The surprising origins of wave-particle duality

February 21, 2024 3:44 PM

Everything acts like a wave while it propagates, but behaves like a particle whenever it interacts. The origins of this duality go way back.
posted by ShooBoo (19 comments total)

Man, every time I see a video or read an article talking about the various double slit experiments it weirds me out all over again. Every. Single. Time.

Many have commented that “It’s like nature knows whether you’re watching it or not!”

I wish they would have expanded on this. As I understand it, it's not so much that nature knows if you're watching as it's that reality is a property that emerges from these quantum reactions.

And how mass comes from these quanta being restrained (by gluons? the nuclear force?). It's constantly interacting trying to escape in every direction at the speed of light at once. So it also resists moving in all directions (since every time it tries to escape in one direction it's also escaping in another direction). It resists movement in relation to the energy level of the quantum particles involved. And that's how mass happens. No interaction, no mass, nothing happens, no reality.

The closer we look the weirder it gets.
posted by VTX at 5:16 PM on February 21 [4 favorites]

From the title, I thought this was somehow going to describe the physical origins of wave/particle duality, like maybe it arose from some early weirdness in the universe and before that everything was one or the other or neither.
posted by solotoro at 7:00 PM on February 21 [5 favorites]

Yeah, I was like “wave-particle duality began in the 1600s? I knew playing all that Mage: The Ascension would pay off.”
posted by No-sword at 7:31 PM on February 21 [3 favorites]

I love this stuff - I’d like to be reincarnated as someone a bit smarter than me to really understand how incredibly *weird* the world is.
posted by whatevernot at 3:35 AM on February 22 [2 favorites]

Is water a particle or a wave?
It seems to travel in waves...
posted by MtDewd at 4:14 AM on February 22

Philosophers: We demand rigidly defined areas of doubt and uncertainty!

Schroedinger: On it.
posted by flabdablet at 9:06 AM on February 22 [7 favorites]

some years ago, I was at a talk given by Robert Anton Wilson. It was cool, fun, worth the price of admission. But it was afterword that I got my big deal epiphany. Various people hanging out by the stage, trying to get a few words with him. I was happy to just listen in.

An older woman said to him, "I was always utterly baffled by the wave-particle stuff, took it almost as an insult to my intelligence. Until one morning as I was driving to work in LA rush hour, it suddenly hit me. Okay, right now, I'm a savage, taking no prisoners as I carve my way through the all the idiots in my way. An hour ago, I was mom, going through the motions, getting the kid out of bed, fed, out the door in time for the school bus. An hour from now, I'll be that nice lady that smiles warmly as people come into the office. If I can constantly switch character as the situations demand, why the hell can't reality?"
posted by philip-random at 11:36 AM on February 22 [6 favorites]

Two things, one origin,
but different in name,
whose identity is mystery.
Mystery of all mysteries!
The door to the hidden.

Tao Te Ching, chapter 1 (translation Ursula K. Le Guin)
posted by protorp at 12:35 AM on February 23 [2 favorites]

A lot of people seem to have a lot of trouble letting go of the question of whether electrons, for example, are "really" waves or "really" particles. The idea of quanta - recognizable, characterizable features of reality that have some wave-like properties as well as some particle-like properties - just seems fundamentally unsatisfactory to such people.

If you're one of them, I would encourage you to introspect enough to be able to express clearly to somebody else exactly what a satisfactory explanation of anything actually looks like to you. Have you in fact been expecting all of Nature to shoehorn itself into some tidy set of categories that you're already familiar with? If so, how do you justify that expectation?

I'd also encourage you to study at least a little bit of mathematics. Not with the aim of acquiring enough of it to help you deal directly with quantum mechanics, just to get comfortable with contemplating and manipulating at least some kinds of patterns and relationships that are never encountered in ordinary day-to-day experience. 3Blue1Brown's YouTube channel offers a tasty and accessible starter menu.
posted by flabdablet at 4:22 AM on February 23 [3 favorites]

The most amazing fucking practical application (.... for certain values of "practical") of quantum probability that I have ever had the privilege of learning about is the Elitzur-Vaidman bomb tester, a concept explained in this gleeful prof in an MIT open courseware lecture. There is no math or any scientific expertise necessary to understand the central aspects of this video, you can safely tune out the math when the lecturer brings it up, but before you watch the video, please read the background explanation below.

