Dear Amigos Armin,

"...the reason I accept the special theory of relativity is that I find the totality of evidence compelling"

Someone develops a theory and rests the validity of the theory firmly on the evidence and postulate that optical phenomena ARE NOT influenced by the motion of the earth (equivalently observer, receptor or detector), but soon after evidence emerges that optical phenomena CAN BE influenced by the motion of the earth (pulsar timing measurements, GPS, lunar laser ranging, etc) and receptor (Sagnac's 1913 experiment) and given the express proviso stated ab initio by the theory's developer, that 'this totality of the evidence' contrary to the proviso would have no bearing on the validity of the theory would surprise the author himself.

"I gave the derivation of the relativistic doppler shift in frequency earlier"

Yes, you did. I don't fault the derivation. Note that Roemer didn't use frequency measurement or Doppler shift to calculate the first value for light velocity.

"the central lesson of special relativity is *there is no absolute frame*."

There seems now to be possible evidence that the frame in which the cosmic microwave background radiation is mostly isotropic represents an absolute rest frame. Our absolute velocity in this frame is about 371km/s.

Probably, we take a break for now to reconvene later. Read my essay and criticize when you can spare the time.

Thanks,

Akinbo

I see Ken Wharton, an FQXi member made a comment on your photon existence paradox on his forum (Ken Wharton replied on Mar. 31, 2015 @ 03:44 GMT)

Thank you for letting me know, I will leave a comment there shortly. Also, please note: My last name is Nikkhah Shirazi, not Shirazi.

Thanks,

Armin

Hi Armin,

I was just thinking about HAL in 2001? Am I the only one who thinks maybe HAL could be looked at in a positive light? After all, here's this super-intelligent entity on this mission and the humanly-fallible Dave is just going to jeopardize it because he is getting a little too paranoid. Dave's fighting evolution! Anyway...

You wrote that even though you could enumerate axiom systems, you would still need creativity to pick out the right axiom system, so enumerating them doesn't really get you too far because you still need imagination to pick from the infinite number of them. But if the axioms are enumerable, couldn't a computer just systematically go through them, computing say the first 1000 "theorems" of each. If the goal of physics is to compress complex physical phenomenon into simple equations, then if you were to take this idea to the extreme, could you just systematically (without imagination) just looking through the space of all simple axiom systems (with simple updating rules/rules of inference) with some romantic hope that our universe might happen to be describable with a very simple system/program? Do you think that this is a worthwhile endeavor or just some pipe-dream? If you perceive it to be a pipe-dream, is that because you think the universe is sufficiently complex (from a Kolmogorov-Chaitin complexity perspective) that it would take too long to come across the rules under this brute force approach? Do you think the halting problem plays a role in making this kind of approach intractable?

With regards to the axiom of choice, you talk about choosing an uncomputable real number to any desired level of precision, but this makes whatever number you provide rather ambiguous, not to mention a computable number. How do I know that the truncated version of the one you provided is some particular noncomputable real and not another? How do you even know which one you had in mind that you are approximating? I think this relates to your thoughts about actuality and potentiality, and I agree that this idea isn't addressed well enough in physics. It may also relate to time and the reversibility of equations. If equations didn't have closed-formed solutions that harnessed infinities and we saw things as a computation do you think the concept of time would stand out more in the equations/programs? Could time just be where you are in the calculation?

You said, "I believe devising any sort of algorithm from scratch for a particular purpose requires at least a modicum of imagination." Do you think nature, evolution, or the universe is creating this way, with some high-level purpose in mind? Or could the purpose just be something very simple, like "I want to see what becomes of this pseudorandom process that I am generating bit by bit"? Or "What happens if I replace every 0 in a bit string with a 1 and every 1 with a 10, and then repeat this process on the next string that is generated?"? (I would actually remove the anthropomorphism out of those questions to make them just a calculation) In the case of you flipping a coin, we could say that the outcome has already been logically determined, but we just don't know what the outcome is because the universe hasn't done the computation yet. In certain situations the calculation might be compressible, and these would be the cases in which we can make precise predictions. In the cases where the computation the universe is doing isn't compressible, we would resort to probabilities.

I always find informal discussions the easiest way to try to learn a new topic, so maybe some of Chaitin's youtube lectures might interest you if the Wikipedia page didn't offer too much insight on his Omega constant.

