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

...From my European Journal of Physics article perhaps you could guess that I would find exciting any research concerning your "universal Schrodinger equation." Keep it up!

"Mathematical tools necessary to implement these ideas include a synthesis of multicategory theory and categorization in abstract algebra, involving interchangeability of objects, morphisms, elements, and relations." The seeds of those tools are in Gauss Disquisitiones Arithmeticae and Riemann's "Natural Philosophy." I believe Grothendieck's use of category theory re-discovered a few ideas already present in Gauss, and even more, Riemann.

"For example, zeta functions, and hence the Riemann hypothesis, are connected to

quantum field theory via noncommutative geometry and the theory of motives " You've read the book "Zeta and Modular Physics (2010)"? Maybe the link to relativity is there. I would link their discussion to Riemann's approach to Dirichlet.

Thanks for the reference to Connes. I've only read his earlier work on Riemann's hypothesis. If you ever want to win a million dollars you should try to prove Riemann's hypothesis. You could apply your ideas to Connes' proof and/or your paper's "complex Hilbert spaces whose elements represent probability amplitudes of point particles, self-adjoint operators whose eigenvalues are interpreted as the possible values of measurements, and time evolution according to the Schrodinger equation." I would approach the Hilbert-Polya conjecture through Heisenberg/ Von Neumann's "mathematical causation" and Von Neumann/Wigner's "observational algebra."

Riemann wrote down he proved "Riemann's hypothesis" and only needed to "simplify the expression." But from my paper you know what he meant by "expression." Still, if you pay close attention to what Riemann thought about his hypothesis, i.e. pay attention to the historical-foundational context, you could come up with the proof. You certainly have the required talent.

Hope at least some of this helps. I'll give it more thought and send you comments that are not half-baked. I look forward to read more of your work. Best, Juan.

Great Article. I will reread again -

Regarding the ending, quoted as follows:

"Finally, the dimension of space as well as its curvature might vary

with \energy density," though the effect might be immeasurably small"

This appears consistent with CIG: www.CIGTheory.com in that the volume of Space (i.e. dimension of Space) is tied to energy density / / / Full curvature = black hole; no curvature = vacuum energy/Dark Energy; partial curvature = Dark Matter, and each is all %"c" dependent

THX

doug (comments still welcome)

Dear Ben,

I will prepare an article on detailed derivation of spacetimes from generalized formulation in Liouville space.

Here t-causality is associated to the approximated Hamiltonians used in general relativity and quantum field theory, whereas tau-causality is associated to the fundamental Hamiltonian. The distinction between "tau" and "t" is mentioned in my essay. A more detailed discussion of both and of the limits of the use of coordinate time "t" is given in the monograph by Pavsic --reference [3] in my essay--. E.g., Pavsic denotes the fundamental Hamiltonian by H and the approximated Hamiltonian used in quantum field theory by H_0.

Regards

Hello Ben,

Thank you again for your comments on my essay, which to me are among the most valued of all the comments I've had.

I saw your recent point about objects ageing, in relation to the point I made about the residual effects of time dilation. The emphasis in my essay is simply to set out the clues we have, and draw broad conclusions from them, rather than going into detailed attempts to interpret them. Because I think it's possible to arrive at a conclusion that way, and to reject block time via simple deduction, it seemed a good way of keeping the essay simple. But of course these questions can be examined in far more detail, and from there it's a case of choosing between two or three initial avenues.

I've read your essay today, will read it again, I found it excellent in a number of ways. The overview of the whole landscape of physics you give in the first half is important and very useful, particularly at a time when things are getting a bit fragmented. It not only helps that you've summed up the landscape as a whole, but - like myself and not too many others - you've included comments on the mindset of the physics community over the 20th century, which helps with understanding about attitudes, and how and why the general view has shifted over time.

In relation to the second half of your essay, what I'll say now is simply a personal opinion, not a criticism of your particular view. And I tend to agree on the assumptions you reject. But I suspect that the way forward, when we find it, rather than involving shuffling the underlying principles and making some go from fundamental to emergent, while others go from emergent to fundamental - which several essays here do, though none better than yours - will instead involve finding some truly new concepts. However, it may be that rearranging the bits of the puzzle we have will also be needed, and I do see that you bring in new principles, and that you may recover established physics from them. So it's certainly too early to tell, and I very much wish you luck with it, and with your essay.

