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.

"Disgrace indeed, to be caught in a metaphysical position"
J. S. Bell,
Free Variables and Local Causality, Speakable and Unspeakable in Quantum Mechanics p. 101

A little dry Scottish humor!

I downloaded and started reviewing the paper yesterday. And I agree there are interesting points. But I am unsure whether this is something that creates anything new or testable.

Now, I'm just a guy who does computers and has an interest in physics. I do not have the skill, actually, I probably do, but I don't have the patience for the mathematics.

This really is a very interesting time, but I'm unconvinced that Palmers theories are more than a shoot from the hip approach.

There are a few on some of the FR physics threads that make a cogent argument that pure mathematics is divorced from physics. This is an easy argument to reject on it's face, but there may be way more to it than we can imagine now.

All of the experiences in early physics dealt with something that was perceived to be dense and continuous. One could make an argument that this view had to at least start being rejected with Plancks work.

Here's the deal: If the physics gives us results that contradict the predictions of the mathematics, we have to toss out the math, not the reality!

Einsteins work as much as I understand it depend on a dense, continuous four dimensional world. But Bell's arguments show GR is incompatible with quantum logic. Not just in the scope of the very tiny neighborhood of a particle, but macroscopically.

So it seems to me that what we are seeing is a change from physics being something concerned with centimeters and seconds and whatever (a physical geometric model) into something concerned with set theory and topology (a looser abstract model).

And I applaud the author for moving in that direction. I have long felt that the ultimate answers were going to be more in the abstract world.

What use is it to posit an abstract theory that has no phenomenological basis? That's kind of like a computer graphics program drawing a picture of the most beautiful woman you could ever imagine.

Interesting exercise, maybe, but ultimately, a waste of time leading to frustration. Some good effort needs to be spent looking at the wherewithals of abstract models and how to "value" them. Thumbs up!! Thumbs down!! A Roman kind of thing. If we are dealing with totally abstract, untestable models, we might end up throwing the baby out with the bathwater. And I'm not sure we would have lost anything!

"Depends on what the meaning of 'IS' is."
Bill Clinton

So we'll see, I guess. This is a preliminary paper. But he admits the base and results are non-computational, so I'm not going to hold my breath or lose any sleep over it...

As you said earlier, there’s no “there” there!

Or, to sow my age and re-use a worn expression, “Where’s the beef???”

You can’t “prove” something by definition. If he were to walk up to us with a notebook and say “Here’s the set” are we simply supposed to take his word for it? What if someone else arrives with another notebook and says “That’s not the set! This is my set and it’s the real set!!”

What do we do, flip a coin?

Something very fundamental is missing here.

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