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Ian Durham: on 9/3/11 at 20:09pm UTC, wrote That's interesting. Hmmm. Well, we just spent 8 days discussing time at...

Sridattadev: on 8/10/11 at 15:45pm UTC, wrote Dear Dr. Ian, The simple mathematical truth zer0= i = infinity can be...

Tony Way: on 6/14/11 at 1:06am UTC, wrote You argue, persuasively to my mind, that our epistemic knowledge of reality...

Georgina Parry: on 6/6/11 at 10:58am UTC, wrote Dear Ian, Congratulations on being a prize winner. Well done. You answered...

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Quantum Replicants: Should future androids dream of quantum sheep?
To build the ultimate artificial mimics of real life systems, we may need to use quantum memory.

October 18, 2017

CATEGORY: Is Reality Digital or Analog? Essay Contest (2010-2011) [back]
TOPIC: In Search of Continuity: Thoughts of an Epistemic Empiricist by Ian Durham [refresh]
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Author Ian Durham wrote on Feb. 14, 2011 @ 15:45 GMT
Essay Abstract

Is the universe digital or analog? In this essay I argue that both classical and quantum physics include limits that prevent us from definitively answering that question. That quantum physics does so is no surprise. That classical physics does so is rather unexpected. In fact, I argue that classical physics is itself really nothing more than a convenient approximation. Either way, it turns out that our knowledge of the universe is discrete and so it is extraordinarily difficult, perhaps even impossible, to determine the underlying continuity of the universe itself.

Author Bio

Ian Durham is Associate Professor and Chair of the Department of Physics at Saint Anselm College in Manchester, New Hampshire. He is the founding editor of the American Physical Society's _The Quantum Times_ and is a member of FQXi. This essay is dedicated to his father-in-law who passed away quite suddenly as the essay was being completed.

Download Essay PDF File

James Putnam wrote on Feb. 14, 2011 @ 23:23 GMT
Dear Dr. Ian Durham,

Very well written essay. I have a question. I agree that our knowledge is discrete. I would be interested in your opinion about this viewpoint: I think the reason is that, as I see it, mathematics is the art of providing shortcuts to counting. We must count things. For example we count both points and lines. However, we cannot count what a line is. The line is continuous. There is nothing internal to it for us to count. It can be approximated as a near infinite series of points. But, that practice reveals our limitations and not those of reality. In other words, mathematics can never be used to describe an analog nature. Furthermore, this limitation of ours causes us to theoretically see discreteness and not continuity.

We imagine continuity. We visualize continuity. If we cannot learn that which has never been made known to us, then, our ability to think continuity comes from an analog property of the universe. Is mathematics misguiding us about the nature of the universe? I am not considering the interpretations that we assign to the properties that we believe ourselves to be counting. I am thinking only about an inherent limitation of the process of counting and its substitutes.

Your professional analysis is appreciated. Please use this as an opportunity to expand upon your essay.


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Author Ian Durham wrote on Feb. 15, 2011 @ 00:46 GMT
Thanks James. I like your insight, though I disagree (which isn't to say either one of us is right or wrong). I'm a mathematician in addition to being a physicist and I think mathematics does a perfectly suitable job handling continuity. It is when it is applied to reality that things get all muddled.

There's a lot of interesting work out there on this problem of continuity purely from the mathematical point-of-view (which is why I say either of us could be right - the matter is far from settled despite what most mathematicians might think). Strichartz in his Way of Analysis does an interesting job of "defining" the real numbers and in the process defining what mathematical continuity is (he is basically giving the standard view as derived from Cauchy and Weierstrass). It is admittedly quite appealing and worth a read and I will confess to teaching from this point-of-view when I teach analysis. But I still find it troubling when we start to use real objects instead of mathematical abstractions.

This, of course, brings up the whole question of the ontological status of mathematical objects (abstractions) themselves. I suppose that is an entirely different discussion.


Lev Goldfarb wrote on Feb. 15, 2011 @ 02:25 GMT
Hi Ian,

In my essay I have explained that "discrete" means simply non-continuous, while "continuous" we know only from the mathematical models. So in which sense are you using these terms?

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Author Ian Durham replied on Feb. 16, 2011 @ 20:23 GMT
Hi Lev,

I'm not sure I understand the second part of your comment - unless, of course, you agree with my conclusion (continuity is merely a mathematical "ruse").

But I take "discrete" to be the opposite of continuous. In my essay I hint at (and would have expanded on, given more space) the fact that there are different notions of these things - some mathematical, some physical.


Lev Goldfarb replied on Feb. 16, 2011 @ 23:12 GMT
Yes, Ian, I agree.

But the situation with the "discrete" is quite different: first of all, we don't have a definitive concept/model of the discrete, and second, I believe, when we get one, it will not be the same mathematical "ruse".

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Author Ian Durham replied on Feb. 18, 2011 @ 04:01 GMT
Maybe. I mean, I think I see where you're going, but it's quite a novel idea, if I'm understanding you correctly.

Personally, I don't think discreteness is a "mathematical ruse." I only think that about continuity. Or, rather, I think our knowledge about the continuity of the universe itself is a mathematical ruse. It is entirely possible that the universe *is* continuous, but we simply can't determine if it is or not because we're limited by a discrete "lens," as it were.

Alan Lowey wrote on Feb. 15, 2011 @ 11:19 GMT
Hi Ian, you sound like an intelligent guy who's mathematically minded so I want to put to you this quandry regarding another ancient Greek:

Newton's inability to consider a particle model for the force of gravity has left a legacy where the ideology of a spacetime continuum has been set in stone. His equation negates the possiblity of a particle for the force of gravity. If he had considered the Archimedes screw as a GRAVITON he would have included an element of ORIENTATION in his simplistic equation, wouldn't he?

Best wishes,


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Author Ian Durham replied on Feb. 16, 2011 @ 20:24 GMT
Hmmm. Why does his equation negate a particle model for gravity? Coulomb's law is similar and yet we have a very successful particle model for electrostatics.

Alan Lowey replied on Feb. 21, 2011 @ 12:23 GMT
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

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Alan Lowey replied on Feb. 23, 2011 @ 17:11 GMT
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

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Mike wrote on Feb. 15, 2011 @ 19:30 GMT

Enjoyed the essay. As previously posted on your blog, I think that David Deutsch generally has the right approach to this question. In short, he thinks that “within each universe all observable quantities are discrete, but the multiverse as a whole is a continuum. When the equations of quantum theory describe a continuous but not-directly-observable transition between two values of a discrete quantity, what they are telling us is that the transition does not take place entirely within one universe. So perhaps the price of continuous motion is not an infinity of consecutive actions, but an infinity of concurrent actions taking place across the multiverse.”

Sorry to hear about your father-in-law. These things are always difficult. All the best to your and your family.


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Author Ian Durham replied on Feb. 16, 2011 @ 20:26 GMT
Thanks Mike. It was quite a shock and we're still grappling with it (especially my kids who were very close to their "opa").

Anyway, as you well know I'm not a huge fan of the multiverse concept so I'm not sure Deutsch's argument resonates with me, but I believe I said something similar on my blog.

Nevertheless, it's good to have healthy debate on the issue!

