Heisenberg's 1925 Quantum Mechanics Paper

Here is a good new video: How Heisenberg Discovered It. There is more detail here.

It is largely on Heisenberg's famous 1925 Umdeutung paper.

In his article, Heisenberg described a new framework for quantum theory that was based on observable parameters (parameters that could be measured in scientific experiments), such as transition probabilities or frequencies associated with quantum jumps in spectral lines, rather than unobservable parameters, like the position or velocity of electrons in electron orbits. Thus, Heisenberg used two indices for his re-interpretation of position, corresponding to initial and final states of quantum jumps. Heisenberg used his framework to successfully explain the energy levels of a one-dimensional anharmonic oscillator.

Mathematically, Heisenberg used non-commutative operators in his new multiplication rule, i.e. generally A B ≠ B A for quantum quantities A and B. This insight would later become the basis for Heisenberg's uncertainty principle.

This theory beme quantum mechanics, and has been well accepted for a century, described in textbooks, and applied to a trillion dollar industry.

The bizarre thing is that now the leading popularizers of quantum mechanics seem to not understand Heisenberg's first paragraph. The latest offender is the Veritasium channel. I have criticized many others on this blog. What they have in common is that they refuse to accept that quantum mechanics is about observables, and argue that the theory must mathematically represent unobservables.

In their jargon, the unobservables are called hidden variables, and the belief that they should be incorporated into the theory is called realism.

The 2022 Nobel Prize was given for the experimental proof that local hidden variables are impossible. John von Neumann had said so in his 1930 treatise, and the experiments were just confirmation of what the textbooks have said since 1930.

Maybe all the textbooks are wrong, but that is like saying that perpetual motion machines are possible, or that rockets can go faster than light. Anyone making such a claim needs to explain how everyone else has been so wrong for so long.

They do not, of course. They mainly give some silly argument about how QM would be hard to understand if it included the unobservables. Of course that is true, because the whole point of QM since 1925 has been to exclude the unobservables.

When you hear people demand realism, they are essentially demanding commuting hidden variables to represent unobservables. The whole point of QM is to avoid such things.

Another trouble point is the supposed quantum nonlocality. I have come to the conclusion that this is a misunderstanding or rejection of probability, and doesn't even have anything to do with QM. If a theory predicts probabilities, as all physical theories do, then it says there is a chance something happens and something else does not happen. Assume that something involves at least two spatially separated events. As soon as you run an experiment and see that something happens, you immediately learn that something else did not happen, and that conclusion is the supposed nonlocality. You can call this nonlocal, but that is silly as the same thing happens in any theory.

Einstein's Notion of a Principle Theory

Einstein scholar Galina Weinstein

Einstein's distinction between principle theories and constructive theories is methodological rather than metaphysical. Principle theories such as thermodynamics and relativity articulate empirically distilled constraints that delimit admissible microphysical models, while constructive theories remain provisional and revisable....

In late 1919, following the British eclipse expeditions that confirmed the light-bending prediction of general relativity, Albert Einstein agreed to write an explanatory article for The Times of London. Written in German as “Was ist Relativitätstheorie?” and published in English as “Time, Space, and Gravitation” [7, 8], the article was intended not merely as popularization, but as a methodological clarification of the kind of theory relativity is.

In the essay, Einstein contrasts constructive theories (konstruktive Theorien) with principle theories (Prinziptheorien) [7]. This distinction is not merely classificatory but methodological and epistemological in character [22].

Here is that 1919 Einstein paper:

There are several kinds of theory in physics. Most of them are constructive. These attempt to build a picture of complex phenomena out of some relatively simple proposition. The kinetic theory of gases, for instance, attempts to refer to molecular movement the mechanical thermal, and diffusional properties of gases. When we say that we understand a group of natural phenomena, we mean that we have found a constructive theory which embraces them.

But in addition to this most weighty group of theories, there is another group consisting of what I call theories of principle. These employ the analytic, not the synthetic method. ...

The special relativity theory is therefore the application of the following proposition to any natural process: "Every law of nature which holds good with respect to a coordinate system K must also hold good for any other system K' provided that K and K' are in uniform movement of translation."

The second principle on which the special relativity theory rests is that of the constancy of the velocity of light in a vacuum.

No, relativity was not developed as a principle theory. FitzGerald proposed the relativity length contraction in this 1889 paper:

I have read with much interest Messrs. Michelson and Morley's wonderfully delicate experiment attempting to decide the important question as to how far the ether is carried along by the earth. Their result seems opposed to other experiments showing that the ether in the air can be carried along only to an inappreciable extent. I would suggest that almost the only hypothesis that can reconcile this opposition is that the length of material bodies changes, according as they are moving through the ether or across it, by an amount depending on the square of the ratio of their velocity to that of light. We know that electric forces are affected by the motion of the electrified bodies relative to the ether, and it seems a not improbable supposition that the molecular forces are affected by the motion, and that the size of a body alters consequently.

