Abstract: **Incompleteness is not just a consequence of our finite neurobiology. Quantum Physics says that Incompleteness is how the universe works**.

Einstein famously pondered whether Quantum Mechanics could be considered complete. He looked, very fruitfully, at nonlocal effects. Einstein and his collaborators asked:

*Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?*

A. Einstein, B. Podolsky, and N. Rosen*Phys. Rev. 47, 777 – Published 15 May 1935*

However a more direct, simpler answer was possible: **Quantum Mechanics is obviously incomplete in comparison to the (erroneous) Weltgeist Classical Mechanics gave us**. Quantum Mechanics does not allow us to have as complete a knowledge of the world as we thought possible. And no, this observation is not a rehash of the Uncertainty Principle… which actually is not an overall principle, since it has been experimentally violated in 2021.

Some philosophers, observing we know just part of reality, claimed that all we know is therefore illusion. However, pontificating that we are certain about uncertainty or incompleteness in some certain cases doesn’t make everything a complete illusions… This silly position emanated from Plato. That’s so obvious one would not have to tell it to a toddler.

So Platonism “All-Is-An-Illusion-I-read-It-In-A-Cave” was already found “embarrassing” by Aristotle, 24 centuries ago, “because these people are friends”

There are forms of incompleteness. Neurobiology always considers portions of reality, on a “need to know basis”. But sometimes the sensitivity of the human eye and its neurons is down to ONE photon: can’t beat that. Moreover the problem of incompleteness does not just have to do with biology being finite…

Nor do we have, when considering incompleteness, to harness the mathematical axiom of infinity and brandish theorems of Gödel or Tarski about incompleteness, which can be deduced from it. Although these theorems attracted a lot of attention, they are very specialized aspects of so-called “Second Order logic”, and the importance non-specialists give them mostly reflect the ignorance of said non-specialists. Biological incompleteness and Quantum incompleteness, my subject here, are much more primordial and important.

**Incompleteness arises straight from physics: arguably, reality, as depicted in Quantum Mechanics, is INTRINSICALLY incomplete (relative to what Classical Mechanics took, erroneously, for granted). In Quantum Mechanics, completeness is just a need-to-do basis. **

Look carefully at the axiomatic of Quantum Physics. Given an experimental situation, one sets up a Hilbert Space H the ** eigenbasis** of which is made of possible outcomes of said experiment. The experiment is by definition partial, a part of reality, and thus so is H. This Hilbert Space H is intrinsically a partial consideration. This is a trivial, thus very deep observation. PARTIAL CONSIDERATION IS HOW QUANTUM PHYSICS WORKS… Because any Quantum measurement is inside a Hilbert space specific to that measurement.

**That any Quantum realm, this Hilbert Space H it is made of, has constraints turns on its head the worries of Einstein about Quantum Physics being incomplete (applause!) Quantum Physics is not incomplete. Instead Classical Mechanics assumes freedoms we do not have**.

Lest I be accused to illusionary logic, I will need to dig into the argument. What’s the difference with Classical Mechanics? The argument I make is then highly non trivial and controversial… because, should it be correct, it demolishes at the most basic philosophical level a new technique in physics called “* Quantum Trajectories*“… and yet I do believe in the work of some physicists using those “Quantum Trajectories”…

When we deal with a classical system, all initial conditions can be considered (and then those get plugged into a Partial Differential Equation). Not so in Quantum Physics. Consider the setup of the original EPR: two regions, A and B, vastly separated in space. Measuring in A constraints measurements in B. This has been verified experimentally outside of the light cones (so the Quantum Interaction is superluminal). There is no such a constraint in Classical Mechanics.

**Thus Quantum Physics restricts our freedom. We are not free to expect any outcome by making any measurements: the outcomes have been restricted, sight unseen** [2]. But it also means that, however restricted they may be, incomplete descriptions of reality can be full. Thus bemoaning that what may appear to be a partial description is an illusion is silly: partiality can be full and dynamic.

Patrice Ayme

***

[1] What should be viewed as well-knowns philosophical errors of the past often enjoy great Internet applause. The gist of it was that human reality was an illusion because it comprised just a fraction of “reality”. Hence the need for “objectivity”. This is a variation on Plato’s Cave Argument.