Anonymous wrote on Feb. 15, 2011 @ 23:52 GMT
Dr. Durham

Hi. I thought your essay was very good. In regard to your point about the overuse of mathematics as a means of interpreting physical processes, I totally agree and would like to add a related point about infinite sets in relation to physics:

The main issue I have with measuring the size of an infinite subset relative to the size of the set from which it was extracted relates to my background in biochemistry and is as follows. Mathematicians say that if you start with a single, initial set of all the positive integers and then pull out the subset of even integers and pair off the evens in the subset one-to-one with all the integers in the initial set, then you can see that because of the one-to-one correspondence, the number of elements in the subset is the same as in the original set. This is a thought experiment, but it is still an experiment and should use proper experimental technique. However, the pairing off method uses very bad experimental technique, I think. That is, the system to be studied is the single original set of all the positive integers. The experimental processing is pulling out the subset and pairing it off with the elements in the original set. The results from this experimental processing on two separate sets (ie, equal set sizes) are then assumed to be the same as in the original single set. This is similar to studying the interactions of a cell nucleus with the rest of the cell (ie, the cytoplasm) by pulling out the

nucleus, putting it in a separate test tube from the rest of the cell,

studying it there and assuming the results of the processed, separate

nucleus-cytoplasm systems are the same as in the single, whole cell. They may be but often are not, and so this assumption could be totally incorrect. These types of assumptions are not tolerated in biochemistry because it's well known that processing can create the possibility of experimental

artifacts (errors introduced by processing), which means that the results after processing don't reflect the situation in the original system. This bad experimental technique shouldn't be acceptable in mathematics either. Even if you say that mathematics is in its own abstract realm, it's also still used in the physical realm of physics. Its use of bad experimental method makes the use of infinities in physics problematic, IMHO.

I also address the role of infinite sets in physics in the second part of my FQXi assay ("Reality is digital, but its perception as digital or analog depends on the perspective of the observer").

Any feedback you may have would be welcome. Once again, very nice essay!

Roger Granet

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Author Ian Durham replied on Feb. 16, 2011 @ 20:30 GMT
Thanks Roger.

I guess I don't have a problem with "bad experimental technique" in mathematics because, to me, mathematics is not an experimental science. I think our mistake is in assuming that mathematics represents some kind of universal "truth." I have no trouble accepting the fact that we can have infinitely countable and uncountable sets and other oddities in mathematics. Mathematics is either right or wrong, in a sense. It's more black and white than science which is fine. We just have to remember that science is about modeling and sometimes our models contradict one another. Mathematics, unlike science, is entirely self-consistent.


Juan Ramón González Álvarez wrote on Feb. 16, 2011 @ 13:14 GMT
Dear Ian T. Durham,

I have loved your discussion of infinitesimals. Effectively, those exotic objects have evaded mathematicians during three centuries, giving a long controversy, which is still open!

You cite Robinson's work on "Non-standard analysis"; but, as you must know, this modern analysis has received criticism by other mathematicians. For instance, Connes is trying to obtain...

view entire post

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Author Ian Durham replied on Feb. 16, 2011 @ 21:11 GMT

Thanks for your comments. I have a few replies.

First, regarding Robinson, I certainly am no fan of his and I did not cite him in such a way as to say I supported his conclusion. I simply cited him in order to point out that someone had attempted to "vindicate" Newton and Leibniz in recent decades.

I agree that time is a complicated and funky problem (and I'm looking...

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Juan Ramón González Álvarez replied on Feb. 18, 2011 @ 20:13 GMT
Dear Ian,

I am glad to see that we agree on such issues as Robinson's non-standard analysis, time, and the non-geometric interpretation of gravity. Let me to answer to some few issues.

I understood your claim on that Dt must have a non-zero lower bound. I remarked the same in my message when said that the relativistic uncertainty relations introduce such lower bound for time. Indeed,...

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Author Ian Durham replied on Feb. 19, 2011 @ 16:21 GMT

I beg to disagree with you on a number of points.

First, I completely disagree with your claim that simply because c is a constant, Dx/Dt must trivially go to dx/dt. This is true *mathematically.* My point is that it makes no sense *physically.* I think I made it fairly clear *why* this makes no sense in my essay.

Now, before addressing your next points, let me first...

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Rick P wrote on Feb. 16, 2011 @ 18:54 GMT
Bang on. One was worried for a while that you weren't going to do it. But happily you did.

Another Aristotlism: "That which moves does not move by counting." Of course we can't be absolutely certain about that, but he was probably right.

Sorry about your father-in-law. I've been there.

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Author Ian Durham replied on Feb. 16, 2011 @ 21:11 GMT
Thanks Rick.

James Putnam wrote on Feb. 17, 2011 @ 21:05 GMT
Dear Dr. Ian Durham,

Could you please say something succinct to make clear why there is this distinction:

"What does it mean for something to be physically continuous? Does it mean the object can't be broken down into individual parts or does it simply mean the individual parts are intrinsically linked?

For example: A line is continuous; however, it might vary several ways in width and direction along its length. This is the simplest example I thought of to question the distinction between 'individual parts' and 'intrinsically linked'. Personally, I see the interaction of particles of matter to be analogous to, though not nearly so simple, as this example portrays.

I assume that there is a distinction that is not properly represented by my example. I would appreciate a combined mathematician's and physicists viewpoint. What do you think?


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James Putnam replied on Feb. 17, 2011 @ 22:52 GMT
Dear Ian,

I decided I should make it clear that I do not understand how an example of a line broken into pieces and separated completely would have any relevance to what is occurring in our universe. Any clarity that you can offer would be appreciated.


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Author Ian Durham replied on Feb. 18, 2011 @ 03:57 GMT

So, my statement there simply leaves open the possibility that we might be able to define some slightly different "version" of continuity. So, for instance, perhaps a pair of entangled particles, even if separated by light-years, could somehow be considered continuous. Personally, I don't think so, but I could imagine someone trying to make that argument.


Albert wrote on Feb. 19, 2011 @ 17:06 GMT

Interesting work but I do not agree with some of your key points.

I did not fully understand your position about Zeno's paradoxes. I also agree that we have all the mathematical answers. But I sense you tried to avoid answering directly whether supertasks are possible in nature.

Finally, I do not agree with the following statement:

"This would seem to imply that epistemic states are ultimately discrete on some level: our knowledge of the universe is discontinuous."

It is my understanding that this essay contest deals with the ontology of spacetime, not our epistemic states. These states are modified as science progresses and new experiments are performed.

and finally I do not also agree with this statement:

"Classical physics, with its inherent continuity, is nothing more than a convenient myth."

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. I think the myth is "it from bit". This is what we should be targeting, in my opinion of course.

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Author Ian Durham replied on Feb. 19, 2011 @ 22:20 GMT
Actually, the most successful theory of all time, as measured by how closely it matches experiment, is QED.

"It is my understanding that this essay contest deals with the ontology of spacetime, not our epistemic states. These states are modified as science progresses and new experiments are performed."

Actually, this essay contest deals with reality. Reality is more than merely spacetime. 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.

Member Dean Rickles replied on Feb. 20, 2011 @ 01:19 GMT
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.



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Edwin Eugene Klingman replied on Feb. 20, 2011 @ 01:34 GMT
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

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Thomas J. McFarlane wrote on Feb. 20, 2011 @ 06:27 GMT

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.



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Author Ian Durham replied on Feb. 25, 2011 @ 02:07 GMT

Thanks for the comments. I've printed your essay and it is on my "to read" list!


Juan Ramón González Álvarez wrote on Feb. 20, 2011 @ 13:52 GMT
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.

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Author Ian Durham replied on Feb. 20, 2011 @ 21:42 GMT
> which means that you have not answer to my points.

Indeed. I do not claim to know everything.

Juan Ramón González Álvarez wrote on Feb. 20, 2011 @ 13:54 GMT
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....

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Juan Ramón González Álvarez replied on Feb. 20, 2011 @ 14:03 GMT
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.

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Author Ian Durham replied on Feb. 20, 2011 @ 21:58 GMT
I think you are still fundamentally missing my point, as Dean also made clear.

I know full well that physicists believed in discrete electrons as early as the 19th century. Indeed, Newton proposed a particle theory of light even earlier! The question is, did they concurrently believe that *reality itself* was discrete? How about time? Or space for that matter? Believing that something *in* reality is discrete does not mean that one must believe reality *itself* is discrete.

Regarding QFT versus QM, you are mistakenly equating "different" with "contradictory." QM and GR are contradictory in certain respects. QM and QFT are not. You are taking Dirac's comments entirely out of context.

