Einstein was right. There is no ‘spooky action at a distance’
Why we don’t need multiverses or conspiracies to understand quantum theory.
Why we don’t need multiverses or conspiracies to understand quantum theory.
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Quantum theory is one of the most successful theories of all time. It is considered to be the ultimate, all-compassing formulation of physics. Prior physics theories from Newton’s laws to thermodynamics all are considered approximations of our quantum reality. Even the planets orbiting the Sun, are, as far as we know, quantum objects as are we.
While we cannot prove that quantum theory applies to everything because in some cases its effects are too small to measure, we know that everything we see is made out of atoms which are bound by forces. Atoms and forces certainly do obey quantum theory. Countless experiments have proved it. Those quantum atoms and forces cannot combine together to create something that is fundamentally not quantum.
Yet, unfortunately, experiments on atoms and tiny subatomic particles such as electrons and particles of light called photons suggest that our intuitions about how the world works at the human scale do not apply at the quantum scale.
The first problem between how we believed the universe worked before quantum theory was developed in the 1920s and after is that quantum theory does not predict definite locations for particles until they are measured. This fact is demonstrated by the famous and bizarre double slit experiment.
The outcome of this experiment is so bizarre, most physicists consider it the breaking point between classical and quantum physics. There is no classical explanation.
You can read details about the double slit in my article:
We don’t understand quantum physics
The most intuitive understanding of it doesn’t workmedium.com
The key insight of the double slit experiment is that particles can be interpreted as waves impacting a detector all along its surface. Yet, the detector only ever registers the particle at one location. This bizarre result suggests one of two things: either the wave is a fiction we invented to describe our uncertainty in the particle’s actual location or the wave somehow collapses upon impacting the detector.
The wavefunction interpretation gained hold in quantum physics mainly because there was no other way to describe what was going on at the time. The idea that it represents uncertainty doesn’t work because we see results as if the particle passed through both slots at once. You cannot eliminate the “wave” part of a particle’s description in favor of the “particle” part . The best you can do is reduce it by scattering some other particle off of it to see where it is.
Albert Einstein, in a letter, called the wavefunction collapse idea “spooky action at a distance” because the wavefunction had to collapse everywhere in the universe. Einstein believed that to mean that the part of the wavefunction at a location A had to know that the part of the wavefunction B was the place where the particle would actually appear.
To his mind that implied some kind of instantaneous communication between A and B, in violation of Einstein’s theory of relativity which says that two points cannot communicate faster than light. No wonder he was put out of joint about it!
Einstein wanted physicists to accept a principle based on relativity that all events were “local” meaning that they could not instantaneously communicate with other points. If something anywhere happens, it has to communicate at the speed of light. If you deny this principle, then you are saying that quantum physics is nonlocal.
This type of nonlocality where a single particle is smeared out across space however is fundamental to physics. Quantum physics uses this concept to build a consistent description of what we see in nature, and it is perfectly compatible with relativity. What Einstein failed to understand in this early letter was that what we understand to be real isn’t the same in quantum physics as in classical. It isn’t like we can actually send messages faster than light, which would cause problems for relativity.
The fundamental problem with sending information faster than light is that it can, under certain circumstances, reverse cause and effect. If you send a message faster than light, because of the strange, time-bending aspects of relativity, it means that you can inform somebody of something that is about to happen to them. You can do this by sending a message faster than light to somebody, in a rocket, say, traveling close to the speed of lights. Then, they send a message back, also faster than light. Because of relativity, the second message reaches you before you sent the original message! Not only is cause and effect reversed, but it can create causal paradoxes. For example, what if the second message informs you not to send the first message? That’s how you get “grandfather” paradoxes.
Nonlocality in the sense of a particle or multiple particles being smeared out across space is difficult to avoid in quantum physics.
The idea that any hidden information is exchanged across time and space, however, which is what physicists now call “spooky action at a distance” is another matter. And that’s what we are going to talk about now.
