What Is Space?

> There are a dozen different possibilities for what the photon has done - a dozen different universes, if you like. As long as the photon never interacts with anything else, this bundle of a dozen universes can act much the same as a single universe. Certainly if you're just looking at a telescope, all dozen versions of that telescope are behaving the same, so they behave like a single unified instance.

Well that's interesting you bring it up this way.

If what you said is possibly true, then light could be a carrier of things like multi-dimensional spin, or possibly where dark matter really comes from (inter-dimensional interference).

I know Greg Egan has discussed the possibility of infinite orthogonal dimensions that energy can leak into. And by energy conservation, the result would be things like dimensional rotation and other effects we cannot yet perceive.

One theory is that the EM-Drive uses a rudimentary version of this effect. We're all still awaiting the results.

> No. The evolution of quantum systems is unitary and conserves energy.

I'm guessing that all the tiny parts of the wave function basically can't interact and collapse so just continue on forever. I don't see a conflict with unitary or conservation of energy. But these tiny pieces of wave function should continue to play their role in general relativity, gravitation, etc. That's my wild guess.

To pursue wild guesses, my guess is need a solid foundation in the physics. So, I tried again with quantum mechanics. I got a famous text. It claimed that the wave functions form a Hilbert space. Tilt! No way! They can be points in a Hilbert space, but a Hilbert space is complete which from some simple examples of convergence mean that the space has to have a lot of points (wave functions) that are not differentiable and not even continuous!

Then in QM I got to where they differentiate a Fourier transform. Okay. They are doing a differentiation under the integral sign. But, can't always do that. So, I get out a book with details, right, W. Rudin, Real and Complex Analysis, that is darned, fully, careful about such things. He has a nice chapter on the Fourier transform and does differentiate it. But he also justifies the differentiation by using the dominated convergence theorem which he also proves with great care in his early chapters on measure theory. Okay, that case of differentiation under the integral sign does work. So, then, back to the physics. But the physics lectures (an MIT thing) were never clear at all about such differentiation, were not even clear about their use of the Fourier transform, and never mentioned the dominated convergence theorem. Bummer. Further, soon it became clear that physics guy was going to be sloppy: He said that a wave function is differentiable. Okay. Then, seemingly amazingly, he went on to add that it is also continuous. Of course it's continuous: Every differentiable function is continuous.

So, for the unitary stuff, okay, I studied unitary top to bottom, side to side, from Halmos, in group representation theory, for the polar decomposition, etc. I'm eager to see the role in quantum mechanics. But I suspect again I'll have to get the math from math books, not the physics books!

I want to be careful about unitary, and the claim that no information is destroyed, etc. Careful. Really careful. Much more careful than that.

Heavily physics checks itself with experiments and, then, feels free to be sloppy with the math. But for considering wild stuff such as for goofy situations for wave functions, two particles entangled, the Einstein-Podolsky-Rosen (EPR) "spooky action at a distance", symmetry giving a conservation law, across billions of years and light years, I want the math correct right down to Bourbaki and axiomatic set theory -- no more of this sloppy stuff!

The sloppy math is why I left physics and continued with math. Now I'm ready, with enough solid math, to return to parts of physics, but just out of curiosity! I'll continue with the MIT QM lectures to get out of them what is there I don't know, but often I will have to be holding my nose over how he does the math. It's old for me: My ugrad physics prof kept telling me "Let's don't get hung up on the math". Well, I did and would say "Let's get the math straight. If we are going to differentiate under the integral sign, then let's hear about the dominated convergence theorem. And, by the way, for this stuff about integrating over unbounded sets, for that mostly we have to junk the Riemann integral and use the Lebesgue integral, so, let's do that. Let's start with sigma algebras, etc., something I never heard about in physics class!"

So, I can't push my wild guesses without more physics, and there I want to be careful about the math!

> The rest of your post is discussing philosophy,

I'm trying not to be philosophical and wondering if by now we have enough data so that we can talk about purpose without being philosophical. Sure, that we have that much data now is a long shot!

> What makes you think it was deliberate?

It looks like it might be a deliberate case of our being denied information that might let us see behind the curtain, that is, see more of how the universe is working.

> (that predicts that no information can propagate faster than the speed of light).

How we get from special relativity to that, I want to check out in detail.

Also there is the EPR "spooky action at a distance". Sure, the usual statement is that this does not permit communications faster than the speed of light, but I've seen no careful, detailed argument and want to check this out.

