Ian (nor me) is saying that the theory is not continuous, but only that our knowledge of the world is discontinuous (and must always be so). This is also true of general relativity, and Einstein was aware of this. Indeed, it was just this lesson that led him away from the non-generally covariant field equations he had initially fixed on. The observable content, according to Einstein, was given by point-coincidences: only these respect the diffeomorphism invariance of the theory - the point was originally Erich Kretschmann's, but Einstein refashioned it.

The consensus still remains that something like these relational point-coincidences exhaust what is observable in GR (Bergmann, Komar, Jim Anderson, Bryce DeWitt, and a host of others worked very hard on establishing this conclusion). So even if this essay competition is about the ontology of spacetime (which it isn't), we quickly stumble into epistemological terrain.

Best,

Dean

Dear Ian Durham,

Re: "Actually, the most successful theory of all time, as measured by how closely it matches experiment, is QED."

Over 60 years of QED calculations of the anomalous magnetic moment [up to 12,000 Feynman diagrams involved in the latest such calculation] have produced the eight [or so] place accuracy of QED. Then, after this calculation is made, I believe the fine structure constant [upon which it is based] is adjusted, based on the results of the latest calculation of the anomaly. In my mind, this would lead, over 6 decades to a very accurate 'correlation' between these two.

One issue that has bothered me is that, as of 1998, the vacuum energy, which is central to QED, was found to be overestimated by QED by 120 orders of magnitude. It would seem that this would call for 50 years of QED calculations to be redone, but I don't believe that this has happened. Am I missing some basic point here?

Also, just a few years ago, the proton was assumed to contain a significant contribution from the virtual 'sea of strange quarks', but this has not turned out to be the case. I don't know whether to lay the blame for this at QED's door or QCD's door, but it would seem to be related to vacuum energy.

What bother's me is that 'virtual particles' seem to be the best imaginable 'fudge factor' because the particles aren't measured [to my knowledge] but simply provide the means to 'fit' calculations to reality.

And finally, the recent recent QED calculations of the proton radius based on the experimental data from 'muonic hydrogen' is off by 4 percent. Since this is the simplest possible system one would expect better of QED. Does this mean that QED now has one place accuracy? [Which would put it in the same realm as QCD.]

I have generally been unable to get answers to these [and related] questions, and I wonder if you could help me understand what's going on.

Edwin Eugene Klingman

Ian,

Excellent essay. Parts of it resonate considerably with the views in my essay. One of the most interesting points is where you write,

"But what if the only way to get information about ontic states is through epistemic states? Further, what if the epistemic states themselves are discrete? How could we even determine if the underlying ontic states were continuous or not if the 'lens' through which we view them is discrete?"

I would go even further to ask how we could even determine if the underlying ontic states exist at all. In what sense is it meaningful to talk of such ontic 'things in themselves' if we never have any direct access to them, even in principle? We are of course free to create speculative models to give coherence to our empirical observations (and it is the job of science to do so), but what is gained by the additional step of attributing a non-empirical ontic reality to a hypothetical 'somewhat' that such models supposedly describe?

Thanks again for the fine essay.

Regards,

Tom

@Ian,

"Regardless, the point of my essay is that the epistemic states through which we access the ontology of spacetime (reality, whatever) necessarily limit the amount of knowledge we can obtain about the ontology of reality."

Our epistemic states change constantly as technology progresses. Even until recently, we didn't know anything about fundamental particles, DNA, even the composition of close by planets. Thus, I view your argument as a distracting issue, a red herring.

You have avoided dealing with the main issue, which is failure to unify discrete QM with analog GR.

I get the feeling there is confusion in your argument between what we think we can know about reality and what it may turn out we can know about reality.

In other words, you have not proved that what we can know is all we will ever know.

@Dean

"Neither Ian (nor me) is saying that the theory is not continuous, but only that our knowledge of the world is discontinuous (and must always be so)."

In my opinion "discontinuous knowledge" does not imply that we cannot have knowledge about a continuous world. You have not proved that. Furthermore, I find universally quantified statements like "and must always be so" sort of dogmatic. Do you know what the future holds?

I also disagree on a most fundamental level. There are many instruments physicists use that are purely analog in nature. Analog computers have been used for years to simulated dynamical systems. The knowledge those instruments provide is analog in this sense. Specific measurements may refer to discrete instants in time but those devices offer analog knowledge. Knowledge is not only the set of all discrete measurements we can get but also the means by which those measurements are obtained. Unless you can prove to me that the way we obtain knowledge is not knowledge in itself.