Quantum physics gets around relativity by saying you can not send information, meaning messages, faster than light. It relies on the randomness of quantum measurements for this.
Let me demonstrate with an example.
Imagine, for example, that I meet a shadowy dealer at a market — say the back corner of a Renaissance Faire — who offers to sell me a pair of magic coins. Whenever I flip one, the other one, when I next flip it, always gets the same result, heads or tails. The result is instantaneous, so, if I flip one on Earth, and the other at Mars or Alpha Centauri or the Andromeda galaxy, anywhere, the results will be perfectly correlated. Heads for heads, tails for tails.
Because of Einstein’s relativity, we can’t always even tell which one was flipped first, but that doesn’t matter since the two are identical and identically correlated.
The seller demonstrates the coins and, lo and behold, they seem to work!
I have great and noble plans for these coins. I could use them to win money. Imagine how fantastic it would be to know the outcome of a supposedly random process? But surely I can use these for science instead. I will solve the great problem of how to communicate faster than light.
Should I buy the coins?
Why not?
The reason is because no information can be transmitted from one to the other. I cannot influence the outcome of either coin to my advantage. They do not accept information as an input.
This means that, no matter what tricks I try to devise, I cannot send a message from one to the other.
And this is exactly how quantum phenomena seem to work.
In the 1960’s John Bell formalized the idea in his famous Bell’s Theorem which showed not only how correlated two quantum measurements are but when measurements can be considered entangled.
Entanglement is simply an expression for a situation like with the two coins. Two particles that are entangled appear to share state and so the outcome of measuring one is correlated with the outcome of the other despite both being supposedly random. They are random, but correlated.
So, the coins will, sadly, not allow faster than light communications, but that doesn’t answer the question: does physics really allow action at a distance?
John Bell thought so but he recognize a flaw in his reasoning. It might be possible that outcomes are just correlated from the beginning of time or at least from some point in the past. For this to work, my coins would have to always show heads or tails not because they are communicating but because some event in the distant past caused both of them to always have the same outcome no matter when I chose to flip them.
Bell immediately dismissed the idea as silly and nonsensical. It seemed like an admission of defeat: the outcomes are correlated because that is the way of the universe. It means replacing spooky action at a distance with spooky action in the past.
Yet if outcomes are correlated and one doesn’t cause the other then surely that means they have some common cause. (This is known as Reichenbach’s Common Cause Principle.)
Either they are exchanging information faster than light or the two coins are “conspiring” together to create the outcome.
Like conspiracy theories, we can reject the magic coin theory and suggest, instead, that our explanation is wrong. Perhaps entangled particles are more like flipping one coin and then writing the result on two slips of paper. We send one to Bob and the other to Alice. If Bob’s says tails, he automatically knows that Alice’s says tails as well.
Unfortunately, quantum mechanics does not precisely let us get away with this, as John Bell knew, because how you measure particles appears to affect what you measure. With entangled particles, that means that how you measure a particle A affects what you will measure of B, no matter how far apart they are. The magic coin analogy appears to stand. For example, if I look for polarization of light at a particular X-Y alignment, the alignment of my apparatus will affect the polarization of entangled light somewhere else in the universe. That means that if the correlation between polarizations has a common cause, then my decision on how to align my experimental apparatus has to have the same common cause because it is part of the outcome.
You can see the slippery slope here. If the outcomes of experiments and scientists’ decisions about how to measure phenomena are correlated with each other, then science tells us nothing about the universe. It is all just a big joke. A joke on us. A joke on the universe.
It turns out that if you reject this idea, and you don’t change anything else about how you understand what entanglement means or the properties of quantum particles you are stuck with magic coin interpretations of quantum physics.
Many physicists, because of these problems, have run towards fanciful interpretations like the Many Worlds Interpretation of quantum theory. It’s not the measurements, it’s us splitting into more and more copies.
