The Quantum Tower of Babel

"If God is a mathematician, in what dialect does She/He/They/It speak?"

In the past few weeks, I've gone down what you might call the quantum foundations rabbit hole - talking to a dozen researchers and reading enough papers to fill a small library. What I found was... concerning.

Imagine you're learning a new language, except everyone who claims to speak it has their own private dictionary. And instead of helpful corrections, you get drawn into ancient blood feuds about whether "mesa" means "table" or "tablecloth" or possibly "the experience of eating at a table."¹

This is roughly what it's like trying to understand quantum foundations research in 2025.

The field has splintered into a dozen different dialects, each with its own interpretation of basic concepts. It's as if we've spent ninety years having a debate where everyone is talking past each other so completely that we can't even agree on what we're disagreeing about.²

As Sabine Hossenfelder puts it, "The major problem with quantum mechanics, it seems, is that we can't agree what the problem is."

This would be merely amusing if we weren't still struggling with the same foundational issues - quantum gravity, dark matter - that researchers a century ago did.

It seems unlikely that any progress is possible until this mess is properly cleaned up.

Here are a few ideas on how we might start to sort this out.

Interpretations, formulations, modifications, and nonsense

“If God is a mathematician, in what dialect does She/He/They/It speak?” - John Horgan

The difference between interpretations, formulations, modifications and plain old nonsense has to be crystal clear.

You can formulate quantum mechanics in Hilbert space, phase space, configuration space, or real space. Some calculations are easier in one formulation but that doesn’t mean it’s more correct. As long as the mathematical map between them is sound, they are equivalent.

This is completely analogous to the situation in classical mechanics. For many problems, the standard Newtonian formulation in real space is perfectly fine. But formulations like the Lagrangian one in configuration space or the Hamiltonian one in phase space are more convenient for a certain class of problems. And if you want to carry out calculations in Hilbert space, you can use the Koopman-von Neumann formulation. Each formulation has its merits, but they're mathematically equivalent.

There is absolutely nothing controversial about this.

And yet virtually all work is done using the Hilbert space formulation, while other formulations like the Bohm-de Broglie formulation are still largely ignored for mostly sociological reasons.³

People often point out that most calculations can only be done using the Hilbert space formulation. This, however, ignores the obvious fact that approximately 1000x more manpower so far went into developing the necessary calculation tools for the Hilbert space formulation. If, say, the Bohm-de Broglie formulation had been discovered before the Hilbert space formulation, the situation would probably be reversed. Physicists might now be arguing that the Hilbert space formulation is too abstract and complicated compared to the more intuitive Bohm-de Broglie approach.

Modifications, on the other hand, actually alter the theory's mathematical structure and predictions. Examples include collapse models like GRW theory . These aren't just different ways of looking at quantum mechanics - they're genuinely different theories that can be tested experimentally.

Last but not least, interpretations provide different philosophical frameworks for understanding what the mathematical formalism means. They don't change the mathematics or predictions, but rather offer various metaphysical perspectives on what's "really" happening. The Many-Worlds interpretation and QBism are examples of different ways to philosophically interpret the same underlying mathematical structure.

Different formulations certainly might hint at different interpretations.

But if anything, the fact that we have multiple equivalent formulations should give us pause when considering any single interpretation too dogmatically.

Again, this is no different from the situation in classical mechanics.

Most straightforwardly, we can look at classical mechanics as a framework describing inert objects pushed around by forces. We can also interpret it by observing that Nature seems to be driven by a desire to extremize the Action. You could certainly also cook up an interpretation by staring long and hard at Hamilton’s principal function.

But there is no reason to claim that any of these points of view is more correct than another.

Most importantly, no one should get confused by nonsense like the “Copenhagen interpretation,” which really doesn’t deserve to be called an interpretation at all. It’s a collection of vague philosophical statements that don’t make much sense no matter how long you stare at them.⁴

In summary, these four categories - formulations, modifications, interpretations, and nonsense - serve distinct purposes and shouldn't be conflated.

Instead of fighting against each other like fans of different sports teams, researchers should focus on building bridges between different formulations and leveraging each one's unique strengths for different types of problems.⁵

Modifications deserve to be tested, interpretations to be discussed but not dogmatically held, and nonsense to be ignored.

“There is a pleasure in recognizing old things from a new point of view […] there is always the hope that the new point of view will inspire an idea for the modification of present theories, a modification necessary to encompass present experiments.” - Richard Feynman

Put genuine quantum weirdness into the spotlight

While most researchers do agree that quantum mechanics is weird, there’s hardly any agreement on what exactly is weird about it.

