Time Symmetric Quantum Mechanics

Practically a century ago, Albert Einstein challenged the advent of Quantum Mechanics, perhaps most well-known through the phrase “God does not play dice with the Universe”. Today I want to provide a short, cursory introduction to my favorite flavor of Quantum Mechanics, which provides an answer to why God might want to play dice with the Universe, as well as provide interesting insight into Free Will. Let’s start by looking at what the two main branches of physics – classical mechanics and quantum mechanics – have to say about the nature of reality.

Classical Mechanics consists of the physics (electromagnetism, celestial mechanics, etc) which describe the macroscopic world. One key characteristic of the physical laws in this domain is that they are deterministic in nature. Given a set of initial conditions, one can predict future trajectories. In addition, objects are considered to have precise historical trajectories. The classic example is billiard balls. Given some initial force by the que stick in a given direction, one can determine exactly where those balls will end up. The billiard balls also had precise historical trajectories along the way, in that they followed a definite path at a definite speed across the pool table. So, what does this say about free will? If we are just large collections of molecules, which were set in motion at the beginning of the Universe (amongst many, many other molecules), we’re all just like those billiard balls bouncing around. All our actions and thoughts are pre-determined by the initial conditions of the Universe, which leaves zero room for Free Will. Not looking promising so far, but let’s move on to Quantum Theory. 

Quantum Mechanics (QM) is an altogether different story and a very exotic place. A simple example is a quantum particle which has only two spin states – spin-up and spin-down. (Spin is equivalent to a top spinning, or even the Earth rotating, but in QM spin states are quantized, or restricted, to certain values) Classically, one would expect the physics to be able to predict whether one would get spin-up or spin-down upon measurement. Instead, QM says the best one can do, even in principle, is predict the probability of what one will get upon measurement. For a physicist who is used to being able to precisely predict outcomes, this can be a bit disconcerting, which is partly why Einstein said “God does not play dice with the Universe”. Perhaps even more troubling than the probabilistic nature of the predictions is that before measurement the particles are considered to be in a superposition of spin-up and spin-down, which would seem insane in the classical world. This applies even to the particles position, meaning they do not have well-defined historical trajectories. As unfounded and strange as this all sounds, it is well verified over the past century via experiment. So, what does this say about free will? QM still presents us with an undesirable picture for free will. Here, we have a set of potential outcomes where multiple actions, or thoughts, might be possible, but they are completely left up to chance. Whether you got the bacon crisp or avocado burger for lunch was not your choice, but rather left up to the “flip of a coin”, perhaps in your neurons.

This probabilistic nature of Quantum Mechanics has been an area of great debate and intense study for the past century. Why would reality take on such a bizarre nature? Anyhow, this is how it would all seem … so far. This is what the two big pictures in physics seem to say about the nature of reality at first glance. Let’s take a look at Time Symmetric Quantum Mechanics (TSQM) and see how things change. 

Both areas of physics above assume that time is solely linear, flowing from past to present to future. If A happens before B and B happens before C, then what happens at A can effect B and C, and what happens at B can effect C. But, what happens at C will never effect what happens at B and A, and what happens at B will never effect what happens at A. This is cause and effect as we normally view things. TSQM mixes things up a bit, but in very subtle ways. Standard quantum mechanics has a wave function (the mathematical object that encodes the above mentioned probabilistic outcomes) that propagates forward in time (from A to B to C). TSQM consists of two wave functions – one propagates forward in time to the present and the other propagates from the future to the present. In other words, the outcome from a measurement obtained in the present (say, at B) depends upon information from the past (what happened at A) and the future (what will happen at C). (I would like to stress this is a very subtle type of retrocausality that in no way violates our everyday notions of cause and effect. I will get a bit more into this below). Modern experiments seem to suggest that what happens at C, can indeed effect measurement at B. See the reference links provided below.

Yakir Aharonov is one of the founders of TSQM and the insights this formulation contains.