We don’t have to give in to such flights of fancy, however. Instead we can come to a new understanding of a concept that is so intuitive to physicists that it is taken for granted. This concept hasn’t really changed since physics separated from religion, and it is one core assumption John Bell made on his way to spooky action. Without that assumption, Bell’s theorem falls apart.
That concept is called a hidden variable.
A hidden variable is a property we are attempting to measure with our double slits or other experimental apparatus. Location is a hidden variable, as is momentum, spin, charge, mass, and so on. Properties like hidden variables are distinct from measurements. They are part of the essential nature of particles, waves, and forces, always cloaked in secrecy. Physics is intimately concerned with how to obtain knowledge of these, but physicists, rather than give up their classical intuitions about what properties are, chose very early on to believe in magic coin conspiracies.
Take an ordinary coin as an example. It has two sides. The two sides are the sum total of properties it has {heads, tails}. When it is flipped and lands, it takes on a value from that set, heads or tails. These properties are exclusive. If it is heads, it is not tails. If it is tails, it is not heads. If you have two coins, you just multiply the states {{heads, heads}, {heads, tails}, {tails, heads}, and {tails,tails}}. Each is distinct from the others. The truth of each implies the negation of the others.
Quantum properties don’t work like this. In fact the mathematical description of the theory contains nothing like it. You can have a quantum property be both heads and tails, even though these are contradictory in classical physics. If you have two coins, you can have subsets of contradictory states {heads, heads} + {heads, tails} for example. Truth does not automatically imply negation of alternatives.
That doesn’t mean that the particle has both of those values at the same time in the sense that both are true, mind you, it means rather that the particle’s value is nonlocal or delocalized, smeared out across the values. That is why you can have results like the double slit experiment which could never happen if a particle had a definite location. Contrary to what Einstein thought, delocalization doesn’t imply action at a distance because there is no interaction or influence between distant points.
Another feature of classical physics is that when you add new, independent properties to an object, they just add new dimensions to your space of properties. For example, suppose I throw my coin instead of dropping it. As it flies through the air, it has both a position and a momentum at each moment in time. Thus, I can represent my coin as living in space made up of its position and momentum as well as heads or tails at any given moment in time {10 meters, 1 kg m/s, heads} for example.
In quantum physics, some properties turn out to be mutually exclusive to one another. Your particle can have one but not the other. That applies to position and momentum. It also applies to spin along different axes (x,y,z). So spin in the z axis is exclusive from spin in the x axis.
A common misconception is that you just can’t measure both position and momentum — that is how Heisenberg’s uncertainty principle is often interpreted — yet the particle somehow has those properties, hidden from view. That is wrong. We can’t measure them both because they cannot both exist at the same time. There’s nothing special about the measurement of quantum particles. It is reality that is counter-intuitive.
So, if we go back to the idea of the coin I threw existing in a position, momentum, and heads or tails space, a quantum coin cannot live in such a space. It must live in a space where position and momentum are mutually exclusive {10 m, heads} or {1 kg m/s, heads} with the missing property undefined.
Like Marty McFly existing simultaneously with 1955 Doc Brown, position and momentum should not exist simultaneously.
It turns out that you can take this concept from single particles to many particles spread across time and space, including pairs of entangled particles.
Let’s see what happens when we apply this idea to entanglement.
For compatible properties, like spins that are both aligned on the z axis, entanglement works like mailing the results of a coin toss to Alice and Bob. There is no spooky action at a distance and no problem.
When measuring incompatible properties, like z-axis spin of one particle and x-axis spin of the other, what you can infer about the particle’s state at a prior time are mutually exclusive sets of properties.
That is why when John Bell came up with his famous theorem and he, like most physicists, assumed that quantum particles lived in a space of classical properties, it led him to magic coin thinking. It led a small minority to imagine that all experimental outcomes were determined at the Big Bang. They did not consider rejecting the hidden variable.
Thus, the question is no longer about action at a distance at all but what is real?
