Oleg, if I understand correctly, you and I have very little disagreement when it comes to the physics of the large. Our potentially biggest problem is that when the math indicates the path-length of a light ray is ZERO, I embrace that as reality. To me, I accept that our observable universe is actually the complex geometry described by Minkowski, Penrose and others. I consider it more than just math. Penrose's twistor space directly deals with zero path-lengths by representing light rays as single points.

I don't have major problems with anything before this paragraph in your last comment. There are some things that I would phrase differently, but they are minor points compared to what lies beyond the quoted paragraph.

Concerning this paragraph itself, I don't share your fascination with null geodesics, but that's okay: beauty is in the eye of the beholder. I actually agree that Minkowski geometry is more than just math: it is a physical model of our spacetime, tested and found accurate.

But let's go to the next couple of paragraphs.

I presume the physics of the large must somehow be the same as the physics of the small. Reality is reality.

Physics of the large is not necessarily the same as physics of the small. Properties of a crystalline solid (say, gold) are very different from those of a single gold atom. For instance, a crystal has rigidity, a single atom does not. I suspect that you may mean something else by that, like there should be a universal theory that describes everything from the Planck scale to the scale of the Universe. It's a pipe dream. Physics is a patchwork of theories applicable each in its own domain. Quantum mechanics is useful on the scale of a few angstrohms, but no one in his right mind applies it to the description of, say, airplane motion. It is neither practical, nor necessary. That said, different patches of physical theory overlap with one another and they must agree in the overlap region. Indeed, we know that equations of quantum mechanics reduce to classical physics when we deal with large objects (Schroedinger's cat notwithstanding). Relativistic dynamics turns into Newtonian at low velocities. And so on. At the moment, however, quantum physics does not patch up with general relativity, so this is an area of current research. Nonetheless, a theory that will eventually unify the two on the small scale will not be a theory of everything. It will be a theory useful in its realm of mind-bogglingly small distances and high particle energies. However, it won't supplant either quantum mechanics or general relativity outside of that realm.

With this is mind, it provides basic explanations for quantum experiments like Delayed Choice Quantum Eraser. It is a geometry problem with light rays being points.

Oleg, having read Penrose's book, would you agree that Penrose's twistor theory provides a basic explaination for this experiment (especially since is was done with light and not heavier particles)?

This is your fantasy, TP. Penrose has never said anything that could be interpreted in this way. We have gone over his book over and over and there is nothing even resembling that. I completely disagree with this (mis)characterization.

If we presume the twistor-string theory gains acceptence, it will result in something I pointed out multiple times. It is ironic that it looks like it is easier to solve the riddle of combining the physics of the cosmos with quantum physics than it is to explain our everyday world.

What you pointed out multiple times falls into two categories: (a) things long ago accepted by physicists such as the shortcut in Minkowski space. (b) mischaracterizations of passages in Penrose's book, like Minkowski geometry somehow explaining quantum entanglement. (Sorry about being blunt, but since you are summarizing our dialog for the lurking reader, I have to call a spade a spade.) Penrose has never suggested that. I have just explained to you that twistors are quantized like everything else and that quantum physics is not a consequence of twistor math. Yet for some reason you still cling to this totally bogus claim. It's your right to say whatever you want, but it's also my right to point out that it is complete BS.

IOW, it is our everyday world that is "weird" not Quantum Mechanics.

Whatever you say. Weirdness is a subjective characterization.

This is why I think Penrose has already presumed his twistor theory and quantum gravity are correct (even if he is missing some of the details). He has already moved on to the followup problem, providing a complete model for decoherence. And, no decoherence model would be complete without explaining the Schrödinger's cat Gedankenexperiment.

A careful reading of the book suggests that Penrose is much more modest in his assessment of twistor theory. In Ch. 33.14 The future of twistor theory? (p. 1003) he writes:

but did I not complain, in Chapter 31, that a weakness of string theory was that it was itself largely mathematically driven, with too little guidance coming from the nature of the physical world? In some respects this is a valid criticism of twistor theory also. There is certainly no hard reason, coming from modern observational data, to force us into a belief that twistor theory provides the route that modern physics should follow.

