New Law of Physics Could Explain Quantum Mysteries

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.

Now he may or may not be correct about this.. for ultimately this might lead to some sense of predestination.

The Feynman Path Integral, by the way, explains why predestination seems to be an ingredient of QM (in fact, the Principle of Least Action, which the FPI is an extension of, says the same thing in classical mechanics.) You can describe physics as the result of a Lagrangian in which the past and future are connected by functionals acting under some constraint. In this view, the end points appear to determine all the paths between them, which indeed they do: under the action of the constraint -- The Principle of Least Action -- this results in a single trajectory through phase space (in classical physics) or a set of trajectories in QM.

Completely equivalent to this is the Hamiltonian formulation of mechanics. In the Hamiltonian perspective, starting points are arrived at by application of the time-evolution operator. As you may know -- but for the benefit of passersby -- it is a first year grad-students' exercise to prove these two formulations are mathematically equivalent (after you struggle through Goldstien.)

So something that seems entirely predestined (Lagrangian mechanics) can arise from something where states move through time purely from one infinitesimal starting point to the next under the influence of the Hamiltonian, and vice versa. The reason two so fundamentally different ways of looking at time evolution appear the same is that the underlying physical principle -- The Principle of Least Action -- governs both.

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."

I think you are getting close to understanding what they are trying to get at, but rejecting the point by referencing the weakness of standard Quantum Mechanics to deal with this question as the reason this solution can't work when the contrary is exactly the point.

This Invariant Set Postulate concept is that QM is ignorant of the existence of the "reality" that is the Invariant Set and thus predicts possibilities that are within this Set and those which are outside of this Set, but only those which are within the set are manifest in "reality"

To go to your basic point about smooth functions and a smooth predictable volume within the Universe, this idea sees this volume as a much more complex space wherein many functions may have described the Volume but only a select few indeed do. The insight is that the Quantum Mechanical states possible are restricted to a specific set of states that are only a small group of the states that would otherwise be possible and this set of real possibilities is what we term as physical reality.

What I see missing from this discussion is the fact that the "Invariant Set" must by force be collapsing and thus I am unsure about the name Invariant which would imply that all events throughout all time are already pre-ordained and though potentially not predictable are yet inevitable.

My best guess is that this is not the meaning Palmer has meant to project by using the term Invariant, but that is the limit of this description.

This statement is wildly false. what you are describing is in fact what QM already DOES DO.

You missed my point completely. The analogy deals with mathematical simile and has nothing to do with this putative theory, AT ALL.

The insight is that the Quantum Mechanical states possible are restricted to a specific set of states that are only a small group of the states that would otherwise be possible and this set of real possibilities is what we term as physical reality.

The part of what you say here that is actually correct is not an insight at all. Dirac commented on this informally in the 1930's and it was made part of a serious theory by Feynman. The other part of your statement is, once again, wildly false. If you have a background in physics, you have forgotten what you learned in grad school. If you don't, please Google "Feynman Path Integral." It is a key observation of the theoretical basis of QM that even physically disallowed paths through phase space must contribute to the ultimate trajectory of a state through phase space. This principle is thoroughly established in so many theoretical and experimental results that a theory that does not incorporate this concept CANNOT be correct -- and incidentally, this article does not claim that the "new theory" disallows "unreal" Lagrangian functionals to contribute to a trajectory; it simply says they are not manifest in the Invariant Set... Well, again, SO WHAT? QM already says EXACTLY the same thing: that is the point of the Feynman Path Integral.

While this understanding is deep and internally pleasing, it is limited as many models in physics in requiring that a boundary of consideration exists where specific boundary conditions can be stated and maintained. F=Ma only exists after all of the confounding and interfering terms are removed. This allows for a purity of exposition of the underlying principle when the messy chaotic details would just get in the way.

However, this is not the real world. The real world and more specifically physical reality is the all of the interactions all of the time including the simple ones governed by simple physical or chemical interaction but also including those that are modified by the force of choice and intent that are driven by analysis, subjectivity and even whim.

One admits that human intention limited as it is modifies the great events of time and space very little, but that they can at all is a question that begs to be answered in the presence of the proposition that an INVARIANT set of quantum possibilities may exist. Normal physics does not concern itself with attempting to predict the intentions of the experimenter or scientist or boy at the corner drug store, but this theory posits that all of this is preordained if the Set is truly fixed. Worse, it is the very function of the collapse of possibilities into the reduced set that represents the remaining possibilities that provides the arrow of time making it irreversible. However, I am reading way to much into this. I have to actually dig at the original discussion to make any more or less of it.