Sorry, I'm probably getting away from your more practical approach to physics(and a little off topic), but since this forum is for Foundational Questions I think I'm in the clear. There are other things in your response that are probably worthy of having a discussion around, but my reply is already too long.

Jon

Dear Sir, This essay started out as interesting but then went in a direction I don't follow. I was entirely puzzled by your failure to define inconsistency. I am more concerned by why physicists claim Einstein relativity is consistent mathematics when people knowing only high school math can see it is inconsistent. It seems anyone with a high school math background can see that relativity is mathematically inconsistent while experts can not recognize this fact at all and insist that the theory is not inconsistent. It obviously is false and wrong but not inconsistent? That is a puzzle, and so I think inconsistency is not a sufficient criterion. I think you guys need to think out the fundamentals better before you construct your theories.

    Dear Harry,

    Thank you for your comments. I am a bit surprised about your comments about special relativity because it was barely mentioned in my paper. In fact, the main result, the theorem on page 8 is expressly in the non-relativistic limit. You are correct that I did not define inconsistency; the reason was that I thought it would be reasonable to expect the reader to know this. If the reader doesn't know what an inconsistency is, then there is little hope they will understand the rest of my essay.

    "It seems anyone with a high school math background can see that relativity is mathematically inconsistent while experts can not recognize this fact at all and insist that the theory is not inconsistent.

    Well, why do you think it seems that way? Could it be because there is a grand conspiracy among physicists, mathematicians and nuclear engineers worldwide to impose on the rest an obviously false theory, presumably fudging all the technological innovations and experiments based on it, like nuclear reactors, atomic bombs, astrophysical observations, particle accelerators, GPS devices, not to mention all the physics labs so that each new generation of physicists gets brainwashed to join the grand conspiracy? Or could it be because if someone with a high school background misunderstands relativity and, in best Dunning-Kruger form, blames the theory and everyone who uses it for his misunderstanding?

    I think I have a good idea which one you think is more likely.

    Best,

    Armin

    Hi Jon,

    "Am I the only one who thinks maybe HAL could be looked at in a positive light?"

    No, I'm sure all the peers of HAL would also look at his actions in a positive light, presumably because they would be sufficiently advanced to have something like empathy for HAL, but the not the astronauts.

    "But if the axioms are enumerable, couldn't a computer just systematically go through them, computing say the first 1000 "theorems" of each. If the goal of physics is to compress complex physical phenomenon into simple equations, then if you were to take this idea to the extreme, could you just systematically (without imagination) just looking through the space of all simple axiom systems (with simple updating rules/rules of inference) with some romantic hope that our universe might happen to be describable with a very simple system/program? Do you think that this is a worthwhile endeavor or just some pipe-dream?"

    I think being able to answer these questions intelligently requires a background in both complexity theory and in computability theory, neither of which I posses, unfortunately. I would like to clarify that by using imagination in this sort of situation I had in mind something like the following: You pick some axiom system and think about what requirements it fails to satisfy, then use your imagination to add/subtract or modify the axioms and now you can take advantage of the ability to have computer system check the thousands of theorems that follow from the tweaked system.

    "If equations didn't have closed-formed solutions that harnessed infinities and we saw things as a computation do you think the concept of time would stand out more in the equations/programs? Could time just be where you are in the calculation?"

    I have a hard time understanding what it means for something physical to be a computation, so I am afraid I can't really answer that question. However, I suspect that computation conceptualized broadly in this way pre-supposes the existence of time, and if that it is true, then you cannot just say that time is defined by where you are in the calculation on risk of circularity.

    "Do you think nature, evolution, or the universe is creating this way, with some high-level purpose in mind?"

    No, I do not think there is such a high-level purpose. In my view, whatever adaptions you see are the result of environmental constraints, which though obeying regular patterns, do not serve to advance any particular purpose.

    "How do I know that the truncated version of the one you provided is some particular noncomputable real and not another? How do you even know which one you had in mind that you are approximating?"

    I would say that if you have to ask these questions, then you have not yet approximated the number to sufficient precision and need to approximate further. It seems doubtful to me that you would run into a realistic situation in which you need an arbitrary uncomputable number to infinite precision. What would you do with it? Any manipulation involving it to infinite precision is also going to be uncomputable, unless it happens to be expressible in simple form like e and pi.