The hypothetical scenario they begin with is: you have a large bag of mixed-quality but identical-looking bombs, say 100 of them, half of which are duds. The only way to test whether a bomb is working or not is to try to trigger it using a photon (or electron, or a pebble, even!) aimed at the correct spot - if it doesn't explode, it's a dud, and if it explodes, it was a working bomb. Obviously this test is not much use if you're trying to extract live bombs for use in your war or whatever. Is there some other way to get at least some guaranteed-to-work bombs from your pile, without exploding them?

It turns out there is a way, using the magic of quantum superposition, i.e. the interference and interaction patterns of PROBABILITY waves. We, in our regular reality, tend to think of probability as a hypothetical, an imaginary construct. But in quantum mechanics, probability is tangible reality with measurable outputs - like, in this case, a single photon's probability waves "interfering" with one another and a single particle's possible path superposing onto its own self to create outcomes you can hold in your hand, like an unexploded bomb that we can guarantee with total certainty that it WILL work. It's completely non-intuitive and mind-bending, but it is true, and the Elitzur-Vaidman bomb tester proves it.

The Elitzur-Vaidman Bomb test uses a setup known as the Mach Zehnder Interferometer. It's not a hundred percent necessary as such to understand the MZI to understand the EVBt, like, if you are willing to take it on trust that the MZI's outputs are what the lecturer says they are for reasons unknown to you but known to others, then you can be merrily on your way. But the MZI is actually very easy to understand and the only science concepts are needed to understand it are:

1. If there is a sine-wave pattern, and you phase shift it by pi radians, then it becomes an exact mirror image of itself. If you phase shift it by 2*pi radians then it's not shifted at all, it is back to its original phase.

2. If there are two beams of light, both going in sine wave patterns, and they meet, they will interfere with one another, i.e. interact in some way. In particular, they will cancel each other out if one of the beams of light is phase shifted by exactly pi radians from the other one - and this is known as destructive interference. Two sine wave patterns interfering with one another will add up and amplify if both of them are "in phase" - and this is known as constructive interference.

3. Bouncing a beam of light off of certain mirrors at a 90 degree angle can shift its phase by exactly pi radians.

A good explanation of the Mach Zehnder Interferometer setup is here in this under-5-minute video (you can stop at 6:49 when it hits the mathy bits, that doesn't matter) - and if you prefer a text-and-image based explanation then look here at the beginning of this web page- or you can find another very clear explanation here on this page.

I hope you all will enjoy this quantum nonsense as much as I did. It is absolutely wonderful and makes me hug myself in glee every time I think about it!
posted by MiraK at 10:13 AM on February 23 [4 favorites]

Mach Zehnder is definitely going to be a character in my next space opera.
posted by philip-random at 10:22 AM on February 23 [3 favorites]

I think the discussion usually gets a little muddled when talking about nondeterminism:

Despite the proposal of hidden variables to attempt to reconcile wave-particle duality into a single deterministic framework, all experiments point to nature still being non-deterministic, as you cannot predict the outcome of an unmeasured, wave-like trial with any more accuracy than the Schrödinger’s equation’s probabilistic approach.

The Schrödinger equation is deterministic. It describes how a quantum system evolves over time, and there's only one way it can evolve. I think the article is referring to the Born rule, which is probabilistic. But the problem is that when people use the Born rule to talk about measurement, then you have to talk about wave function collapse, and then you have to define when, exactly, the wave function collapses - what counts as a measurement? The Copenhagen interpretation has the Heisenberg cut, but I find it deeply unsatisfying because of how arbitrary it is.

