The Paradigm of Kinematics and Dynamics Must Yield to Causal Structure by Robert W. Spekkens

Sean Gryb

Hi Rob,

Always good to hear from you too! Thanks for your detailed comments.

It's encouraging to hear that we seem to be coming to similar conclusions from the same philosophical motivations but different physical problems. I think it points to the strength of the principle that: "empirical indiscernables are physically identical" (not that "snappy" I have to admit!!). I've often thought of this as the core idea in Mach's principles but haven't been able to come up with a catchy slogan either. Regarding Leibniz, I don't think he explicitly mentions scale (or Mach either) but you should really check with Julian, who could tell you for sure.

The theorem I mentioned is one of the primary motivations for Causal Set theory, so Rafael could probably give you an exhaustive list of references (and he could probably explain the theorem more carefully than me). However, I think the original result was in: Journal of Mathematical Physics, July 1977, Volume 18, Issue 7, pp. 1399-1404. There are probably more modern versions though. I think there is a discussion and proof of this in Hawking and Ellis.

Regarding global structures like anomalies, boundary terms, and the AB effect. It would be interesting to see if one could reproduce these effects through a restriction of knowledge. Maybe this is naive, but wouldn't this restriction itself be just a kind of replacement for holism in the sense that it acts as a kind of global restriction on the system? In any case, I am coming to think more and more that these kinds of effects might be very fundamental.

Cheers,

Sean.

[deleted]

I just read your essay. I need to read it again for greater depth. I usually give these a couple of readings. I am pondering what you are saying. I think it comes down to the Bell statement

P(XY|ST) = sum_λP(X|Sλ)P(Y|Tλ)P(λ),

where the ontic variable is ultimately a summation or dummy variable. This means that what ever the analyst assigns to λ it is independent of the constituent subsystems. Your further implication is that any assignment of ontic variables for the constituent systems is then observer dependent and physically irrelevant.

In my essay I conclude something related to this. I remove the notion of locality from field theory. This is different from the statndard notion of locality, where in QFT this is commutivity of fields on a spatial amplitude fixed by a coordinate condition. However, for noncommutivative spacetime, say quantized spacetime or fine grained detail on a D-brane, quantum nonlocality occurs with gravity and this QFT construction is no longer afforded. The result, based on a reference of mine in this essay, is that the configuration variables of particles are gauge-like dependent. This means the universe consists of only one of each type of elementary particle, such as there is only one electron. The multiplicity of electrons, from the electron kicked up in energy by photosynthesis of one of my tomato plants, one electron in your computer passing through a logic gate, or one in a white dwarf exerting its degenerate pressure to hold the star up, and all the others, are due to a gauge dependent holographic projection of that one electron onto what we think of as local configuration variables.

In this setting the standard QFT approach to assigning field variables φ(x_i,t) at points on a spatial manifold is an observer dependent procedure which is not fundamentally correct. Consequently what you appear to advocate may have deeper implications with quantum gravity.

I am not well read on the subject of causal sets. However, this does suggest that the ontic variable is a sort of gauge-like "processor" that structures a network between nodes of events in the universe.

Cheers LC

[deleted]

Dear Robert,

In related to the hidden variable theories you mentioned in the essay, I have a different thinking that I hope you may find it interesting. Nothing mathematical fancy, I find that the bosonic quantum field can be reconciled from a system with vibrations in space and time. The model has some unique features that seem to be extendable to gravity and non-locality of quantum theory.

Is there really no reality in quantum theory

Your feedback will be valuable.

Hou Yau

Stephen Sycamore

Dear Sean and Robert,

When you make that important statement (Sean):

"However, even in this rigorous setting there is a problem with the interchangeability of kinematics and dynamics: there can be global properties of the fibre bundle itself that can show up in the physics. An example of this is the Aharonov-Bohm effect that would be relevant to your model of the electromagnetic fields vs potentials. Similar things, like boundary terms, can appear during Legendre transforms which imply real differences between the Lagrangian and Hamiltonian. The chiral anomaly is yet another example relevant to the Standard Model."

