Posted on 08/18/2009 10:37:08 AM PDT by LibWhacker
The Invariant Set Postulate differentiates between reality and unreality, suggesting the existence of a state space, within which a smaller subset of state space (reality) is embedded.
(PhysOrg.com) -- Since the early days of quantum mechanics, scientists have been trying to understand the many strange implications of the theory: superpositions, wave-particle duality, and the observer’s role in measurements, to name a few. Now, a new proposed law of physics that describes the geometry of physical reality on the cosmological scale might help answer some of these questions. Plus, the new law could give some clues about the role of gravity in quantum physics, possibly pointing the way to a unified theory of physics.
Tim Palmer, a weather and climate researcher at the European Centre for Medium-Range Weather Forecasts in Reading, UK, has been interested in the idea of a new geometric framework for quantum theory for a long time. Palmer’s doctoral thesis was in general relativity theory at Oxford University in the late 1970s. His studies convinced him that a successful quantum theory of gravity requires some geometric generalization of quantum theory, but at the time he was unsure what specific form this generalization should take. Over the years, Palmer’s professional research moved away from this area of theoretical physics, and he is now one of the world’s experts on the predictability of climate, a subject which has considerable input from nonlinear dynamical systems theory. In a return to his original quest for a realistic geometric quantum theory, Palmer has applied geometric thinking inspired by such dynamical systems theory to propose the new law, called the Invariant Set Postulate, described in a recent issue of the Proceedings of the Royal Society A.
As Palmer explained to PhysOrg.com, the Invariant Set Postulate is proposed as a new geometric framework for understanding the basic foundations of quantum physics. "Crucially, the framework allows a differentiation between states of physical reality and physical 'unreality,'" he said.
The theory suggests the existence of a state space (the set of all possible states of the universe), within which a smaller (fractal) subset of state space is embedded. This subset is dynamically invariant in the sense that states which belong on this subset will always belong to it, and have always belonged to it. States of physical reality are those, and only those, which belong to this invariant subset of state space; all other points in state space are considered “unreal.” Such points of unreality might correspond to states of the universe in which counterfactual measurements are performed in order to answer questions such as “what would the spin of the electron have been, had my measuring apparatus been oriented this way, instead of that way?” Because of the Invariant Set Postulate, such questions have no definite answer, consistent with the earlier and rather mysterious notion of “complementarity” introduced by Niels Bohr.
According to Palmer, quantum mechanics is not itself sufficiently complete to determine whether a point in state space lies on the invariant set, and indeed neither is any algorithmic extension to quantum theory. As Palmer explains, in quantum theory, states associated with these points of unreality can only be described by abstract mathematical expressions which have the algebraic form of probability but without any underlying sample space. It is this which gives quantum theory its rather abstract mathematical form.
As well as being able to provide an understanding of the notion of complementarity, the two-fold ontological nature of state space can also be used to explain one of the long-standing mysteries of quantum theory: superpositions. According to the Invariant Set Postulate, the reason that Schrodinger’s cat seems to be both alive and dead simultaneously is not because it is, in reality, in two states at once, but rather because quantum mechanics is ignorant of the intricate structure of the invariant set which determines the notion of reality. Whichever point (alive or dead) lies on the invariant set, that one is real. The notion of quantum coherence, which is reflected in the concept of superposition, is, rather, carried by the self-similar geometry of the invariant set.
With superposition seemingly resolved from the perspective of the Invariant Set Postulate, other aspects of quantum mechanics can also be explained. For instance, if states are not in superpositions, then making a measurement on the quantum system does not “collapse the state” of the system. By contrast, in Palmer’s framework, a measurement merely describes a specific quasi-stationary aspect of the geometry of the invariant set, which in turn also informs us humans about the invariant set.
