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Why Understanding Space Is So Hard

nautil.us

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Re: Why Understanding Space Is So Hard

#61

Post by [deleted] »

grondilu wrote: post #50
kazinator wrote: post #24

The question "would space still exist if matter disappeared" is posed with an ontological bias which influences the answer. A better question is: does a universe in which there is nothing (and never has been) still contain space? (Though a better question, I wrecked it by introducing "never", which presupposes that the universe has time---even though it contains nothing, and therefore no events take place.) The quest…

I've struggled several times to formulate this question properly. I'm not convinced by your formulation. I'll give it an other try. Does space have an existence per se, that is regardless of the matter it contains, or is it just a mathematical framework for the interactions between particles?

[deleted]

Re: Why Understanding Space Is So Hard

#63

Post by Gravityloss »

fennecfoxen wrote: post #13
xyzzy4 wrote: post #10

Earlier quoted context omitted.

How can a dimension be under a size? The four regular dimensions (3d and time) can go infinitely in any direction.

Well, how can you go on forever without falling off the edge of the Earth? The surface of the Earth two-dimensional, and approximately flat... but there's small positive curvature, so you're continuously wrapping around to a different part of the space. The surface of the Earth can be meaningfully understood as a two-dimensional surface that possesses finite dimension. A three-dimensional space can be close to flat b…

I find these videos explaining things in an interesting way. https://www.youtube.com/watch?v=_k3_B9Eq7eM There's also a part 2.

Re: Why Understanding Space Is So Hard

#64

Post by gkya »

grondilu wrote: post #50
kazinator wrote: post #24

The question "would space still exist if matter disappeared" is posed with an ontological bias which influences the answer. A better question is: does a universe in which there is nothing (and never has been) still contain space? (Though a better question, I wrecked it by introducing "never", which presupposes that the universe has time---even though it contains nothing, and therefore no events take place.) The quest…

I've struggled several times to formulate this question properly. I'm not convinced by your formulation. I'll give it an other try. Does space have an existence per se, that is regardless of the matter it contains, or is it just a mathematical framework for the interactions between particles?

This requires a definition of space. For your question to be logical, space should be taken as the thing that is among and around matter. Then on it may be researched physically. Buf if space is taken to mean the thing that exists among and around perceivable matter, then your question becomes obscure, as this means that space is matter, but just not perceivable. And therefore it exists, also without relation.

Re: Why Understanding Space Is So Hard

#65

Post by danbruc »

klank wrote: post #58
Animats wrote: post #53

Earlier quoted context omitted.

Centrifugal force is an abstraction, but angular momentum has physical reality at the subatomic level. See Feynman, chap. 17.[1] Photons have angular momentum, even though they don't have a meaningful size. This is strange, but it's reality. [1] http://www.feynmanlectures.caltech.edu/III_17.html

Angular momentum could be encoded in the wave function. http://arxiv.org/abs/0807.3930

That is a trivial fact, the wave function of a system completely describes the state of the system and that of course includes the angular momentum. But the wave function has nothing to do with a physical wave with physical properties, it is a pretty abstract construction and the physical properties are essentially encoded in the base vectors of the Hilbert space. I only skimmed the paper but I didn't come across something that plausibly argued that the wave function is the fundamental physical entity.

Re: Why Understanding Space Is So Hard

#66

Post by colordrops »

Animats wrote: post #53
colordrops wrote: post #49

Earlier quoted context omitted.

Angular momentum is an abstract concept, and an emergent property. It doesn't exist inherently in an object.

Centrifugal force is an abstraction, but angular momentum has physical reality at the subatomic level. See Feynman, chap. 17.[1] Photons have angular momentum, even though they don't have a meaningful size. This is strange, but it's reality. [1] http://www.feynmanlectures.caltech.edu/III_17.html

I mean angular momentum of macroscopic objects, which the spin of particles has little to do with.

Re: Why Understanding Space Is So Hard

#67

Post by klank »

danbruc wrote: post #65
klank wrote: post #58

Earlier quoted context omitted.