Regarding the speed of light as a constant, in fact it is merely a maximum value that can be obtained. It is known to be lower than its vacuum value in objects (e.g. water, crystals, etc.). Further, there have been suggestions (and some claim to evidentiary support) that it is variable under certain constraints (see work by Magueijo and others - I think I spelled his name wrong, but I don't have his papers handy).

Author Ian Durham replied on Feb. 20, 2011 @ 22:06 GMT
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.

Robert Spoljaric wrote on Feb. 21, 2011 @ 09:25 GMT
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,


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Author Ian Durham replied on Feb. 25, 2011 @ 02:04 GMT
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.

Robert Spoljaric replied on Feb. 25, 2011 @ 03:01 GMT
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.


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Author Ian Durham replied on Feb. 26, 2011 @ 15:40 GMT

I'll print out your essay and read it. I'm interested in what you have to say on the topic.


T H Ray wrote on Feb. 21, 2011 @ 11:45 GMT

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.


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T H Ray replied on Feb. 21, 2011 @ 14:42 GMT

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.


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T H Ray replied on Feb. 21, 2011 @ 15:59 GMT
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.


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Author Ian Durham replied on Feb. 25, 2011 @ 02:09 GMT

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.


Christian Corda wrote on Feb. 21, 2011 @ 17:24 GMT
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,


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Author Ian Durham replied on Feb. 25, 2011 @ 02:11 GMT
Thanks Christian!

Juan Ramón González Álvarez wrote on Feb. 21, 2011 @ 21:30 GMT

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...

view entire post

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Neil Bates wrote on Feb. 24, 2011 @ 02:28 GMT

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 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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buy proviron wrote on Feb. 24, 2011 @ 20:54 GMT
Det finns uppenbarligen mycket att veta om detta. Jag tror att du gjorde några bra saker i funktioner också. Fortsätt arbeta, bra jobb!

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Author Ian Durham replied on Feb. 25, 2011 @ 02:14 GMT
Thank you (I think?)! (I'm guessing that bra jobb means good job in, maybe, Swedish??)

Ben Baten wrote on Feb. 25, 2011 @ 02:10 GMT
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...

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Author Ian Durham replied on Feb. 25, 2011 @ 02:24 GMT
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.

Juan Ramón González Álvarez replied on Feb. 25, 2011 @ 12:23 GMT
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.

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Juan Ramón González Álvarez replied on Feb. 25, 2011 @ 12:46 GMT
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.

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Anonymous wrote on Feb. 26, 2011 @ 08:18 GMT
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.

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Author Ian Durham replied on Feb. 26, 2011 @ 23:45 GMT
I will add your essay to the list of them that I am reading.

Indeed, the divide between analog and digital lies in how we perceive reality.

Lawrence B Crowell wrote on Feb. 27, 2011 @ 00:26 GMT
The relationship between the continuous and discrete aspects of the world seems to be an example of a complementary principle. I am not sure how this can be formally demonstrated. Yet it appears that wave functions and continuous structures of that nature are not directly observed, whereas what we do observe are particle or the discrete event of a particle occurrence.

Your essay was pretty good and enjoyable.

Cheers LC

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Author Ian Durham replied on Feb. 27, 2011 @ 17:52 GMT
Thanks, I'm glad you liked it! I think the continuous v. discrete debate was actually at the true heart of the original complementarity principle. If you read Bohr's writings and those of people who adhered to his principles, I think you'll find that this is precisely at the core of what they were talking about.

Juan Ramón González Álvarez replied on Feb. 28, 2011 @ 19:23 GMT
Dear Lawrence B Crowell,

What "complementary principle"?

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nikman replied on Mar. 1, 2011 @ 18:54 GMT

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Peter Jackson wrote on Feb. 27, 2011 @ 00:54 GMT
Dear Ian

I'll need to read your essay again more carefully and will do so, but your response above to Robert Spoljaric interested me as much and seemed to be fully consistent with the basis of my own essay rather than the ruling paradigm.

There also seems to be a similar strong consistent and broad 'new physics' theme emerging in a number of others, including our current leader Jarmo, also Edwin, Robert, Willard, Georgina, Rafael and the list goes on.

Do you think FQXi may at last be engendering the fundamental paradigm shift it was conceived for? or do you feel the new green shoots will be trampled on yet again? or are not worth nurturing? I'd be interested in your views on mine and the above if you have time to add them to your list!

Best of luck.


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Author Ian Durham replied on Feb. 27, 2011 @ 17:56 GMT

Unfortunately, I'm a bit of a cynic so I don't necessarily think FQXi is engendering any paradigm shift (though I think it does a great deal of good). There are just too many people out there who see FQXi as an organization of cranks (ignoring the fact that there are five Nobelists among us).

That said, there may be a slow shift happening in foundational circles. But I don't think anything will truly change until there is a major breakthrough in experiment. Just my opinion (though one shared by a few other people).


T H Ray replied on Feb. 28, 2011 @ 11:51 GMT
I find it hard to understand why one would identify radical reversals of known science with a great creative surge of knowledge, when the facts say otherwise. Arguably, the most revolutionary ideas in physics in the last 300 years -- Einstein's -- were founded in the revolution that Newton started, not in any new way of doing physics. Even now, where relavitity meets quantum mechanics, most bets are on quantum field theory to extend Einstein's work, not overturn it.

Regardless of the charatcerizations of popularizers, objective knowledge viewed in an objective manner is hard won and incremental -- like the process of evolution itself.


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Author Ian Durham replied on Mar. 1, 2011 @ 14:56 GMT

Yeah, I agree with you. In fact that's a bone of contention I have with field theories. That's also why I'm not a huge fan of Kuhn's "paradigm shift" interpretation of the history of science.


Peter Jackson wrote on Feb. 27, 2011 @ 19:05 GMT

Thanks. Cynicism seems difficult to fight in current conditions, and experimental results now seem consistently defined by the ruling paradigm not the other way round. Who would now volunteer for the 'crank label by being inconsistent?!

If you really are am empiricist I really do hope you might look over my essay and advise what may be physically wrong with the empirically consistent solution to unification at it's heart.

You'll need to slow down and think carefully at a few key points. It appears it's only lack of that care that has prevented the solution being seen before now.

There was something very moot late in your essay I'd like to return to, in the meantime I'd be richly honoured by any views on mine. (2020 Vision, a model of discretion..)

Best wishes


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Author Ian Durham replied on Mar. 1, 2011 @ 14:58 GMT

I will promise to look over your essay. I have a stack I have to read so it may be awhile before I get to it, but I promise to do so before too long.


Georgina Parry wrote on Feb. 28, 2011 @ 08:49 GMT
Dear Ian,

I have just had a quick read of your essay. I was very pleasantly surprised as I had thought it might be far to complicated for me to understand. I will certainly read it again when I have more time and am less tired.It is written in an accessible and clear way.

The introduction is excellent. You are the first, that I have read , who plainly asks what is actually meant by continuous and discreet, as well as asking what is meant by reality. You are right to highlight the limits to objective knowledge. We can not know because our knowledge is limited by the need to make detections and interpret them. There is some overlap with last years question here.

Any way It looks like you have done a very good job of addressing the essay question in an enjoyable and relevant way.

I was sorry to hear of the loss of your father in Law.

Good luck. Georgina

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Author Ian Durham replied on Mar. 1, 2011 @ 15:08 GMT

Thank you so much for the kind words! I am glad I made it accessible. It gives me faith that I'm in the right line of business (teaching at a small college, I mean).

There is definitely some overlap with last year's question. In fact it has made me consider putting together a longer treatise on the subject that includes both last year's and this year's essays, perhaps as the core of a class I might offer.


Member Tommaso Bolognesi wrote on Feb. 28, 2011 @ 16:30 GMT
Dear Ian,

your essay has the merit, I think, to discuss with more clarity than other participants the distinction between the ontological and epistemological spheres.

