Thursday, March 04, 2010

Quantum Interactions Create Space-time

The notion that spacetime is an emergent phenomenon is, by my reckoning, being proposed by an increasing number of thinkers. Physicists and philosophers working in quantum gravity and quantum foundations are turning to the idea that the spacetime of relativity is not fundamental, but rather something which arises from a more fundamental world of quantum mechanical systems and their interactions.

I just saw a reference to one such argument which was made a few years ago in an article by Avshalom C. Elitzur and Shahar Dolev called “Quantum Phenomena Within a New Theory of Time”. This was published in the 2005 collection Quo Vadis Quantum Mechanics?, Avshalom C. Elitzur, Shahar Dolev, Nancy Kolenda, Eds.

Elitzur and Dolev examine several puzzles over the nature of time in quantum mechanics and are led to the hypothesis that quantum interactions (measurements) themselves are responsible for the creation of spacetime.

A couple of quotes from section 17.10, titled “An Outline of the Spacetime Dynamics Theory”:

Could it be, then, that the two phenomena – time’s passage and wave-function collapse – are not only real, but the latter is the very manifestation of the former? A wave function, after all, is a sum of many equally possible outcomes, while the measurement brings about the realization of one out of them, the others vanishing. Is this not the very difference between future and past? And is collapse not elusive because it creates the elusive ‘now’?

Suppose that there is indeed a ‘now’ front, on the one side of which there are past events, adding up as the ‘now’ progresses, while on its other side there are no events, and hence, according to Mach, not even spacetime. Spacetime thus ‘grows’ into the future as history unfolds.

What role does the wave function play in this creation of new events? The dynamically evolving spacetime allows a radical possibility. Rather than conceiving of some empty spacetime with which the wave function evolves, the reverse may be the case. The wave function evolves beyond the ‘now’, i.e., outside of spacetime, and its ‘collapse’ due to the interaction with other wave functions creates not only the events, but also the spacetime within which they are located in relation to one another. The famous peculiarities of the quantum interaction – nonlocality, the coexistence of mutually exclusive states, backward causation and the inconsistent histories presented in the previous sections, thus become more natural.
   Can the reciprocal effects of spacetime and matter – the celebrated lesson of general relativity – thus possible gain a quantum mechanical explanation? Perhaps it is the wave function, we submit, that is more primitive than spacetime, and the spacetime connecting the two events is the product of their interacting wave functions.


Thomas J McFarlane said...

On the face of it, there seems to be a problem with this proposal due to the fact that the Schrödinger equation has time built into it already. How can time emerge from wave functions that are themselves solutions of an equation that presupposes time already as a background?

Steve said...

Hi. Good question.
There are two levels. They're making a distinction between the emergent spacetime of relativity, which is a purely geometric structure derived from the distribution of the measurement events, and the underlying background time of the wave functions.

The reason I think this is worthy of consideration is that the spacetime of relativity has no concept of the flow of time anyway, so under this vision that is accounted for by the underlying more fundamental quantum time.

Doru said...

I find the Space-time Dynamics Theory to be a very valid argument.
Even from a philosophical perspective, the wave function seems to be transcending the space-time bound as a more fundamental ontological explanation. The real problem we have here is the problem of mind and consciousness. Space and time is the only solution we have for this problem.

Steve said...

Hi Doru: with reference to your last sentence, I think we need time for consciousness, but I'm not sure we need space (as we have normally understood it).

TechTonics said...

John Baez: ..."there's no "time operator" in quantum mechanics!

Since the underlying quantum formalism has no time operator, the Schrodinger equation, which is super-structure, adds time to bridge QM to General Relativity, or microcosm to macrocosm where humans insist upon time recognition. I don't think the objection offered by McFarlane is fundamental. Refer to quantum gravity.

TechTonics said...

I group my interests in philosophical musings under the category, Causality and Machine Learning, or the case of how did Causality evolve/emerge a time- perceiving consciousness? Here is a real good paper on the problem of time within quantum gravity.
Prima Facie Questions in Quantum Gravity Authors: C.J.Isham

I wish now to consider in more detail three exceptionally important questions that can
be asked of any approach to quantum gravity. These are: (i) what background structure
is assumed?; (ii) what role is played by the spacetime diffeomorphism group?; (iii) how is the concept of ‘time’ to be understood?
One of the major issues in quantum gravity is the so-called ‘problem of time’. This arises from the very different roles played by the concept of time in quantum theory and in general relativity. Let us start by considering standard quantum theory."

Steve said...

Thanks very much for the link. I looked at what Baez said about time not being an operator in qm. This is an idea that t isn't like the other observables and there is some debate about whether the time/energy uncertainly pair is unlike the position/momemtum pair, etc. I think regardless of this, a time parameter is still a fundamental part of qm, as it indexes our experiences in the situations qm is used to describe.

TechTonics said...

QM is not a universal theory. GR is a universal theory in which time is considered fundamental. In QM time is not an operator meaning it is not an observable. The time in the S.E. parameter is arbitrary so that is why I say it is not fundamental. In the chapter under discussion, Zeh is cited as a reference, and within the article, Aharonov is mentioned which is why I selected them as authoritative resources. Zeh
Time in Quantum Theory

... "For this reason, von Neumann [3] referred to the time-dependent --> Schrödinger equation as a 'second intervention', since Schrödinger had invented it solely to describe consequences of time-dependent external 'perturbations' of a quantum system.