Angular momentum could be encoded in the wave function. http://arxiv.org/abs/0807.3930

That is a trivial fact, the wave function of a system completely describes the state of the system and that of course includes the angular momentum. But the wave function has nothing to do with a physical wave with physical properties, it is a pretty abstract construction and the physical properties are essentially encoded in the base vectors of the Hilbert space. I only skimmed the paper but I didn't come across som…

Not meaning to argue that the wave function is a physical entity but rather that particles aren't required to "exist" as a physical entity to explain experimental data.

Re: Why Understanding Space Is So Hard

#69

Post by Animats »

colordrops wrote: post #66
Animats wrote: post #53

Earlier quoted context omitted.

Centrifugal force is an abstraction, but angular momentum has physical reality at the subatomic level. See Feynman, chap. 17.[1] Photons have angular momentum, even though they don't have a meaningful size. This is strange, but it's reality. [1] http://www.feynmanlectures.caltech.edu/III_17.html

I mean angular momentum of macroscopic objects, which the spin of particles has little to do with.

No, they're the same thing. Feynman: "Now we would like to discuss the idea of angular momentum in quantum mechanics—or rather, the characteristics of what, in quantum mechanics, is called angular momentum. You see, when you go to new kinds of laws, you can’t just assume that each word is going to mean exactly the same thing. You may think, say, “Oh, I know what angular momentum is. It’s that thing that is changed by a torque.” But what’s a torque? In quantum mechanics we have to have new definitions of old quantities. It would, therefore, be legally best to call it by some other name such as “quantangular momentum,” or something like that, because it is the angular momentum as defined in quantum mechanics. But if we can find a quantity in quantum mechanics which is identical to our old idea of angular momentum when the system becomes large enough, there is no use in inventing an extra word. We might as well just call it angular momentum. With that understanding, this odd thing that we are about to describe is angular momentum. It is the thing which in a large system we recognize as angular momentum in classical mechanics."[1]

Yes, it's weird. Yes, it's not intuitive. But it's very real. Many experiments, such as the classic two-slit experiment, have confirmed the stranger predictions of quantum mechanics.

[1] http://www.feynmanlectures.caltech.edu/II_34.html

Re: Why Understanding Space Is So Hard

#70

Post by danbruc »

klank wrote: post #67
danbruc wrote: post #65

Earlier quoted context omitted.

That is a trivial fact, the wave function of a system completely describes the state of the system and that of course includes the angular momentum. But the wave function has nothing to do with a physical wave with physical properties, it is a pretty abstract construction and the physical properties are essentially encoded in the base vectors of the Hilbert space. I only skimmed the paper but I didn't come across som…

Not meaning to argue that the wave function is a physical entity but rather that particles aren't required to "exist" as a physical entity to explain experimental data.

I would say nothing is required to exists. Just take the idea that our universe may be a simulation, then nothing in the universe is real. It could then be that the real universe out there is similar to ours or we could be the Game of Life of the real universe which could be totally incomprehensible to us with concepts that aren't even imaginable in our little world. Or take Last Thursdayism, the idea that the universe somehow came into existence last Thursday with fake memories of the past in our all heads and so on. Or Solipsism. There is no way you could ever find out that something like that was true or not.

We just have to make some assumptions about the nature of the universe and accept them as axioms, otherwise you can not even start to draw conclusions. Some assumptions may look more reasonable then others but I guess that is more or less an illusion, last Thursdayism looks only unreasonable because you have already rejected the idea and accepted some other assumptions.

So what is real? Particles? Fields? Wave functions? We pretty surly don't know. Some will say the fields are the real things because they give us virtual particles and that matches experiments, others will say that fields are not real because they have gauge symmetries - gauge redundancies - and how can something that is underdefined be real? It seems certainly possible that we will be able to rule one or another view out in the future because they can not accommodate some new discovery but we are probably not yet there and there is definitely no consensus.

Not to forget that there are quite a couple of new directions in the last years and decades, like space and time emerging from entanglement, the holographic principle, gravity as an entropic force and what not. There is probably a good chance that some or all our fundamental concepts of physics as of today will not survive the next century, millennium or million years. I mean they will still exist as useful approximations but no longer been seen as fundamental.

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