Thus, I am afraid your argument is not even sound.

Dear Ian Durham,

The arguments that Edwin Eugene Klingman is giving for rebating your claim that QED is the most precisely tested theory are part of a more general argument given by me in my post of the day 16. I copy and paste:

"The experimental support of quantum electrodynamics is excellent but it must be put in a right context. In the reference 6 in my Essay, I wrote: "Four main remarks may be done about the relativistic experiments and observations: (i) Precision tests of relativistic quantum electrodynamics are not normally carried out by directly comparing observations and experimental results to its theoretical predictions; (ii) the same tests are satisfied by formulations of relativistic quantum electrodynamics that are mutually incompatible between them; (iii) the experiments and observations only consider a very limited subset of phenomena; and (iv) both relativistic quantum electrodynamics and the relativistic quantum field theory are involved, at least indirectly, in some puzzling observations and glaring discrepancies". And then analyzed each remark by separate in the following two pages."

Edwin Eugene Klingman recent remarks belong to my early points (i) and (iv). You did not reply to my remarks about QED, but I see in your recent reply to Edwin Eugene Klingman that you confess to not having a proper answer at the moment, which means that you have not answer to my points.

Dear Ian Durham,

The relation (Dx/Dt) = c = (dx/dt) has not only mathematical sense but physical meaning, because a measurement of the left hand side ratio (Dx/Dt) implies the measurement of the right hand side ratio (Dx/Dt), both ratios being equal to the speed of light. The issue of relativistic localization is studied with great detail in the reference 6 cited above in a previous post. The physical explanation of why dx/dt can be measured can be obtained from the study done of dx and of dt. In your Essay you affirm that we cannot measure the instantaneous speed, because --as you repeat again above-- "Delta t must have a non-zero lower bound". However, when we repeat the analysis for x, we find that this lower bound for Dt does not prevent us from measuring the value of c, by the technical reasons stated in previous posts.

Regarding the relation between quantum mechanics and quantum field theory, you repeat some well-known trivial stuff, such as that time is absolute in quantum mechanics or that in relativistic quantum field theory we study functions of spacetime (x,t). However, nothing of these trivial stuff addresses the technical points stated in my previous posts, neither in the references cited in my own Essay. For instance, in my previous post, I remarked a very specific property of x where QM and QFT are clearly in contradiction, as is well-known, and even cited a standard textbook in QFT, where this contradiction is emphasized.

Dirac emphasized his disagreement because QED (QFT) was not compatible with QM. Dirac thoughts were given in my Essay and I partially quoted a relevant part in a previous post from mine. They key point here is that QFT does not reduce to QM, as Dirac stated and how has been rigorously proven in the references cited before. About other aspects of your post, the rest of references cited in my Essay give very detailed technical responses.

Effectively, as I have just emphasized "there exist limits where that discreteness is indistinguishable from a continuum", but this does not imply your claim that "classical physics is a myth". In fact, I am just saying the contrary than you! Classical physics is not myth, but a limiting case of quantum physics.

Your analysis of the car speedometer resembles the Schrödinger-cat paradox. This old paradox was based in a naive (without any mathematical rigor or experimental support) interpretation of the quantum theory, where a cat would be in some strange quantum superposition unless some physicist would look to it. But as our modern understanding of the quantum theory reflects, the cat will be classical even if no physicist is present at the lab. The same can be said about the car and the engineer. The car will be not classical or not according to engineer's boss choices about the number of decimal places in speedometer. With independence of the precision of the car's speedometer, this will be a classical car, not one in some weird quantum superposition between New York and Paris, for instance. The same argument hold for your appeal to bathroom scales; with independence of its precision, you will be not superposed between bathroom and kitchen.

You repeat your comments about QED being the most accurate physical theory ever developed, but again you omit the technical details. I already put your statement in a right context in my first post of day 16!

You add now that QED is "ultimately a discrete theory". But this is another exaggeration, because QED is a theory of quantum fields and the quantum fields are continuum objects (with continuum spectral decomposition and continuum basis). Moreover, QED also treats volume and others properties as a continuum.

You are right on the existence of different views regarding history. However, not all the views are in the same footing (for instance, the view that Einstein played no role in the development of relativity is maintained by some very few historians, but their view is strongly rejected by the rest of historians). Regarding the history of the atomic theory, it is broadly accepted by historians of science (and I do not know anyone who disagree!) that chemists of the 18th and 19th were the first to develop a scientific theory where the Universe was considered to be composed of tiny particles called atoms. I have given arguments, the names of relevant scientists as Dalton, and how using this discrete model, they were able to explain empirical laws then without any explanation.

