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What Is Spacetime, Really?

blog.stephenwolfram.com

91–100 of 122 posts

Re: What Is Spacetime, Really?

#91
post #85
post #63

Earlier quoted context omitted.

1: they aren't. They don't need to be, and they cannot be. Simulate the first step of the first machine, then the first step of the second machine, then the second step of the first machine, then the first step of the third machine, then the second of the second, then the third of the first, then the first of the fourth, and so on. Every step of every program/machine is eventually reached. For the same reason that th…

Chaotic functions of continuous real variables are not computable. Computable physics assumes a discrete lattice, which the universe is not proven to be.

Hm, I was not aware of that.

What about for, uh...

It occurs to me that I'm not exactly sure what a chaotic function of continuous real variables is.

Is it like, one where iterating it gives chaotic results, or?

What if, instead of variables over the reals, using variables over the computable reals?

Re: What Is Spacetime, Really?

#92

In the beginning was a graph, more like diamond than graphite. Every node in this graph was tetravalent: connected by four edges to four other nodes. By a count of edges, the shortest path from any node back to itself was a loop six edges long. Every node belonged to twenty-four such loops, as well as forty-eight loops eight edges long, and four hundred eighty that were ten edges long. The edges had no length or shap…

That's a pretty neat idea. Then you could have gravity caused by structure -- the closer the nodes are to each-other, and the more nodes in an area there are, the easier the nodes fall into a lattice/crystal -- making masses attract.

And conversely space could just be a limit to information density.

If that's roughly what Wolfram was saying, I'm sorry, I couldn't read his jerk-session.

Re: What Is Spacetime, Really?

#93
post #92

In the beginning was a graph, more like diamond than graphite. Every node in this graph was tetravalent: connected by four edges to four other nodes. By a count of edges, the shortest path from any node back to itself was a loop six edges long. Every node belonged to twenty-four such loops, as well as forty-eight loops eight edges long, and four hundred eighty that were ten edges long. The edges had no length or shap…

That's a pretty neat idea. Then you could have gravity caused by structure -- the closer the nodes are to each-other, and the more nodes in an area there are, the easier the nodes fall into a lattice/crystal -- making masses attract. And conversely space could just be a limit to information density. If that's roughly what Wolfram was saying, I'm sorry, I couldn't read his jerk-session.

Or the lattice is infinite in all directions, and is "pulled" against. So even as local objects want to fall into lattice, the fact that the network is infinite "pulls" the "space" away from the lattice.

So close together the lattice force works, but it is weak across long distances, in comparison to the pulling force of the rest of the lattice out towards infinity.

I really have no idea what I'm talking about.

Re: What Is Spacetime, Really?

#94
post #64

Earlier quoted context omitted.

This conversation has given me lots to think about and I was ready to let it trail off. But wanted to answer you just out of respect. My mistake was thinking that he was proposing something about the nature of physical reality. Ie. that physical reality was literally a network of interconnected nodes at its fundamental level. Something along the lines of macroscopic -> atomic -> sub atomic -> wolfram-nodal. A la, str…

No, I don't think that's it. He is saying that physical reality is literally a network of interconnected nodes at its fundamental level. I think you're still assuming that these graphs have to be embedded in some space to be real. If we get fundamental enough, we can go below geometry, into algebra. For a less abstract example, what's the radius of an electron in modern physics?

These graphs have to be embedded into a computation device to be real and changing in time. To build such a computation device, maybe you need time and space. It could even be that our Universe is of the minimum complexity required to build a computation device capable of computing the graphs that describe our Universe.

Re: What Is Spacetime, Really?

#95

Maybe a physicist could help me out: the idea here of treating space as a simple discrete network, and particles just being emergent behavior sounds very interesting. But doesn't this violate Bell's Theorem, that no local hidden variables could completely explain quantum mechanics?

Loop Quantum Gravity (LQG) and Causal Dynamical Triangulations (CDT) are two theories of quantum gravity that describe spacetime as arising from a network of sorts. For LQG, spacetime emerges from a spin foam quite elegantly. And for CDT things are also quite elegant. I'm not aware of either violating Bell's Theorem, but quantum gravity isn't my specialty.