This appears partly inspired by this 1988 Heaviside paper. That is, solid objects are held together by electromagnetic forces, and those fields were known to be warped by motion. Relativity was the constructive consequence.

The relativity principle that laws holding in K must also hold for K' was essentially what Lorentz proved in 1895.

Einstein seemed to disavow all of this when quantum mechanics was discovered. He was happy to avoid the question of how the FitzGerald contraction works on the molecular level, but refused to accept a quantum theory that did not explain the Heisenberg uncertainty on an atomic level.

It is interesting that in 1919 Einstein was still using 1895 terminology, and not saying that the laws of nature must be in covariant equations, or that the laws must be well-defined on a non-Euclidean manifold.

Weinstein posted some other goofy papers recently, including this on Einstein EPR entanglement, and this comparing Heisenberberg-Schroedinger to the P=NP problem. The Heisenberg and Schroeding theories were mathematically equivalent, but she has a whole paper analogizes them to things that are completely different.

Aaronson's Latest Quantum Computer Assessment

Dr. Quantum Supremacy, aka Scott Aaronson, posts his latest judgment on the feasibility of quantum computers.

In brief, quantum supremacy has not been achieved, but he still has hopes based on theoretical considerations from 30 years ago, and recent progress in quantum gate fidelity.

And he hints that at some point, researchers might hold back on public announcements, just as 1940 research into fission bombs avoided publishing how to build a bomb.

I think that artificial general super intelligence is potentially a lot more dangerous than quantum computers, and so there would be more reason to hold back on that. Maybe OpenAI or Google or Microsoft is holding back, but I doubt it. They are locked in a high-stakes competition.

He makes this ominous comment:

Similarly, at some point, the people doing detailed estimates of how many physical qubits and gates it’ll take to break actually deployed cryptosystems using Shor’s algorithm are going to stop publishing those estimates, if for no other reason than the risk of giving too much information to adversaries. Indeed, for all we know, that point may have been passed already. This is the clearest warning that I can offer in public right now about the urgency of migrating to post-quantum cryptosystems, a process that I’m grateful is already underway.

The US government is migrating to post-quantum cryptosystems, but I don't think those estimates will help any evil-doers. So far, the quantum computers can only factor 15 = 5x3. It will take quantum computers 50 years to crack today's cryptosystems, even if it is possible.

Veritasium goes Full Retard

This YouTube channel has nearly 20 million subscribers, and a lot of truly excellent videos. But the latest release get physics badly wrong.

The Experiment That Breaks Relativity

Veritasium 19.7M subscribers

Dec 18, 2025
How an argument between Einstein and Bohr changed quantum mechanics forever.

A tipoff is when it says that all the textbooks are wrong:

7:09 - Physicists tell a version of this story, you know that you will find in physics textbooks 7:15 and in pop science books and that you know physicists tell amongst ourselves that 7:20 what happened was Einstein and Bohr had a great debate and Einstein was unhappy with quantum mechanics ...

33:29 - We did do this experiment again, and the number, we got very much agreed with quantum mechanics, 33:41 but this is one of the most misunderstood experiments in all of physics. - You'll find in all sorts of physics textbooks and papers 33:48 and whatnot, that what Bell's theorem proves that it rules out local hidden variables or local realism. ...

35:00 it's a really deep misunderstanding that shows up in almost every single textbook on the subject. - So what does Bell's theorem really prove?

No, the quantum mechanics textbooks are right, and this video is wrong.

Here is the textbook explanation of quantum mechanics.

Position and momentum do not commute, and do not have definite values until observed. There is a Heisenberg uncertainty. If you measure both, your answers will depend on the order of measurement.

This contrasts with classical mechanics, where these variables have values independent of measurement.

Einstein and Bell wondered if maybe quantum mechanics could be reformulated as a classical theory. Bell cleverly formalized classical theories as theories of local hidden variables, and proved a theorem that such theories differ from quantum mechanics. Experiments then confirmed the quantum mechanics that everyone believed since 1930.

That was the end of the matter, for all serious thinkers. But some pursue some loopholes to this argument. Namely nonlocal theories, many-worlds, and superdeterminism.

Where Veratasium goes off the rails to make three fundamental errors.

(1) That simple entanglement examples show that quantum mechanics is nonlocal. The given example is to produce two related particles, such that a conservation law tells you that observing one immediately tells you something about the other.

The same thing happens in classical mechanics. This does not distinguish classical and quantum theories, or local and nonlocal theories.

(2) That "realism" means a classical theory, so if you believe in reality, you have to accept classical mechanics and reject quantum mechanics.

