Essay Abstract

We argue in detail why spacetime geometry (or pregeomtry) is most likely analog. While there are many negative arguments against discreteness and all positive reasons appear to be severely misguided, the continuum is necessitated by the principle of locality. I give a detailed expose why locality is our best guiding principle in a search for unified laws of nature.

Author Bio

The author did a bachelor in physics and mathematics, as well as a masters in physics at the university of Leuven. Later on, he did a PhD in theoretical physics at the university of Gent followed by a postdoc position in Utrecht. Since then, he has held several postitions in the private/public sector.

Download Essay PDF File

8 days later
  • [deleted]

Hello Johan,

It was interesting to read your paper to try figure out your reasoning and find motivation for your starting point of the I think I've come to conclude that I don't share the general guide you use to construct your theory, but I do share several notes of yours.

"but what is never said is that quantum eld theory is a theory of hidden variables. Indeed, reality consists here in Fock space, an ill de ned Hamiltonian"

I understand what you mean and I fully agree.

But while I think you take this to excuse more of the same, I disagree as I reject it and suggest that no such "hidden variables" are allowed. These "frozen" variables do carry information, and I think disrespecting those are the missing link to understand the origin and unification of interactions.

About the continuum you pose the question such as "is there a reason to abandon the continuum model". Ie you are already having that as a prior conception, giving it more inertia.

"discretization sacri es many things as we have just seen and it hasn't rewarded anybody in a substantial way until now."

It's true that discretized techniques (beyond those that are just approximated solving method; these don't count here) seem underdeveloped. But I there are many deep arguments, that are rational and in line with the scientific ideals, that suggest that it's not the discretized models that approximate analog reality, but the other way around.

The most clear perspective IMO is if you consider the problem of quantifying and constructing measures on evidence. Basically counting evidence, and use it to form rational expectations. Now, how do you construct measures of entropy by counting microstates if the set is uncountable? Then you start considering limits and comparing convergence rates, but then the complexity disrepsect the finite information bound if you believe that a finite system only encodes and proces finite information. This is the simplest argument I find.

This is why I unfortunately loose track of the rest of your logic here, as I fail to accept the initial premises that makes up the first matemathical entities in your reconstruction.

I wish you luck with your work though! Obviousl none of my arguments means anthing to your results, it just means that - until it's mature and make explicit predictions to be tested, all there is to judged is the rationales for your construction - and unfortunately I don't find your logic of reasoning to answer all the traits I expect from such.

What I do like is that you do acknowledge several "issues" and try to find some creative solutions! I hoped that your reasoning would converged to mine, but perhaps the mismatch is due to my ignorance. There are several other lines of reasoning in your paper(and book) that I do share, that are deviating from normal thinking but the overall direction is too much structural realism for my taste to the extent that I interpret your spirit correct.

/Fredrik

    Dear Fra,

    The hidden variable perspective in QFT is in my opinion a deep consequence of relativity. Indeed, relativity forces the hidden variable perspective upon us (for example, the notion of a particle becomes contextual), something which Einstein deeply realized and is entirely absent in the Eculidean world. Furthermore, you do not seem to realize that classical gravity is a theory of hidden vanables; likewise is classical Maxwell theory. Moreover, all these theories do not even specify at all what is being measured and we certainly do not measure a metric or measure stick.

    Concerning your arguments of information, they are as misleading as all the others I have discussed for several reasons:

    (a) nobody knows what information is, for that you need to know the fundamental atomistic degrees of freedom and go over to a density matrix instead of a state description. Doing this requires already an artificial split between entity and the rest of the universe. But the universe is holistic and identities are emergent, not fundamental at all.

    (b) Nobody says that one needs to be able to measure or know information. While such attitude is certainly minimalistic, it is utterly wrong. For example consciousness is a hidden variable which has no materialistic interpretation.

    (c) There is not reason why local information is finite; actually it should be infinite otherwise you break local Lorentz covariance; a principle which should still be valid in quantum gravity (because it has been tested experimentally on earth).

    In that respect, why would you think that we cannot grasp infinity? For sure, everything we can write in a symbolic language is finite, but there is no good reason to suspect that we cannot create things which require an infinite amount of basic information. For example, writing the figure 1 on the blackboard is such an activity (at least if you consider the number one quantum mechanically).

    Furthermore, you have clearly not read the entire text: I started out by questioning those reasons to abandon the continuum, but I have also offered deep reasons FOR the continuum.

    Concerning the underdevelopment of discrete techniques, this is not a matter of an insufficient number of people working on it, but an inherent limitation of discreteness. Alas, 10 pages do not allow me to explain all this in sufficient detail.

