# Radical new foundations for both quantum theory and space-time

1. Aug 11, 2013

### marcus

This was just posted

http://arxiv.org/abs/1308.2206
Energetic Causal Sets
Marina Cortês, Lee Smolin
(Submitted on 9 Aug 2013)
We propose an approach to quantum theory based on the energetic causal sets, introduced in Cortês and Smolin (2013). Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links and conserved at each event. Fundamentally there are amplitudes for such causal processes, but no space-time. An embedding of the causal processes in an emergent space-time arises only at the semiclassical level. Hence, fundamentally there are no commutation relations, no uncertainty principle and, indeed, no hbar. All that remains of quantum theory is the relationship between the absolute value squared of complex amplitudes and probabilities. Consequently, we find that neither locality, nor non locality, are primary concepts, only causality exists at the fundamental level.
9 pages. Article companion to http://arxiv.org/abs/1307.6167

2. Aug 11, 2013

### strangerep

I'm puzzled why only energy and momentum are taken to be fundamental, with no mention of intrinsic spin, afaict. Their momenta seem to be 3-momenta, and there's nothing distinguishes each such momentum, hence one would expect a rotational symmetry and hence intrinsic spin.

Also, the Poincare mass$^2$ Casimir is assumed -- cf. eq(6) of 1308.2206, but no mention of 2nd Poincare Casimir.

Or did I miss something important?

3. Aug 12, 2013

### marcus

Good reminder. Cortês and Smolin are apparently preparing for a series of four articles, two of which have appeared. Although Pauli matrices and twistor formulation occur in the first article, which is suggestive, I don't see anything that addresses your question. But we have two more of the series to look forward to. I'll list the titles, starting with 1307.6167 and 1308.2206:
The Universe as a Process of Unique Events
Energetic Causal Sets
Fundamental Irreversibility in Cosmology, to appear.
Partly emergent quantum mechanics, to appear.

4. Aug 13, 2013

### Quantumental

Is this deterministic?

5. Aug 13, 2013

### xk_id

Can anybody comment whether those are sensible ideas?

6. Aug 13, 2013

### marcus

I hope some other people respond to your question. I'll just give my personal reaction.

With something this radical we have to wait and see. At present there are only two people (Smolin and Cortês) in the whole theoretical physics, foundations, quantum gravity research community that are working on this. We have to see if some young researchers take up the idea whether it develops some momentum. We also have to see how the other two papers work out. S&C plan a series of 4, I listed their titles earlier. So far we've seen only the first two.

By contrast,take Loop gravity. It is very conservative in a sense. It retains the essential principles and much of the conceptual content of what has been successful in the past: GR, QFT. Lattice gauge theory. It is in reach (thru cosmology) of making testable predictions and has attracted phenomenologists like Aurelien Barrau.
So it does not make a radical leap.

S&C idea, Energetic Causal Sets, departs from all the established precedents and makes a highly risky radical leap. However if you want my opinion, I do indeed think it is SENSIBLE.
To me it looks highly logical, ingenious, economical conceptually, and at this stage remarkably fertile. It gets a lot out of a very limited set of concepts, really very little machinery.

If I were a 27 year old postdoc working in Loop gravity, would I jump into ECS? No. I would keep an eye on it and see how it develops over the next couple of years. I would not jump into the arms of every extremely radical idea that comes along and looks sensible, like it MIGHT succeed.
I would keep on working in the more conservative and populous line of QG research and just keep an eye on this very interesting ECS gamble,to see how it goes.

You said you wanted a comment. I hope somebody else volunteers something more insightful. This is the best I can do for now.

7. Aug 14, 2013

### Chronos

Any notion of causality as fundamental, imo, implies some sense of determinism. This is not a revolutionary idea. It does, however, raise questions about the 'fundamentality' of statistical probability. I think this is a promising avenue to be explored.

8. Aug 14, 2013

### friend

Thanks for the link, marcus. You know I'm a fan of foundational issues in QM.

A couple of things strike me with this paper. One is, how can you define momentum without first assuming a background spacetime in which something can move? Or for that matter, how can you have causality between topologically disconnected points without a medium (spacetime?) to transmit that causality?

