On the Foundational Assumptions of Modern Physics by Benjamin F. Dribus

Benjamin,

I thought your theory was deductive. That is, "causal relations" can be formulated as an assumption (analogous to Einstein's 1905 assumptions) from which (and possibly from other assumptions) you are going to deduce conclusions, Minkowski spacetime in particular. Now I see I was wrong: there is no deductive theory.

The following wisdom of yours is breathtaking:

"Regarding the constancy of the speed of light, "speed" means "change in distance per unit time." Distance and time are both metric concepts. When one begins with something other than a metric, "speed" must be viewed as a secondary, rather than a primary, concept. No assumption must be made about it whatsoever."

Pentcho Valev

Dear Pentcho,

You were right the first time. I do assume the causal relations to be fundamental. Minkowski space is not "deduced," but recognized as a large-scale approximation. No assumption is made (or needed) about the speed of light because it is not a fundamental concept. Take care,

Ben

Dear Jonathan,

Thanks for the feedback! You raise some excellent points that give me an excuse to talk about certain technical issues that might otherwise have been considered overkill. I must hurry to go teach my class, but will get back to you later today. Thanks also for the paper. Take care,

Ben

Dear Georgina,

Thanks for the message. The last two sections were a little compressed because of the length requirement, and I could only state short versions of my ideas in a rather formal way without much explanation. That part represents several hundred pages of my own work. You certainly should not feel any personal shortcoming from not understanding the details, because by itself that part raises more questions than it answers. Since the topic of the essay contest was which existing assumptions are wrong, I didn't feel justified in spending more than a few pages at the end introducing new theory. Anyway, thanks for persevering through it! Take care,

Ben

Then don't mislead the reader by saying in the essay that you will "recover" established physics from your new principles:

"Recovery of established physics at appropriate scales from these principles is a challenging problem due to their parsimony, with the standard model likely more dicult to recover than general relativityｮ ｨｮｮｮｩ ﾅmergence of ﾍinkowski spacetime is the first step toward the standard model as well as toward relativityｮｮｮ｢ｼｯpｾｼpｾﾁt least in my understanding this means that you first state your new principles and then physicsｬ ﾍinkowski spacetime in particularｬ somehow emerges from themｮ ﾔhis is tantamount to deductionｮ ﾉf it is notｬ you will have to justify your original ｨeuphemismｩ theoretical approachｮｼｯpｾｼpｾﾐentcho ﾖalev

Hello again Ben,

I have a lot of thoughts to share about causal structure, though I have not finished my first read-through of your essay yet. So I figured I should cross post a comment I left on Robert Spekkens' forum, regarding how we look at kinematics and dynamics. To wit..

The notion that kinematic states and dynamic evolution are separable seems to carry over from the subject-object distinction in English and other European languages.

It is a peculiar left-brain dominated preoccupation, which necessitates measures like Korzybski's "the word is not the thing." In Chinese, by contrast; one cannot describe a thing apart from its process, and even the individual strokes in a character tell the story of how that pictogram evolved.

So this gives you one more thing to reflect on. I'm just returning the favor, since you gave me a lot to think about - in terms of thoughtful questions about my essay content. I have been very busy, this past week or so, but I shall be interested and available to engage on this subject matter as long as there is something worth talking about.

All the Best,

Jonathan

Dear Ben,

You've got my highest note!

I hope you keep the first place and win the contest, 'cause you deserve it!

Good luck.

Gene Alexandrescu

Hello yet again, Ben and everyone;

I'm following my muse, by sharing a few more thoughts before reading further, as they respond to comments you left on my essay forum and Ian's. First, yes; Twistors are way cool, because they address the objection of Grothendieck, that geometric points omit too much essential information. In twistor theory, rays are more fundamental than points, which I believe are a special case. This strongly suggests a causal element, and incorporates the idea of forward motion in time, revealing that the fabric of spacetime is emergent. As I understand it; the paper by Witten - after his meeting of the minds with Penrose - showed connections with String Theory, but mainly proved the concept and paved the way for others. Work by Nima Arkani Hamed and Freddy Cachazo involving twistors and S-matrix theory has been especially productive.

But my intuition is that the emergence of spacetime and structure proceeds most simply or elegantly from the octonions, as I mentioned in my essay. One paper by Connes emphatically states "Noncommutative measure spaces evolve with time," but I came to believe that as the Planck scale is approached, geometry becomes non-associative as well - so we must examine the implications of this to have a full understanding of dynamism at the smallest spatial scales and at the universe's time of origin. We know that the octonions are the most general number type, where the quaternions, complex numbers, and reals are a subset thereof. If we assume, as suggested by my departed friend and colleague Ray Munroe, that the imaginary dimensions in octonionic space are at the outset space-like, and the real dimension is time-like - some things fall into place nicely IMO.