But you don't actually need to add wave function collapse to quantum mechanics. If you don't, then you get the many-worlds interpretation. It is completely deterministic, but still explains why measurement appears to be nondeterministic: when you measure something, you become entangled with all possible measurement outcomes. From the point of view of each version of you, only a single outcome was observed, with a probability given by the Born rule. However, from the point of view of the entire quantum system, every outcome was observed, but there are more worlds with outcomes that would have a higher probability given by the Born rule.

For me, the many-worlds interpretation is the simplest way to think about quantum mechanics: everything is quantum, everything evolves according to the Schrödinger equation, and there's no wave function collapse or quantum-classical dividing line that separates entanglement from measurement. There are, however, infinite copies of "you" experiencing every possible outcome of each quantum interaction.

I think the Copenhagen interpretation lives on because most people feel uncomfortable imagining copies of themselves in an infinitely branching quantum universe, and all of them experiencing a deterministic timeline unfolding with only the illusion of free will. Many-worlds is also untestable, because by definition the different branches of the wave function can never interact with each other.

But I think that even if something feels uncomfortable, and even if it can't be tested, if it falls out of the simplest model we have that's consistent with observations, and the only way to avoid it is to add arbitrary new assumptions to the model like wave function collapse and the Heisenberg cut, then we should still take it seriously.
posted by april of time at 9:43 AM on February 24 [2 favorites]

I'm the other way. I refuse to take any claim about reality seriously unless it can be tested.

I'm also quite internally hostile to the idea of any feature of reality being "governed", as opposed to described, by any mathematical formulation.

To my way of thinking, the Schroedinger equation is the best yet devised for constructing a predictive model of how any specified set of initial conditions will evolve over time. It encapsulates what we can know about the outcomes of that evolution.

When we set up some kind of interaction between some system we're modelling per Schroedinger and a detector capable of directly interacting with that system so as to interrogate its behaviour, the wave equation plus the Born rule gives us probabilities for the outcome of that interaction that are absolutely testable.

But the wave equation does not and cannot tell us what's actually happeningbetween the measurements we make in order to plug numbers into it and those we make to check the predicted outcomes. Only actual measurements - interactions between the quanta being modelled and the quanta that form part of some measurement apparatus - can do that. The "collapse" of the wave function is simply the point at which it ceases to be our best source of information about what's going on in the world.

The most parsimonious explanation I can think of for why the wave function and the Born rule work the way they do is that the wave function genuinely is probabilistic - statistical, in fact - and has to be because every part of reality is ultimately unique. There are ways that natural processes proceed, and the wave function neatly summarizes those, but specifically what happens in any given experiment is ultimately non-replicable because of that uniqueness, and in practice determinable only by making measurements. Everything interacts with everything else always and everywhere because ultimately every particle is entangled even if we have no way of finding out what with, making it simply not feasible to know in advance exactly which of those interactions will turn out to be consequential within the confines of any given experiment.

This view preserves determinism as a principle, in that if we could specify every quantum number for every particle in the Universe then we could in principle set up a wave equation for the whole shebang, and the wavelength involved would end up so small as to track all subsequent behaviour to arbitrary precision. In practice, though, it's not even feasible to construct a complete wave equation for the content of one of my farts. Closest we get to practical determinism, then, is the tautology that only what will happen will happen. And sometimes the fastest way to find out exactly what that will be is just to wait and see.

I see the Heisenberg cut not as an inherent property of any system under test, but rather another choice that we make as investigators and modellers of that reality. Making a measurement in the QM sense amounts to arranging for the system under test to interact with apparatus whose specific construction allows us to get away with not using QM to describe and predict its behaviour to whatever accuracy and precision we require.

I vastly prefer not taking that pack of furious handwaving seriously to taking either Copenhagen or Many Worlds seriously. Especially since the only thing we can actually do with any of this, regardless of metaphysics, is shut up and calculate.
posted by flabdablet at 10:50 AM on February 24 [4 favorites]

The most parsimonious explanation I can think of for why the wave function and the Born rule work the way they do is that the wave function genuinely is probabilistic - statistical, in fact - and has to be because every part of reality is ultimately unique.

Mixed quantum states describe probabilistic distributions of wave functions and can be used when we don't know which wave function we're in. But I don't think the wave function itself can be probabilistic - what would it be a distribution of?

