Spacetime as a consequence of something else: ER=EPR.

There's so much I don't know about GR that talking about interpretations and physics trends is a dangerous matter, specially if my words are intended to be, you know, taken seriously. That's the reason I try to focus in learning instead of trying to develop things on my own. And I don't always succeed anyway, so look at that.

Nevertheless sometimes comes the time when you find something interesting and you have to share it and... Well, hell, this is my blog, right?

I have found recently the ER=EPR conjecture and I have tried to learn a bit about it. Shall we talk about it a little? I'll go on with Schwarzschild metric inside the Earth a little bit later. :)

Emergent what?

You all know the Internet: you start looking at kitten photos and you end up in the dark alleys, you know, learning about spacetime emergence from quantum mechanics.

It's not a new song, as you may know. I've been actually joking with a fellow engineer about developing an emergent theory of spacetime based on fluid mechanics -the joke is, BTW, it's already done. The thing is spacetime is so hard to quantize that describing it as the consequence of something else underneath, seems (to some physicists, at least) like a good idea. I'll deal with the fluid mechanics in a later post; for now, let's focus.

So from reddit I went here and from there, to here. And I found a little "paper" of my muse. No, not her. Him. Who? You know who: part time job as captain Ahab, part time job as Charles Darwin impersonator, full time awesome Leonard Susskind. Fancy that! That's too British... I'll USA the language a little, sorry.

What does ER=EPR mean?

ER means Einstein-Rosen. Like in Einstein-Rosen bridge. We have not discussed it yet but as summary, is a special type of metric in which two singularities can collapse into a wormhole. It is mathematically correct and therefore, theoretically possible. I was going to put the Stranger Things' reference for the upside-down, but Sam Neill works better. Even if there are important buts, like ER doesn't say you can pass through the wormhole, and... You know, all the other stuff about hell and blood and angst and such.

Have you seen Inception? A little bit like it. Photo from the spanish wiki, as usual.

EPR stands for Einstein-Podolsky-Rosen. Long story short it's a famous paradox Einstein put on the table a long time ago. You see, Einstein was not fan of quantum mechanics, specially when it came to say that entanglement (which is technically an instantaneuos action at distance), is what it is: an instantaneuos action at distance. This violates the locality and therefore doesn't get well along relativity. But it fuc*ing happens, so no victory for Einstein in that.

What the ER=EPR conjecture states is that maybe, entanglement can be explained by an Einstein-Rosen metric, and hence, no locality is violated and everyone is happy and there was much rejoicing.

What did you said about emergent consequences?

Yes. It turns out, there are elegant ideas that say that spacetime can be a consequence for something else, which can explain why spacetime is so hard to quantize. The part that I'm going to write a bit is the one I have found today. This. And it's so mind blowing that hurts.

TL;DR: It can be no more than a mathematical curiosity but, if you take a Hilbert space with certain properties and you add to the mix the quantum entanglement, it turns out you can obtain a "spacetime like" curvature which arises from the math.

Why a Hilbert space? Not a clue on GR, so don't expect I have clues in quantum mechanics either, but it guess they try to explain a particular region of space through a finite dimensional Hibert Space. Which is somehow acceptable for some interpretations (not all, not the most popular) of quatum fields theory. 

Where does ER=EPR stand in all of this? It stands in the very end of it, because using the Hillbert space interpretation and all the stuff the paper points out, returns the conjecture as another consequence. And that's heavy. It does not prove anything (everything are hypotheses and conequences of them), but it's remarkable because somehow, it packs up all together in something that does not seem like random.

Why is this mind blowing? Well, technically is far from that because it lacks like a bazillion details to be useful but, what makes this atractive is having an origin for spacetime that can give something to begin with, something where attack the problem. If spacetime curvature is a consequence for a series of quantum states, maybe there's a way to warp it, to control it, in a much more reasonable way than putting crazy amounts of energy into the cauldron and crossing fingers.

I should dig into it a little bit more, but for today, I'm done. :)