There is a (minor) point on which I tend to disagree, or at least I need clarification. You write:

"This idea simply formalizes the somewhat intuitive notion that causality is somehow related to continuity. To get a better conceptual understanding of this, suppose two events, A and B, are causally connected. Then there must be some way to get information from one to the other without exceeding the speed of light (or, more formally, they must be either timelike or lightlike separated). If spacetime is discontinuous, how do we know that this information couldn't 'jump around' from point to point? Continuity guarantees that the information follows a nice, orderly 'path' between A and B. This should make it easy to see the conceptual attraction of a continuous reality."

I really do not see the coupling between causality and continuity as something that matches common intuition. In particular I am not sure I understand what you mean by writing that one might be worried by the possible uncontrolled jumps of information (possibly messing up causality, you probably imply) under a discontinuous spacetime assumption.

I am indeed tempted to say that a discrete spacetime assumption, as embodied in a partial order/directed-graph model (a causal set) would create less problems to intuition, as far as causality flow is concerned, due to the explicitly represented paths that information may follow in the discrete structure: you explicitly indicate which event influences which other event. (And Lorentz distance, in the continuum, in nicely approximated by graph-theoretic longest-path distance, in the discrete setting.)


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Author Ian Durham replied on Mar. 1, 2011 @ 15:24 GMT
Thanks Tommaso!

I understand where you are coming from in regard to the directed graph approach (in fact, I would go one step further and use category theory). But what I was saying was that, at least to some people (this is obviously not all), a causal spacetime would necessarily seem like it had to be continuous. In fact, Hawking and Sachs wrote an interesting article on this back in the '70s and suggested that, at least in macrophysics, causal continuity should be a fundamental postulate.

My argument, which was brief due to length restrictions, essentially is as follows. Imagine a simple 2-D spacetime with coordinates x and t. If spacetime is continuous, then we can think of it as an infinite "world-sheet," so-to-speak, and we can overlay our x and t axes anywhere on it. Now, in a discontinuous spacetime, we can think of it rather as a collection of disconnected points. It makes no sense to globally overlay x and t axes here because x and t are not defined in between the points. So the x and t can only be defined locally *on* the points. But then, it might be perfectly possible for information to hop from point to point even if it is "sideways." It would seem to violate a macro-causality, though wouldn't really on a micro scale since spacetime would only be locally defined. At some point I should work up some diagrams to help better explain what I am trying to say here.

Member Tommaso Bolognesi replied on Mar. 2, 2011 @ 18:31 GMT
Dear Ian,

thanks for spelling my name correctly, and not with swapped doubles, as many people in your continent do.

I am afraid I still don't see your point. Perhaps the source of confusion is in the idea of trying to bring around the x-axis and t-axis on a discrete structure exactly as one would do on a continuous manifold. (I do understand that you are not the one who wants to do this!) This is inappropriate. On a causal set (our discrete structure) one cannot rely on cartesian axes for obtaining the space and time values of an event. So, it is true, as you wrote, that x and t are not defined in between the points, BUT they are not even defined *on* the points: if one insists for having definite (x, t) coordinates for an event, he should embed the whole causal set in a manifold, and read out the coordinates from the latter. These would be coordinates relative to a specific reference frame. But one of the nice features of causal sets is that they describe the pure causal structure of events while abstracting from any specific embedding/frame, in the same way as Lorentz distance is invariant for all inertial observers.

So I still do not see why it should be easier to be trapped in the erroneous belief that information might hop from point to point, and event 'sideways', w.r.t. a discrete structure, than to be trapped in the analogous error w.r.t. a continuous structure, picturing information jumping outside the light cone.

But, as I said, this was really a minor point. Thanks for the pointer to Hawking and Sachs. I have one for you, if you are interested: a one-page discussion of causal sets by R. Sorkin. My essay is in line with those basic ideas, but departs from them in the causet growth dynamics, which in my approach is algorithmic and fully deterministic.


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Author Ian Durham replied on Mar. 3, 2011 @ 13:44 GMT

It wasn't too hard to get your name right - I just copied it from your postings! ;) Seriously, I am used to everyone butchering my own name (especially when they try to pronounce it) so I am sensitive to such things.

Anyway, I think I see your point. I'll have to study causal sets a bit more closely, though before I can say for certain. I'll take a look at Sorkin's article. Note that Hawking and Sachs do approach it from a set-theoretic standpoint.



Ken Wharton wrote on Mar. 1, 2011 @ 05:15 GMT
Hi Ian,

Another nicely constructed and argued essay -- and of course I'm glad you arrived at the conclusion that the next question to ask is whether it's possible to have a "quantum" theory that's not discrete. I'm looking forward to hearing more of your thoughts on that topic.

Only a couple of nitpicks:

- I didn't follow your leap from "imprecision" to "discontinuity". Yes, measurements are imprecise. Does that mean the knowledge we gain from them is "discrete"? Well, maybe, but that's not how I tend to think of the word. But then in your conclusion you used the word "discontinuous", which I think is a much stronger claim (and more akin to how I view "discrete" in the first place). Was that word a slip, or is that what you really mean?

- In my view of the world, "Classical, Newtonian physics" did indeed have competition after 1788 via Lagrange. A point I like to make, because I still don't think that people have properly wrapped their heads around how different variational principles are from what Lee Smolin calls the "Newtonian Schema".



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Author Ian Durham replied on Mar. 1, 2011 @ 15:44 GMT
Hey Ken,

Thanks! I've read yours, by the way. I just haven't had a chance to post my comments yet (or did I?). Regarding "discontinuous" v. "discrete" I do, admittedly, use them interchangeably in that essay, though they are not necessarily the same. In the sense that I'm using it, I'm saying truly continuous measurements are not technologically (perhaps physically) possible due to the imprecision of measurements. I'm not sure how to better explain it, but basically continuous measurements require instantaneous measurements (or at least the ability to make them) and the latter are physically impossible.

I'm not sure I see how Lagrange's variational principles differ from Newtonian mechanics. In fact, Newton was the first to develop variational principles (famously, though perhaps apocryphally, in a debate with the Bernoulli brothers).


Constantin Zaharia Leshan wrote on Mar. 3, 2011 @ 10:45 GMT
Dear Readers,

There are three kinds of the essays in our contest: 1) the essays with original physics research where all physics' information was created by their authors. Often such essays seem to have errors because they often contradict orthodox theory. 2) There are essays-stories about physics which contain generally known physics' information copied from the textbooks or papers and author's commentaries (for example Jarmo Makela, Singh, Durham, Funakoshi and so on). Such essays have ARTISTIC VALUE only but not scientific value; usually these essays-stories do not have any errors by definition because all physics' information was copied from the textbooks and other published papers. 3) There are essays of mixed type containing mixed information. It is clear that the authors of the essays-stories have advantages because their essays never contain errors since all Physics' information was copied from the textbooks.

What kind of the essay must FQXi community support? If we support the essays-stories, we'll transform FQXi into the entertainment community. For example, instead of my ''interpretation of quantum mechanics'' I could send the jokes about Bohr, Einstein or stories like Gamov's ''Mr. Tompkins in paperback''. It would be very interesting and fun. Another option is to create artistic essays-discussions with Einstein, Bohr, or Aristotle following the example of Jarmo Makela. In this context, the next logical step is to organize a banquet for the authors of essays where we tell jokes and funny stories about physics. What is our purpose?

Since the goals of the FQXi (the "Contest") are to: Encourage and support rigorous, innovative, and influential thinking about foundational questions in physics and cosmology; Identify and reward top thinkers in foundational questions, therefore I ask readers to vote for essays with original research rather than for essays-stories. In this way we'll encourage the fundamental physics research but not entertainment essays.