    Kind regards,

    Johan

    • [deleted]

    Dear Johan,

    While I respect your original ideas but I got more confident now that we have quite different ways of reasoning.

    It will not change anything, but maybe the discussion here might invite others to comment!

    > The hidden variable perspective in QFT is in my opinion a deep consequence of > relativity. Indeed, relativity forces the hidden variable perspective upon us

    Although much simpler argument than yours, this REMINDS me of an argument that H Nikolic made in an old paper. I'll try to see if I find it. That was if I remember correctly an attempt to related hidden variable theories with strings, and argue that the extended nature of a particle, follows from the relativistic and realistic view, roughly similar to a string.

    > Furthermore, you do not seem to realize that classical gravity is a theory of > hidden vanables; likewise is classical Maxwell theory. Moreover, all these

    > theories do not even specify at all what is being measured and we certainly

    > do not measure a metric or measure stick.

    I certainly do realize. Again, the diffence is that I think you use this to bring in more of the same; IMO the classical models are not near any "standard". I seek an intrinsic measurement theory.

    > (a) nobody knows what information is, for that you need to know the

    > (b) Nobody says that one needs to be able to measure or know information.

    Except the statements needs to be clarified, I say so. The requirement of inferrability, and that any opinion must be rationally justified in terms of counting evidence, is a basic demand I have on an intrisitic model of inference.

    So I disagree that it's wrong.

    > (c) There is not reason why local information is finite; actually it should

    > be infinite otherwise you break local Lorentz covariance; a principle which

    I have a different understanding of lorentz covariants. Lorentz symmetry is related to 4D spacetime, and in my view this is constructed as an emergent sturcture, and lorentz symmetry is only completely well defined in the continuum apporoximation.

    > In that respect, why would you think that we cannot grasp infinity?

    I can't convince you I think, but it just causes too much problems with representation and processing time. IT seems to me that it would lead the infinite inertia, infinites, cosmological constants that 122 orders of magnitudfe off scale etc.

    I see that you see how discrete problems creates all kinds of problems, I see it the other way around :) And the problems you mention I think can be solved, by allowing symmetries to be emergent and explain in the continuum limit.

    But my kind of discreteness is subjective, not objective. Two observes doesn't necessarily agree about the discreteness.

    > Furthermore, you have clearly not read the entire text: I started out by

    > questioning those reasons to abandon the continuum, but I have also offered

    > deep reasons FOR the continuum.

    I did read it, but like you start with the continuum and look for reaons to abandon it (and conclude there are none), my stances is that of information processingg and rating evidence, in the discrete sense, and I see no convincing arguments that continuum is a more basic starting poitn than discrete ones. Even the real numbers are construced from limits of Q. I just think that the LIMIT is not physical.

    > Concerning the underdevelopment of discrete techniques, this is not a matter > of an insufficient number of people working on it, but an inherent limitation > of discreteness.

    And probably lack of good ideas in the direction :)

    /Fredrik

    Dear Fra,

    An intrinsic measurement theory will contain hidden variables: {}the devil is in the details and you should think it through.

    Furthermore, it is clear that there is no unique rational interference based on available evidence. This will lead to multiple logics, each with their hidden rules and therefore we are in the same situation again.

    Concerning the emergence of local Lorantz covariance. Experimental evidence suggests that no violation of Lorentz covanriance may even happen on scales of 10^{-20} meters. And probably, it will be so for much higher scales too. The problem is that nobody knows how to make this even precise and it are all buzzwords so far.

    You do not seem to have actively worked with discrete structuresz, I have. I can guarantuee you that after 30 years people still cannot free themselves from the continuum. For example, in discrete theories, one should not even use the number Pi, since that one is tied to the continuum. The problem of discretenesz is the lack of locality and this is not merely a cosmetic property you know.

    There are plenty of good ideas regarding discreteness. It is however so that the most natural ones all give the wrong answers ! But some people appear to ignore this fact due to religious reasons.

    Kind regards,

    Johan

    • [deleted]

    Dear Johan,

    > An intrinsic measurement theory will contain hidden variables

    I'm not sure what you mean, I guess it depends on what we mean by hidden variables. The intrinsic measurement theory doesn't exists yet, so I guess you judge your expectation of this.

    But I might guess and the the hidden variables/structures are in my view not hidden ad hoc, they are rather formerly visible but frozen and hidden. So to understand the hidden variables, I think one has to understand the origin of them; which I connect to that part of history that lead to the current, but whose reason is forgotten in the present state.