Moreover, as is well-known to historians of science, electricity was considered to be made of discrete negative particles before the 20th century:

"Now the most startling result of Faraday's Law is perhaps this. If we accept the hypothesis that the elementary substances are composed of atoms, we cannot avoid concluding that electricity also, positive as well as negative, is divided into definite elementary portions which behave like atoms of electricity."

Those discrete units of electricity were named "electrons" by physicist Stoney in the 19th, who added about his paper "On the Physical Units of Nature" the following: "I called attention to this minimum quantity of electricity as one of three physical units, the absolute amounts of which are furnished to us by Nature, and which may be made the basis of a complete body of systematic units in which there shall be nothing arbitrary".

As a conclusion, the affirmation done in your Essay on that everyone before the 20th century believed in a continuum Universe is one without historical basis.

A mistake in my post, the part where it says:

"The relation (Dx/Dt) = c = (dx/dt) has not only mathematical sense but physical meaning, because a measurement of the left hand side ratio (Dx/Dt) implies the measurement of the right hand side ratio (Dx/Dt), both ratios being equal to the speed of light."

must be corrected to:

The relation (Dx/Dt) = c = (dx/dt) has not only mathematical sense but physical meaning, because a measurement of the left hand side ratio (Dx/Dt) implies the measurement of the right hand side ratio (dx/dt), both ratios being equal to the speed of light.

Dear Dr. Durham,

Thank you for a truly enjoyable essay. And my sincerest condolences for your father-in-law.

I do have a question. In my essay is a generalisation of the energy of a photon ('the Light'), which is that 'indefinable fusion' of the continuous and discrete, mentioned by de Broglie. Further, 'the Light' is the only 'quantum' theory that necessarily follows on from classical physics, and unequivocally demonstrates "Classical physics, with its inherent continuity, is nothing more than a convenient myth."

Therefore, is 'the Light' ontic, epistemic, or both?

All the best,

Robert

Ian,

The thing I most appreciate about your essay -- and it's a great one -- is the recognition of the difference between mathematical continuity and the continuity of physical experience as enshrined in classical physics. Yes, it brings into question the very meaning of objective knowledge and its relation to ontology.

I expect you'll continue to be the very model of a modern mathematician. Gilbert and Sullivan get no apologies from me. :-) I mean, putting aside what we're "not supposed" to look at closely in the way we see the world (Monet is a better example than Van Gogh, in my opinion), mathematics always deals with what lies beneath, as basic structure -- point and line and number. Yet the evolution of graphic art from flat images to perspectives incorporating a point at infinity anticipates the progress of mathematics incorporating that same image, in the abstract, on C*. If we need reasons to think that the ontology of mathematics connects with that of physics, we can always find them.

I'm sorry for the loss of your father in law. Even though the event is inevitable, it seems that nothing prepares any of us for it.

Good luck to you.

Tom

Hi Ian, his declaration of universality or put simply "every object attracts every other object equally in all directions" is a BIG assumption which is then set in stone within his gravity equation. No wonder it can't be reconciled with particle based QM! Why did no-one at the time of Newton consider the Archimedes screw as a mechanical method for explaining the force of gravity, his spooky action at a distance?? The history of science would have been very different if someone had imo! Best wishes, Alan

Ian,

Having read again more carefully, please indulge me in correcting a slight inaccuracy that I think has been responsible for many misunderstandings of general relativity. On p. 7, you characterize spacetime in general relativity as being modeled on a four dimensional Lorentzian manifold. Not quite true. It is a four dimensional pseudo-Riemannian manifold of Lorentzian metric properties.

This is important, especially for the relativity-doubters (with which this forum abounds) because it explains classical gravity symmetry and time reversal symmetry. The manifold is pseudo-Riemannian because every Riemannian manifold is, in fact, orientable. The non-orientability of Lorentz invariance ("all physics is local") informs us of the relationship of "empty space" to matter -- it was Einstein's (and Mach's) desire to reduce physical epistemology to the properties of matter alone. Lorentz invariance with spacetime produced a model finite in time and unbounded in space.

Tom

My apologies. I did not know that "Lorentzian manifold" is a special case of the pseudo-Riemannian manifold until I looked it up. (I was unfamiliar with the term.) Other points re relativity still hold, nevertheless.

Tom

Hi Ian,

once again, you wrote an excellent Essay. In particular, I enjoyed with the "EVERY GOOD MYTH NEEDS AN ANCIENT GREEK".

Have my condolences for the death of Lawrence Brod.

Best regards,

Ch.