“Aharonov accepted that a particle’s past does not contain enough information to fully predict its fate, but he wondered, if the information is not in its past, where could it be? After all, something must regulate the particle’s behavior. His answer—which seems inspired and insane in equal measure—was that we cannot perceive the information that controls the particle’s present behavior because it does not yet exist.” (*)

“Nature is trying to tell us that there is a difference between two seemingly identical particles with different fates, but that difference can only be found in the future,” he says. If we’re willing to unshackle our minds from our preconceived view that time moves in only one direction, he argues, then it is entirely possible to set up a deterministic theory of quantum mechanics.” (*)

In fact, Aharonov decided to mix things up and instead of making a claim like, “God does not play dice”, he decided to ask a question. What advantage would there be for God to play dice? Is there something we are perhaps missing, that could make us realize there is a deeper reason why nature would at first appear probabilistic. As it turns out, TSQM suggests there is indeed a larger picture we are missing here. 

Consider the following three principles:

(1) Genuine Free Will 
(2) Cause and Effect 
(3) Retrocausality 

The first two we are well familiar with and, for the most, take for granted. The third is introduced by TSQM. At first glance, all three seem to be mutually exclusive to each other. Free will seems to be prohibited by classical and quantum theory, as discussed above. All your choices are determined, or effected by a preceding physical cause, meaning they can never be truly free (and QM alone didn’t offer much help here). Retrocausality seems to contradict both. How can one have retrocausality without violating our normal notions of cause and effect? And, if there is a “destiny” out there waiting for us (let alone reaching back in time to effect the present), how can we have free will, or choose our own destiny? 

It turns out the “rolling of dice”, or the probabilistic nature of Quantum Mechanics, is exactly what one needs to allow those three principles to live together! To set Einstein straight, this is why God plays dice! 


When taken in a larger context of a reality which allows a richer structure for spacetime, a seemingly bizarre and perhaps undesirable facet of reality suddenly becomes not only enlightening, but useful beyond our wildest imagination. Not only that, the probabilistic nature of the reality at the quantum scale seems to indirectly imply free will, even if at first glance it appears to be a stumbling block to it. In addition, for the three above-mentioned principles to exist harmoniously it would appear we need a richer view of time than our normal linear time, specifically one that allows for the type of retrocausal influence found within TSQM.

That these three can harmoniously exist within the framework of TSQM has been shown by physicists working in the field, although a comprehensive paper outlining the specifics is still waiting to be published. I’ll try to quickly cover some of the basics of how this works and will dig into it more in a future blog post. Of course, this will be stated in terms of a scientist having free will, or free choice, over what he does and does not measure. 

In a subtle fashion, Mother Nature protects free will choice from “destiny”, by making it so one can never be sure if what they observe in the present is really a wave function (i.e. “destiny”) propagating back in time or just error in the measurement process, which is a ramification of the type of measurement used within TSQM – weak measurements. No matter what way they have come at this problem, they cannot get around it. It is only by examining all the measurements (past-present-future) after the fact, that one is able to decipher what really happened. In this way, free choice in the present, as to what measurements one can take, are protected from these subtle retrocausal influences. Further, it has been shown that it is precisely the probabilistic nature of QM that is needed in order for (1) free will, (2) cause and effect, and (3) a subtle retrocausality, to all exist harmoniously. 

As you may already know, I also explore parapsychology on this blog, so I can’t help but point out that this is the kind of direction physics needs to head in to accommodate a phenomenon like psi. One type of psi experiment shows that folks seem to react (on an unconscious level) to certain stimuli 1-10 seconds before the stimuli actually happens. This is screaming for a richer view of reality, like the one presented in TSQM, which does allow information from the future to leak into the past. TSQM doesn’t yet provide a mechanism for psi, but it does begin to open up a new window to reality that at least seems conducive to the existence of psi.

I would imagine this blog post has raised a number of questions, even if potentially providing a number of fascinating answers to some other questions. I hope to cover more in future posts I am planning to write about TSQM. Stay tuned!