"Smears" as an analogy in quantum physics?

[SolarpunkFan]

My understanding of physics is (I guess) slightly better than that of my average country-people (not a particularly high bar to cross though). From a physics class in primary school I recall the teacher stating that particles in the quantum realm aren't exactly "particles and waves at the same time" but rather entities that have some properties of particles and some properties of waves.

I don't know if that's incorrect, but a recent article here got me thinking of an analogy for quantum particles. That particles on that scale are less like discreet entities but more like "smears" of mass-energy.

I'm not sure if this is a good analogy or not (or if this is a good post for that matter), but it's something I'd like feedback on. If only to know how much I don't know.

[Surlethe]

First of all, I'm a mathematician, not a physicist.

That's one way of thinking about a particle, it's useful when you're approaching classical quantum mechanics from the perspective of the Schrodinger equation. According to this perspective, a particle or system has a wavefunction, which is a complex-number-valued schmear over all the possible positions of the particle. It evolves according to the Schrodinger equation.

However! I'd caution you that this is just an analogy. It's a metaphor for understanding a mathematical model. The model itself is only a tool for predicting observations. In fact, the Schrodinger equation is not even compatible with relativity, so its predictions only apply in a low-speed regime.

For a different perspective, here's a lecture by Feynman:
[youtube]https://www.youtube.com/watch?v=xdZMXWmlp9g[/youtube]

[SolarpunkFan]

However! I'd caution you that this is just an analogy. It's a metaphor for understanding a mathematical model. The model itself is only a tool for predicting observations. In fact, the Schrodinger equation is not even compatible with relativity, so its predictions only apply in a low-speed regime.

For a different perspective, here's a lecture by Feynman:
[youtube]https://www.youtube.com/watch?v=xdZMXWmlp9g[/youtube]

Thank you! I suppose the initial post I made was rather sparse, but mostly because I didn't know what else I could say about it.

[Feil]

Little correction - classical QM is indeed incompatible with relativity, but it works fine in high speed regimes in which its axioms (specifically, that spacetime is euclidean) are met. Conversely, it doesn't work in low speed regimes where spacetime has a significant curvature over the scale of the relevant quantum event.

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When we refer to the wave nature of a particle, we're referring to a probability wave, not a mass wave (like you'd see at the beach), or an energy wave (like a photon), nor a pressure wave (like sound).

Think about a set of two dice. You've probably seen this distribution in math class at some point.


When we roll the dice, we will find them at one discrete position on that number line, 2 through 12. It doesn't even make sense to ask if they're smeared out over the number line.

Now let's say we ask, "where are the dice before we roll them?" The real answer is "That's a meaningless question, we have to roll the dice before they have a discrete position." But if we needed something close to an answer, we could describe that probability distribution: "Well, it's in position 2 with 1/36 chance, position 3 with 2/36 chance, and so on."

Particles work the same way, except they have (at least in classical QM) an unlimited number of positions that they can fall into, so their probability distribution is continuous, and must be described with a waveform function rather than a list of discrete probabilities. Instead of rolling dice to find out where they fall on the number line, we interact with particles by bouncing something off of them to find out where they are in space.

"But where was the particle before we bounced something off of it?" demands Monkey-self. "It must have been there all along, or we couldn't have bounced something off of it, right? And where is it now, after we bounced something off of it?" Monkey-self is stupendously skillful when it comes to identifying possible mates, climbing trees, avoiding predators, and getting enough of the right stuff to eat without eating any of the wrong stuff, but he's having a lot of trouble with this.

Well, Monkey-self, it's the same "place" as where the dice roll was before we rolled the dice. And it's gone to the same "place" as the next dice roll is waiting for us to roll it. We can talk about probabilities, but the only real answer is that the question has no meaning.

[Surlethe]

I ran across this on Twitter, may well be relevant: https://aeon.co/ideas/the-concept-of-pr ... -you-think

[SolarpunkFan]

SNIP

Okay. So the gist of it is that the states/positions the particles can be in is large so unless it gets perturbed (say, by another particle) we can't know for certain as to exactly where or what state it is before or after observation (which involves interacting with and thus perturbing the particle), only where or what state it could probably be in?

A rough (and likely incorrect) analogy in my head is of having a ball inside of a gymnasium that can only be observed by bouncing another ball off of it. We don't know where exactly it is before observation (because we can't "see" it before then) or after observation (because bouncing another ball off of it changed its momentum, velocity, etc.), we can only say with certainty that it's somewhere in the gymnasium moving approximately in so-and-so manner.

Hopefully I'm more right than wrong on that one. And I thank you all (presently and maybe in advance) for your patience. And I'm sorry if this counts as a thread necro.

[Feil]

That's a good analogy, but drawing macroscoping analogies to the behavior of subatomic particles will always get you into trouble eventually.

The basketball really is somewhere specific before we bounced something off of it, and it really does go somewhere after we bounce something off of it. We may not know where it is, but if we throw our pingpong balls at a place where it isn't, we will miss it, and if we throw them at somewhere where it is, we will hit it. Our ignorance is a description of us, not a description of the ball.

This is not true for a subatomic particle like an electron. The electron really is a probability wave, like the next number rolled by a set of dice. It doesn't have a location to find, the act of finding it determines a location for it to be at the moment of observation, which we describe as "collapsing the waveform." But it doesn't learn where it was all along, the way we would for a basketball. It wasn't smeared out, it wasn't in one place, it didn't not-exist and then pop into existence. It wasn't in any state that we can imagine a macroscopic object to be in, because macroscopic objects don't have wave-nature on the scale at which we interact with them.

