I left you a message.
You knew the message was coming. You also knew that you wouldn’t understand it. Not until you asked me.
The message came instantly from me to you. It didn’t come by radio or fiber cable at the speed of light. It was immediate. Yet, it told you nothing. You would have to ask me what it meant.
Here is the message:
“up”
I told you it made no sense.
I have a similar message. Mine says:
“right”
If we knew each other’s messages, we would know something important, something that, a century ago, nobody thought you could know.
That was until 1935, when Albert Einstein gave his two cents to a paper that would rock the small world of quantum physicists.
The problem is entanglement.
The paper was titled “Can quantum-mechanical description of physical reality be considered complete?”
Entanglement is a hard topic to understand, even for physicists. It is so difficult that nailing down exactly what it was and how it worked took decades. Still, nobody knows what it means.
Entanglement comes from conservation laws in physics.
These laws tell us that certain quantities have to add up. Energy, momentum, angular momentum, and charge cannot be lost or found.
Those conservation laws are absolute, but quantum physics gives particles wiggle room in how they obey them when there is more than one particle involved.
That is how particles get entangled.
Conserved quantities come in pairs of complementary properties. You can measure one but not the other in a single experiment on a single particle. For example, you cannot measure both the position and momentum of a particle.
If you’ve heard of Heisenberg’s uncertainty principle, it is that idea, but uncertainty is a bad way to understand it. It makes it sound like the problem is in your measuring apparatus. The problem is reality.
Particles have a property called spin, which is their angular momentum. For massive particles like electrons, spin has three components that we call x, y, and z. Photons only have two, x and z.
Spin components are complementary properties. If you measure x, you can’t measure z. But it turns out that you can know both if you have particles that are entangled.
Suppose you prepare an experiment that produces two photons so that they must have opposite spin, A and B. You might get that from the decay of a pion.
Since you don’t know what spin each photon has, you need to measure it, but you can only measure the x or z component of each photon.
Luckily, if you measure the x of A and the z of B, you can infer that the z of A and x of B are the opposite. That is because the two photons are entangled. For example, if A’s x is “up” and B’s z is “right”, then B’s x is “down”, and A’s z is “left”.
Is this surprising?
In 1935 some physicists thought it was a big deal that you could do this because it seemed to violate Heisenberg’s principle, but it wasn’t, and Einstein knew it.
Einstein was after bigger game.
In my last article I talked about how Einstein insisted that quantum physics was incomplete. Entanglement was a big reason.
According to quantum physics, when these two photons move apart, they remain connected, as if they are a single particle in two different locations. Worse, the particles do not have a definite value for spin until the spin is measured.
Einstein had two deeply held beliefs about the nature of the universe: locality and realism, and, with these facts, quantum theory appeared to violate both.
Locality means that every thing that happens, happens at a particular time and a particular place. A single thing cannot happen in two places. It must be two things happening. And two things can only be related based on signals that travel at or slower than the speed of light, never instantly.
Realism means that everything in the universe that can be measured has a definite state before it is measured. In other words, if I measure a particle to have a particular spin, it must have had that spin before I measured it.
Einstein insisted that quantum physics would not be complete until it met these two criteria. But the great quantum physicists Bohr and Heisenberg disagreed. Heisenberg was distinctly anti-realist while Bohr was not necessarily anti-realist but believed that what was real depended both on the observer and the observed, so he was comfortable with getting different results from different kinds of experiments on the same particles.
Here is how entanglement appears to violate Einstein’s beliefs:
Violating Realism
According to quantum theory, photon A and photon B do not have definite spins before they are measured. Instead they have a range of probable spins encoded in an entity called the wavefunction, but, because their spins are opposite, the spin of one must determine the other. When you measure the spin, however, it becomes definite and immutable. Thus it doesn’t become “real” until measured.
