Radical new foundations for both quantum theory and space-time

[Jimster41]

Thanks Marcus, that is helpful. I have the later CS papers and Wieland also. I appreciate the guidance on piece-wise efforts at digestion. I had assumed I would be missing too too much without the first concepts from CS. I started with the (WW) paper but the geometry made me woozy, so I very much appreciate the outline you give at a very high level (with more context, I am looking forward to trying it again) and your impression that the coincidence of the two approaches is notable.

My understanding, such as it is of C&S 2013 paper (anyone who would correct me here please do):

• Axioms: 1)EnergyMomentum conservation, 2)Causal direction from event I to Event K (an event generator or clock), 3)A coherent gradient metric for EnergyMomentum (I think that's what 3 is)
• They derive a model by defining a virtual coordinate system, or "cost surface" for solving "action" given Axioms 1,2 and 3. It spits out a coordinate system like (Minkowski) space-time. (wow...)
• They chain (or network) some of these models together and show that they obey GR in-variance, you can accelerate one part of the network and the solution still works, because accounting gets done at each event boundary, clock stays local.
• They do the whole thing as a Twistor. here I am completely lost which is frustrating because they call this formulation ("... elegant"). Oof.
• They iterate a 2d model network in which the "event generator" favors events with similar pasts to define the next event, to show how momenta conservation under asymmetric time can show time symmetric or reversible behavior. The plots are spooky cool.
• They run the 2d model but evolving to favor maximally different pasts. A single past event dominates the future. Huh? I think this is super interesting. What if the selection rule used by the event generator had time structure itself, like maybe it traverses a range of history differences at a constant rate, as if the clock was counting something down or up - that affected event selection, or it was looping a selection gradient related to recycled or tapped past selections (partially non-local) anything that would cause events selected for interaction to reflect some time-coherent but "externally defined" (aka a-temporal) connection. Like Chronosynclasticinfudibulation... (Vonnegut me!)
• Wait, I think that's what they are doing in the last section (non-local interactions). Starting to investigate what happens when there are some hidden variables driving the event generator's selection rules... Spook-Like.

I got to say also, this whole thing (aside from being really cool) where the universe is like a big computer with a clock running registers based on rules reminds me of "Deep Thought" from Hitchhiker's Guide To the Galaxy.

Thanks again,

 

[RUTA]

"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."

Of course, you can't have concepts like momentum and energy without spatiotemporal measurements, i.e., you have assumed the existence of a spacetime metric. So, if your fundamental processes carry p and E, then fundamentally you have space-time.

 

[marcus]

"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."

Of course, you can't have concepts like momentum and energy without spatiotemporal measurements, i.e., you have assumed the existence of a spacetime metric. So, if your fundamental processes carry p and E, then fundamentally you have space-time.

I wouldn't say "of course" though : ^) There is at lease one small research literature in which energy and momentum play an important role without the existence of a globally defined space-time. In other words, in the context of that line of research by those researchers (e.g. Laurent Freidel, Giovanni Amelino, Jerzy Kowalski, Lee Smolin...), you have NOT "assumed the existence of a spacetime metric" when you talk about energy and momentum

I would have imagined that you knew about this, RUTA. Since you are sensitive to the different ontological approaches people take.
http://www.newscientist.com/article/mg21128241.700-beyond-spacetime-welcome-to-phase-space.html
http://en.wikipedia.org/wiki/Relative_locality
http://arxiv.org/abs/1101.0931
http://arxiv.org/abs/1106.0313

Mind you, I don't personally espouse or advocate that particular research initiative, and I wouldn't presume it is relevant to what we are talking about in this thread, namely ENERGETIC CAUSAL SETS as studied by Cortes and Smolin. This ECS is something new, not explicitly related to the 2011 papers on Relative Locality. But in this case, too, one is assuming that there is something which is conserved, which is prior to the definition of a spacetime. And which does NOT require one to assume that one already has a spacetime metric. : ^)

Maybe one of us should write to Cortes and Smolin and urge them not to use words like "energy" and "momentum" in a pre-geometry context. Advise them to make up different words to use, for the sake of semantic peace and harmony. Maybe they could be persuaded to use the word "Vigor" and call the mathematical structures they are investigating by the the name "vigorous causal sets" (VCS) instead of "energetic causal sets" : ^)

BTW Wolfgang Wieland has something similar to ECS he is studying (google "Wieland new action" to get his July 2014 paper) and he has a conserved quantity which he calls "volume". But this is also prior to the construction of a metric. So one cannot say that his having a conserved quantity called "volume" flowing through a bunch of interacting tetrahedra necessarily or "of course" presumes the prior existence of a spacetime.
Or so I think, anyway. If you have a look at the New Action paper you may conclude otherwise. Wieland's model has been called CAUSAL SPIN FOAMS.
I suppose that CSF and ECS could turn out to be closely related, or even the same theory.