There are ways that natural processes proceed, and the wave function neatly summarizes those, but specifically what happens in any given experiment is ultimately non-replicable because of that uniqueness, and in practice determinable only by making measurements. Everything interacts with everything else always and everywhere...

We talk about measurements because we like to model the quantum system in an experiment as a closed system, isolated from the rest of the universe. I agree with you that everything interacts with everything else, so this model isn't realistic, because the experimental apparatus, and the humans running the experiment, are also part of the system.

In that view, a measurement is a series of interactions between the experimental object, the experimental apparatus, and the experimenter, causing all of them to become entangled. We've become coupled with all possible outcomes of the measurement. But that means there's multiple versions of "us" for each branch of the entangled wave function, just like how when two particles that aren't human-scale (and therefore on the other side of the Heisenberg cut) interact, they become entangled without "measuring" themselves.

This view preserves determinism as a principle, in that if we could specify every quantum number for every particle in the Universe then we could in principle set up a wave equation for the whole shebang, and the wavelength involved would end up so small as to track all subsequent behaviour to arbitrary precision.

So in normal quantum mechanics, if you knew the wave function of the entire universe with perfect precision (in other words, the universe could be described by a pure quantum state), you still couldn't predict the outcome of every measurement, even in theory. For any basis where a quantum object isn't in superposition, you could always measure it in an orthogonal basis - in that case, it's not a problem of lack of knowledge. Many-worlds avoids this by saying you can still predict the outcome of every measurement if you don't collapse the wave function and include the multiple branches of the universe's wave function as part of the "outcome."

But it sounds like you might be talking about something like pilot wave theory? That is a statistical interpretation of quantum mechanics, where you could in principle predict every measurement if you had perfect knowledge. The problem is that it's nonlocal. Many-worlds is local.
posted by april of time at 12:10 PM on February 24 [1 favorite]

Everything interacts with everything else always and everywhere because ultimately every particle is entangled even if we have no way of finding out what with, making it simply not feasible to know in advance exactly which of those interactions will turn out to be consequential within the confines of any given experiment.

As a layman, this really resonated well with me as an argument against the many worlds theory.

I don't really have a horse in this fight. I think most of these theories have merit and think all should be pursued. I'm really loving following this conversation.

Please, carry on. :)
posted by VTX at 12:47 PM on February 24 [1 favorite]

In that view, a measurement is a series of interactions between the experimental object, the experimental apparatus, and the experimenter, causing all of them to become entangled.

Right. And to the extent that it is feasible to identify and characterize all of the quanta involved in that entanglement, it would be possible to extend the particular wave function that we're using to model the experimental object so as to account for all its new entanglements as well.

But that's not feasible. So what we always do instead is rely on what we know about the structure and function of some measuring apparatus to interpret its interaction with the system under test, and then treat the information arising from that interpretation as a measurement of that system. We perform a Heisenberg cut, not because the wave equation is in principle incapable of describing all of the experimental object, the experimental apparatus and the experimenter as a single entanglement, but because at quite small system complexities it becomes practically infeasible to do the required calculations and "taking a measurement" is just more informative.

We've become coupled with all possible outcomes of the measurement. But that means there's multiple versions of "us" for each branch of the entangled wave function, just like how when two particles that aren't human-scale (and therefore on the other side of the Heisenberg cut) interact, they become entangled without "measuring" themselves.

I don't think that this multiple-versions-of-us interpretation is justifiable.

As you pointed out earlier, the wave function is deterministic. For as long as we remain content to model the system we're looking at asa wave function, nothing in that model implies that multiple versions of the system exist.

The key to the difficulty is this idea of "all possible outcomes of the measurement". From my vantage point as a strictly practical tautological determinist I take it as self-evident that there can only ever be one outcome of any given measurement, which is the outcome that is actually measured. My preferred interpretation of the verifiable fact that we cannot know in advance what that measurement is going to reveal about any given experiment is that every experiment is unique. The only objection I can think of to that observation is that it is so blindingly obvious as to be dismissible as trivial.