The analogy does, however, work well as long as you push your ignorance of the ball's location from a description of yourself (how reality actually is for basketballs) to a description of the ball (how reality actually is for electrons, etc). It also scales well when we consider that there could be more than one (subatomic) "ball" in the basketball court. We can imagine a whole rack of basketballs, flung in all kinds of directions, bouncing off of one another. They definitely interact with each other, and when they interact, they have no choice but to interact by bouncing off of one another at discrete positions and momentums. So, how do we reconcile the fact that the balls MUST be bouncing off of one another discretely, with the fact that we know (from experimentation) that the "balls" really DON'T have discrete location until we observe them?

The response of classical QM is to say that all the balls form an entangled system of probability waves acting on other probability waves. This is mathematically robust. With sufficient computational power, one can use regular wave mechanics - the same exact ones you would use to calculate the acoustics of a concert hall or calculate the behavior of ocean waves or design a stealth fighter jet - to compute the wave behavior of an entangled system as a giant bunch of probability waves interacting with one another. Then a single observation-interaction anywhere on the system will cause the whole entangled system to collapse into the subset of its possible states as allowed by the observation.

To snap back from the analogy for a second - an electron interacts with everything around it all the time, not just some scientist in a lab. We have to square this with our experiments that prove that an electron has particle nature when it's interacting with things, but wave nature up until the point that it interacts with something. The popular responses to this conundrum are the following:

"The magical soul riding around in my head, but discrete from my brain, is the only authorized observer in the universe, and nobody and nothing else exists unless I'm looking at it. Get me some patchouli and crystals, STAT."

"This doesn't make any damn sense, but the theory and all its predictions, even the insane ones, are 100% robust, so get over yourself, do the math, and leave the philosophy to the guy with the patchouli."

[SolarpunkFan]

That's a good analogy, but drawing macroscoping analogies to the behavior of subatomic particles will always get you into trouble eventually.

This is not true for a subatomic particle like an electron. The electron really is a probability wave, like the next number rolled by a set of dice. It doesn't have a location to find, the act of finding it determines a location for it to be at the moment of observation, which we describe as "collapsing the waveform." But it doesn't learn where it was all along, the way we would for a basketball. It wasn't smeared out, it wasn't in one place, it didn't not-exist and then pop into existence. It wasn't in any state that we can imagine a macroscopic object to be in, because macroscopic objects don't have wave-nature on the scale at which we interact with them.

It is, after all, only an analogy.

That being said, this is really fascinating stuff. It's one of those things that you can't truly "picture in your head" you just have to deal with what the math tells you.

To snap back from the analogy for a second - an electron interacts with everything around it all the time, not just some scientist in a lab. We have to square this with our experiments that prove that an electron has particle nature when it's interacting with things, but wave nature up until the point that it interacts with something. The popular responses to this conundrum are the following:

"The magical soul riding around in my head, but discrete from my brain, is the only authorized observer in the universe, and nobody and nothing else exists unless I'm looking at it. Get me some patchouli and crystals, STAT."

Ah yes, the magic brain poof woo. Though I've known beforehand that all it really takes is an interaction to collapse it. Whether that interaction be from observation or a stray cosmic ray doesn't really matter all that much when it comes to that scale.

[Feil]

One quick clarification / aside:

Just because Relativity and classical QM are axiomatically incompatible doesn't mean we can't use them both on the same phenomena, combine their predictions, and get good results, under many / most circumstances. For instance, consider nuclear physics, the sub-field that describes how atomic nuclii decay, fission, and fusion. In nuclear physics we run Relativity equations and QM equations for pretty much everything, constantly plug in the outputs of one theory as the inputs of the other, and everything works just fine. The fact that they rely on incompatible axioms doesn't mean that they generate incompatible predictions or have mutually exclusive predictive domains.

[SolarpunkFan]

One quick clarification / aside:

Just because Relativity and classical QM are axiomatically incompatible doesn't mean we can't use them both on the same phenomena, combine their predictions, and get good results, under many / most circumstances. For instance, consider nuclear physics, the sub-field that describes how atomic nuclii decay, fission, and fusion. In nuclear physics we run Relativity equations and QM equations for pretty much everything, constantly plug in the outputs of one theory as the inputs of the other, and everything works just fine. The fact that they rely on incompatible axioms doesn't mean that they generate incompatible predictions or have mutually exclusive predictive domains.

Of course. IIRC that only becomes a problem in phenomena that are simultaneously very dense (relativity) and very small (QM), like black holes or the universe before inflation occurred.

[Feil]

IIRC that only becomes a problem in phenomena that are simultaneously very dense (relativity) and very small (QM), like black holes or the universe before inflation occurred.

As far as we know. But... QM is the study of stuff we can manipulate in labs, and relativity is the study of stuff that's easy to see. And there's a whole lot of the universe that's apparently invisible and too far away for us to manipulate in labs, and it's absolutely baffling. As far as we can tell, about 95% of the universe's mass-like and energy-like stuff just comes from what looks for empty space for what looks like no reason at all. I don't have the education to give an educated opinion. But given how fundamental Relativity and QM seem to be to the way everything in our tiny little 5% seems to behave, my money is that the nature of most of the mass-energy-stuff in the universe is hiding behind whatever blind spot gives us "spacetime is euclidean because QM is accurate" and "spacetime is not euclidean because relativity is accurate" as the two most well-supported facts in science. If we ever solve that problem, maybe we'll get to peek behind the curtain and see what "dark matter" and "dark energy" are up to.