A new perspective on quantum entanglement
Fluctuating histories is one hypothesis that challenges the standard view.
Quantum entanglement is an often misunderstood phenomenon. To the uninformed it may seem banal, easily explained with ordinary probability theory. To others, it is a spooky and magical phenomenon with mysterious implications on the nature of reality.
In truth, it is a little of both. Ordinary probability theory can explain it if you discard some of your ideas about how reality works, as I explain below. Spooky action at a distance though it may appear, that is only true if you fail to think about it multi-dimensionally.
First of all, what is quantum entanglement? In simple terms entanglement is when you have two or more quantum systems like photons, for example, that have a single quantum state. If you want the technical definition, the Von Neumann entropy of the combination of systems is lower than the entropy of the individual systems. Von Neumann entropy is the quantum analog of ordinary entropy and describes the degree to which a quantum state is “pure” or “mixed”.
Mixed states just refer to ordinary probability such as the case where I flip a coin and hide it. The state is a mixture of heads and tails because I haven’t seen it but I know it is one or the other. Because the coin has two possible states, the entropy is non-zero (proportional to the log of two).
Pure states refer to the quantum superposition of states where a particle is in two or more states at the same time. Thus, if I have a quantum coin in a superposition of heads and tails, it is not heads or tails but heads and tails until I observe it. Because heads and tails is one quantum state and not a mixture of two, it has zero entropy.
Let me be clear: it is in one definite state not one of two probable states despite the randomness of the outcome.
An entangled set of states means that the coupled systems are “pure” rather than “mixed” as a whole. (You can also have mixtures of pure states but let’s keep it simple.)
That is important because it is possible to show that when I have two entangled particles, such as two photons with opposite spin that I can get from pion decay, and I measure one, the other must be correlated depending on which component of spin I measured. Photons have two spin components, e.g. x and y. If I measure perpendicular spin components, they aren’t correlated at all. If I measure parallel spin components, they are completely opposite. If I measure them at some angle with respect to one another, then they are correlated according to the cosine of the angle I chose.
Entanglement truly is as if measuring one transmitted the information I measured to the other because what I measure at the other one seems to depend on how I measured the first one.
Imagine that I create two photons and send one towards my extraterrestrial colleague at Alpha Centauri (A) 4 lightyears away and the other to scientists on the starship Bohr (B) traveling in the opposite direction 4 lightyears away. If the researchers on the Bohr and those at Alpha Centauri measure them at about the same time, they will find their results correlated with one another. Yet there is no time for that information to travel between them at even the speed of light.
I’ll get to what is weird about this in a moment, but first a little digression on how measurement in quantum mechanics works.
An experimenter is only able to measure one component of spin in any coordinate system. That is because of Heisenberg’s uncertainty principle. (Spin components do not commute is the technical term.) Like position and momentum, once I measure one spin component of a single particle, I cannot measure the other. I can, however, measure one component of one particle and the other component of the other entangled particle and know the complete spin state of the two particles by combining the two measurements.
For example, if I measure the x component of A to be positive, and the y component of B to be negative, then I know the y component of A is positive and the x component of B is negative.
(Podolsky of Einstein-Podolsky-Rosen paradox fame claimed this was a serious problem with quantum theory, but it really isn’t. After all, nobody says that you can’t know the complete spin state of a single quantum particle. You just can’t measure them both from a single particle.)
When I make a measurement of a quantum particle in a pure state, I cause the state to “collapse” into one observation of that state. What that means nobody knows, but it appears as if measurement (the interaction of the particle with a macroscopic measurement apparatus) somehow changes the reality of the particle from quantum to classical probability.
Getting back to our interstellar experimenters, the correlated result of A and B is not unusual since the two photons were created together. The problem is that they are correlated with one another in proportion to the cosine of the angle between the spin component measurements that the two experimenters chose to make. That is not possible without some kind of communication between the two. For a mixed state where, e.g., I created two photons separately with classically correlated spin (meaning I just prepared particles with particular spins of my own choice) and sent them off, the correlation would be linear in the angle. The only way that my ET friends and those on the Bohr can get the correlations they see is if the photons are not independent of one another when they are measured. This is the basis for what is called Bell’s theorem, the theory of quantum measurement.
But since these two photons are 8 lightyears apart when they are measured, how can they not be independent? Doesn’t that violate the speed of light restriction on communication? Isn’t it spooky action at a distance?
The word for this is that quantum states are nonlocal, and it all depends on what you think quantum mechanics means.