The Invariant Set Postulate appears to reconcile Einstein’s view that quantum mechanics is incomplete, with the Copenhagen interpretation that the observer plays a vital role in defining the very concept of reality. Hence, consistent with Einstein’s view, quantum theory is incomplete since it is blind to the intricate structure of the invariant set. Yet consistent with the Copenhagen interpretation, the invariant set is in part characterized by the experiments that humans perform on it, which is to say that experimenters do indeed play a key role in defining states of physical reality.
Yet another quantum mechanical concept that the Invariant Set Postulate may resolve is wave-particle duality. In the two-slit experiment, a world where particles travel to areas of destructive interference simply does not lie on the invariant set, and therefore does not correspond to a state of physical reality.
Among the remaining mysteries of quantum mechanics that the Invariant Set Postulate might help explain is the role of gravity in quantum physics. As Palmer notes, gravity has sometimes been considered as an objective mechanism for the collapse of a superposed state. However, since the Invariant Set Postulate does not require superposed states, it does not require a collapse mechanism. Rather, Palmer suggests that gravity plays a key role in defining the state space geometry of the invariant set. This idea fits with Einstein’s view that gravity is a manifestation of geometry. As such, Palmer suggests, unifying the concepts of non-Euclidean causal space-time geometry and the fractal atemporal geometry of state space could lead to the long-sought theory of “quantum gravity.” Such a theory would be very different from previous approaches, which attempt to quantize gravity within the framework of standard quantum theory.
Palmer’s paper is an exploratory analysis of this Invariant Set Postulate, and he now hopes to develop his ideas into a rigorous physical theory. Just as global space-time geometric methods transformed our understanding of classical gravitational physics in the 1960s, Palmer hopes that the introduction of global state space geometric methods could give scientists a deeper understanding of quantum gravitational physics. And, as suggested above, combining these two types of geometry might help lead to the long-sought unified theory of physics.
Great article, thank you.
It’s not that the electron might be here or there, it’s that both locations make sense simultaneously, until the nature of the observation thereof chooses one over the other, making the other nonsensical and thus nonexistent.
Kinda like $1.00 in change could be 4 quarters or 10 dimes - both answers are correct, until something dictates the reality includes one dime or one quarter, which in turn dictates the reality of the rest of the coins accordingly.
QM tells us we’re asking the wrong questions.
His theory explains why the “probability” component of QM isn’t.
Sorta like how part of Algebra didn’t make any sense until someone came to grips with “square root of -1” - the answers are real numbers, but to reach them you have to go thru “imaginary numbers”. Likewise, to solve real-world physics you have to go thru the “imaginary space” of quantum mechanics.
Yes, the "reality" set is always static...until it changes and becomes the new reality.
However, in the "unreality" set...all "change" and all potential states exist. Since we are in the reality set, we can only see reality.
However, we can imagine unreality.
Sheesh. That's a boatload of conceptual thinking to digest over the next decade or so...
Beautifully stated! If the neat little box of reality begins to bulge and have hair-balls sticking out of it, just get a bigger box and stuff the whole thing into it. Works until it happens again...
You were correct!
He rejects superposition then says QM is incomplete. But offers no way to find out how to complete it, or if it can be supplanted.
We already knew that QM is talking about an infinite space/infinite dimensional model that has far more possibilities than the solutions that (might appear to) match the observables.
Some people call them eigenvalues. He calls them “invariant sets”.
You say potato...
I gathered that the reality portion was that which is static regardless of dimensionality or measurability (i.e. the atomic weight of X is Y). The unreality was that which is dynamic or incapable of accurate measure dependent upon the dimensionality or measurability.
...ok, now I’m confused.
Besides, this seems to be a rehash of the “hidden variable” theory.
I’d love to see this guy in the ring with J. S. Bell!!
Sooooooo does this mean the guy can tell me who’s gonna win the Super Bowl?
B4L8r
I think, therefore I am. Or not. ;^)
In my field, electrical engineering, when finding mathematical solutions, we would always end up with the real part and the imaginary part.
We would ignore the imaginary part as an unreal artifact.