If we interpret the imaginary components of octonions as the freedom to vary by a specified amount, it is natural to consider those dimensions as space-like extents. But making the observation (ontological?) that structures must have a duration in time in order to exist; the last sentence of the preceding paragraph can be seen as a kind of procedural formula. In octonionic space, things can evolve through seven dimensions in sequential relation - as possible directions afforded by a specific range of play - but the next step is always time-like, and this creates specificity or definiteness. Briefly stated; non-associativity makes the octonions not only evolutionary (a la Connes' comments about NCG) but also procedural. Multiplying or dividing with octonions is sort of like putting together or taking apart a watch - where you have sub assemblies that must fit together in a specific way.

Intriguingly; I've been working on a universal theory of measurement or determination, and some of the behaviors noted above appear to be emergent. For example; the postulates of projective geometry have a connection or can be a generator...

More later,

Jonathan

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

Dear Benjamin,

I have read your essay with great interest (even if I am not sure if I fully understand your causal metric hypothesis idea). I think you might like to read something that was once intended to be my diploma thesis (in a quiet longer and more complicated version). : About the length of world lines ... (my essay)

My abstract could be like this:

There is a way to test if the metric (based on the notion of distance, given by the Minkowski norm) tying space and time to space-time really exists.

By using an assumption that is (WLOG) weaker then the assumption that has been used to derive Minkowski norm, we can see that reversed triangle inequality (one of the three conditions that have to be met for space and time to be a four-dimensional metric space) is violated. Thus space and time can not be seen as a four-dimensional metric space.

I would be happy to hear what you think about it.

Kind regards,

Frank

Dear Ben,

I'm glad to have finally read your essay. Frankly, I'm most impressed that your clear and insightful discussion of established theories in the context of their "explanatory and predictive power." There are a few of observations I'd like to discuss more fully. Unfortunately I've never been a student of physics or mathematics - although I have isolated and corrected critical problems in the design and implementation of some of the very largest and most complex 'early' information systems. I'm kinda like the Sam Spade (or Peter Faulk) of systems analysis - but you're way too young for those 'detective' 'character' references. Please bear with me - I'll eventually be very direct...

Dark Matter

As you know by reading my essay on the establishment of dark matter by applying simple Keplerian relations to compound structues of massive objects (spiral galaxies), I stress the historical events contributing to DM's adoption. While Zwicke is often posthumously credited with the 'discovery' of missing mass in galaxy clusters, in fact there WAS then undetected 'missing mass' in galaxy clusters: the enormous amount of hot gaseous intracluster media (ICM) later found to be a strong source of then undetected x-rays. The ICM is now thought to be around twice as massive as the ordinary matter contained within clusters' galaxies, although that alone did not solve the problem. For many decades, physics paid no attention to that missing mass. No, historically the 'discovery' of dark matter can only be attributed to the work of Vera Rubin and her collaborating astronomers in the 1970s.

During that time, Rubin often said things kind of like 'we thought they'd orbit the galactic bulge just like planets' because in fact that was the extent of the gravitational analysis performed. Others thought and said things like 'we evaluated them just like smaller scale planetary systems but that didn't work at large scales.' That is very simply how the conception arose that established gravitational theory failed at larger scales.

But it wasn't the scale of the application that was the inherent problem - it was simply the improper application of grossly simplified methods of gravitational system evaluation that produced the problem addressed by dark matter. Dark matter allowed astronomers to justify their continued very convenient and expeditious use of grossly overly-simplified methods of gravitational evaluations - then 'correcting' them with the 'dark' 'fudge factor'.

There was no fundamental theoretical breakdown, only very complex configurations and distributions of billions of discrete masses that had to be properly represented and evaluated. I can't assess their mathematical methods, but please read at least two of my essay's references:

James Q. Feng and C. F. Gallo. "Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies." Res. Astron. Astrophys. 11 (December 2011): 1429. doi:10.1088/1674-4527/11/12/005. arXiv:1104.3236v4.

J. D. Carrick and F. I. Cooperstock. "General relativistic dynamics applied to the rotation curves of galaxies." (2010). arXiv:1101.3224v1.

I think both of these unrelated, more appropriate, gravitational evaluations illustrate that problems that seem to require dark matter for solution are not theoretical in nature, but in the difficulty of their proper application to large scale, exceedingly complex, compound distributions of masses. It seems to me that general relativity my hold some advantages in terms of properly representing those complex and diverse masses...