But we don't actually need to posit an endlessly bifurcating universe to account for all our experimental outcomes, because each such outcome is the outcome of some specific experiment, each of which can be distinguished from all the other similar experiments by virtue of having happened at some other place or time. All those extra versions of us who end up with different experimental outcomes than ours are strictly imaginary.

All we need to do is have the humility to understand that our models are only models - descriptions, not prescriptions - and that it's completely reasonable to expect that information we leave out of any model's inputs, which we might do because we don't have it or because we consider it irrelevant or because it would make the model unwieldy, could easily have relevant consequences for its outputs.

On pilot wave theory: I've never been happy with the idea of a "pilot" wave that "guides" particles. I'm happier to assume that what guides any given particle is its relationships with everything else in its entire history, and to interpret the wave equation as a beautiful statistical description of the ways in which those histories pan out in practice.

Non-locality, then, speaks only to the likely infeasibility of collecting all potentially relevant inputs to any model of reality we might wish to construct, and causes me no discomfort.

All that stuff about modelling the entire universe as a single wave function? Purest handwavium. I recommend not taking any of that the slightest bit seriously. Getting serious about any argument over what we could do "in principle" is always a mistake, because the only thing any of them amount to is that things would be so different if they were not as they are.
posted by flabdablet at 11:05 PM on February 24 [1 favorite]

And to the extent that it is feasible to identify and characterize all of the quanta involved in that entanglement, it would be possible to extend the particular wave function that we're using to model the experimental object so as to account for all its new entanglements as well.

I meant that the experiment would become entangled with its environment after the measurement is made, but not before. You can extend the wave function to include the environment before the measurement, but it would be a separable state, not an entangled one.

We can tell the difference. Here is an experiment: I put a qubit in the superposition state |0⟩ + |1⟩ (omitting the normalizing factor). I flip a coin and measure the qubit in the Z basis if the coin is heads, or the X basis if the coin is tails.

If the experiment is not entangled with the environment, then we are in a 50-50 mixture of |e_H⟩(|0⟩ + |1⟩) and |e_T⟩(|0⟩ + |1⟩), where |e_H⟩ represents the environment where the coin landed heads up and |e_T⟩ represents the environment where the coin landed tails up. In the |e_H⟩ case, I measure in the Z basis, so I would get 0 with probability 0.5 and 1 with probability 0.5. In the |e_T⟩ case, I measure in the X basis, so I get 0 with probability 1. The expected value is 0.5 × (0.5 × 0 + 0.5 × 1) + 0.5 × 0 = 0.25.

If the experiment is entangled with the environment, then before we flip the coin we are in a 50-50 mixture of |e⟩|0⟩ and |e⟩|1⟩. After we flip the coin, we are in a 25-25-25-25 mixture of |e_H⟩|0⟩, |e_H⟩|1⟩, |e_T⟩|0⟩, and |e_T⟩|1⟩. In the |e_H⟩ cases, we measure whatever state we're entangled with with probability 1. In the |e_T⟩ cases, we measure 0 or 1 with probability 0.5. The expected value is 0.25 × 0 + 0.25 × 1 + 0.25 × (0.5 × 0 + 0.5 × 1) + 0.25 × (0.5 × 0 + 0.5 × 1) = 0.5.

As you pointed out earlier, the wave function is deterministic. For as long as we remain content to model the system we're looking at asa wave function, nothing in that model implies that multiple versions of the system exist.

By "multiple versions," I mean a superposition, which is deterministic. I think this is a logical consequence of taking seriously the idea that the experiment and the experimenter become entangled after a measurement. If you started in |e⟩(|0⟩ + |1⟩), and then "measure" (become entangled with) the qubit, you end up in |e₀⟩|0⟩ + |e₁⟩|1⟩, where |e₀⟩ is the environment where the experiment measured 0 and |e₁⟩ is the environment where the experiment measured 1. From the perspective of each environment, it sees only one outcome. But the wave function tells us that both exist.

From my vantage point as a strictly practical tautological determinist I take it as self-evident that there can only ever be one outcome of any given measurement, which is the outcome that is actually measured.