Does it follow that dynamics is to be preferred to kinematics where there is that departure? In other words, kinematics has a larger set of constraints and may not be as malleable in conforming to global properties and boundary terms. A case in point is the Aharonov-Bohm effect you mention which is not readily modeled by U(1) topologies. Relativistic kinematics seems to require a force fit into any even marginal compliance with SU(n) topologies.

Steve Sycamore

Sean Gryb

Hi Steve,

That's a good question. I don't have a good answer but I will think about it.

It may be that these global things - like global anomalies, boundary terms, and the non-trivial topology of the gauge bundle - should have their own status in a theory. In my view they play an important but mysterious role in physics. It may also be that Rob is right: that we can just accommodate them through a restriction on knowledge. My guess is that this restriction would have to be of a slightly different nature but I could easily be wrong!

Cheers,

Sean.

Tobias Fritz

This is a very insightful essay!

It might be worth mentioning that computer scientists have long recognized the fact that kinematics and dynamics do not have separate observational meaning. This can be formalized in terms notions like bisimulation. There ought to be a definition of bisimulation for theories of physics!

Robert Spekkens

Tobias,

Can you tell me more about the notion of bisimulation? I'm intrigued.

Bob Coecke

It's the cornerstone to concurrency theory:

http://en.wikipedia.org/wiki/Bisimulation

The right mathematical context in which it lives is coalgebra. Next year in Barbados: coalgebra quantum foundations. Both of you are of course invited!

[deleted]

Robert Spekkens,

I recently made a comment on the viXra blog about bisimilation and its relevancy to your causal structure in the sense that it allows the incorporation of bi-directional causation! I made the comment before I read these comments here and as soon as I saw this comment I thought I would direct your attention to a good paper on bisimilation: http://www.cs.unibo.it/~sangio/DOC_public/history_bis_coind.pdf. This paper examines the history of bisimilarity in the context of computer science, Modal Logic, and set theory.

Robert Spekkens

Dear anonymous,

Thanks for the reference! It's clear that bisimulation is relevant to what I want to do. I'll definitely have a look at the paper.

Robert Spekkens

Steve,

The fact that it is possible to describe any such constraints within each of the possible choices of kinematics that one can make (i.e. any section of the fiber bundle) seems to me to support the notion these constraints are not part of the conventional distinction between kinematics and dynamics and rather something that is either part of the causal structure or something else that must supplement the causal structure, as Sean suggested. I think it's a really interesting question and I probably need to learn much more about these anomalies to answer it properly.

Best,

Rob

Vladimir Rogozhin

Dear Robert! Excellent in-depth analysis in your essay. But why not have the depth of the ontology? Modern physics and mathematics - science not ontologically grounded. Today dominate the operational theory without the necessary ontological foundation.

Correctly, you have to look deep first structure. Bourbaki is a good title "mother" or "generative". Now, as for the physics and mathematics necessary first structure-mother. The concept of "causality" - a category of relationship (Immanuel Kant) ... What are the most fundamental relationship that is unconditional?

There is a fine principle of "coincidence of opposites." Also there is another good old principle of the triunity, who was not Isaac Newton.

In my absolute generating structure to form the basis of dialectical triad only absolute (unconditional) state of matter. This structure, which Umberto Eco calls "missing." "The truth must be drawn ..." (A.Zenkin) ... and ontologically grounded .... There is no other way to truth... My rating-9. Sincerely, Vladimir

[deleted]

Robert,

Congratulations, your excellent essay is in the top 35 essays of this contest. I wish you good luck in the final evaluation too.

As a final conclusion of your essay, please summarize in a few sentences, which of our 'Basic Physical Assumptions' are wrong in your opinion?

Anonymous

Robert Spekkens

My essay argues against the prevalent assumption that any proposal for a physical theory should separately specify kinematics and dynamics, that is, a space of physically possible states and a law describing how these evolve in time.

