Video: Quantum Gravity Breaks Causality -- And You Can Compute With It

Transcript

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Flip the switch and the light turns on. “Duh,”  you might say. Physicists say “causality”. Lights  

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don’t turn on by themselves and then make  switches flip. And that sounds all well and  

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fine except. Quantum physics screws it up. In quantum physics, lights can turn on and  

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make switches flip, in some sense.  And as if that wasn’t crazy enough,  

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some physicists now say you can actually use that  to build better computers. Let’s have a look.

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Quantum particles can be in two places at  once. We call this a “superposition” of two  

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places. That’s definitely weird, but it gets  weirder. The maths of quantum mechanics says  

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that this shouldn’t just be the case for small  particles. In principle, it could happen for  

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anything, molecules, bananas, cats. This is why Schrödinger was going on  

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about a dead-and-alive cat, because it’s there,  in the mathematics of quantum mechanics. So why  

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don’t we ever see dead-and-alive cats? It’s  because for large objects like bananas or  

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cats these quantum effects disappear very  rapidly, due to tiny interactions with air  

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molecules or the cosmic microwave background.  This is called “decoherence” and is the reason  

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why the quantum-typical behaviour only shows up  for small objects if you measure quickly enough.

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Ok, we only observe it for small  objects, but in quantum physics,  

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things can be in two places at the same time  indeed. And if the thing that’s in two places  

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has a mass, then it has a gravitational pull. And that gravitational pull, according to  

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Einstein, means that space-time itself curves  which then affects the motion of other objects. 

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The often-used analogy is that of a heavy ball  on a rubber sheet seems to attract other balls  

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towards it, even though it’s really just the  curvature of the sheet that makes it happen. 

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But how does space-time curve if a massive  particle is in two places at once? Well, we  

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don’t know. For this we would need what physicists  call a theory of quantum gravity, that describes  

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the quantum properties of space and time. However, most physicists think in any such  

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theory of quantum gravity, space-time itself  would exist in superpositions, so it would do two  

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things at the same time. And if that is right,  that has some very interesting consequences.

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You see the issue is that the curvature of  space-time affects which event can causally  

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influence another event. Let’s take two events  and call them A and B. For these two events to  

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have had any causal relation it must be possible  for some influence to go from one to the other,  

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and that can’t go faster than the speed of light. So if we draw space on the vertical and time  

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on the horizontal axis, and as usual say  that light travels at a 45 degree angle,  

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then for A to be a cause of B, the event  B must be in this area. It’s called the  

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inside of the future light cone, just so  you’ve heard it. If B was down here instead,  

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then it could be a possible cause of A. But  not any event is causally related to any  

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other. Suppose they both sit here next to each  other, then neither can be a cause of the other.

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But here’s the thing. Space-time curvature can  change causal relations. Yes it can. Remember that  

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time near a black hole passes slower. I’ll denote  the passage of time with ticks on the vertical  

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axis. If I put a black hole on the right, then  A can now influence B because time runs so slow  

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at B. If I put the black hole on the left, then B  can influence A. Alright, you might say, so what.

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Well now imagine that the black hole is in  both places at the same time. So which event  

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can influence which one. If A was flipping  a switch and B was the light turning on,  

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then it seems that, depending on how spacetime  is curved, either the switching caused the light  

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or the light caused the switching. This means that if you want to  

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give quantum properties to space-time, as  most physicists think has to be the case,  

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then causal order goes out of the window. And  just in case you think this sounds like nonsense,  

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Sabine probably just made this up  so she has something to talk about,  

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I’ll leave you a reference in the info below.  It’s called an “indefinite causal structure”  

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which you could now say still sounds like  nonsense, but now it’s scientific nonsense.

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Then again some of you might say  this is actually pretty cool,  

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effects coming before their causes. But of  course the fine print is again that this  

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really only happen for teeny tiny things because  these quantum effects are so fragile. Then again,  

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physicists deal with small objects all  the time, don’t they? And that brings up  

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the question of what you can do with it.  You can use this for example to compute.

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Suppose you have a quantum computer and you  have these quantum properties of space-time  

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which scramble up the causal order. You then can  use this to do several computational operations  

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at the same time. Take one number, call it  x, and say you want to add another number,  

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say 3, and then multiply with seven. If  you do it in two different orders then  

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you get both (x+3) times seven and x times  7 plus three, so you have actually done two  

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different calculations. At the same time! If you have an algorithm that uses both  

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operations, you can use that speed up the  calculation. And this is just an example  

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where you change the order of two operations.  The more operations you have the more ways  

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you can exchange them. This means that in  principle, quantum gravity can make quantum  

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computers even faster. And yes there are  some people who have worked out the details.

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So let me be clear that this isn’t something  which is going to happen any time soon, because we  

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haven’t get even measured the quantum properties  of space and time. Though there are several  

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experimental groups working on trying to do this,  as I have discussed in several previous episode.

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But this is one of the reasons why I think  quantum gravity is not just interesting for  

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theoretical reasons or merely philosophy.  It could one day indeed have technological  

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applications. The other conclusion you can  draw from all this is that if quantum gravity  

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gives rise to such indefinite causal orders,  then maybe that means that gravity shouldn’t  

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be quantized in the first place.  I think Albert would prefer this.

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Yes, I've been talking about quantum physics  again. It's without doubt one of the most  

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exciting areas of science at the moment,  though I may be a bit biased. If you want  

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to learn more about how quantum physics works,  you can check out my course on Brilliant.org.  

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It's a beginners course that you can take without  any background knowledge. It'll introduce you to  

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topics such as interference, superpositions  and entanglement, the uncertainty principle,  

6:59

and Bell's theorem. And afterwards, you can  continue learning more about your favorite  

7:04

topics in science, computer science, or math.  All courses on Brilliant come with interactive  

7:10

visualizations and follow-up questions. It's  really an easy and fun way to learn something  

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new. And of course I have a special offer  for viewers of this channel. If you use my  

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link brilliant.org/sabine you'll get to try  everything Brilliant has to offer for free  

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for a full 30 days and you'll get 20% off  an premium annual subscription. Link's in  

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the description below so go and check those  out. Thanks for watching, see you tomorrow.