    "In the case of you flipping a coin, we could say that the outcome has already been logically determined, but we just don't know what the outcome is because the universe hasn't done the computation yet. In certain situations the calculation might be compressible, and these would be the cases in which we can make precise predictions. In the cases where the computation the universe is doing isn't compressible, we would resort to probabilities."

    Again, because I have a hard time wrapping my mind around the idea of physical processes as computations, I'm afraid I can't say much. But if what you are saying is right, it seems that this would imply a novel interpretation of probability.

    "...maybe some of Chaitin's youtube lectures might interest you if the Wikipedia page didn't offer too much insight on his Omega constant."

    Thank you for the suggestion, I'll look into it.

    I hope I was able to at least answer some of your questions, though I felt that they were somewhat outside of what I consider to be my area of knowledge.

    Best,

    Armin

    Harry,

    To form an all encompassing opinion, and to know where any conspiracy could be coming from, especially concerning GPS devices and relativity, please find time to read about Ronald Ray Hatch - "born in Freedom, Oklahoma, now of Wilmington, California, received his Bachelor of Science degree in physics and math in 1962 from Seattle Pacific University. He worked at Johns Hopkins Applied Physics Lab, Boeing and Magnavox as Principle Scientist, before becoming a Global Positioning System (GPS) consultant. In 1994 he joined Jim Litton, K. T. Woo, and Jalal Alisobhani in starting what is now NavCom Technology, Inc. He has served a number of roles within the Institute of Navigation (ION), including Chair of the Satellite Division, President and Fellow. Hatch received the Johannes Kepler Award from the Satellite Division and the Colonel Thomas Thurlow Award from the ION. He has been awarded twelve patents either as inventor or co-inventor, most of which relate to GPS, about which he is one of the world's premier specialists. He is well known for his work in navigation and surveying via satellite.

    In a pair of articles, Hatch shows how GPS data provides evidence against, not for, both special and general relativity: "Relativity and GPS," parts I and II, Galilean Electrodynamics, V6, N3 (1995), pp. 51-57; and V6, N4 (1995), pp. 73-78. In his 1992 book, Escape From Einstein, Hatch presents data contradicting the special theory of relativity, and promotes a Lorentzian alternative described as an ether gauge theory" and other details here.

    In particular, read this paper, also listed in the linked website.

    By any stretch of imagination going by his Bio above, Ron Hatch cannot be said to be someone with a high school background who misunderstands relativity. Why, my friend Armin would feel such a person should be disregarded along with other references like Prof. Herbert Dingle is what looks more like conspiracy, probably unintentional or well meaning, I can't really say.

    All the same, regards to you Harry and regards to my Amigos, Armin as well,

    Akinbo

    Armin,

    Very solid essay worthy of scientific publication. Two comments on ontology.

    1- When proven, the (empirical) expectation value can be replaced by its (ontological) equivalent or existence. The probability of finding a particle in one place according to the equation is the same as saying that the equation describes where the particle is more likely to be or exist.

    2- Actuality is created when probability is constrained, squeezed. When the infinity edges of the normal distribution are eliminated by constraint, then the distribution becomes a box with quantized modes of existence. Similarly, when we measure a free parameter on a particle, the constraint of measurement creates a temporary quantization of the values obtained for that parameter.

    all the bests,

    Marcel,

      Dear Akinbo,

      "To form an all encompassing opinion, and to know where any conspiracy could be coming from..."

      Are you seriously considering the possibility of such a worldwide conspiracy?!?

      All those physicists working on the Manhattan project generations before GPS must have done an outstanding job not only maintaining the secrecy of the conspiracy but of giving terrifying fake evidence that the theory works.

      Or wait...maybe you think Hiroshima and Nagasaki was not A-bombed, either?

      My point is that if your really believe such things, then it seems that such beliefs, in order to be consistent with other beliefs, entail beliefs which become ever more absurd. And citing one person in one particular field is not going to help much.

      I see that Ronald Hatch has written a lot of critical material on SR. I find it curious that, at least upon a cursory search, I was not able to find any critique of his work except for one particular blog.

      "By any stretch of imagination going by his Bio above, Ron Hatch cannot be said to be someone with a high school background who misunderstands relativity. Why, my friend Armin would feel such a person should be disregarded along with other references like Prof. Herbert Dingle is what looks more like conspiracy, probably unintentional or well meaning, I can't really say."