Violating Locality
When we do measure the spin of photon A, it automatically determines what you will measure at photon B, but only to the degree that your measurement is correlated with the measurement done at A. What is measured at photon A appears to be instantaneously transmitted to photon B so that it “knows” both what spin it should be and what kind of measurement was performed. That knowledge does not give the person doing the measuring any new information, but it is impossible to explain experiments within standard quantum theory without invoking some kind of information transfer.
You can quantify that by looking at how the angle between your spin detectors affects what you measure at each photon. If you measure x and x for the two photons, your angle is 0 or 180 degrees. If you measure x and z, it is 90 or 270. But if you measure in between x and z, it could be 30 or 45 or some other number.
If there were no information transfer, you would expect your measurements at different angles to obey the red line below, a perfectly linear correlation between angles. When your detectors are parallel or perpendicular, you can pretend that information isn’t transferred because the blue and red line cross at those angles. But otherwise, the correlation is nonlinear, meaning information must have been transferred not only about what was measured but how it was measured.
In quantum field theory, this information transfer happens over all of time and space, from the Big Bang to the end of time and from Earth to the end of space if there is such a thing.
Nothing for Nothing: The Balm of the Many Worlds Interpretation
You can resolve these problems by a Many Worlds Interpretation: for example, you can restore realism and locality by saying that each value of particle spin exists as a a definite value in a copy of that particle in a separate universe within a multiverse. The apparent transmission of information from one photon to another is an illusion. Instead, you, meaning a copy of you, have been split into a particular universe where it appears that way. This is easy to understand but hard to believe and, so far, scientifically useless.
The MWI is useful for making us feel better about the confusing aspects of quantum theory, but, because it assumes quantum theory is complete, it tells us nothing new about the universe, and it cannot be verified because it makes no new predictions. It is a balm for our angst but, because we take no risk on a new theory, we get nothing in return.
Playing with Fire: Modifications to Quantum Theory
You can also restore them by modifying quantum theory but not easily — not without giving up something.
David Bohm, for example, introduced his guiding wave to guide particles and communicate for them, which restored realism but not locality. He was not able to remove the instantaneous communication between particles.
There are many other variants and reinterpretations. Most are not that popular anymore while some, such as Lindblad equations, seem to be becoming more so.
Modifying quantum theory is like playing with fire, you often get burned. Quantum theory is, after all, a 100 year old edifice and the most successful physical theory of all time. Bohm’s theory falls on its face in trying to repeat that in every detail. Beyond that, you are forced to more exotic modifications, almost all of which introduce some element of randomness to the universe. Most also fail to restore locality.
Thinking about quantum theory intuitively is hard. Even the relatively benign theory of quantum mechanics where particles stay particles and Einstein’s relativity is not in play causes problems. Once you transition to quantum field theory, many of the assumptions those modifications rely on disappear. Theories like Bohm’s start to break down.
How to think about entanglement intuitively
Imagine having a God’s eye view. Go back to the entangled photons. You are watching photon A propagating away from photon B. Imagine that its spin is a little arrow pointing perpendicular to its motion at the speed of light. The arrow moves about randomly and discontinuously.
Now you watch photon B moving in the opposite direction at the speed of light. It also has an arrow moving around randomly. The odd thing is that whenever photon A’s arrow moves to point somewhere else, photon B’s arrow moves to point in the opposite direction instantaneously. No matter how many light years they get from each other the arrows move in lock step with one another. It is as if they are one particle in two places.
The only way you can imagine this happening is that they are somehow connected, either by a guiding wave function that allows instantaneous communication, or perhaps something built into the nature of the universe.
Expanding Locality
Suppose we take another look at locality and try to expand our definition of it. Look at the photons four dimensionally. Imagine the path each photon takes. The two together form a single structure. This structure is not a point structure, but a set of lines (called world lines). There are two lines connected at a single point in space and time where the photons became entangled.
Suppose that these world lines are the real particles, not points in time and space, but lines through time and space. And those particles are able to communicate along these world lines back to their point of origin, back in time. If that is so, then it makes sense that these entangled particles would be able to share information “instantaneously” because they are communicating back through time, reconciling their state all along the world lines.
