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Discussion Starter #1
I recently read about how a geometric shape called the amplituhedron makes a pre-existing quantum equation simpler to compute but I didn't really understand. I searched the web to try to understand what amplitude but found the explanations confusing. The way people try to explain these concepts it almost seems like they don't want you to understand.

I figure at least one INTP on this forum understands quantum mechanics. Can anyone explain quantum mechanics, entanglement, amplitudes, locality, unitarity, the amplituhedron, what we know, and what we have left to solve?
 

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Honestly I think the only way to understand something this new in a field of science that is relatively new is to actually have a degree in it. You'd need a degree in quantum mechanics to understand this stuff since even the people who discovered it don't fully understand it yet.

Also the wikipedia pages for all the things you're wondering about my help if you haven't already read them.
 

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Looking at the list of authors on that arXiv paper, I'm pretty sure that less than 50 people in the world understands what this amplituhedron thing is. But if Ed Witten spoke on it, then it's probably a real and interesting discovery.

Unfortunately I don't think anyone here has the time to give a detailed intro to quantum mechanics. If you want to self-learn QM I suggest:
 

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What the hell... why haven't I heard about this amplituhedron until now? This is amazing!

Unfortunately, my interest in quantum mechanics and theoretical physics in general is just a hobby. I have yet to dare to venture into the mathematics behind it and so couldn't even begin to answer your question. I did some quick internet research on this amplituhedron thingy, though, and came away with the impression that you need a pretty thorough understanding of the math behind pretty much the entire history of quantum theory - some of which involved equations long enough to fill all the pages of a large book, apparently - in order to properly understand how to work with the amplituhedron mathematically.

In other words, there's probably not much hope of being able to do this and actually have some understanding of the meaning of all your calculations without having already spent half a lifetime seriously studying quantum mechanics.

For people like myself who want to gain as deep an understanding of the subject as possible without actually dipping our fingers into all that ugly math, this is a good read:

https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/

And a pretty picture:
amplutihedron_span.jpg
Not that you can accurately depict an N-dimensional object on a 2-dimensional plane, but I guess they needed some kind of visual, and it looks pretty :cool:
 

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I recently read about how a geometric shape called the amplituhedron makes a pre-existing quantum equation simpler to compute but I didn't really understand. I searched the web to try to understand what amplitude but found the explanations confusing. The way people try to explain these concepts it almost seems like they don't want you to understand.

I figure at least one INTP on this forum understands quantum mechanics. Can anyone explain quantum mechanics, entanglement, amplitudes, locality, unitarity, the amplituhedron, what we know, and what we have left to solve?
Quantum Mechanics is mainly what we call the theories developed mostly in the first half of the 20th century to describe the behavior of subatomic particles. It gives us the probability of finding particles in certain states. What you're asking about though with the amplituhedron is Quantum Field Theory, which is basically relativistic Quantum Mechanics.

Locality is basically the idea that particles can only be influenced by their immediate surroundings. If you and I are alone in a room and someone shoves you, then clearly I was the one who shoved you. That's basically the principle of locality. Entanglement is a phenomenon that happens with subatomic particles where an entangled particle is either influenced directly by a particle far away, or by some superluminal (faster than light) intermediary.

The amplitude they're talking about is the scattering amplitude, which is basically just a probability we can measure experimentally during scattering experiments. The specifics probably aren't very interesting without the math.

Unitarity is the idea that if we add up the probabilities of all the possible states, they have to add up to 1. In other words, if we add up the probabilities of all the possible outcomes of the experiment, they have to add up to 1.

The amplituhedron is basically a new technique for solving certain problems in quantum field theory. We usually have to use computers to solve them. The amplituhedron is a shortcut that's been shown to work for some simplified problems (they don't actually describe real world experiments), which means it might work for other problems.
 

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Thank you for the explanations! I'm more up to speed now. So entanglement is a real thing but the question there is how is that possible. And the only theory so far is superluminal communication. The ampituhedron helps with the statistical equation.

I wonder what the effect of entanglement is in the grand scheme of things. What is it for?
 
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