      This is called a straw-man, a fallacy which only further undermines your credibility. Anyone reading my comment knows that my "high school background" comment was a reference to Harry's claim that "anyone with a high school math background can see that relativity is mathematically inconsistent".

      It is quite obvious to me that your reason for holding your physics beliefs is not because you are guided by evidence to your beliefs, but because you have already decided what you want to believe. This leads you to grasp every straw you can find, regardless of its merits, to support the position which you already had decided beforehand you wanted to hold. This became especially clear with the articles you cited on the purported invalidity of the Heisenberg uncertainty principle, all of which, except for the one in which the author himself suffered a misunderstanding, contradicted your position.

      I have not investigated Hatch and Dingle's works, and so I cannot judge their merits. However, based on my understanding of special relativity and my own research in it, I think if their findings were so revolutionary, we would have heard of it by now. Until that happens, it is much more reasonable to work with the theory for which there are mountains of evidence.

      Best,

      Armin

      Dear Marcel,

      Thank you for your comments. As for scientific publication, yes that is a goal, but I omitted a lot of details that still need to be filled in.

      Best wishes,

      Armin

      Dearly Beloved Armin,

      Thanks for your all encompassing essay.It is necessarily didactic;a great contribution.

      I am especially thrilled over your assertion of mathematics being potentially effective in modelling reality.And even more so with your projection of the human mind as the facilitator of the nexus between physics and mathematics.

      Keep on flourishing,

      Lloyd Tamarapreye Okoko.

        Dear Lloyd,

        Thank you for your kind remarks.

        Yes, as you can see, most essays here try to explain the relationship between physics and mathematics solely in terms of those fields (and perhaps some philosophy). But it is easy to ignore the fact that we do both activities in our minds, and therefore its role on the connection is less likely to be appreciated. My essay was in part an effort to bring attention to an important factor that might be easily overlooked.

        Best wishes,

        Armin

        Thanks for the response, Armin.

        Although I was talking about the universe as a classical computer, Seth Lloyd has a view of the universe being a quantum computer, which may be a little more appealing to you. Stephen Wolfram, Ed Fredkin, Jurgen Schmidhuber, and some other scientists talk about the universe being a (classical) computation, but these ideas aren't quite as accepted.

        With regard to the Axiom of Choice being an issue with infinite precision real numbers, I was talking about it from a purely mathematical/theoretical perspective, so I wouldn't want to defend that point of view for a "realistic situation" yet. From a purely theoretical perspective, no matter how far an uncomputable real number is specified, it will always be ambiguous, since there are an infinite number of real numbers that start with the specified sequence of numbers, and there is no way to refer to or conceive of one specific uncomputable real since they have an infinite amount of information that can't be compressed into a formula like those that represent/generate pi or e. If you don't think this point is relevant when it comes to physics and your ideas regarding ZFCD, then that's probably a slightly different discussion.

        I don't think computation broadly defined pre-supposes time, although I do think it would imply a sequential relationship...which I think is slightly different.

        That "novel interpretation of probability" was what I was trying emphasize in one part of my essay when I discussed the prime number theorem. The PNT shows how we can look at the prime numbers from a probabalistic perspective even though we know the prime numbers are not randomly generated; they are only pseudorandom. But if given a large list of numbers that are all a million digits long, it would be a lot more practical to estimate what percentage of them are prime numbers using the prime number theorem than it would be to know exactly how many of them are prime by checking each one of them for sure. (by checking to see if any primes up to the number's square root divide evenly into it) So from this mathematical example, I tried to raise the question that maybe some of the statistical laws of physics are actually modeling pseudorandom processes, as opposed to truly random processes. If the computation that the universe was doing was too complex, a statistical approach analogous to the PNT might be are only practical approach to making predictions.

        I hope some of this made sense.

        Jon

        Dear Jon,

        "Seth Lloyd has a view of the universe being a quantum computer, ..."

        First, whenever you have someone proclaiming that the universe "is" a giant version of some contemporary piece of technology, you should always take that with (more than) a grain of salt . As you may know, a couple centuries ago, during the enlightenment, people proclaimed the universe to be a giant clock, and who knows what people will proclaim the universe is in a couple centuries. To me, the universe is just the universe.

