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.
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.
Det finns uppenbarligen mycket att veta om detta. Jag tror att du gjorde några bra saker i funktioner också. Fortsätt arbeta, bra jobb!
Thanks Robert! Excellent question about light. In fact it directly relates to particle physics. In the Standard Model, the fundamental interactions are all mediated by "virtual" bosons. So electromagnetic interactions are all mediated by "virtual" photons, yet, as we all know, at least some of these virtual photons become "real." As David Griffiths says in his excellent book on particle physics, "[y]ou might say that a real particle is a virtual particle that lasts long enough that we don't care to inquire how it was produced, or how it is eventually absorbed." In my mind, I would tend to think that states of "virtual" particles are epistemic while states of "real" particles are ontic, yet there in the example I just cited it is a matter of how long the state lasts! So the "light" mediating an interaction between two closely spaced magnets would, by that reasoning, be epistemic while the light mediating the interaction between you and a distant star that you observe in the night sky is ontic. I would say that qualifies as an interesting philosophical problem.
Tom,
Thanks for the comments. I've printed your essay and it is on my "to read" list!
Ian
Tom,
Thanks for the comments! No need to apologize about "Lorentzian manifolds." My essay for last year's contest tried to make the point that one of our problems is language. I sometimes think we have too much jargon, some of which can give different impressions.
Ian
Dear Ian,
I onjoyed reading your essay. Several of the issue that you discuss have been paradoxical for ages and have not been resolved satisfactory. There is, however, a way to get around those issues, which I will explain below by addressing them specifically.
1. Page 4. the second expression for the average speed makes the assumption that the limit can be determined, because dt (read d as Greek delta) can be made arbitrary small. This is not the case. As I describe in my essay, for electrons, dt has a lower bound equal to 10 exp (-20) sec. A The electron would cease its existence by 'making it smaller'. In other words, mathematically, one can determine the stated limit, but it is unphysical. The velocity of a massive particle is well-defined, even although dt is different from zero. The velocity of a particle does not need to be described in terms of a mathematical limit at all: a definition in terms of a discrete ratio is sufficient, i.e. v = dx/dt, where dx and dt are constrained by quantum condition (4) stated in my essay. In this way, an electron can be assigned a velocity without measuring this (see page 6 of your essay where you discuss the issues around this).
2. Page 5. Classical Light. I assume you mean light described in terms of classical theory.
3. Page 5. "by Brukner and Zeilinger to argue that the continuum is nothing but a mathematical construct, a view I wholeheartedly endorse". I do not necessarily agree with this view. As I describe in my essay, continuity needs to co-exist with discreteness. In the theory I describe, two underlying continuous fundamental fields are needed to explain the existence of particles, interaction between particles, and dynamically emergence of local discrete space and time.
4. Page 5. "So what happens in the limit as dt --> 0 for classical light?" As I indicated under 1., dt cannot be smaller than 10 exp (-20) sec. Light cannot be attributed a discrete time, unless one wants to define it as wavelength/c. The latter is not very useful, since the time would be wavelength dependent.
5. Page 5. "Suppose we decrease dt while leaving dx unchanged. As dt gets smaller and smaller, it implies we are measuring the difference between x1 and x2 more and more rapidly. Lest we forget, classical physics limits how rapidly information can propagate. At some point, without changing dx, we will be empirically prevented from further reducing dt since the ratio of dx to dt cannot exceed the speed of light. So, if we wish to take dt --> 0, we must take dx--> 0 in order to keep the ratio at or below the speed of light."
There is an implicit assumption made that dt can be made arbitrary small, which is not the case as I explained earlier. For a stationary electron dx=0, while dt=10 exp (-20) sec, such that the ratio dx/dt=0 and there is no issue with violating the speed-of-light as one would get by assuming that dt can be made arbitrary small. When the speed of an electron increases, both dx and dt increase, but their ratio cannot exceed the speed-of-light c. In my essay, I explain that this is due to the fact that the internal speed of random spatial motion of an electron is equal to the speed-of-light. The details can be found in the second report on my website.
6. Page 5. "The classical theory of light assumes light is a wave which is an inherently non-local phenomenon". Indeed. This result in a paradoxical behavior. However, is is also known that light consists of photons, which propagate at the speed-of-light, and posses a kind of corpuscular behavior when detected. When one assumes that photons are oscillating blobs, then they do not behave as a classical wave. Still, a 'wavelength' can be assigned, which is equal to the length of the oscillation.
I have a few more comments, which I may write up later.
Thanks Christian!
Thank you (I think?)! (I'm guessing that bra jobb means good job in, maybe, Swedish??)
Thanks for the comments, Ben. Regarding your point number 6, the corpuscular theory of light is inherently quantum. No classical corpuscular theory of light was ever successful as far as I am aware.
I think we fundamentally agree. In all your points where you say there's a lower limit to dt (and then you cite it), that's precisely my point. There is a lower *empirical* limit. The assumption that dt -> 0 is a purely mathematical one and is not grounded in reality, as you correctly point out.