If we define locality to mean connected world lines and not events happening at points, then entanglement no longer violates it. And because information is not transmissible from photon A to photon B, it doesn’t violate causality. (You can’t send information back in time or faster than light because all the “information” the two photons share is random.) Two disconnected lines, on the other hand, cannot be entangled unless they are connected by a third line.
Collapsing Locality
Quantum field theory, however, represents these particles as simply inputs to a vast set of a fields that span all time and space. The field connects all particles in the universe capable of interacting. This means that we have to expand our notion of world lines to include fields, but luckily world lines are one dimensional versions of four dimensional fields. So, our definition of locality continues to hold but now covers all of time and space!
With this addition, locality collapses as a concept but everything is local. It becomes meaningless without further modifying quantum field theory.
Free Will versus Locality
There is a loop hole in this problem of locality. Quantum theory suggests that there are correlations between experiments that suggest information is being transmitted instantaneously about the experiment being done. But what if the universe already knew about the experiments and their outcomes in the first place?
Superdeterminism suggests that this strange correlation curve is the result of correlations that occurred at the time of the Big Bang between all matter. Matter is never uncorrelated, including the matter making up you and me. Information is not traveling faster than light. It was always there to begin with because nothing we chose to do was undetermined.
Even though quantum field theory appears to connect all time and space at each moment, that is an illusion. All things in time and space are connected because they are all predetermined from the beginning of time.
Expanding Realism
Einstein did not like randomness, but unfortunately randomness is at the heart of quantum physics. If you expand realism to include random fluctuating values, then you no longer have a problem.
Quantum math tells us that particles have a wavefunction that describes their state, but nobody has ever seen a wavefunction. We might as well assume that the particles’ states fluctuate randomly as they propagate. When we measure the particle, it is like rolling dice. We happen to land on one of the probable values.
In order for randomness to work, however, the world line of the particle again has to be invoked. The world line as a whole is random, not the particle’s state from one time to the next. That is the difference between quantum and classical randomness. You can imagine throwing a set of dice, not at every moment the photons propagate, but only once to determine the entire history of the photons from emission to detection. Once those dice are thrown, the photons can have a definite state for their entire history.
But when are the dice thrown? Is it when you detect the photons or the beginning of the universe? Somewhere in between? When does what we measure become real?
Realism versus Free Will
As long as the dice is thrown at or before emission, we can say that realism is definitely restored. To do that, the particle has to “know” what is going to happen to it.
If the dice are thrown at detection rather than emission, then free will is possible but realism is on shaky ground. Can we say that something in the past becomes real based on an event in the future? That is a much weaker definition of realism than we would like because it means that before the photon is detected is has no reality.
To go to quantum field theory, we expand one dimensional world lines to four dimensional fields. Because of the way fields interact, we end up with the past and future of the entire universe being random and interconnected, including us.
Now there is no way out of it. Every observation and measurement is made predetermined at the Big Bang but real or only determined at the end of time. (Stephen Baxter used this idea in his novel Timelike Infinity.) Life may feel real to you, but, if you want free will, you have to trade reality away and make your life a dream until every interaction of every particle is resolved.
Conclusion
There are other interpretations that avoid the free will problem, but they involve extra dimensions or universes. If we could find evidence for these, that might answer some deep philosophical as well as scientific questions.
The other startling conclusion is that we may already understand quantum theory. We just don’t want to accept the implication. If we have free will, quantum theory makes no sense. If reality is superdetermined, then quantum theory does make sense and Einstein’s locality and realism are restored, but we have no free will.
The choice is yours what to believe. But then again, perhaps it isn’t.
Einstein, Albert, Boris Podolsky, and Nathan Rosen. “Can quantum-mechanical description of physical reality be considered complete?.” Physical review 47.10 (1935): 777.
Bell, John S. “On the einstein podolsky rosen paradox.” Physics Physique Fizika 1.3 (1964): 195.
Hossenfelder, Sabine, and Tim Palmer. “Rethinking superdeterminism.” Frontiers in Physics 8 (2020): 139.