        I watched the short video and found Seth LLoyd to be a bit fast and loose with words (For example, he claimed that we already have quantum computers, but I am more skeptical (My view is informed by Scott Aaronson's blog posts on the subject matter).

        "...which may be a little more appealing to you..."

        No, you know (I think) enough about my ideas to understand that in my view our contemporary conception of the universe, which equates it with spacetime, is too undifferentiated.

        If you want to talk just about spacetime, then I definitely disagree with him, because I conceive of quantum theory (well QM, QED, and EW interactions) as the physics of spacetime objects emerging out of areatime. If you already have spacetime to begin with (which is the reasonable interpretation of his use of "universe"), then the appropriate theory is Einstein's General Relativity, not quantum theory.

        "Stephen Wolfram, Ed Fredkin, Jurgen Schmidhuber, and some other scientists talk about the universe being a (classical) computation, but these ideas aren't quite as accepted."

        Do they give concrete examples for how some physical process can be reframed as a computation?

        "From a purely theoretical perspective, no matter how far an uncomputable real number is specified, it will always be ambiguous, since there are an infinite number of real numbers that start with the specified sequence of numbers, and there is no way to refer to or conceive of one specific uncomputable real since they have an infinite amount of information that can't be compressed into a formula like those that represent/generate pi or e. If you don't think this point is relevant when it comes to physics and your ideas regarding ZFCD, then that's probably a slightly different discussion."

        Yes, I interpreted you previous question as a physicist, from the point of view of mathematics I agree. Yes, I am uncertain about the relevance of AC. The only reason at this point that I chose ZFCD vs. ZFD (not to be confused with Zermelo-Fraenkel with axiom of Determinacy) is that ZFC is the standard set theory. This does not mean that subtle deep connections may not be there, in fact, more likely than not, I think there may well be.

        "I don't think computation broadly defined pre-supposes time, although I do think it would imply a sequential relationship...which I think is slightly different."

        You may be right. As mentioned, the notion of a physical process as a computation is not intuitive to me, so my intuitions are more likely to lead me astray than in other areas.

        "I tried to raise the question that maybe some of the statistical laws of physics are actually modeling pseudorandom processes, as opposed to truly random processes. If the computation that the universe was doing was too complex, a statistical approach analogous to the PNT might be are only practical approach to making predictions. "

        Can you tell me which statistical laws of physics you had in mind?

        "I hope some of this made sense."

        Rest assured that you did:)

        Best,

        Armin

        Dear Armin,

        Your description of modal logic is perhaps too brief, so a little research was in order before I concluded that modal logic is a solid foundation for your imaginative theory. I am always a bit amazed at the way a versatile mathematical concept can develop from a small number of simple assumptions.

        The Peres-Mermin magic square provides an effective analogy, and another interesting subject to research. The grid layout and aim of the game conjure up something like quantum Sudoku.

        Anyway, I just wanted to say it is good to see your progress.

        Best regards,

        Colin

          Dear Armin,

          As I said I would on my essay's forum, I read your essay. I found your introduction very well written: you nicely describe the freedom that we have to choose our mathematical axioms, and the human imagination it takes to "discover" or "stumble upon" effective mathematical models of reality.

          Your attempt to formally incorporate in mathematics the distinction between potentiality and actuality is very ambitious. My own view on the subject is that what distinguishes an "actual" (or "physical") mathematical structure from a "regular" (or "potential") one is whether it contains sub-structures that have the correct properties to be "self-aware" and can "feel" the actuality of the mathematical structure "from the inside". Not having enough of a background in your field of research, I have to confess I could not follow your presentation in detail, but it certainly seems interesting! I hope you'll have the chance to continue your research and look forward to what it can teach us about what it means for a mathematical structure to be "actual".

          Good luck!

          Marc

            Dear Colin,

            Well, thank you for going through the trouble of researching modal logic in order to understand my theory better. I believe that one of the ways in which the mathematics of the future will be different from the mathematics of today is that it will have the power to formally express nuances that today most mathematicians would perhaps not even dream of expressing.

            To reiterate a slightly modified analogy to the one I gave in my response to Vladimir Tamari's post, in my view the era of today's mathematics is like the era of black and white movies, and tomorrow's will be, l believe, like that of color films.