From my perspective, the answer to quantum entanglement has to do with what quantum states really are.
First, let’s imagine what a spin state looks like from the perspective of a quantum particle. You can imagine it like this: the photon has a little needle, like on a speedometer, and it moves about randomly, jumping to different angles as it propagates through space and time. The needle points perpendicular to its path since any component in the direction of motion would be squashed flat by relativistic effects.
Now, if you imagine two photons propagating that are completely (purely) entangled such that their spins are opposite (as from the decay of a pion), then each photon’s needle will point in a random direction, but they will always point in opposite directions, no matter how far apart they are. This means that whether they are two, four, or eight lightyears apart, they will still be choosing pointing angles that are exactly 180 degrees apart at every moment.
(Some would say that the photons aren’t randomly selecting pointing angles but just exist in a moving probability field that embodies all those random angles as potentialities. I find mine easier to visualize, and the two pictures are equivalent. For the mathematically minded, this is just the equivalence between canonical quantum mechanics and Feynman-Kac stochastic equations.)
That doesn’t seem to make sense unless the photons are communicating, but there is a way out.
Consider that the photons are not individual particles but part of a single structure that exists in both space and time called a world line. A world line is simply a photon’s path but in this case we have two photons that belong to a single world line. If you drew this, it would look like a V-shaped graph with the bottom of the “V” being the creation event and the two tops of the “V” being the two measurement events.
The key to understanding entanglement is to see the V as not two separate world lines but as one world line that is bent in time at the point of creation by its entangling event. That is how you think of these things four-dimensionally.
As the photons propagate along the V, at each moment, the V as a whole is selected randomly from a bucket full of possible V’s. (The bucket of V’s is the called the phase space.) Thus, every possible spin state of both photons together is included in the V at every moment. (Technically, the V’s also include different paths from emitter to detector, but we are only interested in the spin portion.) This works without any recourse to quantum probability theory. It is purely a classical probability model but of world lines rather than point particles. Filaments, not billiard balls.
That is the difference.
Aren’t we still talking about instantaneous communication?
Yes and no. What we are talking about is history changing randomly from moment to moment. Thus, there is no communication as in propagation of information from one point to another. Rather, past and present change as a whole rather than the past being fixed and the present changing.
That may sound like a scary proposition, but it is entirely consistent with quantum theory. Particle states appear nonlocal because they are nonlocal objects that exist in both time and space and their histories as a whole fluctuate randomly. Classical systems like gases likewise fluctuate randomly at each moment in time but don’t change their histories. Quantum mechanics implies that the universe is set up like a gas of world lines (or, in field theory, fields) randomly changing but at all times respecting the strict laws of conservation of energy, angular and linear momentum among others.
What about our history? If it is fluctuating randomly, we wouldn’t know because we are changing with it, but I think that it may be farfetched to say that macroscopic phenomena are subject to the same fluctuations, even when they interact with quantum phenomena.
One way out is to go the consistent histories path and say that there is one and only one randomly selected world line for any given quantum system. That is the history, end of story.
My approach is to suggest that quantum histories are dynamical and fluctuate randomly as they propagate through a 5th dimension. Conservation of angular momentum that creates the spin entanglement is maintained because the laws for propagating the world lines in that 5th dimension don’t allow it to be violated. Thus, any change in one particle must be reflected in the other and vice versa without communication between them, and all events remain local. Apparent nonlocality is taken care of by the world line’s nonlocal structure.
When the quantum systems interact with macroscopic systems like us, they decohere, meaning that their fluctuations may be influenced by macroscopic boundary conditions, which, because of their size, act like large reservoirs, absorbing but also influencing.
In other words, measurement can be a two way street that curtails a particle world line’s freedom to fluctuate as much as it retrieves information about that particle’s state.
While you can justify that a fluctuating history model is consistent with quantum mechanics, you can’t justify that classical history also fluctuates even when taking quantum influences (the effects of cosmic rays on evolution for example) into account. So, for now, it may be that much of history as we know it remains set in stone.
Schulman, Lawrence. “A path integral for spin.” Physical Review 176.5 (1968): 1558.
Klauder, John R. “A Langevin approach to fermion and quantum spin correlation functions.” Journal of Physics A: Mathematical and General 16.10 (1983): L317.
Andersen, Timothy D. “A Dynamic Histories Interpretation of Quantum Theory.” arXiv preprint arXiv:2009.04244 (2020).