He goes on to list some known difficulties of twistor theory (like the left-right asymmetry). On the next page he writes:

The main criticism that can be levelled at twistor theory, as of now, is that it is not really a physical theory. It certainly makes no unambiguous physical predictions. My own (over-)optimistic perspective would be to regard twistor theory as being vaguely comparable with the Hamiltonian formalism of classical physics. Hamiltonian theory did not introduce physical changes, but it provided a different outlook on classical physics that later proved to be just what was required for the new quantum theory according to Schroedinger's prescriptions, as described in Chapters 21-23. Twistor theory, likewise, is merely a reformulation that does not necessarily introduce physical changes. The optimistic hope is that its framework might also provide a leaping-off point for some significant physical developments in the future.

I can summarize these passages in a shorter way: at this point, twistor theory is just math. I am quite certain that it is an accurate characterization, one with which even Penrose would agree.

Ergo, Penrose had to explore the role of consciousness and wrote several books and embraced Hameroff's ideas.
I think it's much more prosaic than that. Penrose is a mathematical physicist. Quantum mechanics and general relativity are his cup of tea, so it's natural for Penrose to look to gravity as a cure of quantum conundrums. When all you have is a hammer, every problem looks like a nail. There is no reason at this point to believe that his gravitational model of decoherence is correct. No experiments have been done yet, so it remains a hypothesis, and not a natural one in my book. I personally think that a proper understanding of decoherence will come from active experimental studies in mesoscopic physics, but I have already mentioned that, so I won't dwell on this subject.

Whether or not Penrose is on the right track, I think I understand what he is doing and why.

Sadly, I must tell you that you don't understand what Penrose is doing and I am not sure that I can help you. I tried above to explain what Penrose did with twistors. However, there is certain prerequisite knowledge that one must possess in order to appreciate Penrose's book or my explanations in the previous posts. One needs, at the very least, to know quantum mechanics at the level of a two-semester undergraduate course: canonical quantization, operators, wave functions, that sort of things. I still don't know whether you have that knowledge. Perhaps you could describe your background.

You wrote…

Quantumness does not arise from spacetime, it is applied to spacetime parametrized by twistors.

Thank you for providing the contrary position. On page 962 Penrose was comparing his twistor theories to the alternatives…
"All these ideas concentrate on the construction of notions of 'spacetime' that take on aspects of discreteness of 'quantum' characteristics of some kind. In the remainder of this chapter I shall describe a quite different family of ideas, namely those of twistor theory (to which I have, myself, now devoted over 40 years!) in which there is no discreteness specifically imposed upon spacetime…it does not directly lead to any notion of a 'discrete spacetime'"

I had read this a Penrose identifying something unique about his theory (pride?). I am now rereading this to understand even if discreteness ('quantum') wasn't imposed upon spacetime, that doesn't mean Penrose didn't impose discreteness on his definition of twistor space to allow for quantum phenomena.

I don't have enough mathematical background to judge the degree Penrose artificially force-fit this into his theory. I get the impression that has been a large part of the reason why Penrose's twistor theory has lacked acceptance. Even though no one has managed to poke significant holes in the logic, few can understand it as well as Penrose does. Apparently, Witten was one of the unique few. From the link you provided on the subject…

The emerging link between twistors and string theory arises from the complex-space nature of twistor space. In modern string theory, the space representing the six hidden dimensions is a space of three complex dimensions known as a Calabi-Yau space. The strings themselves are usually taken as lying inside the Calabi-Yau spaces, but these spaces are artificially imposed. In twistor theory, we can put the strings into twistor space instead. The geometrical correspondence between twistor space and the four-real-dimensional space-time of special relativity means that twistor space now does double duty: it simultaneously supplies the needs of both the Calabi-Yau spaces and space-time itself. Accordingly, the strings now become complex curves — Riemann surfaces, to be specific — in twistor space!

Twistor theory has been around for a little over four decades now. Like string theory, it has had more impact on pure mathematics than on clear-cut physical results, but as the string theorists begin to take it up it may just be coming into its own as a physical theory. And, since fully fledged twistor theory calls for just three space dimensions and one time dimension, the first result of this emerging union may well be that those extra dimensions of string theory slip quietly away.

While I wish I could understand it better, it sure sounds promising.

You asked…

Does this help?

Very much so. I want a realistic picture. I expected and accept that it is possible that most of this is Penrose manipulating the math to look good. It wouldn't be too hard to fool me. But I suggest that manipulating math to complete a model is better than trying to impose extra, undetectable dimensions.

If Witten et al can paint a complete model that corresponds to observations and is testable, that would go a long way for establishing the twistor-string theory as a physical theory, IMO.

Let me see if I can summarize things for our listening audience…

In the 1994 debate between Hawking and Penrose, the two of them agreed more than they disagreed. The major disagreement between the two boiled down to the treatment of mathematical models. Penrose tended to argue that models should be developed to explain everything (including Schrödinger's cat Gedankenexperiment) in order to understand reality. Hawkings rejected the notion of pursuing reality because observations is all we have to work with ("Reality is not a quality you can test with litmus paper.") In this vein, it appears that Hawking considers any model that matches observations to be good enough. Oleg, you come across as having more in common with Hawking in this regard (although you seem to embrace Copenhagen stronger than Hawking).

To me, when I see the completeness and beauty of Minkowskian geometry, the math becomes something I can embrace. I don't consider it Truth because I know it could be wrong, but it still seems more than just math that happens to match observations. Especially when I can use it to derive curved Schwarzschild geometry.

This is the point I was trying to get across with my argument against Special Relativity and saying the twin paradox is a geometry problem (twin takes a short cut). Of course the math of Special Relativity matches observations in the SPECIAL case when you pick the correct reference frame and make other assumptions. Like Penrose did in his debate, I point at it and say something is wrong with math that is that incomplete and artificial. The Hawking response is that it isn't wrong as long as it matches observations for the cases in which it is used. But this doesn't make sense to use it when the geometric solution is more complete and more universal.

Penrose's twistor space is a geometric model that is rather complete. It encompasses the spacetime geometry and makes significant inroads in making "an important thread of connection"¦between the physics of the large and the physics of the small."

Oleg, if I understand correctly, you and I have very little disagreement when it comes to the physics of the large. Our potentially biggest problem is that when the math indicates the path-length of a light ray is ZERO, I embrace that as reality. To me, I accept that our observable universe is actually the complex geometry described by Minkowski, Penrose and others. I consider it more than just math. Penrose's twistor space directly deals with zero path-lengths by representing light rays as single points.

I presume the physics of the large must somehow be the same as the physics of the small. Reality is reality.

With this is mind, to me spacetime geometry provides basic explanations for quantum experiments like Delayed Choice Quantum Eraser. It is a geometry problem with light rays being points.

Oleg, having read Penrose's book, would you agree that Penrose's twistor theory provides a basic explaination for this experiment (especially since is was done with light and not heavier particles)?

If we presume the twistor-string theory gains acceptence, it will result in something I have pointed out multiple times. It is ironic that it looks like it is easier to solve the riddle of combining the physics of the cosmos with quantum physics than it is to explain our everyday world.

IOW, it is our everyday world that is "weird" not Quantum Mechanics.

This is why I think Penrose has already presumed his twistor theory and quantum gravity are correct (even if he is missing some of the details). He has already moved on to the followup problem, providing a complete model for decoherence. And, no decoherence model would be complete without explaining the Schrödinger's cat Gedankenexperiment.

Ergo, Penrose had to explore the role of consciousness which resulted in him writing several books and embracing Hameroff's ideas for Orch OR.

Whether or not Penrose is on the right track, I think I understand what he is doing and why.