Also, for what I started with, a photon through a beam splitter, the wave function then in two parts, and then later the wave function parts separated by some large distance, if we have photo detectors for each part of the wave function, then the usual argument/assumption is that at most one detector will get a signal from that photon. So, instantly, across light years, the other half of the wave function is destroyed. But in principle we could detect when the detector got a signal because the other half of the wave function would suddenly not exist and would not have its effect on gravity. We're talking the gravity of half a wave function of a photon; right, small. But in principle ....

> Quantum mechanics isn't dice rolling. It is true that there cannot be a local hidden-variables theory of QM, but QM still has incredible predictive power when discussing the probabilities of experiments.

Two high energy photons cross paths, there at the same time. Maybe they generate an electron-positron pair, and maybe they don't. That's a roll of the dice.

> It is possible in the future that a non-probabilistic view of QM will emerge, it just cannot be both hidden-variables and local.

I saw the Bell's inequality part of the MIT introductory QM lectures. After that lecture, I wanted to see a much, much more careful presentation. Yes, yes, yes, I've heard what 99% of the physics community believes; I took more than enough physics to see how such beliefs are passed out. What I want to know is what the heck the truth is, including about far out possibilities, and for that at least I want the arguments, and the math, about the old stuff, solid.

> If ants could think, they would probably think they're the most amazing thing they know of in the universe. The only reason we think we're so amazing is because we have no competitor to compare to.

Not quite the "only" thing: We have axiomatic set theory as our foundation of math, and there we have pushed hard on its rough edges, e.g., what is decidable. Likely ET can't do better.

Then building on set theory, we have math, and just from the Whitehead-Russell stuff we know how that can be verified by just mechanical means, e.g., just symbol substitution. And we know that some new results can be obtained also just by mechanical means. And I have to doubt that ET can do better in the framework -- for specific math results, sure, ET can be 1 million years ahead of us.

So, basically, we seem to know how solid reasoning goes. I'm guessing that ET can't do better on the techniques of solid reasoning, that is, ET can come up with terrific theorems we have not found yet but is still limited to the same framework I just outlined.

And, ET will have seen all our basic physics and will have to agree with at least 99% of it, no matter how sloppy the MIT QM course is. ET can't disagree with that 99%. For that part of physics, we and ET are in agreement.

So, in some fundamental ways, at least the frameworks, methods, paradigms, we are about as good as there can be.

That's some of why we look special.

And it's some of why we seem to be approaching limits on what we or ET can know about the universe. So, if there is a purpose, then we are seeing about all the evidence there can be about what that purpose might be.

So far, we don't see a purpose. But I was asking if there is some more info that lets us start to guess a purpose?

> The reason it's 3K is that it has been cooling since the big bang and that's the temperature it happens to be today. If it were any other temperature, would that also be a clue?

My point about the 3 K radiation is not that it is not 2 K (as apparently eventually it will be) or 4 K (as apparently it once was) but that it is to us for photons a wall we can't see past. Also the timing is curious: 3 K is darned cold, and it took some astounding detectors to study it; in some years, the temperature will be 2 K, 1 K, etc., and need still more astounding detectors. So, at 3 K, we've come along at about the right time. When big, seemingly independent things agree in time, it looks suspicious. So, we have to suspect that the wall was deliberate. I'm willing to set that guess aside because people are talking about seeing gravitational waves from before the time of the origin of the 3 K radiation -- so the 3 K radiation is only partly a wall. And by analyzing the 3 K radiation, e.g., taking the spacial power spectrum and understanding the acoustic aspects, maybe we can get some clues about before that radiation.

Still, to me, that there is this wall of 3 K radiation, in surprising senses uniform, is one heck of a situation. I'm not, but some people got all wound up and called it the face of God! If there is a purpose, maybe from the shockingly surprising 3 K radiation we can get a clue. Uh, maybe shocking conclusions, e.g., a purpose, need shocking data so that from shocking data maybe we should look for shocking conclusions, e.g., a purpose!

A good talk along those lines is Feynman on algebra http://www.feynmanlectures.caltech.edu/I_22.html

He starts from numbers 1,2,3 etc and gets to eiθ=cosθ+isinθ which he has as 'This, then, is the unification of algebra and geometry'

I've always wondered if you could go further and deduce our spacetime in a similar manner.

I think the reasonable guesses are no purpose and the universe will keep expanding.