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

@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

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.

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Dear Ian Durham,

Dean Rickles replied to Albert, and mixing Albert's viewpoints (I do not agree with all that he said) with the mine (e.g. you name me in a reply to him) only can give up to further confusion. I will repeat my point.

I have said that there exist limits where discreteness is indistinguishable from a continuum, which implies that your claim that "classical physics is a myth" is a complete exaggeration. Classical physics is not myth, but a well-defined subset of physics. Classical physics is a scientific discipline not a myth!

I offered some technical details about my point that you have avoided. Following your example of a car speedometer, I emphasized why a car is a classical object even if you decide to "look closely enough" (in your own words). I also drew the interesting analogy between your claims and the confusion of the earlier physicists regarding the state of a cat (Schrödinger-cat paradox). The cat will be in a classical state, with independence of the observations of the physicists, if any observing the cat at all! Analogously, the car will not be in a superposition between Paris and New York even if you ask engineers for a better car's speedometer.

You say "I know full well that physicists believed in discrete electrons as early as the 19th century." This is again misleading by several reasons. Physicists and chemists developed a scientific theory of matter which contained a discrete unit of electricity, instead of merely believing in discreteness as some philosophers did; these scientists named "electrons" to those discrete units (your term "discrete electrons" is misleading because electrons are, by definition, discrete); they gave the value for this elementary unit of charge; and they emphasized its fundamental role for our understanding of the Universe. Stoney wrote in his paper "On the Physical Units of Nature":

"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 consequence, the claims made in your Essay have not historical basis. Personally, I find really curious that the discrete theories developed by physicists and chemists in the 18th and 19th suggest to you that they would believe that "reality itself" is continuous, whereas you affirmed above to us your belief on that QED is "ultimately a discrete theory", without being aware of that QED is a theory of fields and that the fields are continuum systems (the fields have a continuum spectra).

Regarding the relation between QFT and QM, you opine that I am "taking Dirac's comments entirely out of context". The problem here is not that you ignore what Dirac really said, but that you also ignore the additional technical details and the rigorous references given.

For instance, I remarked one specific contradiction between QFT and QM at least in three occasions, and your response has consisted on completely avoiding to comment about this contradiction the same number of times.

In previous posts I discussed how, contrary to misguided claims done in your Essay, the constant speed of light c can be measured. The fact that the phase speed v = c/n is less than c for materials as water, does not mean that we cannot measure c. You then move away from materials and introduce Magueijo cosmological model where the speed of light c is substituted by a variable speed c*. However, his work is highly speculative (I was discussing our current models based in the universal constant c and how we measure that c in the lab). Moreover, he introduces a larger c* for the early Universe, but maintains a value c for the present Universe. Finally, it must be emphasized that, even if his model was finally verified, it does not change my remark (Dx/Dt = c = dx/dt) about the constant c.

Finally, you add "Oh, and regarding my lack of 'technical details' surrounding the claims of the accuracy of QED, Google 'precision tests of QED' and read what comes up." Again you ignore what is being said. Nobody here doubts of that accuracy. I wrote "The experimental support of quantum electrodynamics is excellent". The part that you omit both in your Essay and in this forum is that accuracy may be put on the right context.

The right context is the following, as I wrote before: "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 has done similar remarks about QED regarding points (i) and (iv), you replied to him confessing to not having a proper answer, you replied me saying more of the same... but now without offering any technical response to any of us, you go up and ask us to read Google hits for "precision tests of QED"! I am sorry to reveal you that this material was already known to us and that, evidently, it does not address the points (i)-(iv).

Dear Albert,

You write:

"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?"

My point was that given our means of engaging with the world is based on discrete events (which in our most mature theories it is), any knowledge we think we gain that goes beyond these discrete events will be inference (metaphysics, in fact). Unless we radically alter our means of engaging with the world (by measurement, using relations between properties) then this will indeed always be so: this strikes me as a generalization that can be made! (I'm not completely happy with the phrase "discontinuous knowledge" in any case, and was led to it by the nature of the discussion).

This relates to your second point. You write:

"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."

I showed in my own essay how the representation (be it digital or analogue) cannot be used as a guide to the nature of the target system being represented, since one can model one and the same target system using either method of representation. Further, I'm not sure what your argument is that gets you from an analogue instrument to analogue knowledge. Given that the analogue/digital distinction refers to representation, I'm not entirely sure what "analogue knowledge" could mean? Knowledge of an analogue world? If so, then my previous points apply.

Best,

Dean

Hi Ian, I'd just like to re-iterate my point about a spinning helix which travels around a hypersphere being analogous to an electric circuit. Imagine you are on the inside of a battery which is connected to a simple loop of wire which makes an electric circuit. Imagine a handle rotates clockwise from the positive terminal as seen from your internal perspective. Now trace this turning handle as it travels along the wire and arrives at the negative terminal of the battery. Which way is the handle now turning from the viewpoint of the battery's interior? Is it clockwise or is it anti-clockwise?

The thought experiment illustrates the important relationship between chirality, loops and mirror images. Incidentally, I learnt from a repeat of QI on TV last night about oranges and lemons. The aroma of a lemon is the exact mirror image of an orange and vice versa. Our olfactory sense, the first one to develop via evolution I believe, is ultra sensitive to right and left handedness of airborne molecules, which I find quite interesting.

Kind regards, Alan

Ian,

Well considered and summary look at the difference between how pure math operates versus limitations of actual measurements, at the "bird's eye view." Indeed, models and measurements are not so dovetailed as the glib idea suggests. This is particularly vexing in the quantum realm. I invite you and others to look at my essay, at http://www.fqxi.org/community/forum/topic/949. There I consider the claim that decoherence in any way resolves the measurement problem, with proposed experiments to confirm my claim that the answer is "no, it doesn't." To me, the MP transcends the issue of discreteness, because (ironically named) realist concepts per se can't fully describe our universe or deal with genuine unpredictability.

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