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.

Oh the thing I am falling all over is the name "invariant set" this name should have a meaning and as you have said above, the actual set should recognize that actions have consequences and that the set of possibilities that may yet be expressed in reality is constantly dwindling and thus not be invariant.

Now this may be an aspect of fractal geometry that I just don't get at this moment, such that the fractal is invariant even though the pattern is constrained as it impacts each boundary.

The goo contained in the middle is unmoved by lopping off a slice from the outside, thus the arrow of time more precisely defines the invariant set which is only invariant by the fact that once a chuck is lopped off, it may never be reattached.

Your last post, is, quite simply, nonsense.

You know, it is amazing when someone comes along spewing bluster and venom. It neither clarifies nor informs. You are arguing that this idea presented as new is in fact, nothing new.

Which begs, why the heck have other folks looked at it and said, mmm.. may be interesting. You cite basic and accepted theory and say, this guy's stuff is nothing at all and thus assume that anyone looking and saying it is interesting is ignorant or stupid or uninformed.

That is your hill and your battle. There isn't enough information in the article to even begin to support or refute your contentions about this mans suggestion.

Given that, your last statement just speaks poorly about your own character, because your point is basically beyond your reach and requires all others to assume that this article is patently wrong at your insistence alone.

Past this, you seem to intend on attempting a conversation that has no relevance to the folks that inhabit this place. I am attempting to bring the relevance of this to me, into my space and as I do, I am disturbed by a specific term, but know that inevitably the answer will be obvious so I just indulge in a bit of speculation.

Your argument is not convincing, and bluster, name calling and put downs don't make it any moreso.

OK, you deserve the reason for the statement.

First, you don't understand the basic principles of Quantum Mechanics. That's no sin. Many people don't. But please don't pretend to if you don't.

Second, you don't understand what this article even says. The author suggests a resolution of the conceptual difficulties of Quantum Mechanics by positing the existence of an invariant subspace which by definition can only include those events which actually occur. Now: either this is already accepted dogma (Feynman) or a statement of a teleological supreme reality (Tipler/Davies), or it is tautology. The first is not new. The second is not science. The third is not interesting.

Third, your most recent post confuses physical and metaphysical approximation. The fact that F = ma never exactly applies because, say fat people or the most distant galaxies exert an influence on physical systems is hifalutin stuff for a Sophomore bull session that has no place in a serious discussion, but it is, in any event, errant nonsense to claim that the invalidity of an exact result invalidates the physical law itself. What laws do you think the fat people themselves obey? No law? F = mv? Or can they make up their own laws? This is the part of your recent post that is not even wrong: metaphysical approximation is NOT physical approximation. You have made a category error in your argument. It is like claiming that we will never be able to discover the color of the number three, because the colors of all the other numbers make it so confusing. And frankly, you made this not-even-wrong assertion in a patronizing tone.

Fourth: you are wasting my time. You may claim there isn't enough here to invalidate this man's claims (something I've said from the beginning when I said I hoped there was more to this idea than the article could convey) but for someone who believes that you've wasted an awful lot of energy trying to defend it all the same, and in defending it you have made claims about QM that are false or misleading. Should I be polite and let the errors stand? I don't mind back-and-forth, but when you attempt to brush aside a factual statement with some nonsense about how this is all intellectually fine and good but there really is no such thing as a basic physical law because it doesn't encompass all of reality, that's pretty much the limit of my tolerance.

Strikes me as being very tautological. New names for old.

If something has real, physical existence, it is part of the invariant set. (As I define the invariant set).

I could just as well say so-and-so is a purple people eater (if in fact he/she was) and be equally correct.

Unless the theory can be used to predict a heretofore unknown QM effect (like a new kind of tunneling or whatever), then it’s not covering new ground.

Eddington discussed this type of reasoning in his “The Domain of Physical Science” in which he kind of admits that at some point tautology is all that’s left. An electron is a particle that acts like x,y, and z. So when you see a particle that acts like x, y, and z, then it’s an electron. Not by discovery. By definition!

As you stated above, Bell’s theorem is a rigorous mathematical model. But Bell also responded to Einstein, in as far as Einstein speculated that we simply might not “know enough” to have QM give us a complete answer.

Bells answer was that there is no local hidden variable theory that is compatible with QM. (when he talks “local” he means a theory that fits with relativity). And the proof here is just as rigorous.

