Quantum mechanics is broken

Quantum mechanics, the brainchild of some of our greatest scientific minds, is broken. Some may object to this, since the theory is one of the most successful ones we have ever had. Indeed, it gives correct results, but that doesn't mean everything is okay. Let me illustrate with an analogy.

Imagine you are driving along and suddenly the check engine light turns on (or whatever indicator your car has). But everything seems to be working fine, so you just keep on driving, although the on-board analytics is trying to show that something is wrong. And you just keep on driving, hoping that it doesn't blow up. You can't know how terribly wrong things are before you take the car apart and look inside.

I am in no way saying that there is necessarily something wrong in the results of the theory. What I am saying is that although we have every indication that there is something wrong with it, we keep on using it. We've been ignoring the quantum check engine light(s) for a century!

Let's go through some of the problems, starting with the most glaring one: the Schrödinger equation cannot be derived. Nope, it cannot be done. Not from first principles at least, because the equation is the first principle. Here's what Richard Feynman had to say about the equation (Feynman lectures III, chapter 16):

"When Schrödinger first wrote it down, he gave a kind of derivation based on some heuristic arguments and some brilliant intuitive guesses. Some of the arguments he used were even false, but that does not matter; the only important thing is that the ultimate equation gives a correct description of nature."

"Where did we get that from? Nowhere. It’s not possible to derive it from anything you know. It came out of the mind of Schrödinger, invented in his struggle to find an understanding of the experimental observations of the real world."

So let's get this straight, we have an equation that was dreamed up out of desperation, and we keep using it because it works. Quantum mechanics is the only area of physics where this is considered to be okay. But this is just a wee bit problematic, since - you know - that's just math. What about the physics?

Doing mathematical fittings to data is a completely acceptable way to solve problems in physics, of course, but the problem comes when someone extrapolates the data. Without a physical description or experimental confirmation, extending a model to new regimes is dubious at best.

This leads us to the next very big problem: there is no universally accepted interpretation of quantum physics. For one, we have the Copenhagen interpretation, which just happens to produce all the same predictions as Bohmian mechanics, although they have totally different properties. Copenhagen is "weird" in the sense that it requires an observer and is intrinsically non-deterministic, whereas Bohmian mechanics is completely deterministic, needs no observer, but is non-local.

So two completely different interpretations, but same results. Mkay. Don't get me started on the many-worlds theory, where everything that can happen, will happen, but in different worlds. And those worlds can even interfere with each other! There are oh-so many different interpretations, and it's a real mess if you ask me.

Anyway, the main point is that the theory has been around for a hundred years, and we still have no idea what it actually means. This problem is just avoided with the "shut up and calculate!" mentality, but ultimately, denial is not healthy.

You might have read from textbooks that the Copenhagen interpretation is the "standard," but make no mistake, it really isn't much better than the others. And actually, Bohmian mechanics has been on the rise recently. In John Bell's words (Speakable and Unspeakable in Quantum Mechanics, chapter 17):

"Why is the pilot wave picture ignored in text books? Should it not be taught, not as the only way, but as an antidote to the prevailing complacency? To show us that vagueness, subjectivity, and indeterminism, are not forced on us by experimental facts, but by deliberate theoretical choice?"

If you have believed that there is some wide spread concensus on the actual physics of the theory, then you have been fooled by popular science media. In reality, there is an ongoing silent battle as to which interpretation is the most bestest, and no-one wants to confess that there has been next to none agreement on the physics.

Alas, one of the things that has plaqued quantum mechanics are the emotional responses (though that is not a problem with the theory, but rather, the people). For example, when David Bohm introduced his interpretation of quantum physics, he met astounding obstacles. Having failed to find an error in Bohms reasoning, Oppenheimer commented the theory with complete emotional rejection (Quantum Sense and Nonsense, chapter 10):

"If we cannot disprove Bohm, then we must agree to ignore him."

Then again, we are always told how the quantum theory is great because it describes nature correctly. Well, it's not so simple. Welcome to major problem number three: how well does the theory actually work? It doesn't work as well as we hope.  I mean, sure, all of the materials science and high energy stuff and so on is just fine, the problem is just more subtle.

Let's take the mathematical models for hydrogen. They are some of the most successful analytical descriptions of nature there are. However, try to do the same for the next heavier element, helium, and everything goes to the crapper. No closed form analytical expressions exist for anything more massive than hydrogen, and the numerical simulations are extremely demanding and inaccurate (when compared to hydrogen).

You would think that since we started this journey from the hydrogen atom a hundred years ago, we would have all of the elements completely described by now. But no, progress has been incremental and analytical modeling of more massive elements is still as far away as it was when we started.

These are some of the several indicators that something is wrong, and no one knows what that something is. Unless we take quantum theory apart, we will never know how bad the situation really is. What we need now is more physics, not more math - so don't shut up and calculate, speak up and think!