Let's dwell a bit on Ch. 33.7, Twistor quantum theory. At the beginning of it, Penrose writes:

What, indeed, does twistor theory have to say about unifying spacetime structure with quantum-mechanical principles? So far, we have merely seen some `cute' geometrical and algebraic ways to describe massless particles, but neither quantum-mechanical nor general-relativistic ideas have yet played any roles. I had better to see to this! [italics mine --OT]

Note that Penrose's program is to unify quantum mechanics and spacetime structure, rather than to derive the former from the latter.

A physicist might guess from that brief passage that the program is to be realized in the standard way, through canonical quantization. First, obtain a classical description of the physical system. Twistor math introduced in previous chapters is precisely that, a classical theory dealing with classical trajectories of massless particles. Next, identify pairs of canonical conjugate variables, such as coordinates and momenta for pointlike particles (Ch. 21.2), the angular variables φ and cosθ for spins, or whatever. Finally, quantize the theory by promoting one variable in the canonical pair to a differential operator. See p. 496, where this procedure is implemented for the case of a nonrelativistic pointlike particle.

Back to Ch. 33.7 (p. 983), where Penrose implements canonical quantization for twistors. He identifies Z and Z-bar as a canonical pair and then promotes Z-bar to a differential operator hbar d/d Z-bar. At that point, twistor theory is quantized. Subsequent chapters deal with the consequences of this quantization.

It is now crystal clear that, contrary to your suggestion, Penrose does not derive quantum mechanics from his twistor description of spacetime. Instead, he applies the standard quantization procedure to twistor theory, the same canonical quantization that has been previously applied to nonrelativistic particles, spin, Maxwell's electromagnetic field and strings. Quantumness does not arise from spacetime, it is applied to spacetime parametrized by twistors.

Does this help?

I really appreciate the time and effort you took in helping me with this. When I asked "…do you see why I feel Penrose directly ties relativistic spacetime geometry to his explanation of quantum physics?"

You answered…

Sure I do.

These little words mean a lot coming from someone of your background. I helps confirm I am not totally clueless (at least on this subject).

It doesn't even bother me that you added…

Still, if I understand his speculations correctly, he is leaning in the direction opposite to yours. His spin networks are an attempt to generate geometry out of quantum physics. You, on the other hand, suggest that it is quantum mechanics that emerges from geometry.

I could only hope my biggest confusion is understanding cause/effect relationships in concepts from which time, itself, emerges.

I never expected to avoid chicken/egg paradoxes. On the contrary, I felt they were a given.

I doubt that I could do better than Penrose at convincing you of the soundness of his logic. However, there is at least one thing I would like to point out to you. You wrote…

Yes, the mathematics of twistors is well suited to dealing with null geodesics. That said, null geodesics are mathematical objects introduced in the framework of the purely classical (i.e. non-quantum) theory of relativity. Null geodesics in themselves have nothing to do with quantum phenomena, much like straight lines in Euclidian space aren't wedded to waves.

If I understand you correctly, this is the aspect of Twistor Theory that Penrose appear to be most proud of. "Quantum phenomena" EMERGES from mathematics that should have nothing to do with it. I was going to try to quote Penrose directly, but that would have required too much typing so please read starting at the beginning of section 33.7 on page 982 and then note the section ends with Penrose illustrating the "chiral nature of twistor theory". IOW, Twistor Space takes on a lop-sided aspect for right and left handedness. In section 33.8, Penrose brings in "Massless fields of mixed helicity-such as a plane-polarized photon, which is the sum of a right-handed and left-handed part". The result of this strikes Penrose "as being somewhat magical." (can't you just feel how much Penrose loves and believes in his math?). Section 33.9 is six pages of Penrose trying to explain "sheaf cohomology" whose ideas "…are fairly sophisticated mathematically, but actually very natural." Penrose uses this to introduce non-locality to the chain of discussion (I freely admit that my attempts to understand it mostly result in only making my head hurt). Section 33.10 explains how positive/negative frequency splitting along with "holomorphic first sheaf cohomology" plays "a direct role in generating deformations of twistor space." This leads to section 33.11 titled, The non-linear graviton. Here, Penrose's quantum gravity falls out of this Twistor Model.