I’ll have to wade through “Speakable and Unspeakable in Quantum Mechanics” again and see if I can absorb any more than the last time!

First, take a breath. You are having a conversation with someone else and me.. and the someone else isn't here.

Written words have limitations and our own prejudices often fill in the blanks. I was trying to give a clean example of the difference between physical "laws" and reality which is messy but generally follows these laws. In engineering, we use all sorts of constants and fudge factors to deal with these problems and move on. But my point is that theoretical models have limits and are only true in a theoretical framework. Not that they are ever actually not true, but they are never sufficient to describe reality as it actually presents itself.

Now, it stuck me, that what this fellow was attempting is very different, because it is a grand generalization that arches over the very fabric of reality and attempts to describe the nature of all possibilities and what is reality that is but a subset of this grand superset of possibilities. Feynman proposes that in terms of quantum physics that the system doesn't have to know in advance where it's going; the path integral simply calculates the probability amplitude for any given process, and the path goes everywhere. After a long enough time, interference effects guarantee that only the contributions from the stationary points of the action give histories with appreciable probabilities. This posits that all of the possible paths resolve to just a few probable paths via means of quantum superposition. And as you talked about, this is why you must consider the paths that are unreal or imaginary as well as the ones that have real solutions because the prediction would be off without their contribution.

However, Palmer is looking at this from an entirely different perspective. Rather than continue to try to explain this, I point you to the link below.

The author suggests a resolution of the conceptual difficulties of Quantum Mechanics by positing the existence of an invariant subspace which by definition can only include those events which actually occur. Now: either this is already accepted dogma (Feynman) or a statement of a teleological supreme reality (Tipler/Davies), or it is tautology. The first is not new. The second is not science. The third is not interesting.

This statement is probably not correct. You have a withering contempt for folks who don't sit in your little holes. It very likely conforms to Feynman (If it is correct, Feynman likely conforms to Palmer) but provides a new means of understanding this because it doesn't rely on superposition or any of a number of oddities that are necessary for Feynman or need to be conformed to in order to be judged as consistent with observations.

Once again, I argue that this paper published in the peer reviewed Proceedings of the Royal Society of Mathmatical, Physical and Engineering Sciences is worthy of more than a glance and narrow minded brush off. Moreso, the actual paper does have enough detail that it can be evaluated for significance but remember it is but a proposition at this point.

The whole text of this paper can be viewed as text or Downloaded as a PDF here:

The Invariant Set Postulate: a new geometric framework for the foundations of quantum theory and the role played by gravity by T.N. Palmer

The paper cited in the previous post is actually worth a read. A number of ideas -- the role of imaginaries and quaternions in QM are interesting, but too poorly developed to actually be sensible, yet.

He quotes Penrose's 1989 The Emperor's New Mind extensively. This is an excellent book and full of many good ideas, and Penrose is certainly much smarter than I am, but this is a popular source, and not a peer reviewed article. I highly recommend Penrose over this paper if you want to read something that will make you think.

The essence of the sense in which this theory departs from conventional thinking can be described by this statement, which the author explicitly rejects:

't Hooft says: ‘... we must demand that our model (of nature) gives credible scenarios for a universe for any choice of the initial conditions’.

Unfortunately, I must agree with Nobel Laureate 't Hooft that this is a reasonable expectation, and although I am accused of a "withering scorn" for people who don't sit in "my little holes," I will hazard a guess that there is no physicist living or dead who would disagree with this requirement, except the author of the paper himself.

If you read the paper, pay particular attention to the section on page 9 discussing ontology and also the section on page 16 concerning non-locality, where the rabbit comes fully out of the hat. What the author ultimately wants us to believe is that all reality is embedded in a nowhere dense subset of phase space (think the Cantor Dust.) All of the details of the theory actually developed to a point to be thought-provoking are hidden in a leap of faith that any state constructed that contradicts his theory "probably" aren't in this set because it has measure zero. This is not proved, and he brushes aside the severe constraints that physics already places on admissible states in phase space without comment. Unfortunately for his thesis, these restrictions would make it highly likely that any physically realizable state is indeed in this set. Therefore he can dismiss the consequences of Belle's theorem or any other counter-intuitive result in QM because thought experiments aren't even admissible in his perverse ontology.

As an aside: the Invariance in "Invariant Set" comes about as a result of the fact that this nowhere-dense fractal set has is postulated to have physical invariance under a set of dynamical laws -- which are not specified. Until they are, there is really no "there, there."

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