 

[RUTA]

I'm just pointing out the obvious -- you can't talk about momentum or energy without a notion of spatiotemporal measure. A kg*m/s is meaningless if you don't know what a meter or a second is.

 

[marcus]

I understood what you were trying to say, RUTA. I can see that from your perspective you were just pointing out the "obvious" : ^)

However these researchers who work with pre-geometric concepts where you do not have an agreed-on spacetime or a spacetime metric as yet do, in fact, use terms like energy, momentum, volume.
Maybe they shouldn't! : ^D
But they do.
And I see them postulating that these prior-to-metric quantities are CONSERVED, even though there is no Noether theorem for miles around. There may in fact be no time, defined as yet, and yet these quantities are conserved. In the pre-geometric structure they are talking about.

It's basically a semantic issue. Do you want them to invent some term like "proto-ergon" so they wouldn't need to say "energy"? Maybe Cortes and Smolin should be calling what they study by some term like "Pre-ergetic Causal Sets".

So, when you say "of course" and "the obvious", I realize these things are obvious to you, but they might not be to those other researchers in their own context. It is fascinating stuff. I hope you google "cortes causal spin foam" and have a look at the July 2014 Cortes Smolin paper. Your comments could be very helpful, if you have some you want to share.

 

[RUTA]

It would be news if they could derive mass, space and time from something else more primitive, e.g., Vigor -- haha, love that. Otherwise, they're looking at something like Einstein's equations which tell you how the spacetime metric is to be "self-consistently" related to the stress-energy tensor.

 

[marcus]

It might help to get a more direct look at what we're talking about. I'll quote from Wolfgang Wieland's July paper. To get it without the link, google "wieland new action". As far as I can see there is no spacetime manifold here, and no spacetime metric. And yet analogs of several tools familiar with traditional GR analysis are present.
==quote http://arxiv.org/pdf/1407.0025v1.pdf abstract==
New action for simplicial gravity in four dimensions

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.
==endquote==
I would suggest reading the paper before jumping to the conclusion that time here is some traditional GR observer's clock time, or that the Hamiltonian conforms to conventional preconceptions.
==quote http://arxiv.org/pdf/1407.0025v1.pdf page 24==
The relevance of the model
The action (50) describes a system of finitely many degrees of freedom propagating and interacting along the simplicial edges. The system has a phase space, local gauge symmetries and a Hamiltonian. What happens if we quantize this model? Do we get yet another proposal for a theory of quantum gravity? Recent results [23, 27, 36, 58] point into a more promising direction and suggest a convergence of ideas: The finite-dimensional phase space can be trivially quantized. The constraints of the theory glue the quantum states over the individual edges so as to form a Hilbert space over the entire boundary of the underlying simplical manifold. The boundary states represent projected spin-network functions [59, 60] in the kinematical Hilbert space of loop quantum gravity.
It is clear what should be done next: For any fixed boundary data we should define a path integral over the field configurations along the edges in the bulk. At this point, many details remain open, and we have only finished this construction for the corresponding model in three-dimensions [58], yet we do know, that whatever the mathematical details of the resulting amplitudes will be, they will define a version of spinfoam gravity [61].

Finally, there is the motion of the volume-weighted time normals, which endow the entire simplicial complex with a flow of conserved energy-momentum. As shown by Cortês and Smolin in a related paper [27], these momentum-variables introduce a causal structure, and allow us to view the simplicial complex as an energetic causal set [51, 52]—a generalization of causal sets carrying a local flow of energy-momentum between causally related events.

==endquote==

 

[RUTA]

If you're going to stick p and E on the links of a simplicial manifold, you can use that structure as a base to specify Regge-calculus-like least action equations to marry up p and E with a spacetime metric. But, still, without a spacetime metric, p and E don't make sense. Putting them on the links of a graph doesn't change that.