Continuing the thread from yesterday…

ON DETERMINISM

In the first post I explained that quantum mechanics teaches us that we cannot know the state of a particle until we measure it. Andre Parsa responded, “each particle does have its own absolute state, a position and velocity etc. [It] is not random, only difficult to measure.”

If Andre is right, then I will concede that the Universe is deterministic. My claim that the future is undetermined relies upon the assumption that particles do not have absolute states. It turns out our disagreement gets right to the heart of quantum mechanics, but to examine it more closely requires bringing the “wave function” into the discussion.

The quantum mechanical wave function depends on both position and time. Manipulated in this way or that, it provides information about its system. For example, if you square the wave function you obtain the probability that a particle exists in the vicinity of position at time . This takes a statistical interpretation of the wave function, one that implies a degree of indeterminacy, i.e. even if you knew everything there was to know about the system, you still couldn’t predict with certitude what the outcome of an experiment would be. This is often referred to as the Copenhagen interpretation.

Let’s further separate these two philosophical interpretations by asking the question, “What was the state of the particle just before measurement?” Andre would say, “I don’t know, but it definitely had one.” I would say, “There was no state. It was all states and no states. It wasn’t anything at all until we measured it.” Given that we can never measure a particle’s position immediately before we measure it, this problem seems intractable.

But Einstein, Podolsky, and Rosen (the latter two also physicists) couldn’t help but think that as a theory quantum mechanics was incomplete. They introduced a thought experiment known as the EPR Paradox to illustrate. They considered the decay of a neutral Ï€ meson into an electron and positron, the latter two flying off in opposing directions towards opposite sides of the Universe. Through conservation of momentum, when one is measured to be spin-up the other must be spin-down.

Andre would say, “Of course! One actually was spin-up and the other actually was spin-down. When we measured we figured out which was which.” He would then go on to criticize me further by saying, “If you honestly believe that measuring the electron’s spin caused it to be spin-up, then the ‘message’ that the positron must consequently be spin-down would have had to travel across the Universe instantaneously to assure that any measurement of the positron would reveal as much, and as we all know information doesn’t travel faster than the speed of light, so there.”

At this point EPR and A would all smile satisfied smiles while humbly admitting that their version of quantum mechanics wasn’t perfect. There was some unknown quantity, some hidden variable within the quantum mechanical wave function that had yet to reveal itself. If the Universe was truly deterministic then such a variable testifying to the particle’s state must exist. The challenge would be finding it.

And people tried. Many “hidden variable theories” were proposed, but none worked. Then, in 1964, my champion, J. S. Bell, proved that any local hidden variable theory is fundamentally incompatible with quantum mechanics.  Einstein once famously quipped that “God doesn’t play dice,” a statement which served as a slap in the face to the Copenhagen interpretation. Had he still been alive at the time of its publication in 1964, Bell’s theorem would have caused him to spit his drink all over the Baccarat table. And in case you’re wondering, there have been many tests of Bell’s Theorem. They have all confirmed its veracity.

This result plays a large part in my belief that the Universe is not deterministic. Assuming quantum mechanics is correct (a fairly safe assumption at this point), there’s no hidden information (as represented by an unknown variable) within the wave function of which we’re unaware. There CAN’T BE. Therefore the measurement (more technically the perturbation) of that aforementioned electron does determine its spin state, and that reality is somehow conveyed to the positron in the form of its opposite spin state.

PR and Andre (Einstein is wiping himself off at the bar) make one last gasp, “But even if we’re wrong, you still can’t explain how information about the electron’s spin can travel instantly across the Universe and effect the positron’s spin. That would violate causality! We may not win, but neither do you.”

Sure, but only if you agree that “information is being sent.” So let’s say the electron is measured as spin-up while simultaneously, a million light years away the positron is measured as spin-down. I claim that no information has been conveyed between those two positions. Why, you ask? