<story><title>A Jewel at the Heart of Quantum Physics</title><url>https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics</url></story><parent_chain><item><author>gruseom</author><text>Is anyone here familiar with this work? I would like to hear more about it. At a minimum, this article is very much better than the usual science blog filler—it contains signs of a genuine conceptual breakthrough. For example:&lt;p&gt;&lt;i&gt;“You can easily do, on paper, computations that were infeasible even with a computer before.”&lt;/i&gt;&lt;p&gt;That doesn&amp;#x27;t happen very often! Or this:&lt;p&gt;&lt;i&gt;[T]he new geometric approach to particle interactions removes locality and unitarity from its starting assumptions. The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry. The usual picture of space and time, and particles moving around in them, is a construct.&lt;/i&gt;&lt;p&gt;That is exactly the kind of thing that happens when one model is replaced with a deeper one.</text></item></parent_chain><comment><author>ssivark</author><text>I&amp;#x27;ve been keenly following this area of research and have heard some of the talks and read some papers. I concur with the sketch given by @gaze.&lt;p&gt;1. The notion of &lt;i&gt;unitarity&lt;/i&gt; is a &amp;quot;common sense&amp;quot; rule that implies that you can consistently assign probabilities to possible outcomes in a quantum mechanical experiment (&lt;a href=&quot;http://en.wikipedia.org/wiki/Unitarity_%28physics%29&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;en.wikipedia.org&amp;#x2F;wiki&amp;#x2F;Unitarity_%28physics%29&lt;/a&gt;)&lt;p&gt;2. The notion of &lt;i&gt;locality&lt;/i&gt; states that what happens on Jupiter better not affect how fast your code compiles this morning (or how experiments run on earth). This is an important postulate, because if this weren&amp;#x27;t true, we might as well give up on doing science as there would be arbitrarily many external influences we couldn&amp;#x27;t take into account.&lt;p&gt;All our experiments so far are perfectly consistent with these two principles. Quantum field theory is the brainchild of the marriage of unitarity  (from quantum mechanics) and the idea of locality (in field theory). Our world view today (&amp;quot;Standard model of particle physics&amp;quot;) is based on this.&lt;p&gt;In practice, calculating answers using this theory is painfully difficult. YOu will add up thousand pages worth of algebraic terms and then your answer will &amp;#x27;miraculously&amp;#x27; reduce to a few terms. This and other observations have inspired researchers to search for underlying structure... leading to what is now being called the &amp;#x27;amplitude revolution&amp;#x27; by some people.</text></comment>
<story><title>A Jewel at the Heart of Quantum Physics</title><url>https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics</url></story><parent_chain><item><author>gruseom</author><text>Is anyone here familiar with this work? I would like to hear more about it. At a minimum, this article is very much better than the usual science blog filler—it contains signs of a genuine conceptual breakthrough. For example:&lt;p&gt;&lt;i&gt;“You can easily do, on paper, computations that were infeasible even with a computer before.”&lt;/i&gt;&lt;p&gt;That doesn&amp;#x27;t happen very often! Or this:&lt;p&gt;&lt;i&gt;[T]he new geometric approach to particle interactions removes locality and unitarity from its starting assumptions. The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry. The usual picture of space and time, and particles moving around in them, is a construct.&lt;/i&gt;&lt;p&gt;That is exactly the kind of thing that happens when one model is replaced with a deeper one.</text></item></parent_chain><comment><author>gaze</author><text>This isn&amp;#x27;t my field (a.k.a. I&amp;#x27;m talking out of my ass), but I can give it my best shot. Usually with QFT you start with locality and unitarity as a sort of starting point. You might hope that you could come up with something much simpler where locality and unitarity come about naturally from the model itself (the goal of physics being to show that &amp;quot;it had to be this way&amp;quot;.) QFT tells us how the world works by calculating scattering amplitudes. You throw n things in, and m things come out with some momentum, some spin, some color, etc. The way we started doing this was with Feynman diagrams... these diagrams tend to look like you have some particles banging off of some other particles, and they behave a little that way, but they&amp;#x27;re actually a notation for integrals in a series that you have to sum over. Hence the genius of the notation... they describe math while looking like something physically relevant. However, they&amp;#x27;re a little weird in that if you interpreted the diagram literally, you&amp;#x27;d find that some of the diagrams involved in an interaction actually aren&amp;#x27;t physical! One might say that the degree of nonphysicality suppresses that diagram&amp;#x27;s contribution. Physicists describe these diagrams as &amp;quot;off-mass-shell.&amp;quot; If you wish to describe an interaction, you figure out all the diagrams relevant to the interaction, calculate them and sum them. When the article says &amp;quot;tons of pages of calculations&amp;quot;, what they mean is you need to sum over a LOT of Feynman diagrams to get an answer.&lt;p&gt;Now, there&amp;#x27;s some newish kinda diagram that&amp;#x27;s gone into use (I think maybe only for N=4 SYM?), which is also used to calculate interaction cross-sections. However, they&amp;#x27;re written in such a way that they always describe on-shell processes, hence why they&amp;#x27;re called on-shell diagrams. I think Zvi Bern had something to do with this. These diagrams have an underlying structure... and mathematicians have started writing similar diagrams recently (as in, they ran into a similar structure recently), but instead of the diagrams being to describe interactions, they&amp;#x27;re used to describe some structure called a positive grassmanian. The positive grassmanian in low dimensions relates to convex polygons... it&amp;#x27;s a simple thing. This guy had this interesting insight that an interaction crossection corresponds to some sort of volume... and in this case, it corresponds to the volume of this polytope described by the positive grassmanian... or something like that.&lt;p&gt;The positive grassmanian says nothing at all about unitarity or positivity, nothing about space or time, but it lets you calculate shit. That&amp;#x27;s very, very cool.</text></comment>