Secondly, they take as postulates amplitudes and the sum and product rules of those amplitudes that allows them to define at least a discrete form of the path integral, which is the essense of QM. So they are not really explaining where quantum mechanics comes from. So I don't see how you can call this a radical new foundation. Or maybe I'm missing something.

9. Aug 14, 2013

### friend

I would have to agree with you here, Chronos. It seems that if one can describe cause and effect with a probability distribution, then one can construct quantum mechanics from scratch.

Last edited: Aug 14, 2013
10. Aug 14, 2013

### marcus

In any axiomatic system there are primitives whose meaning is determined by how they are used (rather than in terms of other concepts).

Causality IS the one-directional arrow connecting two points.
Points are not "topologically disconnected" because they are connected by arrows. How can they be "topologically disconnected" when there is, a priori, no space in which they live and no topology!
Momentum is a primitive concept of the axiomatic system. Its meaning is in how the axioms determine the concept shall be used. So in this situation they do not need space in order to define momentum.

So they are not really explaining where quantum mechanics comes from. So I don't see how you can call this a radical new foundation. Or maybe I'm missing something.

Euclid's axioms you learn as teenager do not explain where geometry "comes from" or why there should be lines and angles in the world of our experience. Same way with axiomatic set theory. The amazing thing is what can logically GROW out of a few postulates if you accept the postulates and start reasoning with them. That is what a foundation is, or so I think.

Axiomatic set theory has become the standard foundation of mathematics. calculus, functions, the complex numbers, vectors, Lie groups, etc etc are all founded on set theory. an ordered pair is a certain simple kind of set, a function is a set of ordered pairs, etc etc.

S&C are proposing a very simple logical board game with very simple chess-pieces and rules governing their use FROM WHICH SPACETIME MAY ARISE if they play the game right. and also from which (putting in as little as possible by hand) quantum theory might arise. So far the proofs are incomplete, it might or might not work. There are some tantalizing suggestions that it might work, but one cannot be certain at this stage.

If it happens to work, people will GET USED TO IT. I think it was the mathematician John von Neumann who said you basically never understand mathematics, you just get accustomed to it.

Last edited: Aug 14, 2013
11. Aug 14, 2013

### friend

That sounds like "shut up and calculate"... That seems contrary to the idea of finding the foundationas of QM.

12. Aug 14, 2013

### marcus

Clearly two different viewpoints. To me it seems like the opposite of "shut up and calculate" which does not involve essential mental/conceptual growth. You just keep on with the familar concepts and routines that you have already assimilated and that people have ALREADY gotten used to.

Fundamental mental growth involves getting used to new ideas/ways of thinking for which there may NOT be any nice pat analogies with our experience as animals of a certain size and mass on a planet of a particular chemical composition talking a particular acoustic babble called English.

What people call "explanation"is often a bunch of metaphors/analogies that give them the feeling that some phenomenon relates to their experience as this kind of organism on that type of planet. But Nature is not obliged to run on rules that already make sense to our type of animal with our type of experience.

I really like what von Neumann (I think it was) said,and to me it is the very opposite of "shut up and calculate". But you do not understand it that way, you think he was saying "shut up and calculate".
OK, it is probably an unbridgeable difference of perspective that we just accept and let be. He was one of the most creative mathematicians that has ever lived. Here are a bunch of his sayings, including that one:
http://en.wikiquote.org/wiki/John_von_Neumann
The truth is often funny, I find

Last edited: Aug 14, 2013
13. Aug 15, 2013

### Berlin

Hi,
I think this is an exciting way to go, but I find two weak spots:
- first, why involve mass in your conservation laws, while mass is just a discrete level in energy space, which is acting 'strange' ( I mean different compared to letscsay photons) only in spacetime? It would conceptually be much stronger not to assume mass and only find those discrete mass levels as some solution! I am pretty sure that Smolin et al have to correct.
- second, the mentionings about h look like nonsense to me. H is still there, they only make it one like it is done in many textbooks before, nothing new here or am I missing the point?

Berlin

14. Aug 15, 2013

### marcus

I see your point, Berlin. What they say about ħ is not essential to their argument, more of a side comment. the way it works out they have this primitive quantity called "momentum" not defined in terms of anything else. They could call it "being" or "existence current" or anything. What it means is determined by the axioms governing the use of the concept.