As you know Penrose, and others, have proposed experiments to test the E=h/t of quantum gravity. If this is shown to be correct, I think it would portend for some very interesting discussions, including those involving the Penrose/Hameroff Orch OR model.

But, for the moment, the twistor theory is not a full-blown physical theory (Penrose admits this on page 1001). However, I am biasedly encouraged by the recent developments you have pointed out on a Twistor-string Theory that have occurred since The Road to Reality was written.

I was going to try to do a summary of all of our discussions, but this comment took to long. Maybe some other time.

Thanks again,
TP

Now, it may be my lack of understanding, but it seems to me that String Theory and Twistor Theory are primarily about explaining the foundation of quantum physics. That would include making sense of "quantum weirdness".

Furthermore, it seems to me that Twistor Theory directly deals with "the geometry of spacetime".

String theory applies principles of quantum mechanics to dynamics of extended one-dimensional objects, strings, much like quantum field theory deals with zero-dimensional objects, particles. Neither of these theories sets out to "make sense" of quantum physics. They take it as a starting point.

Furthermore, it seems to me that Twistor Theory directly deals with "the geometry of spacetime".

Yes, the mathematics of twistors is well suited to dealing with null geodesics. That said, null geodesics are mathematical objects introduced in the framework of the purely classical (i.e. non-quantum) theory of relativity. Null geodesics in themselves have nothing to do with quantum phenomena, much like straight lines in Euclidian space aren't wedded to waves.

Therefore, I am puzzled that you "found no indication" of a connection when I think it was one of Penrose's main purposes of The Road to Reality to provide the foundation for the quantum/geometry connection by starting with basic geometry principles, explaining "basic" Minkowskian Geometry and, finally, presenting his Twistor Theory as a geometric model for establishing "an important thread of connection"¦between the physics of the large and the physics of the small." page 962

In that passage Penrose says: look, twistor algebra is natural for spacetime. Both twistor algebra and quantum mechanics of quantum spins involve complex numbers. Ergo, twistors are somehow connected to quantum spins. However, it's a tenuous relation, which may or may not have important consequences.

Penrose writes further down (p. 966-967): "this provides us with hints as to Nature's actual scheme of things, which must ultimately unify spacetime structure with the procedures of quantum mechanics." From this quote it is clear that Penrose does not have a clear idea about the nature of the purported link between quantum mechanics and spacetime. Vague mathematical similarities usually can't replace physical principles. Recall, for instance, that the description of ac circuits also involves complex numbers. Are these circuits relevant in any way to quantum mechanics? The math can be used in many contexts, but it does not establish a physical similarity.

Do you consider String Theory to be part of Physics ("more than just math")?

No, not yet. A theory must go through experimental testing before it can be accepted as a physical model describing reality. That hasn't happened yet to string theory.

What is your reaction to Penrose saying"¦
"ds^2 = dt^2 - dx^2 - dy^2 - dz^2
is more directly physical"¦the integral ds (with ds>0) being directly interpretable as the action physical time"¦" on page 413 in the chapter titled Minkowskian geometry? (Is it "more than just math"?)

In relativity, the interval gives proper time. Theory of relativity has been thoroughly tested by experiments, so it is more than just math, it is a physical model that describes our world.

One of the reasons I have focused on the light code (null geodesic) in past discussions was from Prenrose statements like"¦ "As far as I can make out, quanglement links are always constrained be the light cones, just as are ordinary information links, but quanglement links have the novel feature that they can zig-zag backwards and forwards in time, so as to achieve an effective 'spacelike propagation'." page 603.

