Professor T. N. Palmer, a contemporary of Steven Hawking, has proposed a new law of physics. It is the Invariant Set Postulate (ISP) which, if it is true, will have profound implications in the understanding of the fundamental nature of the universe. It also claims to resolve the paradoxes of QM, i. e. superposition, wave-particle duality, the measurement problem and non-locality. Essentially, the ISP proposes that the fundamental geometry of physical reality from the quantum to the cosmic scale, is fractal in nature.
From the abstract of his paper published by The Royal Society, UK, on the Invariant Set Postulate
A new law of physics is proposed, defined on the cosmological scale but with significant implications for the microscale. Motivated by nonlinear dynamical systems theory and black-hole thermodynamics, the Invariant Set Postulate proposes that cosmological states of physical reality belong to a non-computable fractal state-space geometry I, invariant under the action of some subordinate deterministic causal dynamics DI.
Reconciling Einstein with QM:
On the one hand, consistent with Einstein’s view, the Invariant Set Postulate indicates that quantum theory is incomplete in the sense that it is blind to the fractal structure of the invariant set and hence DI. With respect to DI, physics is both deterministic (no dice) and locally causal (no spooky effects).
On the other hand, the Invariant Set Postulate provides an objective basis for understanding why the observer is a partner in the very concept of reality. From the Invariant Set Postulate, it is not meaningful to regard an individual quantum system as having any intrinsic properties independent of the invariant set on which the whole world state evolves. The invariant set is, in part, characterized by the experiments which inform humans about it. Hence, the Invariant Set Postulate implies that it is not meaningful to regard a quantum sub-system as having any intrinsic properties independent of the measurements performed on the quantum system. Since experimenters play a role in determining the nature of these measurements, they manifestly also play a key role in defining the very concept of reality. This is one of the key tenets of the Copenhagen interpretation.
On free will:
However, by the Invariant Set Postulate, this is not the case. We humans are conscious beings. As such, we acknowledge as ‘real’ the physical world around us. Hence, by the Invariant Set Postulate, we acknowledge the reality of I. That is, we acknowledge the reality of something which is fundamentally non-algorithmic. As stressed by Penrose (1989), no automaton would be capable of this!
On gravity:
If the geometry of I is to be considered primitive, then the geometric properties of the invariant set which lead to certain regions being relatively stable and other regions unstable should be considered a generalization of the notion introduced by Einstein that the phenomenon we call ‘gravity’ is merely a manifestation of some more primitive notion of geometry—here the geometry of a dynamically invariant subset of state space.
Conclusion:
Principles of invariance and symmetry form the bedrock of physics. Based on a type of dynamical invariance, a new law of physics is proposed, directly relevant at the cosmological level. Specifically, the Invariant Set Postulate subordinates the notion of the differential equation and elevates as primitive, a dynamically invariant fractal geometry in the state space of the universe.
And the TOE?:
It is proposed that the introduction of global geometric and topological methods in state space may similarly transform our understanding of quantum gravitational physics. Combining these rather different forms of geometry may provide the missing element needed to advance the search for a unified theory of physics.
So, it seems that at the most fundamental level, fractal geometry rules, but we have free will. OK?
The proposer of the postulate is climate scientist and physicist Tim Palmer. Palmer completed a PhD at the University of Oxford under the same supervisor that Stephen Hawking had and then worked with Hawking himself at the University of Cambridge on supergravity theory.
I’ve tried to read Palmer’s article, and to understand it. Which I could only very partially…
So take my comments for what it is worth.
I do not quite see if anything empirical can be derived from the invariant set postulate. Especially, when Palmer says that QM “is blind to the intricate structure of the invariant set”, then how can we empirically verify this? So at most the postulate can give us a mathematical framework that reduces the number of presuppositions (an number of natural constants?) needed: from the view of “Occam’s razor” this might be some kind of progress. Otherwise it is an interpretation of QM as the Copenhagen interpretation, the Bohmian interpretation, or the many worlds interpretation. All of these interpretations have some unimaginable element in it. And I think so has the invariant set postulate. Can you imagine the universe as a fractal in ‘state-space’ (which is not space as we know it!), in which the elements of the fractal are real, and the other elements are possible, but not real?