Best wishes, Jonathan

Hello Ben,

well thanks for asking - it's more a book that's needed to answer that. I saw you mention somewere the other things that you 'ought to be doing' at the moment, well I have the same... I would be putting the finishing touches to my book if I wasn't on this site, the publisher is expecting it - but am enjoying the discussion here and learning a lot from hearing other people's views. In the book I compare and explore some different avenues, and different kinds of answers to these questions, and try to use rational thinking to estimate what kind of answer is the most likely. It seems to me that I narrow down the possibilities well, but I'll wait to see what others say. I'd very much value your opinion when it's out, will let you know.

Your contribution here has been enormous, I find your posts in many places, helping to pull people's thoughts together, and helping to focus the general attempts to crack these puzzles. Thanks again, and good luck to you.

Best wishes, Jonathan

Dear Ben,

Your comments all over the place have been a joy to read. I particularly admire your habit of asking 4 to 6 detailed and relevant questions on each essay, and am most impressed with the mental power and will power that drives your output.

In most cases I find myself in agreement with you, and certainly when you state:

"...in any case, the physical ideas ought to come first, and the math ought to be whatever is necessary to get the job done..."

And in another comment to Peter you said:

"My view is that simple physical ideas do sometimes lead to horribly complicated mathematics ... the less you assume, the more you have to explain."

Despite my fascination with your prolific comment trail, it is scattered over a hundred or so essays, so I can only comment on my general impression, which is that you several times stated something to the effect:

"the continuum is too good to be true."

while qualifying this by saying that its mathematical definition (manifolds) is quite complex.

Yes, the simplest physical possibility, the continuum, can understandably lead to horrible mathematical complexity in trying to "capture" this simplicity. In my view simple mathematics (can) lead to horribly complex physics. Integers and binary relations are "unnatural" compared to the continuum, although both can fall out of it.

In prior essays I make the fundamental assumption that the universe began as ONE thing, and therefore any possible evolution (which must have occurred to get to where we are today) could only have come from the one thing interacting with itself. It's easy to turn this into a symbolic equation and, with a few known facts, translate it into a physics equation that leads to the world as we know it. I won't belabor the point here but think that you might find my previous FQXi essay to be of interest.

One point in particular that might interest you is that, while no discrete or quantum value of space, time, or mass falls out of the master equation, a quantum value of 'action' does fall out [which I of course set equal to Planck's constant] in a very simple way.

You are probably way too far down your own path of causal binary relations to reconsider things, but I think that you are spot on when you disentangle the complexity of math from the complexity of physics. If anything, they may be inversely related!

Anyway, thanks again for your wonderful comments. They've made this FQXi event even richer than usual. And, having done my undergraduate work there in the early 60's, I have fond memories of LSU. I hope you're enjoying it.

Best,

Edwin Eugene Klingman

There was a discussion last week comparing shape dynamics with causal nets. I am rather new to both of these approaches to physics. The comment was made that shape dynamics involves symmetric relationships, while causal set theory anti-symmetric relationships. Time evaluated from the Jacobi variational principle

δt = sqrt{m_iδx_iδx_i/(E-V)}

is related to a proper time, or an interval. I might then say that if we multiply by E-V on both sides we get

(E-V)δt = sqrt{m_iδx_iδx_i(E-V)}

where the left hand side appears to be a Lagrangian times an interval of time. This may then be written as

∫d^3 δt sqrt{-g}R = sqrt{m_iδx_iδx_i(E-V)}

We may then break out the Ricci scalar R = R_{ab}g^{ab} and the left hand side exhibits this symmetry. On the right hand side again there is symmetry with the interchange of δx_iδx_j δ_{ij}. This probably needs to be firmed up of course, but I think this captures the idea.

Causal dynamics on the other hand is ordered by events with the idea of building up geometry. So there are orderings such as x < y so that in some product we have xy = -yx. This seems to have some connection with Penrose tensor space theory, where for every symmetric tensor there is an antisymmetric tensor. The relationship between the two is a graded algebra similar to supersymmetry. The symmetric interchange between spatial coordinates in shape dynamics is similar to the symmetric interchange between boson fields. The antisymmetric interchange of events in causal sets is similar to the interchange between fermions ψ(x)ψ(y) = -ψ(y)ψ(x). Hence a causal set is potentially identical in form to a Slater determinant. This then opens the door to a type of functor or category theory which maps elements of geometry to elements of field theory.

Cheers LC

Dear Ben,

Thanks for pointing out the other 'pro-manifold' authors. I have not read most of them yet.

And of course I'll be happy to communicate with you after the contest ends and things settle down.

Best wishes,

Edwin Eugene Klingman

Lawrence,

(Feel free to post at the bottom of my thread at any time; the comments up here are easier to miss.)