I see this as a precursor to the Twistor Theory's geometry where "A light ray in Minkowski spacetime is represented as a single point in the twistor space." page 964

I think he makes it more complicated than necessary. Even without entangled pairs, quantum mechanics demonstrates non-local correlations at the level of a single particle. For instance, if you measure the position of an electron that passed through a slit (or two), there is a finite-size spot where it can be detected, so it is described by a wavefunction that is extended in space. However, once your detector determines the location of the electron, its wavefunction instantaneously shrinks to that single spot and you immediately know that it will not be found at any other location. All these points in spacetime are spatially separated, as in the passage you quoted. What zigzags forward and backward in time in this case? I don't see any reason to think that a purely geometrical "explanation" stands behind all of quantum physics.

Whether or not you agree with this aspect of Penrose's thoughts, do you see why I feel Penrose directly ties relativistic spacetime geometry to his explanation of quantum physics?

Sure I do. Penrose leaves lots of clues that maybe, just maybe, there is some deep connection between geometry and quantum physics. At this point, however, he has no clear idea what the nature of that connection might be.

Still, if I understand his speculations correctly, he is leaning in the direction opposite to yours. His spin networks are an attempt to generate geometry out of quantum physics. You, on the other hand, suggest that it is quantum mechanics that emerges from geometry.

Best,

Oleg

I am glad you read the book, even more so since you liked it. I presume you are trying to be respectful by suggesting that when Penrose concedes Twistor Theory is a MATHEMATICAL model, you take it to somehow mean Penrose is being scientifically humble and isn't actually presenting it as being correct.

Penrose's Black Hole model was purely mathematical. By the time physical evidence was found Penrose, and others, presumed Black Holes existed. The model was too complete and made too much sense to be wrong.

I suggest Penrose didn't need physical confirmation of Black Holes to believe in them.

Likewise, String Theory is purely mathematical. It is clear Penrose treats his Twistor Theory to be on equal, or better, footing than String Theory. Here is what Penrose Said on page 1004 following the quote you gave…

"…the primary case for Twistor theory indeed lies, like string theory (or M-theory) in the strength of its aesthetic or mathematical appeal. The two theories are, however, mathematically incompatible as they stand, because they operate with different numbers of spacetime dimensions."

You also wrote…

However, I have found no indication that he attempts to reduce quantum weirdness to the geometry of spacetime.

Now, it may be my lack of understanding, but it seems to me that String Theory and Twistor Theory are primarily about explaining the foundation of quantum physics. That would include making sense of "quantum weirdness".

Furthermore, it seems to me that Twistor Theory directly deals with "the geometry of spacetime".

Therefore, I am puzzled that you "found no indication" of a connection when I think it was one of Penrose's main purposes of The Road to Reality to provide the foundation for the quantum/geometry connection by starting with basic geometry principles, explaining "basic" Minkowskian Geometry and, finally, presenting his Twistor Theory as a geometric model for establishing "an important thread of connection"¦between the physics of the large and the physics of the small." page 962

You wrote…

If you have any further questions, I'll be glad to answer them.

Thank you. Here are some questions"¦

Do you consider String Theory to be part of Physics ("more than just math")?

What is your reaction to Penrose saying…
"ds^2 = dt^2 - dx^2 - dy^2 - dz^2
is more directly physical…the integral ds (with ds>0) being directly interpretable as the action physical time…" on page 413 in the chapter titled Minkowskian geometry? (Is it "more than just math"?)

One of the reasons I have focused on the light code (null geodesic) in past discussions was from Prenrose statements like… "As far as I can make out, quanglement links are always constrained be the light cones, just as are ordinary information links, but quanglement links have the novel feature that they can zig-zag backwards and forwards in time, so as to achieve an effective 'spacelike propagation'." page 603.

I see this as a precursor to the Twistor Theory's geometry where "A light ray in Minkowski spacetime is represented as a single point in the twistor space." page 964

Whether or not you agree with this aspect of Penrose's thoughts, do you see why I feel Penrose directly ties relativistic spacetime geometry to his explanation of quantum physics?

I have browsed through The Road to Reality and read a few sections more closely. I like the book. It has lots of useful mathematical tricks and I'm sure that some of them will end up in a QM class that I'll teach one day.