Quantum mechanics is not a classical theory. If you define realism that way, then quantum mechanics does not obey local realism. In particular, position and momentum do not have values until observed.

(3) That many-worlds theory somehow provides a way out of the quantum puzzles of locality and realism.

No, many-worlds theory does not, and cannot, explain anything.

John Bell passed away suddenly at the age of 62. 40:05 He didn't know it, but he had been nominated for the Nobel Prize just a year earlier - In a talk he gave in Geneva in January, 1990. 40:14 He said, I think you're stuck with the non-locality. I don't know any conception of locality, which works 40:22 with quantum mechanics. That was eight months before he died.

Yes, some believed that Bell deserved a Nobel for this, but the mainstream view, and the Nobel view, is that Bell was wrong. The 2022 prize was given for some Bell-related work, but the prize citation pointedly avoided giving Bell any credit for his goofy non-locality ideas.

My title refers to this movie clip.

This video is very disappointing. The channel had been very reliable and informative. I have learned a lot. But when you see a video claiming that all the textbooks and top experts are wrong, you probably should not believe it.

In this case, the video is rejecting mainstream physics that has been well-accepted for a century. And it is for the pursuit of goofy ideas that cannot lead anywhere.

Proving the Pythagorean Theorem

Here is a new paper with complicated proofs of the Pythagorean theorem. I don't know why anyone bothers, as plenty of proofs are very simple. Some on the Wikipedia page do not even require any words.

My favorite depends on the fact that in similar figures, all linear dimensions are proportional. Areas are proportional to the square of the linear dimensions.

Given a right triangle, drop a perpendicular from the right angle to the hypotenuse. This makes two new triangles, both similar to the original, and combining to make up the original.

Since the triangles are similar, the areas are proportional to the square of their hypotenuses.

The three hypotenuses are the three sides of the original triangle, and adding the areas of the new triangles gives the area of the original, so adding the squares of the sides must give the area of the hypotenuse.

I like this proof because it is so simple and direct. It does not rely on any tricky cancelations.

Are Particles Real, or Model Dependent?

I found this new video confusing:

Why particles might not exist | Sabine Hossenfelder, Hilary Lawson, Tim Maudlin

Sabine Hossenfelder, Hilary Lawson, and Tim Maudlin discuss the existence of particles, quantum field theory, and ultimate reality.

Are particles just an invention of the human mind?

From Democritus to Einstein, we have assumed the world is made of tiny building blocks of matter. But the more we’ve looked for them, the more they’ve disappeared. Our best theory now proposes the world is better described by ‘fields’ that don’t have the familiar properties of physical bits, things, or particles. Yet physicists still refer to particles, though few seem to agree on their nature. Some say they ‘approximately exist’ and others say that they don’t exist at all. Stranger still, there are ‘quasiparticles’, phenomena that we can treat as particles and enable us to solve equations, but which we know aren't fundamentally real.

They argued about whether a particle is a vibration in a field.

They also argued about how to think about physics, when there are mathematically equivalent descriptions of it.

Even if it 11:10 were true, we're we have that all the 11:12 time in physics and we don't think they 11:14 have to be equal. So, Lorentz had an 11:16 understanding of spacetime where there's 11:18 absolute simultaneity. 11:19 Einstein got rid of it, but you can 11:22 prove in their applications. They make 11:26 the same predictions. Nobody thinks 11:27 they're the same theory. All right? 11:29 There's different theories.

Actually I do think that they are same theory. Most people did in the early 1900s, as it was called Lorentz-Einstein theory (LET). Some said that Minkowski's theory was different, because it was based on a Lorentz-invariant spacetime geometry, but Einstein's was the same as Lorentz's. The main difference was that Einstein postulated the Michelson-Morley consequences.

Einstein's famous 1905 relativity paper has a whole section on simultaneity, but never says there is no absolute simultaneity. Here is how the section ends:

It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it “the time of the stationary system.”

The next section ends:

So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.

So two events can be simultaneous in one frame, but not another. The same is true in Lorentz's theory, as motion makes time run more slowly.

Even today, it is generally believed that the cosmic microwave background (CMB) defines an absolute simultaneity.

It often happens that there are mathematically equivalent descriptions, in which I do not see how one can be more real than the other.

If particles are defined as having definite positions, velocities, and trajectories, then they are certainly not real. Quantum mechanics only says that they look real when observations are made.

Quadratic Gravity is Possible

Quanta magazine has article on quadratic gravity.

I mentioned this before as an obvious alternative way to quantize gravity.

People have been saying for a long time that string theory is the only hope for quantizing gravity. It is completely false. For example, Brian Greene says in a new video:

0:00 String theory is the most potent and powerful approach that we have discovered as a species for blending general relativity and quantum mechanics.

He goes on to say that string theory is still viable as long as researchers want to work on it, and that is how science works.