Here is some of what a honorable retired IT specialist says, while apparently not aware that finding out the nature of reality is what physics does: “*Reality is the set of everything that exists…biological entities, like humans, have no direct access to reality… we don’t experience reality: we experience only stimuli from reality… The wavelengths of light and sound that we are able to detect are only a small subset of all available wavelengths. Our sense of smell is similarly hobbled. There’s a lot of stimuli from reality that we’re missing. The human experience of reality is actually an illusion, albeit one that serves us pretty well*…

*It’s this disconnection from raw reality that explains our need for objectivity. We have no way of knowing what reality is.”*

This sort of all-too philosophical consideration is what happens when people do not know much more than what was already known 2,000 years ago. The nature of reality and the nature of objectivity have been intensely the focus of physics ever since *Henri Poincaré* introduced Relativity and local time, pushing Lorentz’s work to its conclusion… and then Planck introduced the idea of the Quantum, soon boosted by Einstein.

The result is that not anything goes: as I said above, there restrictions in providing and receiving information: Quantum Physics reduces our freedom.

***

[2] Does that mean that the Moon is not there when we don’t look at it? No. The Moon itself is zillions of entanglements entangled together, running its own reality show. No need for us.

Reality is NOT what we make it, as some deranged Copenhagen Quantum Interpretation fanatics had it. It’s more subtle.

June 19, 2021 at 6:43 am |

Patrice, you wrote: “There is no such a constraint in Classical Mechanics.”

I disagree. In classical physics, entanglement is caused by applying a conservation law. At that point, in the EPR type thought experiment you usually know the momentum of both particles provided you know the coefficient of elasticity, and of course you know the momenta of the particles in the given frame of reference prior to the collision that entangled them. First year physics students usually get some sort of question along these lines. The problem with quantum mechanics is you don’t know the initial values in this type of situation, so you do not know the outcome until you make a measurement.

Similarly, I suggest that using a Hilbert space is a mathematical procedure to use, but it does not determine the physics – it is merely a calculation procedure. It does not alter the physics.

LikeLike

June 19, 2021 at 11:42 am |

Dear Ian:

Thanks for the comment. Here is my answer:

Hmmm… Call them A and B. So you say (distorting a bit…) A and B are entangled by a conservation law in either case (that’s the way I have always looked at it), no difference. In classical, once one has measured A, one knows B…. As long as one knew I, the initial point of interaction of A and B. But in Quantum, one can’t know I. Thus the analogy to the quantum situation is doing classical without I.

Given an experimental situation, a Hilbert space is imposed by the geometry. Basically, it works this way:

1) Experimental setup.

2) Computing what the waves will do in such a setup, getting an eigenbasis for Hilbert space H.

3) When a “particle” enters, it is constrained to mostly show up according to the eigenbasis.

Illustration: the ONE slit experiment, diffraction. One has one slit and a distant screen. Given long enough a time, and enough particles, they will tend to end up in a central area and then bands, as Huygens said. So the wavy Hilbert constraints the outcome of the trajectories (supposing there were trajectories as the quantum trajectory theory, QTT has it). Maybe the concept “Hilbert” is superfluous: the geometry of waves constrains.

LikeLike

June 20, 2021 at 5:48 am |

To: patriceay@cs.com

Sent: Sat, Jun 19, 2021 2:53 pm

Subject: Re: difference classical – quantum answer

Dear Patrice,

My comment was essentially that Hilbert space is a mathematical means of assisting calculation of what happens, but it does not cause it. There is no physical entity called “Hilbert space”. Your last sentence covers my view well.

In Newtonian physics, there was no space either. Space was just some sort of background on which the objects were placed, and in Galilean relativity, their velocities were measured in the frame of reference of one of them. “Space” was something like the canvas upon which the painting was done, but in this case only the painting was physical. Of course QFT states space IS physical in that it is full of fields, but if so, really the fields should be added to the space. The answer to your one-slit example depends on geometry, but it cannot depend on which mathematical way you look at it, which it would if the Hilbert space were a real entity.

Ian

LikeLike

June 20, 2021 at 5:57 am |

Dear Ian:

So we basically agree.

In the ONE HOLE experiment, the Hilbert depends not just upon the screen on which particles will materialize, but also upon the energy-momentum of these particles. So it’s Hilbert (screen, energy-momentum). Hawking radiation depends upon QFT and the Schwarzschild radius…. Black Holes have made space real in some sense. This being said, whether Minkowsky’s “spacetime” has meaning is an open question (Einstein did not like the notion; I used to view it as meaningless and confusing, but now I am not so sure)…..

The fact the Uncertainty Principle got busted recently confirms that one has to be very careful with all of this. The great debate is whether QTT is right or not …as De Broglie and Einstein thought. QTT people are basically replaying the debate with Bohr and company with greater experimental detail. They claim spectacular results. I don’t contest the thrilling results, but the method, QTT. I used to believe Einstein-De Broglie… But now I am sort of on the other side, with NONLOCAL pilot waves…

Patrice

LikeLike