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.

## "Smears" as an analogy in quantum physics?

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- SolarpunkFan
- Jedi Knight
**Posts:**515**Joined:**2016-02-28 08:15am

### "Smears" as an analogy in quantum physics?

Slusho is Bloop...

### Re: "Smears" as an analogy in quantum physics?

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.

For a different perspective, here's a lecture by Feynman:

[youtube]https://www.youtube.com/watch?v=xdZMXWmlp9g[/youtube]

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]

*Keep, ancient lands, your storied pomp! Give me your tired, your poor, your huddled masses yearning to breathe free, the wretched refuse of your teeming shore. Send these, the homeless, tempest-tost to me. I lift my lamp beside the golden door!*

- SolarpunkFan
- Jedi Knight
**Posts:**515**Joined:**2016-02-28 08:15am

### Re: "Smears" as an analogy in quantum physics?

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.Surlethe wrote: ↑2019-05-10 10:07amHowever!I'd caution you that this is just an analogy. It's a metaphor for understanding a mathematical model. The modelitselfis 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]

Slusho is Bloop...

### Re: "Smears" as an analogy in quantum physics?

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

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

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

"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.

---

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.

### Re: "Smears" as an analogy in quantum physics?

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

*Keep, ancient lands, your storied pomp! Give me your tired, your poor, your huddled masses yearning to breathe free, the wretched refuse of your teeming shore. Send these, the homeless, tempest-tost to me. I lift my lamp beside the golden door!*