    > Furthermore, it is clear that there is no unique rational interference based

    > on available evidence. This will lead to multiple logics, each with their

    > hidden rules and therefore we are in the same situation again.

    I agree completely. I acknowledge and aim to handle this. This is why rational inference is not a logical necessity. It's a different inference than deductive reasoning.

    This is why my view only makes sens in an perspective of evolving frameworks, and evolving law; rather than "hidden" realist structure.

    > The problem is that nobody knows how to make this even precise and it are all > buzzwords so far.

    I agree.

    > For example, in discrete theories, one should not even use the number Pi,

    > since that one is tied to the continuum. The problem of discretenesz is the

    > lack of locality and this is not merely a cosmetic property you know.

    Absolutely true. I am not blind for this. I don't pretend to have all answers but one related problem I have is to try to understand fourier theory without the continuum backbone, as this proves to be a key step in defining non-commutative structures. I've come only to partial progress but a key question is how to COUNT distinguishable events. In this respect PI is merely a label for one real number. If PI can be defined and distinguished by a finite process, then it does not matter if PI is real or rational. It's neverheless just one number.

    The problem of real numbers is the view where it takes infinite information to either REPRESENT them, or infinite computing TIME to compute them.

    Any number, that happen to be real but not rational, that can be defined or represented in another way, without infinite information or infinite computing times are non-problematic.

    IF we define "PO" as the quotient between circumfrence and diameter of finite sets, then "PO" is simply a rational number which is then numerically "approximately PI", and it could well be that the the limit of PO when the complecity -> infinity (and thus is PI) simply doesn't play a role in physics. Because PO will be good enough for every practicla purpose.

    In fact every single scientific computation made with computers only use 32,64 or 128 bit representations.

    So the argument for the physical justification of the continuum is not that hard IMO.

    > Experimental evidence suggests that no violation of Lorentz covanriance may

    > even happen on scales of 10^{-20} meters

    There is one important point here that is often ignored. WHERE is this lorentz symmetry inferreD? It's inferred in the extremely compelx environment of a laboratory. This is why the continuum makes sense. So it may well be that there is no way to INFER broken lorentz covariance from this perspective. But this is just a special case, corresponding to a compelte descriptive view.

    Therefor the question of how fundamental lorentz covariance is, needs to analyser how the symmetry is inferred. And to claim it's fundamental one needs to make the inference not only from one perspecive (bigcontext-small subsystem) but also from all perspectives. This touches upon unification of QFT and QG. So I hold my bets on this until I see compelte unification of forces and QG, while saving all these things.

    I hope that some other people will jump in here and add some thoughts.

    /Fredrik

      Surrealism is a form of creativity: it is no accident that Belgium hosts the institutions of the European Union :-) Concerning our politicians ... ah well, too many ego's and internal games; fotunately it doesn't really affect the state of the country so far.

      Cheers,

      Johan

      • [deleted]

      I'm swedish but for me Belgium = Makes best beer in the world (trappist).

      /Fredrik

      So, you should read the draft of my book. Then you will discover that the continuum and local Lorentz covariance pose no problem; the evil reszides in interacting QFT. Sometimes, you should put you philosophical prejudices aside and listen to more convincing and conservative arguments, although judgement is and will always be a subjective game.

      Johan

      • [deleted]

      Hi Fredrik and Johan,

      Yes indeed the beers and the chocolate.

      Hello to sweden ...do you know the Dr Naima Benali.It's a friend.She lives in Sweden.

      :)Dear Johan, it's always the same problem, the stupidities are everywhere.But I am persuaded the country will evolve quietly.

      Best Regards

      Steve

      I am not sure, but it is hard to see how to prevent the current situation from leading to early elections. This will probably even further radicalize the positions ... notice that it is the population which votes very differently. Flanders votes right (left has less than 20%) while Walloons vote mainly left. A partial separation is unavoidable and Walloons should better accept it and make a reasonable proposal for Brussels. Continuing like it is now is impossible.

      • [deleted]

      I am desesperated by my wallon politicians, you are right, but you know the youngs think differently.It's a catastrophe here you know in Hainaut near Bergen for example, and you know why.Always this ps which blocks all creations. I am angry as you.It's not possible to continue in these conditions.The ps is the problem here , and of course as it is very small, you imagine the mind of enterprize for the creation of jobs.A pure ironic catastrophe.You know dear Johan, we have all the same hopes and here it's difficult.If the country is quietlty separated, the walloons shall be a small country of 4 millions.Many here aren't against you know.but how , that is the question.It exists stupid persons everywhere in all countries and religions or cultures unfortunally.In all case it's time to find solutions.It's tiring all that.