In non-relativistic quantum mechanics, the time parameter t that appears in the Schrödinger wave function *ψ(q,t) is identified with Newton's absolute time."

[SH: This is how the gap is bridged between the not universal theory of QM and the classical/GR regime which is considered universal, because although time is not observable in GR either, time is considered fundamental, "Spacetime is usually interpreted with space being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions."


Time in the Quantum Theory and the Uncertainty Relation for Time and Energy
Y. Aharonov and D. Bohm
Because time does not appear in Schrodinger's equation as an operator but only as a parameter, the time-energy uncertainty relation must be formulate in a special way.
First, it is not consistent with the general principles of the quantum theory, which require that all uncertainty relations be expressible in terms of the mathematical formalism, i.e. by means of operators [observable], wave functions, etc."

Steve said...

Hi. Thanks Techtonics for your comments. Re:"QM is not a universal theory. GR is a universal theory...":

I've been interested in proposals that turn this 180 degrees around.

In these, GR is seen as an emergent, not fundamental theory; a network of quantum mechanical systems and their interactions would be fundamental. You say the time parameter in qm is arbitrary, and I understand the rationale for saying this, but it's drawn from our experience.

Whereas with GR (and some quantum gravity theories like loop quantum gravity) you can't get our intuitive experience of time back out! The idea of time as one of the dimensions in GR isn't enough -there is no preferred time direction picked out by the theory, it is really just geometry.

A list of posts on theories of this type is at the bottom of this post.

TechTonics said...

Causality First
Rafael Sorkin’s Causal Sets and Fotini Markopoulou’s Quantum Causal Histories.
She finishes with a note on time:
Just as the emergent locality has nothing to do with the fundamental micro-locality,
time and causality will also be unrelated macro vs. micro. So, the theory “puts” in
time at the micro-level (via its causality constraints), but emergent spacetime will
have no preferred time slice –as required in general relativity.

TT: I haven't read as many of those theories as you have. I did read Fotini and was impressed. But you quote her as saying "time and causality will also be unrelated macro vs. micro."
I think GR is still received as a universal theory because humans perceive causality as events unfolding through time. The resistance to accepting QM as a universal theory arises from not understanding the physical result of the double-split experiment, which Feymann described as the "central mystery" of quantum mechanics. Or the causality involved with EPR and non-locality. Classically, the speed of light is precisely determined in terms of a meter which limits causality. In the 13 or so major interpretations of what QM describes about reality, one has time considered as instantaneous which wreaks a bit of havoc with a traditional grasp of causality, and other various QM interpretations about the speed of light. I'm not going to buy a theory which doesn't make testable predictions.
I like most what Penrose had to say in the Foreward to that Quo Vadis book. The theories are incomplete, either QM or GR or both. What bothers me about Fotini's idea is that both QM and GR have experiments which confirm the theories to 99.9999+ accuracy.
It makes me think that there should be a reconciliation possible; but it doesn't seem Fotini is forecasting such a reconciliation with that remark: "time and causality will also be unrelated macro vs. micro." I read her paper over a year ago so my memory is fuzzy. I recall that the root of the debate is over whether the turtle's back is discrete or continuous.

TechTonics said...

I just found this newer paper by Loll, Coupling Point-Like Masses to Quantum Gravity with Causal Dynamical Triangulations
Authors: Igor Khavkine, Renate Loll, Paul Reska (Submitted on 24 Feb 2010)

I have a fondness for Loll's approach because I like fractals. Though Fotini mentions CDT, the paper you linked to her seemed to conflict with CDT in too many ways.

Steve said...

I haven't read that paper yet, but I do feel that the cdt results are "telling us something" about quantum gravity. I think that we probably will get a better motivated and more insightful micro-theory than the cdt one in a future theory.

TechTonics said...

I also found that post by Scott interesting. I've heard it said, like a complaint, that everything is emergent. But maybe that is really an insight.
The Big Bang or the Big Bounce, stars forming and then reforming so that they create more complex elements when they nova, planets forming, life, intelligence and consciousness. This all seems quite unpredictable from the point of origin.
Becoming more particular, von Neumann purposely designed an automata capable of universal computation (UC). Was that emergent? Then Conway designed The Game of Life in 1970. He proved Life capable of UC in 1982. I've read that Life (UC) described as an emergent phenomenon. The cases appear to be different in my view.
There are complex patterns which have rules, that are so complex that it has been proven that no computer can find the rule. How can you distinguish that type of rule from random, as in Rule 30, which is a pseudo-random generator which re-cycles after a "billion billion lifetimes of the universe" (Wolfram).

I found your website after looking into CAs and emergence.
I've really enjoyed reading some so far, of your many available insightful posts. I can read a paper and compare what I get out of it (which never seems to be enough) with your analysis; quite a treasure. Also my first impression of Fotini's paper has improved with aging.

TechTonics said...

