Analyzing entanglement as if it is a stage magician's trick


#1

I have read many attempts to explain quantum entanglement and “spooky action at a distance.” I’ve studied stage magic tricks, so I get used to asking, “How could that have been accomplished without magic?” All of the analogies I’ve read leave holes that allow the effect but require absolutely no unexplainable infinite-distance phenomena. I do believe physicists who tell me, “Trust me, if you knew the math, you’d think this was really weird.” I want to understand better, so instead of asking you to present yet another lesson-by-analogy of quantum mechanics, I’d like to present an analogy and ask you some questions along the way in order to rule out various “cheats” that physics might be using. This will give me an understanding of exactly where the mystery of quantum mechanics lies. I hope you don’t mind my presumption that you’ll take the time to answer.

So, here I go…

Quantum mechanics (QM) says you take two particles, entangle them such that some attribute is simultaneously in multiple states, then separate them by an arbitrary distance. When you measure one of them to ask what the attribute’s actual value is, you can measure the other one at the same moment and the measurement will agree, even if there’s a greater-than-light-speed gap between the two particles at the time the measurements are taken. The spooky action is the “communication” of that measurement between the two particles, faster than light.

The analogy runs like this: I have a bunch of gloves. I pick two of them and then entangle them such that both gloves are simultaneously left-hand and right-hand gloves.

That brings me to the first question…

  1. A lot of magic tricks are solved by a magician’s force right up front. Can I really pick any two particles and entangle them? Or when I get an entangled pair, are they possibly connected for me already? In other words, am I some how tricked such that every time I get an entangled pair of gloves, both gloves are secretly already right-hand gloves but superposition makes it impossible for me to see whether they are both right or both left? This would be akin to asking the audience to showing the audience a deck of black and red cards, then secretly swapping the deck for one that is all red cards and asking them to pick two, then putting the two in front of a flashing blue light — when the light is on, the card looks black; when the light is off, the card looks red, but it is always actually red. Do I really have a free choice of particles?

Ok, assume I really can pick any two particles. Now I entangle them and put them in separate boxes. Let’s call them particle Alice and particle Bob. Or, for the gloves, glove Alice and glove Bob.

  1. What does it mean to entangle them? If this were a stage magic trick, I’d say, “The magician just made both gloves be right-hand gloves just now and then put them each into a box.” The magic would be reshaping the gloves, but that doesn’t require any spooky action at a distance, just some slight-of-hand tailoring… all local effect. If we cannot measure the particles, that means there must be something that we can do with an entangled particle that we cannot do with an unentangled particle. What evidence makes us believe that two particles are actually in superposition when entangled? Put another way, how does the superposition particle’s interaction with the world change?

  2. Now, assuming that the two particles/gloves really are simultaneously in two states, it might be that one state is tagged somehow such that the particles when measured will always be the same. Going back to the deck of cards earlier, if both cards become “really red” when entangled but only look like superposition, then when they stop being in superposition, both cards will be red. No surprise there, and no spooky action at a distance. Do we know there’s no pre-decided state for the particles to settle in? (How do physicists prove that negative?)

Now I give one box to my lab partner and take one box for myself. My partner and I synchronize our clocks and start a 1 year countdown timer. Then we get on space ships and fly away from each other at the same (very high) rate. With my really good telescope, I see my partner’s clock slowing down as we get further apart (time dilation).

  1. When my countdown clock reaches 6 months, is there anything I can measure to assure myself that the particle is still entangled? This is similar to question 2, but instead of talking about the pair, I’m now asking about the lone particle. If I can’t test that the individual particle is still entangled, how do I know that the decision wasn’t made as soon as the two particles were put into their respective boxes (or made as soon as the particles reached some light-cone distance from each other)?

At last, my clock hits zero. I open my box. I see a right-hand glove. Nothing magical about that assuming all the previous questions ruled out a pre-decided state and it really was in both positions, it could have been either one. It just happened to be right. In my telescope, I see my lab partner still not yet having opened his box… it’ll be a while before I see that event. So I turn my space ship around and fly back to the origin point.

My lab partner opens his box when his countdown reaches zero. In his box, he finds a right glove. He is unsurprised, just as I was. He also looks through his telescope and sees me still waiting to open my box (time dilation works both ways). He also turns his ship around and flies back to the origin.

We meet up. We report are results. And we are impressed to find that we both got right hand gloves.

We repeat the experiment 10,000 times. 1 million times. Every time, the gloves match. Now we are really impressed, and we think, “Wow. Somehow the gloves are communicating.”

So, in summary…

Do I know the particles are freely chosen? Can I verify entanglement without breaking entanglement? Can I rule out pre-assigned bias of the state when entanglement breaks? If so, then I agree quantum mechanics is weird. If not, then I’m curious why other people think QM is weird.