I would, however, disagree on two points. First, if we assume an empirical limit on dt, then we need to also assume an empirical limit on dx such that v can never be zero since zero motion for point particles is ultimately prevented by quantum effects as is well-known. Second, on your point number 3, there are ways to take the ontological status of a field out of the theory without altering the mathematics, i.e. the "field" interpretation of the mathematics is only one possible interpretation of them.
Dear Dr. Durham,
Thankyou for the reply. In my essay is a defintion of 'the Light,' which is a generalisation of the energy of a photon. Historically and conceptually this definition precede's the advent of QM.
Based upon what you said above, 'the Light' is both epistemic and ontic. Therefore the reason knowledge of 'the Light' is discontinous (at the subatomic level)is because 'the Light' itself is discontinous. Perhaps you could read my essay and let me know if you think that is correct.
Robert
Dear Ben Baten,
For an electron at rest Dx (D is Delta) is not zero, as you say, but
Dx ~ (hbar/mc),
with m being the electron mass. This is the equation (13) in the Reference 6 cited in my Essay.
Reference 6 rigorously revises these and other topics (for instance, the equation (14) gives the value of Dx for an ultra-relativistic electron with momentum p), explains why those limits Dx and Dt are not fundamental but arise only under certain approximations in the propagators (as the approximate propagators used in relativistic QFT), and corrects other claims that you and Ian are doing here.
Dear Ian Durham,
as explained in my previous posts above, the existence of a lower limit to Dt (D is Delta) does not imply that the instantaneous velocity for light is not defined as, however, you believe.
As I showed, when one considers also the lower limit to Dx one obtains the exact equation for photons
Dx/Dt = c = dx/dt
which implies that expressions as (dx/dt) are perfectly well-defined and measurable.
You correctly point out Baten's mistake about Dx for electrons. However, again the lower limits for both Dx and Dt for relativistic electrons (or other particles) does not imply that the instantaneous velocity for those particles is not defined.
A rigorous analysis of relativistic localization for electrons was given in the reference 6 cited in my . One can easily obtain the next exact equation for fermions
Dx/Dt = (c alpha) = dx/dt
where alpha is one of the Dirac matrices.
Precisely the instantaneous velocity (c alpha) is used in QED to obtain the current density
j = e Psi* (c alpha) Psi
where e is the particle charge and Psi the field
Or in a more standard form
j = e c \bar{Psi} gamma Psi
with \bar{Psi} the adjoint field and gamma another of Dirac matrix.
There are other claims that you do that are corrected in the same reference 6.
Ian,
Indeed. My knee-jerk reaction is a case in point. This part of relativity is abused so widely and often that it's blinded me to checking terms more carefully for definition.
Tom
Dear Ian,
1. You're right that no classical theory of light was ever succesful. That is not the point I wanted to make. Photons are quantum like entities can be detected by particle detectors. In interference experiments they exhibit a wave-like character. This dual behavior could be reconciled by assuming that they are oscillating 'blobs in motion' to which a frequency (temporal periodicity) and 'wavelength' (spatial periodicity) can be assigned and which is detectable as a particle.
2. Your reply: "I would, however, disagree on two points. First, if we assume an empirical limit on dt, then we need to also assume an empirical limit on dx such that v can never be zero since zero motion for point particles is ultimately prevented by quantum effects as is well-known.
This is not correct. We are talking about two different things, namely the internal random motion (Zitterbewegung) and the external observable average motion of a particle dx (which you use in your essay). In case of a stationary particle, obviously, the externally observable motion dx=0. However, the internal random motion is created in 'discrete portions' equal to dx sup 0 = h/mc (Compton's 'wavelength). In my essay I talk about dx sup 0, from which dx sup 0= h/mc can be derived via h v sub 0 = m sub 0 c sup 2 (de Broglie's equation, see (1) in my essay).
3. Your reply: " Second, on your point number 3, there are ways to take the ontological status of a field out of the theory without altering the mathematics, i.e. the "field" interpretation of the mathematics is only one possible interpretation of them."
I would like to remark that, by assuming the existence of two fundamental interacting fields (protofields in my essay or whatever you want to call them) one can show that the existence of massive particles, their interaction, the notion of particle spin, particle charge, mass, wave function all can be explained consistently within one coherent model (see the complex non-perturbative considerations in ref 2/3 of my references). The true nature of those 'fields' will likely never be known: we can only observe their consequences in particle interaction behavior and detectors. The issue with current (multi-body) interaction models is that, unfortunately, either they are too simple or they cut out essential pieces if the math 'gets too difficult'. When applied to the conjectured interacting two protofields it is shown that those cut-out pieces are essential to understand the complete quantum and relativistic behavior of particles. The internally random quantum behavior of massive particles can be identified with Zitterbewegung.
Dear Juan,
See my last reply to Ian in which I have included an answer to the issue you bring up.
Dear Dr. Ian Durham,
Iam a little bit confused of your thoughts on digital and analog nature of reality.Which one is more basic than the other one,analog or digital? Or do you want to say that it lies in our way of perception of reality. Any way historic background upon which you have based your essay is really absorbing.
But,I have other thoughts on the above problem in my essay.Why dont you,please,go through it and have a different view of the problem? Expecting your openion on it.
Best regards and wishing success in the competition.
Sreenath B N.