The concept of space-time is not necessary to make the same observable predictions that Einstein's relativity does, it is a concept that was introduced for mathematical elegance rather than because it was a necessity, so it is already dubious to treat space-time as fundamental. Probability waves from quantum mechanics are not necessary either to make the same observable predictions that quantum mechanics does, so again it is dubious to treat probability waves as fundamental.

Rather, physicists have chosen to treat space-time and probability waves as fundamental, and then they find that they cannot mix the two elegantly, so they look for something else. But in looking for something fundamental from which emerge space-time and probability waves, they are constraining themselves to look into a direction that is again not a necessity, so they are creating their own problems.

Another potential direction would be to do away with space-time and probability waves entirely, but since physicists spend years and years learning these concepts and how to apply them, and since they receive funding to carry out research that makes use of these concepts, they have little incentive to look elsewhere.

I listened to the lecture by Arkani-Hamed. Interesting! But mostly over my head! I wonder if anyone can help me understand something he said. At 1:41:27, he gives his thoughts as to why the idea of atoms of spacetime cannot be right. What do you make of the reasons he gives? Can you help me understand?

For it to be atoms of spacetime, it's very important that those atoms are small, but small in whose frame? There is no universal notion of small in whose frame, you see? ... The table is made out of stuff because the table chooses a frame. But we can't say that about the vacuum without breaking Einstein's symmetries. So, that's why you can't just have atoms of spacetime. The notion of atoms of spacetime is in radical conflict with Einstein's relativity. — Arkani-Hamed

What does he mean when he says that the table chooses a frame?

my best understanding is that atoms of spacetime encompasses vacuums, i.e. a lack of matter or "stuff", and, because atoms are supposed to be matter, that puts a lot of doubt onto whether an atom of spacetime is even a legitimate concept to begin with. (not sure about the concept of einstein's symmetries, but nonetheless that much is basic)

also, "the table choosing a frame," is a bit hard considering that the speaker had just brought up the idea of size when the idea of presence of matter seems to be a lot more crucial. but it only makes sense when considering that the concept of table always means that there is going to be a set amount of stuff in a place, but vacuum again means a lack of stuff, and atoms of spacetime apparently encompasses vacuum to some degree (in whole or in part, not sure).

Thanks for your thoughts.

atoms are supposed to be matter, that puts a lot of doubt onto whether an atom of spacetime is even a legitimate concept to begin with.

There are a number of approaches to combining general relativity and QM that involve treating spacetime as quantized, often as a network. And in some of these, the basic elements of spacetime are thought of as being like atoms of spacetime, which here doesn't mean traditional matter exactly, but just the smallest possible part of something. Some network approaches are loop quantum gravity, causal set theory, and ER=EPR. See this video for example:
Spacetime Atoms and the Unity of Physics (Perimeter Public Lecture)

For an interesting look at the idea of spacetime as a network, see this very interesting article:
What Is Spacetime, Really?

Since I find these ideas very intriguing and intuitively appealing, and Arkani-Hamed makes an objection to atomized spacetime, I'd like to know if his objection is a good reason to reject these approaches. Does what he is saying even apply to these specific approaches? I don't know.

It is actually very easy on a computer to program something spacelike, with any conceivable topology in any number of dimensions, by just defining nodes of a network and linking them in various ways, and then passing information from node to node where they are connected. Something spacelike emerges here from a much more primitive specification.

I personally have serious doubts about the old-fashioned conception of space as simply an emptiness in which matter moves. I don't think it is a mere background. I think that ultimately, matter and spacetime must both be reducible to something even more primitive. And I think that they are probably both forms or modes of the same underlying something. Or maybe a better way to put it is that whatever it is that makes up space, when in a certain configuration, is what we think of as the presence of matter.

Try something. Get a cable, maybe a USB charging cable or something. Now, hold it tight in one spot with your left hand and then, using your right hand, twist it 180 degrees, such that you force the cable to make a single loop. Then, hold that loop in place while you make another near it by twisting in the opposite direction. You now have two loops which, if you allow them to roll close enough to each other, will cancel. Done right, a counterclockwise-twist-loop will cancel a clockwise-twist-loop. But if you have an isolated loop and you prevent the cable from untwisting, that loop can travel, sort of rolling along. Also, notice that the loops effectively shorten the cable. And when they cancel, the cable lengthens. If you have some tension on it, when the cancellation occurs, energy will be released.

Perhaps this is a very loose analogy of what a particle could be. Maybe it isn't a separate thing floating in a background of nothingness at all. Consider that particles and anti-particles, when they come into contact, annihilate each other. Consider also that matter and energy can be converted into one another. Does this make sense if you think of matter really as some sort of substance sitting in space? How can some stuff cancel out other stuff? Maybe it is like the two opposite twists in the cable canceling each other and releasing energy.

Maybe all matter and energy in spacetime is reducible to spacetime geometry. And maybe spacetime is quantized, with its smallest elements simply entangled with one another in various ways.

It has always made sense to me that everything must be ultimately reducible to one thing. I believe in the project that physicists have long pursued of unification. Many of the great advances in physics have been unifications. We have found that what we previously though were distinct phenomena were actually different configurations of something more basic. Different animals are not different substances, but rather different arrangements of the same underlying biochemical things. Different biochemical elements, or molecules, are just different arrangements of atoms. Different atoms are just different arrangements of subatomic particles. Maxwell unified electricity and magnetism. Einstein unified mass and energy. He also unified gravity with spacetime, realizing that gravity is reducible to spacetime geometry. Electromagnetism and the weak interaction were unified into the electroweak interaction. You get the idea. What is the natural endpoint? Complete unification.

There aren't a whole bunch of fundamentally different and truly separate things in the world. Spinoza argued this persuasively, I think. For one thing, it is hard to see how two truly distinct substances could interact.