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Author Ian Durham replied on Mar. 3, 2011 @ 13:40 GMT
Dude, did you even read my essay?? I didn't copy anything from a textbook. As far as I am aware, my argument about the radar gun is unique. Whether or not it is correct is another matter that can be debated in a professional manner. But I fail to see how it does not count as original research.

As for your contention about FQXi essays, you have clearly missed the point of many of them. In addition you seem to think that FQXi's sole purpose is to challenge the "ruling paradigm." That is not true. FQXi's intent is to ask meaningful questions about the universe and stimulate discussion about those questions. I think it does an admirable job in that regard.

Constantin Leshan replied on Mar. 3, 2011 @ 17:20 GMT
I wrote in the above post about the PHYSICAL information and physical laws. Your argument about radar guns is not about PHYSICS; For example, the uncertainty principle is a physical information but not guns, cars, ships and so on - It's about technology.

Your essay use generally known physics information that was NOT created by you. Therefore it is true that the essay contain physical information copied from the textbooks and Internet. I understand that really you learned all this information at the University and then you prepared your essay using your memory. However, it is the same - your essay contains GENERALLY KNOWN PHYSICAL INFORMATION copied from external sources.

For example, infnitesimal changes, parabolic functions, Zeno's paradox, Doppler effect, Spekkens' epistemic interpretation of quantum mechanics - it is generally known information copied from textbooks. If you comments about quantum mechanics and SR it does not means that it is YOUR information: ''Quantum field theory combines quantum mechanics with special relativity and so technically deals with a at (Euclidean) spacetime". You are NOT the creator of this physical information. The essays filled with such information and authors commentaries is not original and contains information copied from general sources as textbooks, papers, Internet and so on.

Please show me the PHYSICAL information created by YOU in your essay.

Also, I don't see any proofs in your essay that the Universe is digital or analog. The discussions about radar guns prove nothing about reality.


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Member Dean Rickles replied on Mar. 4, 2011 @ 10:49 GMT
Dear Constantin,

The FQXi is the "Foundational" Questions Institute. The idea is to probe the foundations of pre-existing theories, perhaps propose modifications to these foundations, or even (if absolutely necessary) to propose entirely new foundations. But really, proposing ENTIRELY NEW, completely original physics should be a last resort. I can think of no example where this method has been fruitful in the past. Take the discovery of special relativity, for example. There is a case in which the equations (the Lorentz transformations) were already "in the textbooks". Einstein reinterpreted them, employing a foundational analysis. Would you accuse Einstein of plagiarising here? An equation on its own doesn't tell us much. We need to know what it could mean. There are, in physics, usually (most probably always) multiple options in how we understand the mapping between equations and reality.

Your request for statements that "prove something about reality" must be, in the end, a request for a foundational (or interpretive) analysis (and an epistemological one at that). The point of many of these competitions (and the submissions) has been to probe just what can be said about reality GIVEN OUR THEORIES. You may think you are being a hard-nosed scientist, a la Feynman or Pauli perhaps, but you are in fact just espousing a very naive philosophical position. Feynman and Pauli might have spoken in a similar way, but their actual work revealed a very different, more sophisticated philosophical understanding.

Finally, I have to agree with Robert Spoljaric that your beef ought to be with FQXi.



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Juan Ramón González Álvarez wrote on Mar. 3, 2011 @ 11:30 GMT
Dear Constantin Zaharia Leshan,

I sympathize with your views.

I only want to remark two things. The first, that it is not true that the "essays-stories" do not have any errors because were copied from textbooks and papers. I have given some examples of the contrary both in the forums and in my own Essay.

The second, that I do not consider Singh' Essay to be only of artistic value (see my 'review' of it as well!).

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Constantin Leshan replied on Mar. 3, 2011 @ 17:53 GMT
Dear Juan R. González-Álvarez,

Thank you for support. In my view, the FQXi prize deserves the people who really are able to create PHYSICS; the prize is not for writers and copiers.

There are a lot of the essays and I do not have time to analyze all. Nevertheless, I'll analyze the Singh' Essay more carefully.



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Lev Goldfarb replied on Mar. 4, 2011 @ 01:17 GMT
I must agree with Constantin Leshan: if, indeed, FQXI intends

"to catalyze, support, and disseminate research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality but unlikely to be supported by conventional funding sources"

the mission which requires a *very rear* kind of expertise, especially now when our overloaded schedules meet with the absolutely unprecedented in the history of science transitional period. This very rear expertise should be found and used effectively. Otherwise, the mission will not be believable, and, which is more, will only *undermine* the future similar undertakings.

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Lev Goldfarb replied on Mar. 4, 2011 @ 07:49 GMT
I'm sorry, I mistyped: of course I meant "very rare" rather than "very rear" ;-))

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James Putnam wrote on Mar. 4, 2011 @ 15:28 GMT
It seems odd that this discussion and the one immediately above it should be occurring in Dr. Durham's forum. He does not agree with my ideas; but, I have found him to be a gentleman and as open minded a scholar as I have ever had a discussion with. He is a valuable resource for which I have not yet had to pay. I think that no one has a better chance for having their ideas evaluated by professionals than what takes place here at I think that my ideas are great. However, until professionals agree, they remain not great. That agreement should it ever come must be for good scientific reasons and given willingly by qualified others. Until then, promoting my ideas are my problem and not theirs.


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Author Ian Durham replied on Mar. 4, 2011 @ 22:53 GMT
Thanks James. I appreciate the kind words (they actually made my day!).

Robert Spoljaric replied on Mar. 5, 2011 @ 12:56 GMT
Dear Prof. Durham,

You are indeed a gentleman, and as such I feel somewhat guilty about you reading my essay. I sincerely thank you for taking an interest, and hope you find it interesting.

I would, however, like to clarify a point I made on the Feb 25th post. 'The Light' as defined in my paper is epistomological. However, it is the *basis* of Relativistic Mechanics, and as such entails a future ontological commitment. There is much left unsaid, but I don't want to spoil your fun!

All the best,


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Robert Spoljaric replied on Mar. 5, 2011 @ 12:57 GMT
Sorry that should read Relativistic Dynamics.

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Chris Kennedy wrote on Mar. 6, 2011 @ 21:06 GMT
Ian - Outstanding Essay!

As an educator - I always look for how understandable an essay can be to nonprofessionals and you hit this out of the park! I think being inclusive is very important as many outside the field often have valuable contributions. You do an excellent job of showing that the act of measuring will always be a weaker accuracy link that what is actually measured. This of course applies to the passage of time as well in our pursuit to determine if it is discrete or continuous.

By the way, if gravity is like a painting, then the problem is that we can't see the individual brush strokes since none have been detected. We assume (well, some of us, but not me) that it must be made of individual strokes despite Einstein's original theory telling us that it is the warping of the canvas itself that gives us the painting. I once had a crazy theory that gravity will ultimately be determined to be a "London Force" of EM. If that ever turns out to be true - at least we will have brush strokes, just not the kind we were looking for.

I will be sure to keep a copy of your essay with me so that the next time I get pulled over for speeding, I can point out the inaccuracies of the radar detection device!

Great job!


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Author Ian Durham replied on Mar. 10, 2011 @ 02:56 GMT
Wow! Thanks so much Chris! I, too, think of myself as an educator. I come from a family of them as does my wife (both my parents, both her parents, my sister, sister-in-law, my grandfather, aunts, uncles, etc. - it's in the blood). You know, your idea about gravity isn't that crazy. A similar thought occurred to me recently (though not specifically related to a London force). I think there is a much deeper connection between gravity and E&M than we realize.

James Lee Hoover wrote on Mar. 7, 2011 @ 18:59 GMT

Your argument is objective and logical. As you seem to say, our view of reality has distortions. I like to compare it to our view of space through earth's atmosphere.

Great essay.

Jim Hoover

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Author Ian Durham replied on Mar. 10, 2011 @ 02:53 GMT
Thanks Jim! That's actually a great comparison, by the way.