George Ellis

Dear Robert

a deep and intriguing essay. The core about causal sets sounds right: I believe there are many indications that gravity is really described by conformal degrees of freedom, and I learned the other day that all of the Standard Model interactions except one term are conformally invariant. Causal set theory is surely a good way to explore. But one somehow has to introduce a scale too at some point.

Your arguments about not separating kinematics and dynamics are intriguing. Of course in a sense that is what Einstein discovered about gravity.

Best wishes

George Ellis

Robert Spekkens

Dear George,

I agree that Einstein's theory of relativity provides further evidence for the conventionality of the distinction between kinematics and dynamics. Concerning the question of introducing scale, you should have a look at Sean Gryb's comment (posted above). Sean is working on shape dynamics, which posits global scale invariance. He points out that the information left in the metric after one does away with the conformal factor is entirely about the causal structure. As I mentioned to Sean in my response to his post (and also in my response to Daniel Alves), the motivation for considering scale to be unphysical is very similar to the motivation for considering the distinction between kinematics and dynamics to be unphysical. I'm certainly sympathetic to the project of formulating our physical theories relationally, as one does in shape dynamics.

Best,

Rob

Jonathan Dickau

Hello Robert,

I have not read it yet, but your essay is on my reading list for today. However, your key point is one I have already given a lot of thought to. 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.

But causal structure is a subject I've been interested in for some time. The challenges posed by the recent Fermi and Integral probe results have called many promising theories like CDT into question, because of problems with achieving Lorentz invariance. And I had some interesting discussions about this matter with Gerard 't Hooft during FFP10, and with some loop quantum gravity folks during FFP11.

So it might be interesting to read what you have to say about this.

All the Best,

Jonathan

Bob Coecke

Hey Rob, nice thingy, but one thing confuses me a bit. As you well know since to told me this, causal discovery is an ill-posed problem and to even have a non-trivial causal structure a joint probability should be degenerate. So how can a causal structure underpin everything? This almost sounds a bit like the causal set paradigm, which you clearly refute in your introduction.

Robert Spekkens

Hi Bob,

It's certainly true that causal discovery algorithms, if applied to finite sets of data, are really just heuristics for identifying likely causal structures. One kind of causal discovery algorithm actually returns a probability distribution over causal structures as its output. In that way, even if one's probabilistic data does not, strictly speaking, exhibit any conditional independences among the observed variables, if it is close to exhibiting such independence the algorithm will identify the most likely causal structure to be one that predicts such independences in the limit of infinitely large statistics. I don't see any problem with positing causal structure to be primitive while granting that we can never be 100% certain of the precise causal structure underlying finite data. Isn't it just like other idealizations in physics? The notion of an inertial observer might be critical to making sense of the special theory of relativity even if, strictly speaking, no observer is every truly inertial.

Best,

Rob

[deleted]

...causality 20 % 40 % 60 % - well half truth or half half falsehood....

Cristinel Stoica

Dear Robert,

I think you are right about the "relativity" of kinematics-dynamics. Originally, I wrote a completely different essay for this contest, in which I explained that the universality of the physical laws (its independence of position and time), as well as the principle of relativity, should not be considered as assumptions, because they can be ensured by extending the configuration space and modifying accordingly the evolution laws. This was based on something I wrote in an older unpublished article, in which I discuss the theories of physics from the perspective of sheaf theory. At the end, I decided to write a completely different essay, about singularities in general relativity, where I have more concrete and published results (Did God Divide by Zero?).

I find brilliant the idea of playing with the kinematics and dynamics to yield an equivalent theory, but which is local. You may be interested in Maxim Raykin's recent Analytical Quantum Dynamics in Infinite Phase Space, who finds a more elegant dynamics for de Brogile-Bohm theory. I would also humbly suggest my own view on QM, in which I try to interpret the quantum weirdness by using only the unitary evolution of the wavefunction, constrained by global consistency conditions (which are intrinsic).

Best wishes,

Cristi Stoica

[deleted]

MAX PLANK:

An important scientific innovation rarely makes its way by gradually winning over and converting its opponents; it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and that the growing generation is familiarized with the idea from the beginning.

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