Quantum Mechanics (QM) has attained a certain level of mystique. You’re not just any old physicist, you’re a quantum physicist. Wow.
I’m not sure why it’s been given this status because the math required to get to grips with a lot of the quantum weirdness is nowhere near as difficult as the math required to understand, say, fluid dynamics or General Relativity.
Today I want to take a shot at describing one aspect of quantum ‘weirdness’. I’m not really going to be able to explain it, though. I am going to try to do this without any math at all - which means that a few of my statements might not be 100% technically accurate, but will carry the ‘flavour’ of the math to, I hope, a sufficiently acceptable level.
We’re going to imagine the following ‘abstract’ experiment. Why have I put this word in quotes here? Well, it does seem to be an abstract and theoretical exercise at first, but (many) experiments like this have actually been carried out in labs across the world.
We imagine a ‘black box’ which spits out pair of particles in opposite directions. What’s actually inside the black box is not relevant - at least at first.
One particle gets sent to Alice, and the other wings its way to Bob.
When the particles reach Alice and Bob, they’re going to measure some property of the particle they receive.
We’re also going to add the restriction that Alice and Bob can only measure one property.
One way to think about the necessity of this restriction is that they’re going to be measuring really, really, really small things. In order to actually make a measurement this tiny little wee parti-glob is going to have to interact with the measurement device. The tiny little thing is not going to emerge from this process unscathed - it’s going to be knocked about, or even absorbed, by the measurement process.
If you shine a light on a golf ball flying though the air - and let’s imagine we do this at night - then the ‘photons’ striking the ball and returning to us might be said to constitute a ‘measurement’ of where the ball is (or, technically, was), and maybe how fast its moving. But we don’t expect the photons to knock the ball out of its trajectory.
If that golf ball gets scaled down to quantum particle size, then being hit by a photon is no longer inconsequential and the now tiny golf ball can be knocked out of its trajectory.
You may have heard about something called Heisenberg’s Uncertainty Principle. This is the idea that in the quantum world you can’t measure everything you’d like to with arbitrary precision. For a quantum particle, if you try to precisely measure where it is, this measurement is going to bugger up your ability to precisely measure how fast it’s going.
The easiest (but not wholly correct) way to think of this is the notion of the act of measurement itself introducing a ‘knock’ - like photons knocking a tiny golf ball out of its trajectory. The light that tells you where this tiny golf ball is introduces a ‘kick’ that means we can’t, now, be fully sure about how fast it was moving.
So, what properties are Alice and Bob going to measure?
We’re going to start off with 2 properties - and we’ll call them colour and texture. The particles that get spit out of the box will be measured to be either red or blue, if colour is measured, and they will be measured to be either rough or smooth, if texture is measured.
The rule here, as a consequence of Heisenberg’s Uncertainty Principle, is that they can choose to measure ONE property well, but not BOTH.
We’re going to write the measurement results as a pair that looks like (Alice measurement result, Bob measurement result). So, we could have (Red, Smooth) which means that Alice chose to measure the colour property and got the result ‘red’, and Bob chose to measure the texture property and got the result ‘smooth’.
At this point, it’s as well to remind ourselves that there really are particles that have properties like this. OK - they’re not ‘colour’ or ‘texture’, but there are particle properties which cannot be simultaneously measured with arbitrary precision, and which have a binary outcome.
So, we set our black box to keep on spitting out these particle pairs and, for each received pair, Alice and Bob will do a measurement.
The results are interesting, to say the least.
Whenever Alice and Bob choose the same measurement to do their results are perfectly correlated. So, if they both choose to measure the colour property the only possible measurement outcomes are (Red, Red) or (Blue, Blue).
However, if they choose to measure different properties to one another, there is no correlation whatsoever in their measurement outcomes. If, for example, Alice has chosen to measure colour and gets the result ‘red’, then Bob, who has measured texture will get the result ‘rough’ or ‘smooth’ at random.
We can summarize this in a table
Our first thought might be something along the lines of the following. OK - these particles have been produced with certain properties and we’re just measuring them. We’re going to use square brackets to indicate the state of these particles - their properties - before measurement. We could have for the particle that gets to Alice
[Red, Smooth]
[Red, Rough]
[Blue, Smooth]
[Blue, Rough]
and there’ll be a similar list of 4 options for the particle that gets to Bob.
Let’s suppose that we have (before measurement)
Alice’s particle [Red, Smooth]
Bob’s particle [Blue, Smooth]
We agree that this is a possibility, right? What if Alice has set her measurement device to measure texture and Bob has set his measurement device to measure colour? No issue there - but suppose Alice, at the very last minute, decides to switch to a measurement of colour too?
Ah - we’d lose the perfect correlation in that case. Clearly, according to our current thinking, this is NOT a possibility for any state (before measurement) of the particle pair.
So, we might conclude, that the above state A: [Red, Smooth] and B: [Blue, Smooth] is not produced by our black box.