Constantinos Ragazas wrote on Mar. 7, 2011 @ 19:06 GMT
Hello Ian,

I've been seeking a dialog with you since my post under your forum on math and physics last spring. This contest provides me another opportunity. We agree generally on the notion that we can only know our measurements (and observations) of 'what is', but not 'what is' the Universe. That much I remember from our brief exchange.

Picking up on this general theme I ask that you consider the following result to be found in my essay. One among many, but what I consider the key finding. The Rosetta Stone, as it leads to many other 'translations'.

Planck's Law of blackbody radiation I prove in my essay is an exact mathematical tautology that describes the interaction of measurement. The mathematical derivation is simple and mathematically irrifutable. It uses continuous methods and does not use 'energy quanta' and statistical mechanics.

I further argue that this tautology explains why the blackbody spectrum obtained experimentally is indistinguishable from the theoretic curve obtained from Planck's Law. Certainly, a mathematical tautology that describes measurement will be indistinguishable from the measurements it describes.

Please read my essay and comment on this result. I also ask your support in getting this result 'peer reviewed' by the 'panel of judges'.

All the best,

Constantinos Ragazas

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Author Ian Durham replied on Mar. 10, 2011 @ 02:52 GMT
Hi Constantinos,

My apologies for not seeing your postings on the forum. Life got a little crazy last summer and hasn't let up. But I am hoping for a renewed respite period here soon. At any rate, I will add your essay to the stack I'm taking to Dallas with me. It wil take me a couple of weeks to get through all of them, but I do promise to do so and to leave comments.



Vladimir F. Tamari wrote on Mar. 8, 2011 @ 15:20 GMT
Dear Ian,

Firstly please accept my condolences for the loss of your father-in-law. I lost mine many years ago but still think of him with great affection and respect.

Your interesting discussion of Doppler effects in connection with the speed of light and relativity reminded me of the fascinating insights and simulations of these topics by my friend Gabriel LaFreniere though he does not deal with the question of granularity of space as such. I would also greatly appreciate it you can read my fqxi essay and the 2005 Beautiful Universe paper on which it is based. I know this means you have to wade through my obviously speculative or half-baked ideas, but it all makes a lot of sense - at least to me! :)

With best wishes, Vladimir

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Author Ian Durham replied on Mar. 10, 2011 @ 02:50 GMT
Dear Vladimir,

Thanks so much. It has been a bit like losing a father (mine is thankfully still alive and well).

I'd be happy to take a look at your essay! I'm spending a week at a conference in Dallas soon and am going to take a stack of FQXi essays with me to read. As for half-baked ideas, some of them turn out to be the best ideas in the end!



Vladimir F. Tamari replied on Mar. 20, 2011 @ 14:15 GMT
Dear Ian

I hope you are feeling better about your loss. I just saw your note dated the day before the Japan earthquake...Sorry to respond to it so late and say thanks for making the effort to read my fqxi paper. I hope it encourages you to look at my earlier longer paper where I have spelled out my theory. Enjoy your conference.

Best wishes from Vladimir

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Peter wrote on Mar. 9, 2011 @ 13:09 GMT

Several mistakes right from your abstract

“In this essay I argue that both classical and quantum physics include limits that prevent us from definitively answering that question. “

Limits are established experimentally in physics, not through argumentation.

“That classical physics does so is rather unexpected. In fact, I argue that classical physics is itself really nothing more than a convenient approximation.”

What is new about this that requires arguing about? Every physics graduate student knows classical physics is an approximation.

“Either way, it turns out that our knowledge of the universe is discrete and so it is extraordinarily difficult, perhaps even impossible, to determine the underlying continuity of the universe itself.”

What is discrete about this knowledge about the universe?

X^2+y^2 = 1

Don’t math equations constitute knowledge or you exclude them from that set?

I was really disappointed by this essay.

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Author Ian Durham replied on Mar. 10, 2011 @ 02:46 GMT
"Limits are established experimentally in physics, not through argumentation."

Um, yeah, that was my point.

"Every physics graduate student knows classical physics is an approximation."

Take a look at some of the essays here by other physicists and you'll find plenty for whom classical physics is apparently not an approximation.

"What is discrete about this knowledge about the universe?"

Did you even read the essay?

"Don’t math equations constitute knowledge or you exclude them from that set?"

Now THAT is an intriguing - and very valid - question. Too bad it was buried in an otherwise condescending post.

"I was really disappointed by this essay."

That's your prerogative. I can't please everyone all of the time.


Alan Lowey wrote on Mar. 10, 2011 @ 12:22 GMT
Dear Ian,

Thank you for replying to my questions earlier w.r.t a helical model for the creation of structure which we observe today. I have been pursuing this line of enquiry and have hit upon something quite extraordinary. I've just talked about it on Edwin Klingman's essay page, so I'll copy and paste it over:

On day-by-day thinking about the novel idea of a mechanical Archimedes screw in empty space representing the force of gravity by gravitons, I have deduced an explanation for the galaxy rotation curve anomaly.

The helical screw model gives matter a new fundamental shape and dynamics which the standard model lacks imo. This non-spherical emission of gravitons is in stark contrast to the Newtonian/Einsteinian acceptance that "all things exert a gravitatinal field equally in all directions". This asymmetry of the gravitational field allows for the stars to experience a greater pull towards the galactic plane, due to their rotation giving more order to the inner fluid matter of the stellar core. Both the structure of the emitter and the absorber of the gravity particles is important. It also has implications for hidden matter at the centre of the galaxies..

I've given the idea some more thought and come to the conclusion that the stars furthest from the galactic centre must have a more 'bipolar nature' than the matter of stars of the inner halo presumably. This is the reason they have wandered towards the galactic plane whilst the halo stars have not. The outer stars' configuration means they experience a greater interaction with the flux pattern of the graviton field. Are the stars of the outer arms simply spinning faster?? We are on the outer edge of a spiral arm and so this would fit with this hypothesis. Our sun could have spin which is higher that that of the average halo star. This relationship between spin and distance from the galactic centre is a fundamental feature which ties in with the suggested mechanism of their creation.

All that is needed is an additional factor of stellar spin speed as well as it's mass and distance from the galactic centre. The relationship should then give calculated values which match those of the observed.

Best wishes,

Alan Lowey

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Author Ian Durham replied on Mar. 20, 2011 @ 01:23 GMT
Interesting. I'll have to give your ideas some deeper thought before I can comment further, but I have a soft spot for astronomy. :)

Author Yuri Danoyan+ wrote on Mar. 10, 2011 @ 19:46 GMT
Thank You for advance for comment my essay

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Russell Jurgensen wrote on Mar. 11, 2011 @ 18:51 GMT
Dear Ian,

I wanted to be sure to say hello before the commenting period is over. I really appreciated your essay and how you discuss that the universe is such that our theories and observations will always be subject to interpretation. Your essay demonstrates a great interest in the science of physics as well as the philosophy of physics. I hope you will have a chance to read my comment on Dean Rickle's essay about the philosophy of how we look at our observations.

Thank you for a thought provoking essay!

Kind regards, Russell Jurgensen

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Author Ian Durham replied on Mar. 20, 2011 @ 01:49 GMT
Thanks for the kind words Russell! I will try to pop over to Dean's essay and read your comments.

Petra wrote on Mar. 12, 2011 @ 11:50 GMT
Mr Durham

A very good essay, thank you. But you say of the subject, which is of physics ~ 'we will likely never know unless we can nd a clever way around the problem of determining the continuity of something through a discontinuous lens.'

You should have found this you have read the essay of 2020 vision. I did, but in thought not in reading. Do see my post. You lead this and I expect read each others? I was interested in your view but saw none from you there. I commend it and more, and hope you support science not yourselves. I wish you and your family well.


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Author Ian Durham replied on Mar. 20, 2011 @ 01:48 GMT
Thank you Petra. I am not sure to what you are referring regarding the essay of 2020 vision.