Also, physicists don't generally take Wolfram's claims about how cellular automata are related to quantum or classical gravity or anything else in fundamental physics very seriously. A New Kind of Science cites very few sources and makes it seem like everything in there is new, which isn't the case. There was loads of criticism about that when the book was released. Nonetheless, it's an interesting idea and if something useful came from the work it would be good.

Re: What Is Spacetime, Really?

#96
post #61

I think Stephen Wolfram fell in the trap, that any continuous dynamical system can be approximated by a discrete one. His position is a bit like claiming the fundamental theory of the universe is Brainfuck. Proof: I can encode general relativity and quantum field theory in Brainfuck, at least to a arbitrary good approximation. The initial conditions are then just the program to simulate GR and QFT plus the initial co…

Why would it be a "trap"? The uncertainty principle hints that something discrete may lie at the bottom. It's clear it's deliberate, not something you fall into due to naiveness. Also, Wolfram isn't the only one in this line of thinking, and this is a topic that rears it's head time and time again in the history of physics.

> The uncertainty principle hints that something discrete may lie at the bottom.

Not necessarily. The uncertainty principle is a direct consequence of some quantities being "the Fourier transform" of each other. You can't play a pure tone unless it extends infinitely in time, and vice versa: You can't play an infinitesimally short sound unless you ring all frequencies. That's all.

And actually, if something discrete lies at the bottom of spacetime, the uncertainty principle implies that there's a maximum energy and a maximum momentum. For the same reason that there's a Nyquist frequency when sampling. So, if anything, our intuition that there aren't such maxima makes the uncertainty principle hint that there's nothing discrete underneath.

Re: What Is Spacetime, Really?

#97
I'm having trouble finding any other references to a notion of a dimension of a graph which is based on howthe number of vertices which can be reached through a path of a given length increases with the length.

I'm finding things like, a dimension of a graph as the minimum dimension of euclidean space where the vertices can be placed and have each edge have length 1, and another thing which seems closer which is based on a metric from the graph, but that is based on the idea of a metric basis, which I don't think is equivalent (in it, a subgraph can have a higher dimension than the graph it is a subgraph of, which I don't think is the case in the version mentioned in this blog post. And one example I'm p sure has finite dimension in the blog post version, but infinite dimension in the other thing, so, I'm p sure they are different things).

Does anyone have any non wolfram references for the notion of the dimension of a graph as is explained in the post linked?

Re: What Is Spacetime, Really?

#98
post #88

Earlier quoted context omitted.

i wish i knew what was so unsettling about the above opinion i'm interested in discussion

I haven't voted on your comment, but here's what stands out to me: (1) It's not written in good style. People who care about how their ideas are received by others take the time to write properly, including capitalization and punctuation. (2) It reads like a middlebrow dismissal. It's critical but doesn't add much of substance on its own through the criticism. Wolfram certainly realizes that he hasn't proven his case…

i appreciate the thought out response.. i'll try to address your points

1) sorry, it's the way i write

2) solid response:

   It's critical but doesn't add much of 
   substance on its own through the criticism. 
what you said there mirrors my immediate reaction to the linked piece by wolfram, and in all fairness i felt it myself of my comment and intended to reply with a more directed response to the piece but found it difficult to find anything to riff off of

    So then the question arises: could one of these simple
    programs in the computational universe actually be the
    program for our physical universe?
this seems to be the base line on which his potential final theory is predicated, but this just reads as a rewrite of the infinite monkey theorem

if the universe is programmable, then surely within the bounds of every possible permutation of computation therein must lie a representation of the universe..?