Whatever units one chooses to quantify "momentum", when space emerges out of their causal web then the natural unit of length turns out to be reciprocal momentum. So then ħ is just a parameter that comes in if you use some other size unit of length. Otherwise it is, like you say, just equal to unity.

Actually in a way the fact that when length arises it turns out to be reciprocal momentum suggests to me that maybe they were right to call it "momentum" in the first place. But it is a primitive of the theory, so in principle there is no "correct"term for it.

This is just a trivial side comment but you probably will like to use LATEX for math symbols and equations. At the top of box where you write the message there is a menu of useful stuff starting with the B I U and ending with the the Ʃ . if you click on the Sigma you get a menu of greek letters and some math symbols, and over near the right end, beside some math arrows, the ħ.
You can write the h-bar either that way or with Latex as $\hbar$ .
Sometimes Latex expressions do not get processed until you click on browser reload.

I think that "momentum" was originally just some Latin word for "motion". http://en.wiktionary.org/wiki/movimentum back in history it was once a primitive vague undefined word for "amount of motion". Gradually we got used to it, and the idea crystallized in our language and our minds as having a definite meaning of the amount of matter (mass) multiplied by the speed it was moving----so it was "amount of motion". Who crystallized this initially vague idea for us? Galileo maybe, or Newton?

Last edited: Nov 10, 2014
15. Aug 15, 2013

### marcus

I think some of the issues that come up when you confront a new foundations proposal have to do with the tension between general principles and practice. Some people refer to general principles as "philosophy".
These folk-sayings, like "shut up and calculate", "not just stranger than we imagine but stranger than we CAN imagine", "what matters with a new mathematical idea is not its truth but its convenience", "you don't understand a new concept, you get used to it", reflect that tension between practical physics-as-usual and concern for deep fundamental or general principles.

Sometimes the appropriate thing to do is NOT worry about general principles---don't ask questions, just continue calculating along conventional lines. Other times it might be crucial to search for what is wrong with your theories at a deep almost philosophical level. To confront (and perhaps replace) the axioms. Doing that may involve learning new words which are not definable in terms of old words, or using mathematical terms in new ways (according to new axiomatics.) The test would then be how well it works---whether it is convenient---say, to provide a common foundation for QFT, QSM (quantum statistical mechanics), quantum theory itself, and 4D dynamical geometry.

Or how well, how conveniently, it works to cure known problems in several areas (GR has singularities, QFT is not general covariant and currently requires a fixed prior geometry like minkowski space) by discovering a single common axiomatic basis.

So sometimes the appropriate thing (even though prevailing theories may be excellent in their limited domains of effectiveness) IS to worry about general principles. And to try out new, possibly quite unintuitive, axiomatics.

I think that is what Cortês and Smolin are doing. And realistically one has to remember that it may fail. It's risky. On the other hand, from a bold attempt that makes some headway in a new direction one can learn ideas. I think it's going to prove a valuable initiative whatever the final outcome.

Last edited: Aug 15, 2013
16. Aug 19, 2013

### Berlin

Partcles with mass are not fundamental

Markus, first of all thanks for the explanation about the scientific symbols. Very difficult on an iphone...

I would like to elaborate on my remark about mass in the conservation laws in the last Cortes/ Smolin paper. My point is that I have the strong conviction that mass should not be part of the starting points of any fundamentel theory. It is understandable that people do it, but it is wrong. In fact, there are many -wrong- reasons why we keep using the concept of "free" particles with mass.

1. History. From Newton on: no asceleration, no force. So, constant movement implies a free particle. But even in Newtonian physics, constant movement is equivalent to no motion at all. You could call this confinement in space..., not free at all! NB, only photons escape this picture. They cannot be captured.
2. Beauty. Currently we are seduced by the beauty of the Dirac equation, including me. SR, particle/ anti-particle, fermion-spin, it's all there. Wow! Easy to switch on gauge forces after this.
3. SR. Maxwell, Lorentz invariance, this is the way to go. All photons stay free as a bird, but particles with mass have a heavy price to pay, so to say. To increase the speed you have to put in more and more energy to ascelerate. In 3-momentum space you will never escape. Sounds like a kind of confinement to me! Right in the center in the right frame...
4. GR. A geodesic only describes a test particle in the limit of small mass..! Free fall in GR is not the same as a free particle, it is a coupled system. And massless particles, like photons, do they escape this picture without contributing to the energy-momentum tensor? I bet they do, but this is only a guess.