#2

Hi.
We are all about two different systems. One with internal ‘error’ correction clock, other with external. You can think on gloves as binary system. If you send stream of gloves, LLRLLR or 110110 in binary. Problem solved.
This is predetermined and contracted communication, sort of, so you don’t need telescope(metaphor for entanglement checker)to check temporal states for particle/code cos it doesn’t matter. Particle can dis-entangle but will ‘self’ correct itself. Only thing is external clock and CRC checker. Polynomials. You can find book about internet protocols and how it works. Larry L. Peterson and Bruce S. Davie “Computer networks a system approach” for example.

Other one, with clocks has ‘built in’ rule. Time saving units or clocks. It’s about they come at the same time, not that we must watch them all the time.


#3

First, understand that with just a single pair of particles you cannot see entanglement at all. If their spin is entangled then whatever axis you measure their spin against then their spin will be either correlated or anti-correlated. But if you just have one pair you can’t detect that correlation. You need to think in terms of measurements on a large number of gloves. That is the only way you can see entanglement.

  1. Yes, you can entangle any two particles. Gloves are a problem because they are not quantum objects with quantum spin and are so connected with their environment that it wouldn’t matter anyway. I’m a decoherentist so I say they aren’t quantum objects exactly because they are connected to their environment. In any case with just one set of entangled objects, you can’t see anything unusual anyway.

Do you really have a free choice? More down below but the short answer is it should not matter.

  1. Entanglement means that there is information about the combined states of the particles but not information about the individual states. For example, say Bob sends one of his gloves to you and the other glove to me. We know the combined state - one left glove and one right glove - but we don’t know the individual states. If you look and see a left glove you instantly know that I have the right glove. Anti-correlated. Say you have a pair of 1/2 spin particles in a bound state such that the spins cancel out. Now if the bound state decays into the two 1/2 spin particles traveling in different directions then one must be +1/2 spin and the other -1/2 spin because of conservation of spin.

  2. Again you cannot see anything with just one pair of entangled particles. You have to think in terms of a large number of particles.

  3. No. You can’t be sure of entanglement with two particles let alone one. And yes when you look at a particle in superposition there should be no surprise. You just see a random plus or minus spin. Same for me when I make measurements on my end. Entanglement is seen in the correlation between our measurements. Even if we both measured hundreds of spin +1/2 particles this does not mean entanglement. This is just polarization. As in polarized light. You are missing an entire dimension of the problem.

Let’s see if I can clue you in on the missing dimension…

Say you have a computer. Every time you push the space bar on the computer it displays either a 1 or a 0. You have no idea how it decides what to display. Maybe it is detecting particles from a distant galaxy or maybe it is just flipping a coin inside. It appears to be random. But is it? For example, if it is running a random number generator then it looks random but is really only psudorandom. How can you tell?

Say I also have a computer that does the same. But say when we both push the space bar at the same time we both get the same result. Our results are correlated. Is this strange? Not really. We could both just be running the same random number generator. This is a hidden variable theory. There is just some process inside the computers that cause them to be correlated despite looking random from outside. This was Einstein’s argument in the EPR paper.

Now say there is a knob on the computers. You turn the knob 30 degrees to the left but it seems to make no difference. You still just see a random string of ones and zeros. But when you compare your string to my string they are no longer perfectly correlated. In general you find that the correlation is equal to the square of the cosine of the angle that you turned the knob. So for 30 degrees the correlation is 0.75. For a hundred tries we should be correlated 75 times and different 25 times. Is this a problem? Not really since you could use the knob input as a seed to the random number generator to get this result. Local hidden variables can still work.

Now say I test my computer and get the same result. No problem.

But what if you turn your knob left by thirty degrees and I turn mine right by thirty degrees? Well if we assume that you turning your knob only affects your bit sequence and me turning my knob only affects my bit sequence then the number of differences can’t more than double from 25 out of a hundred to 50 out of a hundred. In fact it will be less than that because of collisions between which bits get changed. This is Bell"s inequality.

Now what if when we do the experiment the error rate is larger than 50% say more like 75%? This is a problem. There is no way for a realistic hidden variable system to do this. But this is what quantum mechanics predicts for a quantum system.

There is one way around this that preserves local realism and determinism. Say when the General Organizational Director was programming the initial state of the universe she left an Easter egg. If determinism holds then all future events are preordained by the initial conditions. The director could easily select a initial state such that every time I flip a coin I get heads. No matter when where or what coin I flip a heads. Probability does not come in to it because it was selected to happen this way. The Easter egg is preordained.

But what if she had selected the initial state so that every time anyone anywhere does a certain kind of experiment it comes out a certain way? You have no free will to choose what to measure since what you measure and the value of that measurement was set in stone at the beginning of time. The director chose to leave an Easter egg of endless violations of Bell’s inequality. This is called super determinism. I think it is ugly and silly but some people have such an attachment to determinism that they will accept it.


#4

PPNL: This is a useful reply. There are some very enlightening comments in this. It will take me some time to unpack it. The way you described the error rate that rules out hidden variables is particularly clean. Thank you.