Particles don't take "all possible paths simultaneously." Here's why.

Debunking the debunkers...

You’ve probably been seeing viral videos saying particles take “all possible paths.” It’s based on an extreme misunderstanding of path integrals. Let’s disambiguate what the path integral is about and why Feynman’s tool isn’t a literal map of reality.

Firstly, we need to stop saying electrons “go through both slits.” That’s not what quantum mechanics (even textbook QM) says. It’s a hangover from misinterpreting wave functions in 3D space when they really live in something else called “configuration space.” It confuses a calculational trick with physical ontology.

Time for some rigor.

Debunking the Debunkers

People love to say that particles explore every possible path simultaneously—even going back in time or to the moon. Firstly, what is this word “possible”? Possible isn't a physics word. Do you mean to say every continuous path in ℝ⁴? Every once differentiable path in ℝ³? What is it?

And saying “possible” just makes you stop and think… “OK, if quantum mechanically you can tunnel and plenty else that I thought wasn't possible is actually possible, then how informative is saying that the particle takes all possible paths? What is the rigorous domain of ‘possible’?

Furthermore, we’re already including impossible paths classically, like going backward in time and not being differentiable? Why can’t you go through the blocked parts of the slits? Why is that not possible?” There’s a host of questions that occur to a student when this word “possible” is brought up. This isn’t modal logic. It’s better to drop it.

“All possible paths” is echoed because of doctrinal inheritance without thinking, just like “equal footing.”

When you hear someone repeat a certain word or a lexical bundle that they don’t repeat in any other place except in this one specific circumstance, then it’s likely they’ve just inherited it from hearing other people say it.

What is “equal footing,” for instance? Does it mean that they’re the same? No, because there’s the opposite sign on time, but they’re on “equal footing?” What does that mean? Have you seen a math definition of “equal footing”? We’re supposed to be rigorous! Does it mean that you can add or subtract spatial and temporal degrees of freedom? Well, derivative operators can be added even if the order of operators is mixed. I talk about this here with Tim Maudlin.

Anyhow, path integrals are a computational tool (shortcut?), combining unitary evolution and the Born rule for a specific measurement basis.

That cool diffraction grating experiment doesn’t prove particles take all paths. It demonstrates wave optics, which can be calculated using path integrals, but doesn’t necessitate the “all paths” ontology. Wave phenomena explain it just fine.

Dealing with classical electromagnetic waves propagating in our familiar 3D space is a fundamentally different beast than the abstract wave function of an electron, living in configuration space.

Let’s look at the origin story…

Path integrals weren’t invented by Feynman out of thin air to describe particles taking scenic routes. Paul Dirac actually introduced the core idea back in 1932. His goal? To understand the quantum role of the Lagrangian (L = T - V), which felt sidelined by the Hamiltonian-focused (H = T + V) formulations of early QM (Schrödinger, Heisenberg).

Dirac figured out how to express the transition amplitude by divvying up time into tiny intervals and inserting complete sets of states. Feynman, years later as a PhD student, turned Dirac’s formal insight into a powerful calculational recipe, the path integral we know. But notice the motivation: it was about mathematical representation and calculation, not primarily about painting a literal picture of particle trajectories. Feynman himself, in his 1948 review, stated his path integral couldn’t (at that time) calculate anything the standard methods couldn’t.

\(\langle q_f, t_f | q_i, t_i \rangle\)

Now, back to that electron “going through both slits.” This visual relies on thinking the electron’s wave function ψ(x, y, z, t) is like a ripple in the 3D space of the experiment. That works okay only if you have exactly one particle. Add a second electron? Now your wave function (below) is a function on a 6-dimensional configuration space:

\(\psi(x_1, y_1, z_1, x_2, y_2, z_2, t)\)

Add N particles? You’re in 3N dimensions. This ψ doesn’t assign a value (amplitude) at each point in 3D space; it assigns a value to each possible arrangement of all N particles. It’s fundamentally not a wave in physical space!

So, the intuitive picture of a wave splitting and going through two physical slits simultaneously is already a misleading simplification based on the N=1 case, incorrectly extrapolated. The “all paths” story inherits this spatial misconception. The paths being summed over (below) are trajectories in configuration space, not necessarily simple paths in 3D space you can easily draw (unless N = 1).

\(\int \mathcal{D}x(t) e^{iS[x(t)]/\hbar}\)

The standard QM (Dirac-von Neumann) doesn’t actually describe what happens between measurements. If you want to know what the particle is doing when not being measured, you need a theory that does describe the “in-between” (like Bohm, Many-Worlds, or Indivisible Stochastic Processes by Jacob Barandes.