3) 'use case' and 'science as directed utility' seemed explicitly to go hand in hand

4) "... reveal those use-cases untouched by contemporary thought"

one such important use case that showed the inherent utility of relativity was understanding retrograde motion(o), this was the sort of use case i was referring to one where the contemporary thought was unable to reach insight

"an existence where every new finality conjures new questions"

here i'd agree i erred on poetics to allow for some self discovery, what i hoped to express was that every 'final theory', as wolfram puts it or finality as i put it, i think will introduce more questions mocking the title of final

relativity is sussed out and people, as wolfram attested, assume it to be true, but then later find it only reveals, seemingly by conjuring, questions they were unaware of

even einstein, the one person who stood to gain the most by espousing that his theory was 'the final theory', knew relativity to be wanting

it is my impression that i do write 'in spoken language'

when was the last time you heard a capital letter? or 'proper' punctuation?

these are the words i would use to talk to you about this topic

the diction may seem off because i avoid negative constructions:no, not, never, none,etc; with hopes that the a subsequent generation will have the patience to write out even negating prefixes: un-,i-,a-,etc;

i find removing negative constructions is a means of making discussion more inviting and less authoritative

next time someone asks if you've seen some new media, instead of saying 'no' see what reaction something like 'i've yet to have seen it' will afford

if a sentence comes easily as "which isn't that interesting" i will take whatever time necessary to rewrite in order to write out the negative

reading your rewrite:

    The ideas need to work to be useful. 
    We need to think up new ideas. 
    I think we'll always have more questions to answer
could placehold as a rewrite of wolfram's piece

i'll express it as your rewrite on one side of a colon and applicable sections from wolframs piece on the other, ctrl-f confirmation encouraged

    ideas need to be useful: "provides the only successful way 
    we have of describing spacetime"

    we need to think up new ideas: "started on my long journey 
    to go beyond traditional mathematical equations and instead 
    use computation and programs as basic models in science"

    I think we'll always have more questions to answer: 
    "But what would such a program be like?..what’s the basic 
    “data structure” on which this program operates?.." and on and on
so yes, i agree, markedly uninteresting

(o) http://theory.uwinnipeg.ca/mod_tech/node60.html

.. an aside, can we talk to the fact that middlebrow seems the only brow held in contempt, i feel low brow and high brow each have their accepted merits(i) but i've yet to have seen something quantified as being middlebrow used in promotion

i wonder what the says about adjudged middles

(i) http://nymag.com/nymag/culture/approvalmatrix/archive/

Re: What Is Spacetime, Really?

#99
It's interesting to see that, while philosophy has been sitting in the post-Hume doldrums for the last hundred years, physics has gone all the way around and started tackling metaphysics again!

Re: What Is Spacetime, Really?

#100
post #89

Earlier quoted context omitted.

i wish i knew what was so unsettling about the above opinion i'm interested in discussion

I don't find it unsettling but it's not particularly interesting. You can view epicycles as detour before Copernicus, I think that's more of the sense of what Wolfram is referring to as a detour.

wolfram's use of detour seemed like a dismissal of the utility of relativity, i read it as 'a waste of time'.. taking an indirect route when a direct route would have been preferred.. was something else meant by the word? people mock an earth centered universe today but was the idea a waste of time?

what's the alternative to detours? waiting, still, until one is shown the direct route? how will it reveal itself? what defines direct? are there direct and detour routes between wolfram's network nodes?

bones had a hard time appreciating the efforts of his predecessors(o), but does the potential of a future technology rendering a current technology obsolete, barbaric even, mean we should avoid it's utility because it's merely a 'detour'

i think the probabilistic nature of quantum bodies is an incorrect model but i wholly endorse its use in those scenarios in which results are found where they were previously elusive

i think monte carlo descision tree traversal is a misguided method but i wholly endorse its use in those scenarios in which results are found where they were previously elusive

utilise and iterate on best fit 'detours' while still seeking direct routes

my response to wolfram was asking: why call something a detour when everything is a detour, even his unfinished attempt at finalising all detours

i want to make it clear that i encourage wolfram to continue his work on his theory, but careful judging lest ye be judged

hey einstein, “Don’t waste your time working on that!” and, “Please don’t work on that.” it's merely a detour

(o) https://www.youtube.com/watch?v=MMaGnpVaSGQ

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