This installment of our Biggest Ideas in the Universe series talks about Space. As in, the three-dimensional plenum of locations in which we find ourselves situated. Is space fundamental? Why is it precisely three-dimensional? Why is there space at all? Find out here! (Or at least find out that we don’t know the answers, but we have some clues about how to ask the questions.)
The Biggest Ideas in the Universe | 4. Space
This is likely one of my favorite Ideas in the series, as we get to think about the nature of space in ways that aren’t usually discussed in physics classes.
Update: here is the followup Q&A video. More details on Hamiltonians, yay!
The Biggest Ideas in the Universe | Q&A 4 - Space
“Why is there space at all? “. there’s the old saying that time exists so that everything doesn’t happen at once. similarly, we can say that space exists s that everything is not in the same location.
Too complex to discuss here as it is the most complex aspect of the ultimate nature and origin of the universe. Will discuss it to some extent in my coming second book.
Many people have said in popular broadcasts (Through the Wormhole for example) that there are theories suggesting that space is an illusion. Is it possible that entanglement is a little hint that this might be true – we believe that particles are far apart but in reality they share an aspect which remains connected to both particles at all times (like a mini wormhole that remains open between entangled particles). If space turns out to be discreet, does this pose any problem to some of your favorite theories? Is it possible that expansion of space creates new space quanta, like a soap foam? Does the expansion of the universe increase its information content and so every next state has more bits than the previous one and so going back in time mean zipping the universe and losing some bits? I apologize for the long post.
These Biggest Ideas are becoming increasingly delightful.
I hope you’re enjoying presenting them as much as I’m enjoying watching them.
Some preliminary thoughts/fun reactions:
The holographic information principle seems to suggest that physics necessary for complex life could be represented in a 2-d space.
but maybe that doesn’t count as a physical space if interactions aren’t local in that space.
(I may need to find different words for different kinds of space to not get confused.
I tried using italics to distinguish them, but I couldn’t get that to work in this input field)
But Conways game of Life is a 2-d cellular automaton that supports universal Turing machines with only local interactions, so 2-d doesn’t seem to fundamentally exclude intelligence.
In a 4-d space, 2-d manifolds can be knotted, so shoelaces don’t seem like a limitation to intelligence in higher dimensions.
Different ways of partitioning conceptual space, like Hamiltonian vs Lagrangian,
or phase space vs position space, or Copenhagen vs Everett vs de Boglie-Bohm, etc.
seem analogous to different basis vectors in a geometric space.
Fermions with the same spin exclude each other, but Fermions with different spins don’t,
so spin seems to be like an extra dimension in which interactions are local.
1. I asked a high school student if she was familiar with the Hamiltonian from her physics courses. She said, no. Would it be helpful to introduce that concept at the early stages of physics education?
2. If the Hamiltonian approach uses “momentum” as a fundamental concept, is that because “mass” is not fundamental? In other words, it appears that it gets subsumed in the Hamiltonian momentum concept/representation.
Thank you for helping to keep us sane during these challenging times!
In 31:57 I am wondering how would the 3-body problem come into all this? I assume the issue is that it would be impossible in any way to have stable orbits in 4D whatsoever as oposed to the 3-body situation in 3D?
Also, if I understand correctly, we wouldn’t be able to tie 3D laces in 4D space but that assumes the “life” being 3D. Is there something that would prevent life from being 4D in 4D space? Then there would be no problem in making a knot with 4D laces in 4D space.
Hey Dr. Carroll, thanks for the informative videos to keep me occupied during this quarantine.
In each video, you reference a pretty significant amount of mathematics, and then apply this to physical ideas. I am actually familiar with nearly all of the math you reference (manifolds, functional analysis, …) . However, I am ignorant to almost all of the physics outside of popular knowledge – never heard of Kaluza-Klein or a Hamiltonian before your videos! … My question is: Do you know of a reference book which lays out some aspect of modern physics, for a mathematician? I think I am equipped with of of the rigorous maths prerequisites, but have had trouble reading “classical” physics texts, due to them treating math in an informal way. I would love to be learn the math behind the ideas or historical theories which you mention in your videos – it’s most intriguing!
Notability tip: use the “partial eraser” to only erase part of a line. Simply click the eraser in a note, and then you will see the options “whole”, “partial” as well as how thick the eraser is.
The argument about 2d space not being complex enough to support life seems excessively weak to me. We can already make very complex systems in 2d, even with just two different states and a discrete space, such as the game of life or other cellular automata. Our 3 dimensional space isn’t just divided in sections of black and white, we have all sorts of fields with all sorts of interactions between them to create everything we see (and everything we don’t), so I don’t see why a 2 dimensional space allowed the same complexity would be fundamentally incapable of hosting life.
I do not understand the concept of curled up space dimensions. To me generally a dimension has infinite extent – ∞ to + ∞. Do these curled up dimensions have unit of length. When they are curled up do they have extent of -plank length to +plank length (for the reasons of x*p > h). Can there be curled dimension be of arbitrary extent .e.g -1m to +1m. If the curled up dimensions are small and every point will we needs a fourth coordinate i.e. say x,y,z and w to locate a point in 4 spatial dimensions instead of just x,y,z and w being always 0. If w is not 0 wont the thing at that point move out of our perception.
Or do these curled up dimensions are not spatial but are only needed so that we can explain weak gravity because it has a component spread into that additional dimension.