What does he mean when he says that the table chooses a frame? — petrichor

The table is in a frame of reference where the table isn't moving. This frame of reference isn't special, and lot's of properties of the table are going to change when seen from a moving frame of reference or then in a gravitational well. What will be agreed however is causality and the laws of physics governing those causal links will make sense; however, the size of the table and what's happening simultaneously on the table and speed that time runs at on the table all will not be agreed (and so some happenings will be agreed to make sense but for different reasons for different observers; a magnetic field for one will be a electric field for another, Unruh radiation being an even more radical discrepancy in causal mechanism).

The problem of simply "quantizing space" being referred to here is basically that if you imagine a grid of "space-atoms" all around you all equidistant to each other, then from another frame of reference that's moving your space atoms will be compressed along one access and won't line up with their own space-atom grid that their asserting exists around them.

In a single stationary frame, it's no problem filling space time with a grid of "space-atoms" that are smaller than our most precise possible measurements and then just say "particles" jump from one atom to another. And, in a Newtonian space even moving around in the space-atom grid wouldn't be a problem; we can move fast or slow relative the grid. However, relativity has no preferred reference frame and the coordinates of a reference frame get stretched and squashed as seen from another reference frame, and so the space-atom grids would also be stretched and squashed and not line up.

Of course, the physicists and mathematicians working on "space-atoms" (networks, grids, etc.) are working in extremely abstract places to resolve this issue above. Arkani-Hamed is just pointing out the fundamental problem and there's no obvious fix for it. I don't think he's "hard against" any approach to quantizing space, just cognizant of the extreme level of difficulty; however, he is taking the position that space needs to be quantized, that space-time is doomed, which is not the only position (but generally favored by physicists because all observations are necessarily discrete whole numbers, what are usually called "ticks", and the supposition of continuous quantities is unverifiable and so a "more than you need" assumption from the get-go; the problem is Einsteins theories work so well and require continuous quantities to work ... and although QM predicts discrete measurement probabilities ... calculations are done in a continuous, fairly run of the mill, coordinate system; i.e. space is not quantized neither in relativity nor quantum mechanics and there's no obvious way to quantize space in either; it's also not clear to anyone if the problem is fundamentally mathematical or physical, or a strange mix of both).

Thank you! This is helpful.

I am not sure I understand though why the space atoms "won't line up with their own space-atom grid that their asserting exists around them." I can visualize the compression, but not the misalignment.

In the article by Wolfram (link), he claims that special and general relativity can be easily derived from the behavior of a causal network. If you read starting at the section called "Evolving the Network", you'll see what I refer to. What do you make of this? Plausible?

I am not sure I understand though why the space atoms "won't line up with their own space-atom grid that their asserting exists around them." I can visualize the compression, but not the misalignment. — petrichor

In the very simple way that if you "squeeze the grid" so the space-atoms are a half unit a part, those space-atoms won't line up with a grid where the space atoms are a unit apart in each direction.

If postulate space-atoms, the first thing you will do in relativity is compress them as viewed from another reference frame. Unless [insert crazy math here], what this thought experiment concludes is the computation of events must be irrespective of the size of the space-atoms; in otherwords, even if you were using space-atoms as a calculation device they cannot be physical as changing reference frame will and doing the same calculation of events will require postulating a grid of smaller space-atoms to get the same results.

Maybe an easier way to visualize the actual problem [minus crazy math to fix it] that happens. You've done some calculation of a causal events in your reference frame of space-atoms at a given size. By viewing the same events from another reference frame (i.e. viewing the events from relativistic speeds), if the space-atom size is fundamental, then some space-atoms of the previous reference frame "get squeezed out" of the grid in the new frame, if those space-atoms were important to get the result (the prediction of causal events) then they've disappeared and there is not an information mismatch due to changing reference frames. This is fixed by removing the postulate that the space-atom size is fundamental (difference observers cannot agree on the necessary size of the space atoms for the purposes of calculation); for, usually we will switch reference frames to do calculations in an intuitive frame, but this is only a convenience, we can always just keep the frame (the coordinate system) we're in and map out all causal events in that frame; so a length-contracted object will be quite literally "missing" space atoms (the observer in the spaceship decides "10^200 space atoms" axis are required to describe events in the ship, but the stationary observer, using the same size of space atoms, due to length contraction, only has the ship occupy one half of 10^200 space atoms). If the space atoms encode information they literally get lost changing from one reference frame to another.

There is no simple trick to fix this problem.

A property of continuous coordinate systems is they map "onto", without information loss, when stretching and compressing them. So in Einsteins system there are simply no smallest resolution that can "get lost" if you compress even smaller.

The basic problem is literally the same of resizing an image smaller and bigger on the computer: information gets loss (unless the information is encoded in such away that is scale invariant: just like Relativity).

In other words, without solving this problem, the space-atoms hypothesis can be a calculation aid but is not a physical description (i.e. even showing that you can make QM calculations using a grid doesn't provide evidence from grid-like space-atoms): there is no way in principle to decide how big space-atoms are. An analogy is weather simulations that model the atmosphere as a a grid; this is a calculation aid and is a completely non-physical postulate in the model.

In the article by Wolfram (link), he claims that special and general relativity can be easily derived from the behavior of a causal network. If you read starting at the section called "Evolving the Network", you'll see what I refer to. What do you make of this? Plausible? — petrichor

Oh I completely agree with him ...

But these are all speculations. And until we actually find a serious candidate rule for our universe, it’s probably not worth discussing these things much. — Wolfram

Thanks! Thinking about it in terms of rotating, enlarging, and shrinking digital images helps. As I work with digital images a lot, I understand that fairly well.

I'll have to think on this more. I guess its time I actually put some effort into learning about relativity!