      How old are you dear Johan?

      don't forget that never the majority of young walloons votes left because we know who are our corrupted politicians.it's important this point of vue Johan. But you are right , it seems that a quiet and reasonable separtion seems logic.

      It will be easier.In fact it's a quiet harmony between left and right which is essential and not the extremes.....

      Regards

      Steve

      Well, I don't say a separation is mandatory, but more power with the regions certainly is a necessary step. There is for me no reason to be angry but I don't see it evolving in a positive way. Extremes are never good, even not in physics ... see for example the gap between loop quantum gravity and string theory. I am 34 years old, but let us return to the physics and keep Belgium for another forum.

      • [deleted]

      well I am 35 and the strings and loop are falses and a pure joke.

      For the extremists I eat them at my breakfast.In wallonia we have universities and schools also .Our country will be well and will be positive.I dislike the hater and the stupidities.These stupidities decrease the velocity of evolution.

      Steve the Theory of Spherization, a GUT TOE of Rotating Spheres...you see we are skilling also here in Wallonia, even if that doesn't liked by all.

      Ok let's go for physics ,first I see 4 big errors in your essay, you lack of generality, try to find them and we shall discuss perhaps.

      To you belgian human brother

      Steve

      • [deleted]

      You have forgotten unfortunally the percentage in your part of right extremist.

      It's sad that.I hope it's not the youngs....

      • [deleted]

      There are no errors in my essay; normally a discussion proceeds when someone gives away his arguments. I have actually considered the question in full generality; perhaps you do not like my answers or you don't understand the subtleties I tackle but that is an entirely different matter.

      The right extremist part in Flanders covers at most 17 % while the left extremism in wallonia is good for more than 35 %. First, when you speak to someone, you have to get the facts straight; it is something we still learn in the north of the country.

      Johan

      • [deleted]

      Let's have fun my BELGIAN friend , I am going to show you what is the real sciences in total transparence.First my spheres and my theory eat your pseudo sciences.Interesting in all case, good character it's well,but you aren't understand my universal message,thus You are a comic, personnally I dislike the 2, the right and left extremists ,I repeat , but it is not serious, we are all humans, uniques and equals, isn't it? .Keep quiet I am an universalist and I am going to show you your errors, thus of course don't be too much vanitious, just for your future credibility.

      Where have you put subleties, perhaps in your mind but not in your words and still less in your essay.

      Still one thing I am going to take your essay in the details,we are going to laugh, be sure.And don't ask me to go on an other thread, I am going to focus specially on yours, this small work.And of course always with ^politness and civility of course.

      ps I eat the 17 percent as the 35 percent, don't forget that!!!It's the real universality and the real sense of sciences.But Perhaps I must make a course for you.You shall understand perhaps better the real meaning of the entropy and its codes.

      ps2 for my theory, I doubt you can understand its meaning.If you want, read my posts on FQXi since 2 years.

      Friendly

      Steve

      • [deleted]

      Ahahaha in fact I reread,let's me laugh, it's a history of sciences with some ideas of others past thinkers,ahahaha your are a historian in fact,it's that hihi.Your essay lacks of foundamentalism, you mix all without a real generality.(Dirac, poincarré, yang mills ,Cliffors algebras and this and that...it's just a mixing of some ideas, I suspect you don't differenciate the reality and the computing)The most impressing you think you understand.But it's not serious, you can evolve if you learn the real foundamentals.

      If you want I can explain you the real meaning of some basis as our entropy and the uniqueness.We can also superimpose the alephs of Cantor if you want.

      That irritates me in fact that so many pseudos scientists think they understand the realitivity and in fact no they just speak.If you don't understand please don't try!! I want well me but frankly let's be serious nd rational a little.The topic of the essay this year is very spiritual and very general.

      To you thinker.HIHIHIH I am arrogant but nice also,

      Steve, universalist who dislikes the 17 percent of right extremists and the 35 percent of left extremists, logic they are stupids these persons.

      • [deleted]

      There are no errors he says...youn think what your are Eisntein or Dirac or Clifford, it's that. Subtleties, you want a real subtlety about the quantum gravity, here is two of my new equations.....E=(c²o²s²)m and mv1v2V=constant for all physical spheres ...thus for your gravitation, the mass is proportional with the velocities of rotations spinals and orbitals.Still one thing the volumes are also important.The continuum you say....

      advertising no but frankly I have a head of seller or businessman or what.HIHIH Let's me laugh with my guitar.

      Steve

      • [deleted]

      I am not even going to start to disentangle this rubbish but I feel sorry for my walloon friends.

      Johan