Virtually all examples of fundamental quantum weirdness (randomness, discreteness, the indistinguishability of states, measurement-uncertainty, measurement-disturbance, complementarity, non-commutativity, interference, the no-cloning theorem, and the collapse of the wave-packet) do “appear within classical statistical mechanics under reversible dynamics”.⁶

The one genuinely strange aspect of quantum mechanics is the experimentally observed violation of the Bell inequalities.⁷

And yet, there is widespread confusion on what this actually tells us about the world.

The Nobel Prize committee, for example, in their announcement of the 2022 prize, claimed that it shows “that quantum mechanics cannot be replaced by a theory that uses hidden variables.”

This is pretty much the exact opposite of what most researchers would describe as the lessons we learn from Bell-type experiments.

To quote Tim Maudlin in a recent conversation with Sean Carroll:

“The Nobel committee blew it in their press release. They said that what they had done was what proved that von Neumann was right and you can't have hidden variables. The irony there is so delicious. Because Bell became probably the strongest advocate of Bohm's theory or De Broglie's theory, which is a theory with additional variables.”

The different options for understanding the observed violation of Bell’s inequalities need to be spelled out in crystal clear terms and discussed undogmatically.⁸

Right now, potentially interesting options are being overlooked for sociological reasons. For example, violations of statistical independence are dismissed by invoking John Bell’s claim that this would imply “the complete absence of free will”.

Progress is possible

The situation reminds me of the famous parable of the blind men and the elephant. Each man feels a different part of the animal - the trunk, the tail, the tusk - and becomes absolutely convinced they know what they're dealing with.

The man at the trunk insists it's a snake, the one at the tail swears it's a rope, and they all end up in heated arguments about who's right.

In quantum mechanics, we have Bohmians, Many Worlders, relationalists, QBists - each group exploring a different piece of the same puzzle. And just like in the parable, each group has stood in their corner for so long, clutching their piece, that they've forgotten they were all originally trying to describe the same beast.

On top of that, we have mathematicians approaching the problem from yet another direction. They often seem determined to make quantum mechanics sound as unremarkable as possible - as if they're embarrassed by its weirdness. But that's like trying to make Alice in Wonderland "benignly humdrum" by translating it into an axiomatic system.

You haven't explained the talking cats and size-changing potions; you've just hidden them behind a wall of symbols.

The genuinely strange features of quantum theory — like the violation of Bell inequalities — aren’t made any clearer through these approaches. If anything, they become even more confusing.

At the same time, there are tons of beautiful, deep hints where a little bit more attention from people thinking mathematically could help a lot.⁹

Progress in quantum foundations has been glacially slow for the past century, but it doesn't have to be.

The evidence suggests we're being held back more by human factors than physical ones. Many promising ideas were abandoned not because they failed, but because of historical accidents or personality conflicts.¹⁰

Maybe what we need isn't yet another interpretation of quantum mechanics.

Maybe we need something more like couples therapy for physicists - a way to get everyone in the same room, speaking the same language, and remembering why they fell in love with these puzzles in the first place.¹¹

1. For example, there are at least five different notions of “locality”.

2. Yes people do quote “prophets” to make a point. For a frustrating example of what this looks like see this discussion.

3. Even Wikipedia calls the de Broglie-Bohm formulation an “interpretation” when it’s really, first and foremost, a straightforward mathematical reformulation.

4. What is Real by Adam Becker is a great read on the shortcomings of the Copenhagen interpretation.

5. New formulations like this attempt to cast quantum mechanics in the language of stochastic mechanics (à la Nelson) deserve more attention.

6. For a fun example, compare the classical Bandwidth Theorem to the Heisenberg uncertainty principle.

7. This toy model is a fantastic way to get a feel for the Bell inequalities.

8. One of the clearest discussions I found so far is in this paper.

9. One example is the observation that “we could do quantum mechanics with just real numbers, but we wouldn’t get the correspondence between observables and symmetry generators.” The connection between observables and the generation of transformations seems severely understudied. Another interesting topic is explorations of what mathematical tools can potentially be modified without ruining the whole thing.

10. For example, John Bell's derivation of his inequalities in the 70s was inspired by his discovery of Bohm's work, which showed that von Neumann's "proof" against hidden variables was flawed. David Bohm's development in the 1950s was itself a rediscovery of Louis de Broglie's pilot wave theory from the 1930s. Louis de Broglie had abandoned his work after unjustified criticism by Wolfgang Pauli and Hans Kramers.

11. Unfortunately “valley crossing” is not something that is rewarded in the current system.