Penrose gives a nice exposition of the paradoxical aspects of quantum measurement, including quantum entanglement. However, I have found no indication that he attempts to reduce quantum weirdness to the geometry of spacetime. I may have missed something but from what I read I consider that unlikely.

Same with twistors. Penrose views them as a mathematical device that on its own will not solve the problem of quantum measurement but may be helpful one day when we have an insight from experimental physics that requires new mathematics and twistors are it. On p. 1004 he writes:

My own (over-)optimistic perspective would be to regard twistor theory as being vaguely comparable with the Hamiltonian formalism of classical physics. Hamiltonian theory did not introduce physical changes, but it provided a different outlook on classical physics that later proved to be just what was required for the new quantum theory according to Schroedinger's prescriptions, as described in Chapters 21-23. Twistor theory, likewise, is merely a reformulation that does not necessarily introduce physical changes. The optimistic hope is that its framework might also provide a leaping-off point for some significant physical developments in the future.

Once again, twistors and Minkowski space are mathematical concepts that have no physical meaning on their own. Physics is more than just math. That is why I was skeptical of your assertions from the beginning. Reading Penrose only confirmed that.

If you have any further questions, I'll be glad to answer them.

Sal wrote:
Algorithmic means we can describe it in deterministic detail: i.e. "given this condition, this outcome will happen". I don't think we can do that with QM, ever.

QM has nevertheless inspired thinkers to believe that the universe is some kind of computer.

I think that scientists as Chaitin and Anton Zeilinger support this "digital philosophy"

The following website gives an introduction for the layperson
http://www.bottomlayer.com
http://www.bottomlayer.com/bot...

Best
Albert

Rock wrote:

The guys in the Quantum Computing Lab are going to be sorry to hear that QM is "non-algorithmic" or "non-computable."

For that matter so are all quantum physicists who thought they were actually computing quantum physics!

I think it is a mistake to assume that the existence of computers somehow negate the non-algorithmic nature of QM. Computers have to be designed such that the randomness of QM is limited and suppressed. For example:
here

Trenches have been used with success on chip designs to isolate transistors to prevent the unwanted tunneling of electrons between transistors. While they serve this function well, they occupy much needed chip surface area.

When tunnelling will occur cannot be precisely predicted any more than the when a specific radioactive decay will occur. We can predict distributions, not specific outcomes.

Thus we can build computers because we have techniques (such as error correction) or architectures to limit the propagation of unwanted QM randomness and preserve the semblance of deterministic behavior in the computer.

Nano-molecular computers are even more vulnerable to noise from quantum processes, so it takes work to negate the fact QM is not always amenable to the computations we wish to carry out.

Penrose's book Emperor's New Mind dealth with non-algorithmic phenomenon, incompleteness, QM, and AI.

If we treat the universe as some massive computer with all the quantum systems as bits, then yes, we can say QM is algorthimic in that sense, but not in the sense that the algorithm is accessible to us.

One can say, because of Heisenberg uncertainty, the Computer that is the Universe will conspire to behave in a manner that appears capricious to us. So at least from an operational standpoint. the behavior of Quantum phenomena have an aspect of capriciousness and unpredictability, and thus in an operational sense, it is not algorithmic.

Algorithmic means we can describe it in deterministic detail: i.e. "given this condition, this outcome will happen". I don't think we can do that with QM, ever.

Thanks

My impression of the book is that one could spend a great deal of time working out all the puzzles that Penrose sprinkled throughout the book (e.g. page 170 "Do this, by taking advantage of a power series expansion for log z taken about z = 1, given towards the end of [SECTION 7.4]".

It is obvious Penrose is very much the mathematician.

I like to think I am a quick learner, but this took me quite a while to even understand the basics or what Penrose is saying.

I hope to find the time to go through the book again and work out some of the problems. But I don't see it in the near future.

Yes, I agree, Penrose lays out a very detailed case. Which is why I am looking for counter arguments and other ways to look at it.

I thank you for your efforts and hope any headaches you get from reading Penrose's book aren't too severe.