The first part of your sketch seems right to me. Regarding the second part (involving causal dynamics), I am not sure about the meaning of the algebra with the antisymmetric product. I have thought a fair bit about path algebras in this context, and for path algebras acausal products (including anticausal products) are zero. The reason is that this algebraically encodes path sums. For instance, if you partition a "spacetime region" in a causal graph by a "Cauchy surface" (i.e. suitable antichain) then the path algebra element representing all maximal directed paths in the composite region is just the product of the elements representing all maximal directed paths in the subregions.

The obvious thing is take the minus to mean "time reversal" in the obvious sense, but I will have to think about the physical significance of this. The pure causal philosophy is that there is never disagreement between "time" and the "direction of trajectories." In particular, in the causal configuration space, this would correspond to "un-evolution of the universe."

In my original remark about symmetry and antisymmetry I was referring to the order-theoretic definition, not necessarily implying that an antisymmetric algebra is the appropriate vessel for containing information about phases of paths, etc. But perhaps I need to rethink this. The sketch you present is rather compelling. Take care,

Ben

Dear Benjamin,

Your CMH opens a lot of new perceptions and universes. I liked it very much. You also mention : "The initial family evolves to the terminal family", so in your view every universe was in facto initial and becomes terminal, also the conglomeration of universes that forms our "reality".

In "THE CONSCIOUSNESS CONNECTION" I go back to the initiality and limit our universe by the Planck length and time. So "reality" emerges from our consciousness, that is why I appreciate your "thought experiment".

I also saw that Eric verlinde had your attention, his perception of gravity is also in accordance with my idea that only materialistic reductionism is not the only way to research our questions about existence.

I hope that you will read my attribution in the contest, especially your opinion about my "causality" perception.

best regards

Wilhelmus

Ben,

Thank you for stopping by. I am very interested in reading your works. I will be writing to you later today.

James Dunn

Ben,

Thank you for the nice comments over on my essay. I responded over there. While your essay is way over my head in terms of math, the points you made that I think (?) I understood were very good! A few comments are below, but take them with a grain of salt because, as I said, it was kind of over my head. Anyways, they are:

1. I think your way of thinking as illustrated by this quote:

"What I try to do is build up fundamental physics from simple principles like cause and effect. This leads to some rather thorny mathematics, but my view is that the physical principles ought to be simple and well-motivated"

is exactly right, and I wish more physicists and thinkers in general would think this way. If we start at base principles like cause and effect, we have a better chance of building a working model of the fundamentals of the universe that can make predictions than by starting out with high level, assumption-riddled, current physics thinking and working down to more fundamental levels.

2. I totally agree that the assumption that systems evolve with respect to an independent time parameter, and that the universe has a static background structure seem unlikely. To me, if the universe is the "system", time is just the same as a sequential chain of physical events occurring within the universe, with the earlier events in the sequence corresponding to earlier times. If the events A ->B->C are sequentially followed by the events C->B->A, this doesn't mean that time is going backwards because the events C->B->A still occurred after the A->B->C sequence of events. When I hear physicists say that their equations work fine when time is negative, this doesn't mean that time in the real world (not in the equations) can actually go backwards. Also, if time exists as this separate, independent dimension somewhere, I'd like someone to point it out to me now. Where is it?! I can't see it. Also, in regard to the second assumption, I think of the universe a little more holistically where matter and energy aren't occurring against a separate space background, but rather that they're interactions between the units that make up the universe/space.

3. You mentioned on pg. 6 "This means, in particular, that spacelike sections are merely unordered sets, with no independent notion of distance or locality". If I understood this, I think I'd also agree because I think that location of something refers to its position relative to other things within a bigger set of things. That is, while a single existent state may "be" or exist as a location, it doesn't "have" a location within a bigger reference frame.

4. My own view on volume is that to physically exist, any existent state must have three dimensions, and, therefore, volume. I have trouble imagining an actual physical state in which one of the dimensions is zero. Not just infinitesimally small but actually zero. At zero, it disappears. So, three dimensions, or volume, seems to me to be a requirement of an existent state and thus a requirement for whatever existent state makes up our universe.

5. So, is a binary relation just a relationship between two elements in a set/ And, if one element causes the related element to appear, is this a causal relation? If this understanding is right, this makes a lot of sense to me because my own view of existence is that given a fundamental state of existence, whatever this is, this state will somehow cause the formation of identical states around it, these new units will cause the formation of new states around them, etc. and this expanding space of existent states is equivalent to our universe. So, in my view, I think I would say that there's a causal relation between each existent state and the existent states it causes to appear next to it. I have more on this at my website at:

https://sites.google.com/site/ralphthewebsite/filecabinet/why-things-exist-something-nothing

Sorry for the long response. Nice essay and good luck in grad. school!

Roger