I just can't agree. I believe that this paper points to a new way of understanding much. I have seen variants of this general postulation from the state space side which contains all possible outcomes from the beginning of time. The reality that we can observe and live in is the result of the collapse of this greater set of possibilities into actualities that we see as the flow of time.
This paper takes this general concept that has been around and more carefully defines it and relates it to the most vexing questions of "working" quantum mechanics and thus clears away the paradoxes and muddles that point to completely illogical conclusions from the view of standard reasoning, but are completely possible from a quantum mechanical stand point.
This theory explains why what is ... is.. and what is not is not, by proposing a set of possibilities that are, if you would, meant to be.
Now he may or may not be correct about this.. for ultimately this might lead to some sense of pre-destination, but as they state in the article, the system he proposes allows for intention, human interaction, other interaction to determine the state, like picking one chute rather than the other in a water park which points reality in that direction never to return to the same choice point again.
Bob Coeke of Oxford University states: "What makes this really interesting is that it gets away from the usual debates over multiple universes and hidden variables and so on. It suggests there might be an underlying physical geometry that physics has just missed, which is radical and very positive". He added that "Palmer manages to explain some quantum phenomena, but he hasn't yet derived the whole rigid structure of the theory. This is really necessary."
“Can fractals make sense of the quantum world?” by Mark Buchanan
What we have here is a swipe at an explanation and not the whole explanation, but it is sufficiently pleasing that it merits noting and when the whole is proposed, it is very likely that a prediction can be made that can be rejected that would not otherwise be obvious.
Stated very imprecisely, what you are describing is nothing more than the Feynman Path Integral Formulation. Not new.
Possibly, but I think not. The article states, "... the invariant set is in part characterized by the experiments that humans perform on it, which is to say that experimenters do indeed play a key role in defining states of physical reality."
This is a fancy way of putting the rather common-sense position that actions have consequences. Further, however, it lends a temporal aspect to reality -- "the invariant set" is not static per se, but rather unfolds as "observers" (however defined) interact with the existing invariant set.
The concept of predictability fits nicely into this structure: the fact of my deciding to do a thing, at a particular point in time, closes off other possible actions; the reduced set of actions will fall in the vicinity of a future "path," which gets wider with distance from the decision point.
Of course, none of this is particularly new -- it's been the plot of many a sci-fi novel -- but if Mr. Palmer has managed to formalize it in a useful way, that would indeed be new.
Unfortunately, if the "new theory" actually "gets away" from this -- which I seriously doubt it does -- it cannot possibly be correct. Belle's Theorem is not an argument: it is a rigorously correct mathematical result. The Einstein-Podolsky-Rosen Paradox is not a paradox at all: it is a description of what actually happens in our world. Claiming that the correlated spin of one particle doesn't really effect the other at a distance because this is simply "the reality" and the other possible correlated spin state is "not a reality" is tautological.
To take a simpler example: The behavior of sufficiently smooth functions on their boundaries completely determines their behavior throughout the volumes in which they are defined. This is a (admittedly imprecise statement of a) mathematical fact. Consequently we can describe our physics as happening throughout the volume of space-time, or, if we desire, we can consider that reality an illusion for something that is happening simply on the boundary of the universe with the same physical laws (suitably mathematically rephrased on that boundary). This has led to some silly articles about how we may be nothing more than "holographic projections of something that is happening on the edge of our universe." Well, actually, we are, and we are also happening inside the physical volume of the universe, because the two things are not different. The physics is not changed.
Back to the instant case: the fact that the cat lives sometimes and dies other times is not altered by this new interpretation. Unless the "new theory" can actually predict when the cat dies, the uncertainty principle, non-deterministic causality, and all the so-called "paradoxes" remain, and are not answered by hand waving arguments that in some cases the cat lives because that's the way it goes, and in some cases she dies because of the same "explanation."
Sorry, but it has the stench of the weak anthropic principle: either it's trivially true, or it's not science. I hope there is a lot more to this new "theory" than the article conveys.
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