Some physicists say this is a rejection of realism entirely. But in reality (no pun intended) it is only a rejection of classical realism. Particles do have real properties, after all, that are intrinsic to them. They are not determined by measurement apparatus. The notion of wavefunction collapse is completely unnecessary. They exist prior to any measurement. They just don’t look like how we intuitively understand properties to look like since they are smeared out and have mutually exclusive states.
You have to understand how weird this really is though to think about. You cannot visualize a particle, for example, traveling through space at all, even if you could measure it over and over, because its position and momentum do not simultaneously exist. It would be like taking a video in a dark room with a strobe light.
Likewise, you can’t imagine a particle spinning like a top with its spin pointing in any direction you like. Rather, you have to imagine it having components (in some coordinate axes that you choose) which are mutually exclusive from one another.
You can, however, imagine the particle as being at a location and having a z-axis spin component because location and z-spin properties are compatible.
The mutual exclusivity of quantum properties means that you have to be careful when inferring what measurements imply about the states of particles before they were measured. Those states cannot include mutually exclusive properties. Or, to throw some jargon at you, you cannot use incompatible frameworks for interpreting microscopic properties from measurements.
Let’s look at an example. Suppose I have two entangled particles that I prepare and send to Alice and Bob. I have prepared these particles in such a way that their spins (which have positive or negative value in x, y, and z directions) are precisely opposite (+1/2 or -1/2), using the law of conservation of angular momentum. Alice measures the z-axis spin of her particle A. Bob measures the z-axis spin of his particle B. Since these are compatible measurements, Alice can infer that the z-axis spin of particle B is the opposite of hers. Bob can likewise infer that the z-axis spin of particle A is the opposite of his. They will always find that to be true.
If Alice measures her z-axis spin but Bob measures his x-axis spin, suddenly their frameworks for interpretation are no longer compatible. Alice cannot infer that Bob’s z-axis spin is the opposite of hers and simultaneously accept his measurement of the x-axis spin. Likewise, Bob cannot do the same about Alice’s. Rather than having an understanding of the complete particle state, Alice and Bob know nothing more than they have measured about the states of the particles prior to measurement. (For a highly technical explanation, see Sec. 23.5 here: https://quantum.phys.cmu.edu/CQT/chaps/cqt23.pdf.)
If Bob does something like rotates his apparatus by 45 degrees so he’s getting part x-axis and part z-axis compared to Alice’s frame of reference, it makes no difference than if he measured the x-axis. He can only say something about Alice’s particle state based on his measurement or hers not both taken together.
What this means is that we are allowed to know only so much about the quantum world because there is only so much to know — less than we think. Moreover, we cannot combine measurements to build up knowledge of properties that are incompatible. There is nothing hidden from us at all. Spooky action at a distance in the sense of one measurement being able to affect another instantaneously is an error of interpretation about how much those measurements actually tell us.
So why do so many physicists cling to ideas like action at a distance and many worlds?
Partly it is because the mathematics (which is heavy with Hilbert-spaces and projective operators) for this interpretation of quantum physics is very complex and counterintuitive. And since it doesn’t affect the actual outcomes of experiments or what we predict about the world, it feels like, perhaps, a waste of time to try to understand it. Certainly the science writer on the street isn’t going to understand the math. But if we scientists and mathematicians are going to continue arguing about it, perhaps it behooves us would-be philosophers of science to try to understand it before we make blanket pronouncements about physics being nonlocal. Yes it is nonlocal but only insofar as properties are smeared out across space. There are no faster than light influences between locations.
Griffiths, Robert B. “Consistent histories and the interpretation of quantum mechanics.” Journal of Statistical Physics 36.1 (1984): 219–272.
Griffiths, Robert B. Consistent quantum theory. Cambridge University Press, 2003.
Griffiths, Robert B. “Nonlocality claims are inconsistent with Hilbert-space quantum mechanics.” Physical Review A 101.2 (2020): 022117.