This is true, of course, but it doesn't help us make predictions or understand anything about the universe.

But we don't actually need to posit an endlessly bifurcating universe to account for all our experimental outcomes, because each such outcome is the outcome of some specific experiment, each of which can be distinguished from all the other similar experiments by virtue of having happened at some other place or time...

...it's completely reasonable to expect that information we leave out of any model's inputs, which we might do because we don't have it or because we consider it irrelevant or because it would make the model unwieldy, could easily have relevant consequences for its outputs...

...I'm happier to assume that what guides any given particle is its relationships with everything else in its entire history...

Non-locality, then, speaks only to the likely infeasibility of collecting all potentially relevant inputs to any model of reality we might wish to construct, and causes me no discomfort.

This sounds like superdeterminism. You're right that it's consistent with all observations. However:

1. Superdeterminism is not testable. You said earlier that you "refuse to take any claim about reality seriously unless it can be tested." I don't understand how you can use that to dismiss many-worlds without also applying it to superdeterminism.
2. Superdeterminism implies that the universe is conspiring against us to make it seem like nature is consistent with one mathematical model, while in reality being something completely different. That could be the case, but if it were, it doesn't tell me anything about what the underlying reality actually is. So it seems to me like I might as well proceed as if the universe were being honest.

posted by april of time at 8:33 AM on February 25 [1 favorite]

I don't take superdeterminism seriously either. Near as I've ever been able to work out, all of metaphysics is merely word games constructed for the amusement of those of us who like that kind of thing. Batting these ideas around like kittens playing with balls of scrumpled paper is fun, but none of them do diddly squat as far as actual practical predictive power goes.

At best, a metaphysics can serve as a source of inspiration for possible ways to go about constructing models of reality, but the idea that the practical success of any such model in any sense validates the inherently untestable metaphysics that inspired it is, I think, delusional. I see the cognitive dissonance that many people experience when trying to shoehorn testable wavelike behaviour into a metaphysics that doesn't allow any possibility for what they think of as "particles" to exhibit it is a perfect illustration of this.

I have no confidence whatsoever that any metaphysics worth the name could ever concisely encapsulate some kind of "essential" or "underlying" nature of reality; near as I can tell, the only essential quality of reality is raw, undifferentiated existence, and that essence has - as you correctly point out above - no predictive or explanatory power whatsoever.
posted by flabdablet at 10:12 AM on February 25

near as I can tell, the only essential quality of reality is raw, undifferentiated existence, and that essence has - as you correctly point out above - no predictive or explanatory power whatsoever.

But that claim is itself metaphysical, which is my point. Everyone holds some fundamental assumptions about how the universe works - we need to in order to do science. If we think that the universe is telling us exactly what we need to know to make only testable predictions, but not one bit of information more than that - and is in fact obscuring the information we need to know to make true untestable predictions - then that itself is a metaphysical belief.

I don't think there is anything wrong with following our beliefs to their logical extremes so that we can understand their implications, even if there's nothing we can do with those implications. Obviously it's not as useful as testable science, but I don't think it's foolish, as long we we're all aware of the fact that we're just extrapolating.

I'm saying: quantum mechanics is a really good mathematical model of reality. It helps us make predictions that can't otherwise be explained. But there's this weird hack (wave function collapse) that we have to add to make measurement work. What if we don't add the hack? Can we still explain observations then? It turns out we can, and it also has this neat metaphysical implication (many worlds). I think that's interesting.

My understanding of what you're saying is: you don't think wave function collapse is necessary to explain measurement, but you also don't think that many worlds exist. You make an epistemic argument about our lack of knowledge to claim that there is no inherent uncertainty in measurements. I'm saying that this is not possible - it's not consistent with observations - without either nonlocality or superdeterminism. If you also don't believe in nonlocality or superdeterminism, then your argument is not self-consistent because of Bell's theorem, which rules out local hidden variable theories. The only way to explain away apparent nonlocality is superdeterminism.
posted by april of time at 10:56 AM on February 25