Does any of this have implications on the inverse R square in Gm1m2/R^2 i.e. the 2nd power. I think that 2nd power comes from the area (a two dimensional thing) of sphere enclosing gravitational source. If that is true then does it not require only three dimensions?
Reading footnote 48 in your “From Here to Eternity” I visualized the immediate post-big bang expansion as the creation of space and a way, so-to-speak) of dumping energy into this new energy-storing space. Previously I had always envisioned the expansion as a stretching of space. I suspect this space-creation idea is wrong-headed because of the other worldviews in which space is just a metric of distance between objects. Just wondering…
Ooops. Of course I meant your book “From Eternity to Here.”
Hi Sean.. How are u ?You were talking about vanishing dimensions by compactification.. I was thinking about condensed matter systems that are mostly 2d materials.. motion of electrons becomes almost 2 d…but as we know QED is written in 3+1 d. Is Kaluza Klein theory can be applied
to such a case where motion of the electrons become 2d by lattice potentials ?
Q1: could there be a *different* (physical, not phase) 3-d space in addition to ours? Mathematically of course that is easy, but as physics is an empirical science, could we detect a different 3-d space? Could different 3-d spaces interact? Here I am not thinking of Everett-MWI ideas but actually different spaces, each inhabited by their own objects (and fields).
Q2: How big is space? By which I mean our physical 3-d space. Observationally we are limited of course by the speed of light/gravity, but as cosmologists have already inferred that our material universe is larger than our observational limits, could our physical space be truly infinite? And if so, doesn’t an infinite amount of space have implications for how we understand physics (example: the probabilities of certain events occurring)?
There were times when string theorists used to say that the universe is 26-dimensional (25 dimensions of space and 1 dimension of time), then they said the universe is 11-dimensional (10 dimensions of space and 1 dimension of time), and now they say that the universe is 10-dimensional (9 dimensions of space and 1 dimension of time). What is the reason for the reduction in the dimensions of space? Do they know this just from math, or has it been tested? Do you think that string theory would ultimately collapse down to a 4-dimensional universe (3 dimensions of space and 1 dimension of time)?
If you wrap your square into a torus from top to bottom, and then left to right, the hole will be in the “top” of the torus; if you wrap left to right and then top to bottom, the hole will be in the “side”. Is there a topological difference? Can a being living on that torus tell which “way” the hole runs? In a 3-torus, how many holes are there, and does the topology depend on what order you attach the pairs of sides?
How would you physically describe a field?
Is the geometry (or more generally characteristics) of space(time) even a property of nature(i.e objective) or is it just due to the way we perceive the world? Consider the hypothetical scenario in which we have multiple theories of everything (i.e all of them explain all observed phenomena) and they all make the same predictions for all situations (this possibility is a similar to current situation regarding various interpretations of QM). However, the characteristics of space(time) they assume/predict are drastically different. In this case what characteristics of space(time) be considered fundamental?
However, what if we call characteristics of space(time) are just a result of our perception there will be no need consider any set of characteristics as fundamental. This would reformulate the problem why we live in a 4D spacetime, as why we perceive the world as 4D spacetime.
Also, there is the possibility that other living organisms may perceive space (time) in a way which is different from us (note this is just a speculation just like the rest of this comment). This would make us consider if our perception of space (time) is more fundamental than that of other living organisms or not. Also, make us consider if our perception is fundamental or that we are missing some fundamental characteristics/features of space(time) if it even has any.
Hi Sean,
Why are you always combining the words intelligent and life? Just life will do.
The world you want to describe and explain is not different with unintelligent life. Right?
Life is probably not even essential to explain why the world looks like 3 big dimensions. Fysics is about the dead world. Biology is about life…
Kees
There are animals, eg jellyfish, that ingest food and excrete waste through the same hole. Wouldn’t the impossible “three utilities problem” be a better argument against the hypothesis of 2D life? An organism’s organs need to be connected up to interact as a whole and such a system would be severely limited in 2D.
I’m thoroughly enjoying the “Biggest Ideas”. Speaking as one of your innumerate viewers, I find it very accessible.
Richard Dawkins commented in one of his books that you could almost define a philosopher as someone who won’t take common sense for an answer. Having heard the answer to questions like “why space at all?”, I think the same definition might be applied to physicists. Dawkins added that he meant it as a compliment. So do I.
Hi, many thanks for the nice videos.
What about “interactions are local in time” ? Can’t we build a formulation where time is the dependent variable?
Cheers.
How do we know that the three dimensionality of space is not a functional creation of the human visual/sensory system ? In other words 3-dimensionality is the only way humans can explain/envision space. Thank You.
Since I mentioned John Horton Conway: https://xkcd.com/2293/
Hi, I have a question about making sense of real higher dimensional space, and the “curled up and infinitely small” idea really makes me think that it’s not small at all, but the perpendicular direction you travel is, in a sense, “inward”. I don’t know implications this has to what an inward traveling observer would see, but I imagine they might also see the traditional 3D space “at a distance” or “smaller” also.
Trying to be analogous to real world perceptions, like something moving away from you appears smaller, but relative to their local space, they are the same size, obviously. Could this be related to an object seemingly shrinking to an outside observer, but the object itself moving in a perpendicular direction to the X, Y, and Z axis? Basically, is this valid and should I hold onto you it?
Otherwise, I feel like I could only imagine Time being branched perpendicularly. (Traveling between world lines)
Thank you,
an extremely ignorant physics fan