Constantin Zaharia Leshan wrote on Mar. 13, 2011 @ 16:07 GMT
Dear Ian Durham,

I found some errors in this essay:

You write: ''Any interaction necessarily requires an exchange of information''.

It is an erroneous statement; I can show you an example of interaction without any exchange of information. The Black Hole's event horizon is a boundary in spacetime through which matter and light can only pass inward towards the mass of the black...

view entire post

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Author Ian Durham replied on Mar. 20, 2011 @ 01:46 GMT

The black hole information paradox is called a paradox for a reason. If you'd like to argue that it isn't actually a paradox, then feel free. But its existence does not a priori prove that my statement was erroneous.

John Merryman wrote on Mar. 13, 2011 @ 17:07 GMT

"Thus it seems that while it is clearly mathematically possible for an instantaneous velocity to exist, we are physically prevented from ever measuring one!"

Would it be possible for "an instantaneous velocity" to physically exist? It begs the question of whether time is an underlaying basis of motion, on which those mathematically dimensionless points of instantaneous velocity can exist, or is it an effect of motion, such that a dimensionless point of time would freeze the very motion creating the events located on that sequence? Sort of like trying to take a picture with the shutter speed set at zero.

Does the present move along this dimension from past to future, or does the changing configuration of what is present turn the future into the past?

Do we travel the fourth dimension from yesterday to tomorrow, or does tomorrow become yesterday because the earth rotates?

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Author Ian Durham replied on Mar. 20, 2011 @ 01:38 GMT

That's actually a very intriguing observation (although your last sentence is really just an argument of semantics).

Member Moshe Rozali wrote on Mar. 14, 2011 @ 19:26 GMT
Hi there, I enjoyed this essay enormously. To point out one connection to my essay - you correctly identify a connection between causality (and the Lorentzian structure of spacetime) and continuity. I believe this relation can be strengthened by using some ideas from effective field theories, which are elaborated on in my essay, which I offer for your perusal

I also point out that continuity of spacetime in short distances, as seems to be required by this argument, is not necessarily in conflict with fundamental sort of discreteness, albeit of a different type.



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Constantin Leshan replied on Mar. 15, 2011 @ 16:32 GMT
Dear Moshe,

You write: ''you correctly identify a connection between causality and continuity''.

It is a wrong statement, I can show that causality holds even if the Universe is discontinuous.

Durham has the same error: ''This idea simply formalizes the somewhat intuitive notion that causality is somehow related to continuity. If spacetime is discontinuous, how do we know that...

view entire post

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Moshe replied on Mar. 16, 2011 @ 01:06 GMT
I’ve written quite a precise and technical argument, based on general consideration of effective quantum field theories, but I think it is based on the same intuition. Certainly there could be loopholes in the argument (I've pointed out some myself), but if you choose a discrete model out of a hat without carefully considering the question of Lorentz invariance (and hence causality), chances are that it is either inconsistent or in violations of known facts about the real world, or both.

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Author Ian Durham replied on Mar. 20, 2011 @ 01:12 GMT
Thanks Moshe. I'll print your essay out and add it to the stack I'm taking with me to a conference this week. Cheers!


Eckard Blumschein wrote on Mar. 15, 2011 @ 08:38 GMT
Dear Ian Durham,

Since you did not yet answered my question you give me an excuse for not yet voting for you. Admittedly, I will on the one hand appreciate you winning the contest because many of your opinions are close to mine in contrast to less thoughtful and more speculative candidates.

On the other hand, I do not see your uses of Hebrew language justified. The common language of this contest is American English. Given your essay will be printed in the Scientific American, couldn't it be felt a provocation?

Do not take me wrong. When I criticize aleph_2 this does not have any antisemitic reason. Incidentally, Georg Cantor's mother was a Catholic. Hence Georg was not Jewish.

My recent reply to Georgina in my thread 833 tries to reveal the basic mistake behind the Poincaré/Einstein synchronization. Again, this must not be seen as an attack against a Jew. Nonetheless, I see us obliged to not deny serious consequences. Science must not be based on belief.

I wonder how readily you ignored possible consequences from the finding of WMAP: The geometry of universe seems to be flat. Isn't it a foundational question whether or not a basic theory is possibly wrong? I contempt all those who are trying to deceive themselves. In the long run this may only lead from one paradox to the next one. Wasn't the 20th century a century of abundant paradoxes in mathematics and physics?

I repeat my question concerning deception.



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Author Ian Durham replied on Mar. 20, 2011 @ 01:36 GMT
Regarding the Hebrew, it was immaterial to the essay, was supplied with a translation, and was there to honor my father-in-law who was Jewish. I find the mere fact that you brought this up to be disturbing. It would be one thing if I wrote an important portion of the essay in Hebrew, but all I did was put a portion of the dedication in Hebrew. Why the &$%^ should you care?

I don't understand your comment about WMAP. Unfortunately, I do not remember your question from earlier. I have been very busy and I find the software that runs this forum to be annoying and confusing.

basudeba wrote on Mar. 15, 2011 @ 15:26 GMT
Dear Sir,

Your examples of ontic state may be correct to some extent (subject to variations of its mechanical functioning), but that of epistemic state is not correct for the simple reason that knowledge is not probabilistic. Knowledge is the result of measurement and it is the same as wave-function collapse, which freezes the state. Hence, as Spekkens points out, it is no longer...

view entire post

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Author Ian Durham replied on Mar. 20, 2011 @ 01:21 GMT
I think you have misinterpreted what I meant by an epistemic state. In fact, the examples I gave were taken from one of Rob's' papers. The probabilistic state is a state of knowledge in that it gives us a certain *degree* or *level* of knowledge rather than providing complete knowledge and, as such, may or may not describe reality (i.e. may or may not correspond to an ontic state).

basudeba replied on Mar. 22, 2011 @ 23:25 GMT
Dear Sir,

We are an amateur and it is natural for us to misunderstand. But you have not replied to the points raised by us. The only point you covered in your reply is also an admission that it is a borrowed idea and a restatement of what you had told earlier (and which we had refuted with proof).

Even if you have taken something from another Scientists papers, you should have understood it fully before including it in your essay without citation (which gave the impression that it was your original work.) On the face of it, "a state of knowledge in that it gives us a certain *degree* or *level* of knowledge rather than providing complete knowledge" implies partial knowledge. If we are to divide knowledge as "complete knowledge" and "partial knowledge", that must be the darkest day for science, because "a little knowledge is a dangerous thing".

The word Science was derived from the root "scio", which means knowledge. Thus, your interpretation is not science. There is no place for half knowledge in science. Kindly clarify whether you are writting science or fiction?



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Author Ian Durham replied on Mar. 25, 2011 @ 02:52 GMT
Dear basudeba,

I cited Rob's paper and mentioned his name in relation to the exact point you are accusing me of plagiarizing. Please see PAGE ONE (reference number 2). The fact that you somehow missed this blatantly obvious point makes me wonder if you actually read the paper or merely skimmed it. Before accusing someone of dishonesty or ethically questionable behavior, please double-check your facts.

As for your other points, I'm not entirely sure I really understand what you are trying to address.


Alan Lowey wrote on Mar. 15, 2011 @ 17:23 GMT
Hi Ian,

I've replied to your response earlier about Newton's law and Coulomb's law being incompatible for a unification of the forces. Hope you can respond in time.

Best wishes,


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Alan Lowey replied on Mar. 15, 2011 @ 17:33 GMT
I've re-iterated the reply here because I believe it to be so philosophically profound (rightly or wrongly):

"Okay, that's a good point about the similarity with electrostatics, which I've just thought about a bit more. The difference is that Coulombs law assumes "charged" particles, so that they come in two opposite types. Electric charge is a physical property of matter which causes it to experience a force when near other electrically charged matter. The way these two types interact hasn't been modelled by mechnical means, just like gravity itself. Why do like charges attract and opposites repell? The mechanism is an enigma.