Exactly this reference to Penrose makes me a little suspicious:
Another potential objection to the notion that experimental parameters are other than “free”, is that it might appear to make us humans, we who fix these parameters, seem no different to automata. However, by the Invariant Set Postulate, this is not the case. We humans are conscious beings. As such, we acknowledge as “real” the physical world around us. Hence, by the Invariant Set Postulate, we acknowledge the reality of I*. That is, we acknowledge the reality of something which is fundamentally non algorithmic. As stressed by Penrose (1989), no automaton would be capable of this!
(* I is the invariant set).
I do not share Penrose’ ideas on free will, and that his explanation of consciousness should be found in a quantum theory of gravity. And the invariant set postulate explains a little bit too much: the measuring problem, the reconciliation of QM and relativity, wave particle duality etc.
Being a good scientist (I have no reason to think Palmer isn’t one), or even a Nobel price winner, does not make somebody an authority always and on every topic (See for example Brian Josephson, here and here).
But I’ll happily wait if this will be picked up by the scientific community. Until now I have not found any serious response to it: not critical, but also nothing that tried to work it out. So we must wait for Palmer or some colleague:
Future papers will attempt to provide the mathematical detail required to develop this exploratory analysis into a rigorous physical theory.
Yeah, this is famously where Penrose goes off the deep end. It’s like Linus Pauling with Vitamin C.
Sounds from kkwan’s link that this guy is a climatologist. So he really has no business proposing new physical laws; it’s crankish stuff. kkwan has a nose for it.
GdB,
Can you imagine the universe as a fractal in ‘state-space’ (which is not space as we know it!), in which the elements of the fractal are real, and the other elements are possible, but not real?
Do we see this apparent fractal function as physical reality or as an implication of a fundametal (non-physical) mathematical function (i.e natural law)?
Could we say that the physical (real) Universe is constructed in accordance with the natural laws of fractal geometrics?
Yeah, this is famously where Penrose goes off the deep end. It’s like Linus Pauling with Vitamin C.
Sounds from kkwan’s link that this guy is a climatologist. So he really has no business proposing new physical laws; it’s crankish stuff. kkwan has a nose for it.
Ah, well, I would not state it so unpolitical .
Sure is that all the authors about fractal cosmology do not have serious discussing partners in established physics or astronomy. I did not find any article about it aimed at peers.
Palmer might be an exception: at least his dissertation was about relativity, and he seems to be an authority on climate research. And as a ‘quarter physicist’, I can imagine there are parallels between the mathematics of continue media (that can give rise to fractal structures, e.g. ‘fractal smoke’ (see below)) and cosmology. But the absence of real calculations, the deafening silence following his article, and last but not least his reference to Penrose’ ideas about consciousness and free will make me highly suspicious. It seems to me that a lot of people, even on this forum, look for some ‘intricate order’ in the universe, looking for something fascinating that can partially fill up the emptiness left by god.
Write4U - 26 December 2010 02:32 PM
Do we see this apparent fractal function as physical reality or as an implication of a fundametal (non-physical) mathematical function (i.e natural law)?
Could we say that the physical (real) Universe is constructed in accordance with the natural laws of fractal geometrics?
Maybe you should first explain what you are trying to ask?
Write4U - 26 December 2010 02:32 PM
Do we see this apparent fractal function as physical reality or as an implication of a fundametal (non-physical) mathematical function (i.e natural law)?
Could we say that the physical (real) Universe is constructed in accordance with the natural laws of fractal geometrics?
Maybe you should first explain what you are trying to ask?
GdB
Yes, now that I look at it.
I withdraw the question….
Yeah, this is famously where Penrose goes off the deep end. It’s like Linus Pauling with Vitamin C.
Sounds from kkwan’s link that this guy is a climatologist. So he really has no business proposing new physical laws; it’s crankish stuff. kkwan has a nose for it.
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
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.”
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.
He is definitely not a crank, being appointed the Royal Society Research Professor in the physics department at Oxford University, UK, in 2010.
BTW, Albert Einstein was working in the patent office when he wrote papers on the photoelectric effect, Brownian motion and special relativity.
Biddulph (2010) has explained this by applying techniques from deterministic chaos to non-chaotic systems, in particular a computable version of Palmer’s Universal Invariant Set proposition (2009), which allows the apparent weirdness of quantum phenomena to be explained as artefacts of the quantum apparatus not a fundamental property of nature. Waves are shown to be the only means of describing motion, since smooth motion on a continuum is impossible. If a particle visits every point on its trajectory then the motion is an algorithm for each point. Turing has shown that almost all numbers are non-computable, which means that there is no possible algorithm, so the set of points on a trajectory is sparse. This implies that motion is either jerky or wave-like. By removing the need to load the particle with the properties of space and time, a fully deterministic, local and causal description of quantum phenomena is possible by use of a simple dynamical operator on a Universal Invariant Set.
Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system.
Central Principle:
Thus, if a state is to be observer-dependent, then a description of a system would follow the form “system S is in state x with reference to observer O” or similar constructions, much like in relativity theory. In RQM it is meaningless to refer to the absolute, observer-independent state of any system.
On the completeness of QM:
Consequently, if quantum mechanics is to be a complete theory, RQM argues that the notion of “state” describes not the observed system itself, but the relationship, or correlation, between the system and its observer(s).
All systems are quantum systems:
All physical interactions are, at bottom, quantum interactions, and must ultimately be governed by the same rules. Thus, an interaction between two particles does not, in RQM, differ fundamentally from an interaction between a particle and some “apparatus”. There is no true wave collapse, in the sense in which it occurs in the Copenhagen interpretation.
He is definitely not a crank, being appointed the Royal Society Research Professor in the physics department at Oxford University, UK, in 2010.
So? Penrose isn’t a crank, but his ideas about the quantum mechanical nature of the mind are crank ideas. Linus Pauling wasn’t a crank, but his ideas about Vitamin C were.
Again, you seem to have an unerring eye for finding crank ideas ...
kkwan - 28 December 2010 08:38 AM
BTW, Albert Einstein was working in the patent office when he wrote papers on the photoelectric effect, Brownian motion and special relativity.
OK, we’ll see if this guy is the next Albert Einstein. I’m tempted to suggest a bet.
BTW every crank in existence has compared him or herself to Galileo, Copernicus or Einstein. It gets old.
I believe Einstein was working at the patent office because his application for a professorship at a major university was shot down by a department head because he was a Jew.
I believe Einstein was working at the patent office because his application for a professorship at a major university was shot down by a department head because he was a Jew.
I think it was just difficult to find a job. Never heard of any antisemitism in this respect. I found this:
Einstein graduated from his teachers’ training program at the Zurich Polytechnic in August 1900, along with three other students. Two of these students immediately obtained positions as assistants at the Polytechnic, but Einstein was not so fortunate; Professor Weber, a German, was not particularly fond of the student who had renounced his citizenship and relied on his friend’s lecture notes to pass all his classes.
Among his teachers were the German pure mathematician Hermann Minkowski, whose style he found unstimulating, and the Swiss experimental physicist Heinrich Friedrich Weber, in whose laboratory he happily toiled. Einstein was an independent student who did not endear himself to his professors. He succeeded in his final examinations by borrowing lecture notes from fellow students, notably Marcel Grossmann. Upon graduating, Einstein failed to be named assistant by any of his teachers—the usual post obtained by a young scientist working toward a doctorate.
So? Penrose isn’t a crank, but his ideas about the quantum mechanical nature of the mind are crank ideas. Linus Pauling wasn’t a crank, but his ideas about Vitamin C were.
Again, you seem to have an unerring eye for finding crank ideas ...
How about Newton, Godel, Cantor, Darwin, Wittgenstein, Kant, David Hilbert…....?
Michelangelo might have had it. So, too, may Einstein, Socrates and Jane Austen. All are claimed to have had Asperger’s syndrome, a form of autism. What is it about this developmental disorder that can lead to genius?
It is rarely possible to make major advances in science without this narrow intense focus. The lack of interest in emotional issues means that there is far more time available for intellectual mathematical, philosophical, and other scientific pursuits.
Albert Einstein and Isaac Newton both experienced intense intellectual interests in specific areas. Both scientists had trouble reacting appropriately in social situations and had difficulty communicating. Both scientists sometimes became so involved with their work that they did not eat. Newton spoke little and was frequently lukewarm or bad-tempered with the few friends he had. If no one attended his lecture he still lectured to an empty room. When he was 50, Newton suffered a nervous breakdown involving depression and paranoia. After Newton’s death however, his body was found to contain massive amounts of mercury, probably from his alchemical pursuits, which could have accounted for his eccentricity in later life.
Described by David Hilbert, Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of rings, fields, and algebras. In physics, Noether’s theorem explains the fundamental connection between symmetry and conservation laws.
kkwan, I have no idea what point you’re trying to make. That Gödel and Cantor weren’t cranks and so Palmer’s new physical law isn’t crankish? That Palmer has Asperger’s? That anyone with Asperger’s should be assumed to be a genius? That nobody with Asperger’s is a crank?
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