I think these analyses also indicate that the problems involved in gravitational evaluation of large scale structures is not really a matter of scale as much as complexity. Unlike particles in a fluid, massive objects come in varying sizes and masses and densities. Unlike fluid dynamics, it's much more difficult to adequately generalize and simplify the evaluation of their discrete interactions.

Sincerely, Jim

Dear Ben,

Quantum Gravity?

Their of course does seem to be a distinct differentiation in the dynamics of interactions at quantum scales. As you discuss in your essay, foundational theories are evaluated by their explanatory and predictive success. While many think that general relativity's primary advantages over classical gravitation is its predictive accuracy and it's ability to explain HOW gravity works. I can't assess, but it seems to me that much of GR's success in predicting the orbit of Mercury involves a proximity 'fudge factor' of its own. I may have misunderstood...

However, when if comes to explaining how gravity works I think GR is only an incremental improvement over Newton's metaphysical 'attractive' force. As a systems analyst, I can only view GR gravity as a system of abstract dimensional coordinates that very accurately describe the EFFECTs of gravity, not its physical causation. It seems to me that there is no description of any physical aspect of dimensional spacetime that is represented by the described coordinates.

Meanwhile, as I understand the 'vacuum' of dimensional spacetime seems to always contain some kinetic energy that, in flux, is sometimes manifested as 'virtual particles' that do not comply with the universal proportions of matter and and antimatter. It seems that whatever condition(s) that produced the preponderance of matter in the universe is no longer effective. That aside, I think the annihilation of matter-antimatter particles in the vacuum of space is a direct measure of its kinetic energy content. Back to this in a moment...

Its often discussed (like a classroom trick) that gravity is much weaker than the other forces of matter. One demonstration of this is using a small magnet to pick up a paper clip, overwhelming the gravitational 'attraction' of the entire Earth! No mention of that small magnet attracting the Moon, however. My point is that gravity IS fundamentally different that the 'other' forces of matter - IMO it's not a force of matter at all!

It seems to me that the initial or original expansion of universal spacetime must have infused spacetime with all the energy that was not converted into matter. I speculate that gravitational effects are produced by boundary interactions between this kinetic energy of spacetime and the localized potential mass-energy. While all the accelerating/compressing effects of gravity are the direct result of gradient fields of kinetic vacuum energy contracted by localizing potential mass-energy. BTW, Newton's 'attractive force' would be an approximation of the interaction between two opposingly directed gradient fields of vacuum energy.

I think these ideas could be tested by measuring the rate of virtual particle-antiparticle annihilations within a vacuum chamber on Earth, and in orbit or on the Moon. I have no idea of the magnitudes involved (the annihilation rate would have to be av very indirect measure of vacuum energy density), but if gravitation involves the kinetic vacuum energy of space, represented by GR's curved spacetime, there should be some measurable differences within a gradient gravitational field.

I also have some wild ideas about the physical nature of particle mass as the reconfiguration and redirection of wave propagation energy producing the energy absorbing property of inertia, and the particle property of mass as the particle-wave manifestation frequency. But I'm starting to run out of steam.

You'd have to be highly imaginative to have much understanding of what I'm attempting to describe in this last bit, since I don't really know the proper terms, or at least I'm not conversant. BTW, I have mentioned these more fanciful integrated system design ideas to a couple of other authors who have expressed some interest, but we'll have to see. I only briefly touched on these ideas here, but would be more than happy to discuss further if you happen to be interested. The truth is that, if these silly thoughts were by some chance the keys to unlocking the secrets of the universe, my hands are tied, I'm too short and I won't be around long enough to use them. They're free for anyone else to use...

Please do seriously consider my much more grounded interpretation of dark matter, at least. I think it's only a 'fudge factor'. I'm also very skeptical of the accelerating universe hypothesis, but its analytical requirements are not nearly as simple as the silly 'dark matter' incident. I like to consider that the observational evidence centers on the oldest available type Ia SNe observations, those that also represent the prevailing conditions of the earlier universe. But then the discrepancy with standard cosmological models used to estimate distance from redshift are also involved.

I apologize for rambling & appreciate any consideration you might give. Please let me know if any clarifications would be useful.

Sincerely, Jim

Ben,

Although I didn't manage to come up with any insightful questions about your essay, I have to say your participation in this contest has been invaluable.

You have an incredibly keen mathematical sensibility, combined with the rare ability to frame and ask concise, direct questions. I would often read your questions and the author's replies in other essays posted here *before* reading the actual essays. Since the essays here ranged across so many fields of expertise, your questions often helped to provide a middle ground for understanding.

Between your essay and Wharton's, whose Lagrangian perspective really threw me for a loop, I have considerable subject matter to catch up on.

I look forward to watching as your career unfolds.

Dean