If a 'fabric' of spacetime is visualised as the 'mechanism' of gravity, then this fabric is uniform and symmetrical. It therefore can't be the cause of the elctrostatic forces. His equation therefore negates gravity as being behind the eletrostatic force. It therefore renders the unification of all the forces an impossiblity. Therefore his equation must be wrong imo."

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Alan Lowey replied on Mar. 15, 2011 @ 17:45 GMT
lol, edit: I should have said opposites attract and like charges repell. (school was a long time ago)

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Author Ian Durham replied on Mar. 20, 2011 @ 01:17 GMT
Right, I see what you're saying here. I do think there are many unanswered issues here. I'll have to think a bit more about this.

basudeba wrote on Mar. 16, 2011 @ 05:07 GMT
Dear Sir,

We were following your views on gravity and Coulomb's law. Here is our comment on that.

Before we discuss whether the force we were referring to was gravity, we will like to discuss something about force itself. A force is experienced only in a field (we call it rayi). Thus, it is a conjugate of the field. If something is placed in a field, it experiences something else....

view entire post

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basudeba wrote on Mar. 20, 2011 @ 01:54 GMT
Dear Sir,

Further to our comments above, we will like to add the following.

In Coulomb’s law, F = k Q1 x Q2 /d^2. In a charge neutral object, either Q1 or Q2 will be zero reducing the whole equation to zero. This implies that no interaction is possible between a charged object and a charge neutral object. But this is contrary to experience. Hence the format of Coulomb’s law is wrong.

When we said “positive + positive = explosive”, what we meant was the fusion reaction tat leads to unleashing of huge amounts of energy. Its opposite is also true, but since it is reduction, there is less energy release.

Positive + negative (total interaction) = internally creative (increased atomic number.) This means that if one proton and one electron is added to the atom, the atomic number goes up.

Positive + negative (partial interaction) = externally creative (becomes an ion.) This means that if one proton or one electron is added to the atom, the atom becomes ionic.

Negative + negative = no reaction. What actually it means that though there will be no reaction between the two negatively charged particles; they will appear to repel each other as their nature is confinement. Like two pots that confine water cannot occupy the same place and if one is placed near another with some areas overlapping, then both repel each other. This is shown in the “Wheeler’s Aharonov–Bohm experiment”.



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Alan Lowey wrote on Mar. 26, 2011 @ 10:36 GMT
Hello Ian,

I have another bugging question for you. I'm 100% convinced that this proposed 'inclination hypothesis' will be 100x more enlightening than the Archimedes screw model for the graviton/anti-graviton. It's a real eye-opener this one.

The precession of Mercury can be explained in the same way that the 100,000 year glacial cycle can be explained by the inclination hypothesis that has reduced tide raising forces with increased inclination. The reduced tides lowers the distribution of warm equatorial waters to the poles, which induces glaciation in the high latitudes. The combination of these two papers Spectrum of 100-kyr glacial cycle: Orbital inclination, not eccentricity and The 1,800-year oceanic tidal cycle: A possible cause of rapid climate change can be used to reconcile the 1,800 year cycle to the 1,470 year cycle seen in physical data Timing of Abrupt Climate Change: A Precise Clock.

I've scanned a quick doodle from last night which shows how the planet Mercury, due to it's high eccentricity, has very different distances above and below the orbital plane when nearing the planet and when furthest away. This means that the tide raising forces will be very different from one half of it's inclination orbit compared to the other half, despite it only having an inclination angle of around 6 degrees. This difference in gravitational forces from the calculated Newtonian forces is the reason for the discrepancy of it's orbital precession. I need to do the calcs, I know.

This proposed increase in gravitational attraction on the rotational plane of a celestial body has a surprising number of possible examples. This article on the Pan and Atlas moons of Saturn mentions the problem of their formation from ring debris alone, it simply wouldn't happen under the gravity laws. They say that a gravitational 'seed' would be needed which is exactly the same conclusion that the Harvard professors came to when analysing their 360 mile wide innermost core of the Earth Earth's New Center May Be The Seed Of Our Planet's Formation.

Kind regards,


attachments: Doodle.jpg

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Author Yuri Danoyan+ wrote on Mar. 30, 2011 @ 12:14 GMT

I wonder why you did not notice or do not want to notice the radical view that an independent investigator.Remember this name: name,Friedwardt Winterberg


Yuri Danoyan

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Alan Lowey wrote on Mar. 30, 2011 @ 16:53 GMT
Thanks Yuri!

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Alan Lowey wrote on Mar. 31, 2011 @ 10:28 GMT
I've taken the liberty of scanning Professor Taylor's new book where he talks about the current concensus opinion on the cause of the 100,000 year ice age cycle. It's a brillint summary of the situation as it stands. See attached and also attached to the next post.


attachments: 2_Dance_Of_Air__Sea1.jpg, 2_Dance_Of_Air__Sea2.jpg

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Alan Lowey wrote on Mar. 31, 2011 @ 10:29 GMT
Here's the next two pages..

attachments: 2_Dance_Of_Air__Sea3.jpg, 2_Dance_Of_Air__Sea.jpg

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Author Yuri Danoyan+ wrote on Apr. 24, 2011 @ 19:50 GMT
It seems to me very interesting


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Georgina Parry wrote on Jun. 6, 2011 @ 10:58 GMT
Dear Ian,

Congratulations on being a prize winner. Well done. You answered the question in an interesting, enjoyable and relevant way and gave consideration to some issues that I also think are very important. Thank you too for taking the time to participate on your essay discussion thread. I did appreciate your reply.

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Tony Way wrote on Jun. 14, 2011 @ 01:06 GMT
You argue, persuasively to my mind, that our epistemic knowledge of reality is necessarily discrete because of the impossibility of measuring reality instantaneously (or something like that). But you mention, almost in passing, that our epistemic knowledge of reality requires the exchange of information by photons. Could I not also argue that the requirement to use photons to acquire knowledge of reality necessarily makes epistemic knowledge discrete? Imagining myself as an elemental entity, my knowledge of any other entity is acquired only by one photon interacting with me at one instant of time and thereby transmitting to me information about the state of one other entity at one instant of past time with which it has had a single interaction. Thus, "I" acquire information discretely about the discrete state of one "other". If this is a fair description of the process of acquiring epistemic knowledge, then with only one simple assumption, the Heisenberg Uncertainty may become understandable.

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Author Ian Durham replied on Sep. 3, 2011 @ 20:09 GMT
That's interesting. Hmmm. Well, we just spent 8 days discussing time at the FQXi conference, though, so we'd have to be more clear about what we mean by "instants of time" (as well as what we mean by an interaction, which my essay from last year touched on).

Sridattadev wrote on Aug. 10, 2011 @ 15:45 GMT
Dear Dr. Ian,

The simple mathematical truth zer0= i = infinity can be deduced as follows as well.

If 0 x 0 = 0 is true, then 0 / 0 = 0 is also true

If 0 x 1 = 0 is true, then 0 / 0 = 1 is also true

If 0 x 2 = 0 is true, then 0 / 0 = 2 is also true

If 0 x i = 0 is true, then 0 / 0 = i is also true

If 0 x ~ = 0 is true, then 0 / 0 = ~ is also true

It seems that mathematics, the universal language, is also pointing to the absolute truth that 0 = 1 = 2 = i = ~, where "i" can be any number from zero to infinity. We have been looking at only first half of the if true statements in the relative world. As we can see it is not complete with out the then true statements whic are equally true. As all numbers are equal mathematically, so is all creation equal "absolutely".

This proves that 0 = i = ~ or in words "absolutely" nothing = "relatively" everything or everything is absolutely equal. Singularity is not only relative infinity but also absolute equality. There is only one singularity or infinity in the relativistic universe and there is only singularity or equality in the absolute universe and we are all in it.



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