I have been reading your past posts and taking notes. I was hoping to find a consistent
explanation between the ideas explored which shared a common philosophical perspective.
Maybe you can connect all the dots in preparation for writing your book :-)

Philosophers usually dismiss the notion of "strong emergence" because it is magical, transcending causality. Chalmers adopts a type of dualism in suggesting that the only type of strong emergence might be consciousness. Most philosophers describe weak emergence in terms of knowledge (or lack thereof). Weak emergence assumes causality although the rule of the pattern which connects cause and effect is unknown or irreducible.

Apparently the objective universe existed before humans evolved who describe it in theories which can never be proved, thus epistemological constraints. One such theory suggests that the universe expanded at a super-luminal velocity, which I think is faster than causality propagates. At what point can one distinguish some causing event/property as fundamental, from the created event (effect) which follows, and is now described as emergent? The universe was evolving before sentience arose which could experience such epistemological constraints.


The Limit of the Bayesian Interpretation "I read the paper “Subjective probability and quantum certainty” ...

To bring the point home, this particular paper features the discussion of quantum experiments with a certain outcome: the authors show that this outcome is to be interpreted as a certainty of epistemic belief on the part of the observer, not an objective certainty."


Causality: Models, Reasoning, and Inference (2000) by Judea Pearl Preface

"Ten years ago, when I began writing Probabilistic Reasoning in Intelligent Systems (1988), I was working within the empiricist tradition. In this tradition, probabilistic relationships constitute the foundations of human knowledge, whereas causality simply provides useful ways of abbreviating and organizing intricate patterns of probabilistic relationships. Today, my view is quite different. I now take causal relationships to be the fundamental building blocks
both of physical reality and of human understanding of that reality, and I regard probabilistic relationships as but the surface phenomena of the causal machinery that underlies and propels our understanding of the world."


Tech: What primitive or fundamental concept of causality can exist which doesn't also entail the idea of events existing in space which create the following timely t+1 next event? If causality is primitive, how then are space and time considered emergent?
It would seem to me that causality, space and time must all have emerged from a common cause, or, they are all fundamental since causality is defined in terms of, or exists in terms of, space and time and events. Isn't gravity essentially causal? Is everything emergent when viewed from the first few nano-seconds of expansion? Do quantum fluctuations include and explain the plasma conditions?

Steve said...

Thanks for your kind words about the blog. I always appreciate dialogue with others who think about these things. I also appreciate your comment that it’s hard to discern a coherent philosophical story from this format – I should attempt to restate or summarize some of the themes which run through this stuff.

Re: emergence

This is a tricky subject. I had convinced myself awhile back that most examples of emergence in nature were epistemological or explanatory, not truly ontological – with one exception: The collapse of a quantum system when measured.

The idea is that the ordered sequence of measurement events (like the causal set idea) emerges from the underlying dimensionless quantum world of possibilia. So causality, and also time, which is the index of causality, are primitive. Space is not primitive. Space (and the geometric spacetime picture of GR) are derived from the primitive relations between and among the events (“geometrogenesis”).

With regard to mind, the speculative idea is that panexperientialism is true, and so there is a mote of first person experience present in every event. So the emergence of human consciousness is not an additional ontological type of emergence beyond the first type.

Steve said...

Instead of "dimensionless" quantum world, I should perhaps have said "hyper-dimensioned" or something like that..

TechTonics said...

I was talking to a French AIT expert about the term "algorithmically incompressible" as an incorrect description (due to the definition) of describing CAs that must unfold in a simulation, there is no predictive shortcut. Wolram's term, "computationally irreducible" is correct. Anyway, he mentioned in passing that QM thoughts about emergence would depend upon which interpretation one chose.
30. For instance, the Schrödinger equation gives a deterministic evolution of the wave-function. In the "traditional interpretation" of quantum mechanics a measurement "collapses the wave-function." This collapse DOES NOT obey Schrödinger’s equation.
After the collapse Schrödinger’s equation again governs the wavefunction evolution. Randomness enters during the measurement.
"One of the central problems in interpretation of quantum theory is the duality of time evolution of physical systems:

1. Unitary evolution by the Schrödinger equation
2. Nondeterministic, nonunitary change during measurement of physical observables, at which time the system "selects" a single value in the range of possible values for the observable. This process is known as wavefunction collapse. Moreover, the process of observation occurs outside the system, which presents a problem on its own if one considers the universe itself to be a quantum system. This is known as the measurement problem.

SH: So the standard interpretation postulates I think, that there are myriad wave-function collapses in this universe. However the Everett, Many-Worlds, and Many-Minds interpretation postulate a universal wave-function: "However Albert and Loewer suggest that the mental does not supervene on the physical, because individual minds have trans-temporal identity of their own. The mind selects one of these identities to be its non-random reality, while the universe itself is unaffected."
With regard to "panexperientialism is true", isn't that a type of dualism which entails supervience?

Steve said...

No; panexperientialism is meant to avoid dualism by specifying that mental events and physical events are the same things. Neither supervenes on the other. The only dualism here is a dualism of perspectives. Mental events are ones we participate in directly; physical events are the others we infer exist via a third person perspective.