If you try to think of possible states (before measurement) using just the properties of texture and colour you’ll quickly realise you run into problems with the actual measurement results which show this perfect correlation in some cases and no correlation in others. Try it - and see what happens. Can you accommodate the results (perfect vs no correlation), particularly when Alice (or Bob) change their minds about what to measure at the last moment?
There’s something wrong with our notion that the black box spits out particles with these definite properties. We just can’t use these 2 properties alone, together with any notion that they are pre-existing properties generated by the black box.
The idea arose that there must be some hidden variables at play that would explain these correlation properties. The 2 properties of colour and texture were not the whole story.
The idea here is that a correlation may result from an indirect cause. An example of this is to imagine an observed correlation between heart attacks and eating ice cream. Heart attacks, in this hypothetical example, seem to increase in line with an increase in ice cream eating. How could that be?
There’s a hidden variable at play here; that of temperature. An increase in temperature on a sunny day puts an extra strain on hearts, and it also gives rise to an increase in the sale of ice creams.
So, we imagine, the state of a particle after it leaves the black box should be better described by something like
[colour, texture, X]
where X are some extra variables (called hidden variables) that can explain the correlation properties. We imagine the existence of some hidden properties that will get us out of our conundrum.
It all seems horribly abstract but, once again, we should be reminded that things like this exist. Experiments like this have been done (many times). OK, they’re tricky experiments to do but, nevertheless, there are particle pairs that have exactly (analogous) properties to those I’ve described using colour and texture here.
If stuff like this exists in the real world, if we get actual results like this from real experiments, we’d better be able to explain them.
John Bell, in perhaps one of the most profound pieces of physics of the 20th century, came up with a startling answer. He analysed this experimental system using conditional probabilities. He looked at things like the probability that Alice gets the result ‘red’ when she measures ‘colour’ given that Bob measures ‘texture’ and gets the result ‘smooth’.
I’m not going to go into the details, (they aren’t too difficult if you have some familiarity with conditional probabilities), but what he discovered was extraordinary.
What he was able to prove was that if we assumed a couple of ‘sensible’ properties, there was NO theory with these properties that could explain these results.
What are those properties?
One of them is a locality condition. This basically states that any ‘influence’ from Alice’s experiment to Bob’s experiment cannot travel faster than light. In other words, the result Bob obtains could not influence Alice’s result in a way that happens faster than light could have travelled between them.
The other property is that of realism. This basically states that particles are produced with definite properties in the absence of measurement.
He demonstrated that no locally realistic hidden variable theory was able to reproduce the results of this experiment1.
There’s no QM in any of this analysis. No assumption of quantum ‘weirdness’ - we’re just taking a real world experiment, with actual results, and trying to figure out the kind of theory that is capable of reproducing the results.
And then comes the kicker.
QM successfully predicts these results for certain particle pairs (they’re known as entangled particles). Which leads to the inescapable conclusion that QM cannot be replaced with ANY locally realistic ‘hidden variable’ theory.
QM might be replaced with a ‘better’ theory in years to come - but whatever that theory is, we’ve lost forever the cosy and safe notions of locality and/or realism. Whatever is happening at the quantum level, we can’t adopt a theory that pre-supposes the existence of definite properties in the absence of measurement (at least not without sacrificing locality2).
So, our notion that things have ‘properties’, independent of measurement, is somewhat suspect. This is very hard to grasp, because we’re so used to thinking about stuff having real properties - that golf ball that’s just about to hit your head is definitely just there and definitely has enough momentum to crack your skull. But if we do this when trying to solve quantum problems (and, therefore, predict the results of experiments) we’re going to get things wrong sometimes.
In somewhat fanciful and poetic terms it’s as if, at a quantum substrate, all that exists is a sea of possibilities out of which our ‘definite’ world emerges.
It all seems very theoretical - what’s all that got to do with the price of cheese?
Well, quantum entanglement has quite a few practical applications, not least in the possibility of building a quantum computer. There are also some indications that evolution has made use of entanglement in photosynthesis and is the reason why it’s so efficient.
I’m sorry I can’t explain it better. I wish I could explain it better to myself, too.
Technically, with just 2 properties as I have described, it IS possible to construct a hidden variable theory that reproduces these correlation results. It’s a bit artificial, but it can be done nevertheless. If you examine 3 of these binary properties - an example would be electron spin along 3 different axes - then you can’t construct one of these locally realistic hidden variable theories to reproduce the results. I stopped at just 2 in the interests of (hopefully) retaining some clarity.
We’d have to be living in a universe where things happening millions of miles away could instantly affect things happening right here.
Einstein's "spooky principle." Beautifully explained. Our notion of a fixed definable universe is gone. What's happening out there has a lot to do with what's happening in here. Fascinating.
I am always a little puzzled by these thought experiments that are using macro-level concepts (Alice, Bob, cat, train, box, device, measurement) to explore the micro world. As a mathematician I am perfectly happy with accepting that micro stuff is different. But mathematicians are weird, not queer, as well. Anyway, I am learning a lot from your explanation. Thank you!