Furthermore, let’s talk about the math itself. To make these path integrals mathematically well-defined and convergent, you often have to do tricks. These tricks aren’t for kids.

A common one is giving time a small imaginary component (t → t + iε) or performing a full Wick Rotation (t → -iτ), essentially calculating things in Euclidean spacetime (imaginary time) and rotating back at the end. Ask yourself: if the path integral literally depicts reality, does reality fundamentally occur in complex or imaginary time? These are mathematical regularizations needed to make the calculational tool work; the formalism isn’t a direct ontological description.

Path integrals are math, not a literal movie of nature.

Other False Shibboleths

This brings us back to the Veritasium video and the Looking Glass Universe response. The experiment with the laser, mirror, and diffraction grating is cool. However, does it prove particles take all paths? No.

As Looking Glass Universe eventually shows, the phenomenon is perfectly explained by standard wave optics (Huygens’ principle, diffraction). Light waves do spread out (even laser beams aren’t localized), they do hit the whole grating, and the grating does cause diffraction patterns according to well-understood wave physics.

Curt’s aside: Even defining what light is isn’t trivial. Same with defining energy.

The path integral can calculate this outcome (because wave equations can often be derived from action principles), but the wave explanation is sufficient and arguably more direct. Claiming this must be particles taking odd paths relies on the premise that the wave (the laser beam) is perfectly localized and doesn’t hit the parts of the mirror away from the main reflection point. But as the Looking Glass video shows, it demonstrably does!

So, the experiment confirms wave behavior, which can be modeled mathematically via path integrals, but it doesn’t prove the “all paths” chronicle is physically real.

Curt’s aside: I’ve spoken to Mithuna of the Looking Glass Universe several years ago on this podcast here, on quantum immortality and many worlds. She makes great videos.

To summarize, none of the Veritasium video proves that a particle actually takes all these paths simultaneously in reality. The video is filled with a mixture of interpretation-dependent claims and statements that are just incorrect.

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If you’re interested in more of these videos, then subscribe as I speak to physicists, philosophers, and mathematicians about different interpretations of quantum mechanics and the ultimate theory of everything.

Also, on my Substack, I go into more detail about unexamined slogans that even brilliant informed people sometimes perpetuate (e.g., “decoherence solves the measurement problem,” “HUP is caused by the act of measurement disturbing the system,” “distances below Planck length are meaningless”) without rigorous justification or acknowledging the underlying philosophical assumptions. None of these are necessarily true. HUP is right there in the algebra, and the last one assumes operationalism, for instance. Scrutinizing these requires asking for axioms and justifications.

Another falsehood is the idea that erasing 1 bit must dissipate kT ln 2 heat (Landauer’s Principle), underpinning “It from Bit” and “Information is Physical,” where John Norton has long-standing objections to its universal validity.

Soon I’ll be doing a write-up on how John Bell’s theorems depend explicitly on specific causation theories: locality, counterfactual definiteness, and statistical independence aren’t the only assumptions! (notice how “realism” isn’t actually there, despite the pop-sci accounts) Bell ‘64 relied on interventionist causation (problematic for microphysics). Bell ‘75/’90 relied on Reichenbachian factorization or related criteria, which Bell himself doubted and which face objections (e.g., quantum interactions aren’t conditionable-upon “beables” (a John Bell term). Ignoring the dependence on debatable metaphysical causation theories actually neuters the theorems’ purported power to prove non-locality is inherent to QM.

Curt’s aside: Actually, Bell’s 1990 paper modified the assumptions again, trying to get away from strict Reichenbach factorization, but this created other problems by requiring beables specified on a “complete spatial slice” potentially conflicting with statistical independence, as detailed recently by Joanna Luc.

I’ll also be writing about how quantum expectation values <O> aren’t averages of “stuff happening.” The spoiler is that <O> is defined as the statistical average of measurement outcomes weighted by Born probabilities. Mistaking this for an average of the observable’s value between measurements (when nothing is being measured) is a category error pervasive in discussions of the classical limit (e.g., Ehrenfest’s theorem) and semi-classical gravity. You can subscribe for an upcoming podcast with Erik Curiel for more.

I want to hear from you in the Substack comment section below. I read each and every response.

—Curt Jaimungal

PS: Despite these comments, Veritasium videos are a useful go-to resource for an initial overview.