In conclusion, particles with mass do behave 'strange'/ un-free in spacetime. Massless partlcles are much more natural as a starting point for fundamental physics. This would mean that using a Dirac like equation with mass (and adding forces after that) would already be an approximation, a symplification, where fundamental physics has been lost.

I did see that Cortes/Smolin started with massless particles in their first paper, but changed it in their last one. Probably they were -again- seduced by the joy of finding a "free" particle equation (with mass, of course) in the process, using approximations!! You can speculate that not only spacetime is emerging but also the 3-momentum space inside the photon sphere, involving mass...

Berlin

NB, 't Hooft does use massless, c-speed physics in his cell automaton ideas....

Last edited: Aug 19, 2013
17. Aug 19, 2013

### Berlin

Edit:

Correction to my last post: when I said 3-momentum, I actually mean 3-velocity!

Berlin

18. Aug 24, 2013

### audioloop

i think the inverse, full determinism, i.e. predeterminism or fatalism, obliterate causality, sweeps away it .
and the lack of determinism does not entail absence of causation.
determinism is not a thesis about causation.

.

Last edited: Aug 24, 2013
19. Oct 17, 2014

### marcus

http://arxiv.org/abs/1407.0032
Spin foam models as energetic causal sets
Marina Cortês, Lee Smolin
(Submitted on 30 Jun 2014)
Energetic causal sets are causal sets endowed by a flow of energy-momentum between causally related events. These incorporate a novel mechanism for the emergence of space-time from causal relations. Here we construct a spin foam model which is also an energetic causal set model. This model is closely related to the model introduced in parallel by Wolfgang Wieland in arXiv:1407.0025, and this construction makes use of results used there. What makes a spin foam model also an energetic causal set is Wieland's identification of new momenta, conserved at events (or four-simplices), whose norms are not mass, but the volume of tetrahedra. This realizes the torsion constraints, which are missing in previous spin foam models, and are needed to relate the connection dynamics to those of the metric, as in general relativity. This identification makes it possible to apply the new mechanism for the emergence of space-time to a spin foam model.

arXiv:1407.0025
New action for simplicial gravity in four dimensions
Wolfgang M. Wieland
(Submitted on 30 Jun 2014)
We develop a proposal for a theory of simplicial gravity with spinors as the fundamental configuration variables. The underlying action describes a mechanical system with finitely many degrees of freedom, the system has a Hamiltonian and local gauge symmetries. We will close with some comments on the resulting quantum theory, and explain the relation to loop quantum gravity and twisted geometries. The paper appears in parallel with an article by Cortês and Smolin, who study the relevance of the model for energetic causal sets and various other approaches to quantum gravity.
26 pages, 2 figures

http://relativity.phys.lsu.edu/ilqgs/
Tuesday, September 16th
Wolfgang Wieland, PennState
Title: Covariant loop quantum gravity: Its classical action, phase space and gauge symmetries

PDF of the talk (1Mb)
Audio [.wav 36MB]

The 16 September seminar talk presents the results of http://arxiv.org/abs/1407.0025. Download the PDF first, before you start the audio. The talk is well-organized and the slides are rather complete so that one can understand a lot just by reading the slides PDF.

Both regular Causal Sets (e.g. as developed by Rafael Sorkin, David Rideout, Fay Dowker and others) and regular Spin Foam QG (covariant LQG) are active lines of research with important results. This makes it especially interesting to see how the two recent tweaked versions of each can be closely related.

Last edited: Oct 17, 2014
20. Oct 25, 2014

### Dryson

which are transmitted along causal links and conserved at each event

Does this mean that energy traveling along the path of least resistance that arrives at the point of convergence is then conserved into a larger state of amassed properties such as planets and suns or a Big Bang?