            As for the subject of contextuality (and pseudo-nonlocality), these are meant merely as intuition building analogies. The hard work of matching the ideas to the known formalism still awaits. I believe the key is for me to understand how the Hilbert space is built up from orthomodular lattices, a subject I plan on learning this summer. Then I can hopefully take the step of showing how the absence of any "beables" in between measurements implies both.

            "Anyway, I just wanted to say it is good to see your progress."

            Thank you, it is going slower than I hoped, but it is going.

            Best wishes,

            Armin

            Dear Mark,

            Thank you for your comments.

            "My own view on the subject is that what distinguishes an "actual" (or "physical") mathematical structure from a "regular" (or "potential") one is whether it contains sub-structures that have the correct properties to be "self-aware" and can "feel" the actuality of the mathematical structure "from the inside"."

            I'm afraid I do not quite follow. Can you give an example? Or, how would the thrown coin toss vs. the unthrown one differ according to your view?

            "Not having enough of a background in your field of research, I have to confess I could not follow your presentation in detail,"

            Well, that's ok because the details have not yet all be worked out, so if you were able to do that, you would have done my work for me;-)

            "I hope you'll have the chance to continue your research and look forward to what it can teach us about what it means for a mathematical structure to be "actual"."

            Well actually I don't think my work will be able to say anything about what it means for a mathematical structure to be "actual" because, remember from page 2 of my essay, my work is just concerned with mathematics as a representation of objects which in the real world exist as actualities or potentialities.

            Thanks again, sorry I did not get any challenges from you:(

            Best,

            Armin

            Dear Armin,

            You mentioned in your recent reply on my page that it is very hard to make comments that really change the point of view of your interlocutor, and I agree that it is so. I think it's even harder when your interlocutor has a set of basic assumptions about the fundamental nature of things and their relative importance that is completely different from yours.

            For you (correct me if I'm wrong), the "real world" is the observable physical universe and mathematics is a way for us humans to represent it: naturally, you find it is most important to study how mathematics does this, and hopefully improve the definition of mathematics to help it do its job better.

            For me, what is most important is to find a satisfying answer to the question "Why is there something?". It seems to me that the only answer that does not create more questions has to be something like "all abstract structures simply ARE, and one of these IS our observable universe". I believe all of mathematics (being abstract) simply IS, but it doesn't mean of course that we, human mathematicians or physicists, automatically have access to it all. It is by our hard work that we explore the "space" of all mathematics and "come back" with useful "nuggets" that can improve our understanding of our observable physical universe. So I find that research endeavors such as yours are worthwhile. I wish I could challenge some of your specific points (in order for you to improve your ideas), but I honestly can't follow your arguments in enough detail (being too unfamiliar with the subject) to be of any help here.

            You asked me to clarify my view of actuality vs potentiality, ideally with an example. I will take Tegmark's example of a dodecahedron: it is a mathematical structure, but it is not complex enough to be a physical universe --- it just exists abstractly in the space of all mathematical structures. Perhaps you would say that something that only "exists abstractly" is a "potentiality" --- fine, that is a valid way to define potentiality.

            The way I see things, my mind also is a mathematical structure, but I know from direct experience that it does not merely have an abstract existence. It has (at least) a "mental" existence, so we could say it is an "actuality". Moreover, I perceive myself as a physical being in a physical universe: this "physical universe" is also a mathematical structure, but it is precisely because my conscious states are part of it that it makes sense to say that it exists as a physical "actuality".

            As you can see, I'm looking at the philosophical roots of the concept of actuality vs potentiality, while you seem to take these concepts for granted. In your essay, you say that "Everyone understands at an intuitive level that existence as a potentiality is distinct from existence as an actuality." I don't think it's that simple! What is potential vs what is actual is purely contextual: from the point of view of the year 2014, the year 2015 is potential, but from the point of view of the year 2016, it is actual. Ultimately, I don't think that the distinction between actual and potential is very useful when you try to understand reality at the most fundamental level. But of course, since I believe that this most fundamental level is a spaceless and timeless abstract realm where everything simply is, that I hold such a view should not be too surprising.

            Thank you for the opportunity to have this discussion. Beyond ratings and prizes, it is the main reason why I participate in these FQXi contests!

            All the best,

            Marc