Yeah, they're probability distributions, not fields. So electrons, protons and neutrons are still tiny, even though their positions are uncertain. And so atoms are still mostly empty space.

Rather than thinking of space as empty vs non-empty, it might be better to think of space as a relationship between things.

I think you make less commitments of space this way.

That's also the difference between raster and vector modeling of virtual geometry. There is an area on a graph where one literally takes less space on a computer's memory than the other, for representing essentially the same information.

But there are other trade-offs.

Thought you might find this interesting.

https://www.quantamagazine.org/coder-physicists-are-simulati...

In the model you propose, what would I think instead of “this box is full of water”?

I think it’s fine to have the usual view, “this box is full of water”.

But you might also think, “this eyebrow is hairs with not too much space between.”, or “this box is hydrogen and oxygen without too much space between.”

An eyebrow is hairs with a certain spatial density and distance (space) from the eyes. Water is hydrogen and oxygen with relatively less space between than say water vapor.

If I think of space as a magnitude, all the math and forces still work out, but there is “room” for other stuff.

This is what I took from the article as well. Though, it's important to note that the 'billiard ball' particle model is just a model also.

On a related note, as a physics grad, I've been looking into growing evidence that shows consciousness affecting what we observe (i.e. wave-particle duality in this case).

Have you seen Steven Greer's latest film (CE5)?

As a lapsed Cognitive Scentist, I had stopped paying attention to consciousness studies and thought Penrose was full of it. This comment sparked my interest. Will look into this movie but curious for pointers for summaries of recent evidence?

I believe there is non-zero vacuum energy. So "something" is going on, whether it be virtual particles popping in and out of existence, even in "empty space".

Granted, I don't really understand the details of what this means, but that's what I remember of the current science.

Yes, vacuum energy. But that's still probability distributions, and so almost all of the vacuum is empty at any given time.

Most physicists would likely say that there's no point trying to visualize this stuff in mundane terms. Or at least, that's what they were saying the last time I took a physics course.

Modeling electrons as tiny objects that have probability distributions has a weakness. There is no sensible value to assign to the 'tiny'. I mean there is no experiment to determine the 'size' of the electron.

OK, not a physicist.

But what about this?

https://en.wikipedia.org/wiki/Classical_electron_radius

That's essentially just an approximation. In some problems it can be useful to model the electron as having a finite radius, but our current understanding is that particles like electrons are literally infinitesimal points. In that case it's generally more useful for us to use things like Dirac delta functions to model them more accurately.

Check all the disclaimers on that concept, in particular "Attempts to model the electron as a non-point particle have been described as ill-conceived and counter-pedagogic"

“Empty space” is a concept from our scale that becomes absurd at small scale

Do probabilistic interactions necessarily imply a moving particle structure?

Do those fields extend into infinity or is there a boundary that the electrons don't cross?

>If you took an atomic nucleus and bound only one electron to it, you would see the following 10 probability clouds for each electron, where these 10 diagrams correspond to the electron occupying each of the 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d and 4f orbitals, respectively. The electron is never located in one specific place at one particular time, but rather exists in a cloud-like or fog-like state, spread throughout a volume of space representing the entire atom.

If there is no boundary, then the universe itself would be full by that field definition because every electron would be at any point by a very small probability.

You’re not filled with fields or those fields would block neutrinos. Instead we can shoot them though the earth and detect them just fine on the other side. Fields represent possible locations, not actual locations.

For anything that responds to the electromagnetic force, you're filled with fields. For something that responds only to the weak force, you're almost entirely empty space.

In the English-language usage I grew up with, 'occupied' means that there is something there, while 'filled' means occupied to the point where nothing more can be added. The former does not imply the latter.

In this usage, space itself (the 'empty' space of the article's title) is implicitly not something.

This usage may seem to be an accidental issue of language, resulting from an incomplete understanding of physics, but a lot of metaphysics seems to reach the point of hanging on such definitions. One may, of course, agree with both of the points of view expressed in this paragraph.

This whole idea of empty space within atoms is just nonsense using English grammar as a substitute for physics. It's a meaningless statement either way until you define the terms specifically enough. And by doing that, you can choose whatever answer you want. "occupied to the point where nothing more can be added" isn't specific enough because you can still add a lot of photons to a "filled" glass of water, so that means it's not filled by that definition even though it is by common sense. It just shows the irrelevance of everyday words and concepts at the subatomic scale.

Even a neutron star is practically invisible to neutrinos which can easily pass through it despite it's being "filled" with neutrons.

It’s abstract, but we experience this kind of issue with language lot. Think of a box that doesn’t have any objects in it. It’s empty, right? But if it’s sitting on the table in front of you it’s probably full of air.

So in one respect it’s completely empty but in another it’s totally full.

Well, that space is filled, but only because of quantum interactions, and not because it's empty.

If that’s how you want to look at it, everything responds to gravity. But, that’s not what people mean when they say space is filled.

And then there are those who say that space is an emergent property, e.g.

https://www.scirp.org/journal/paperinformation.aspx?paperid=...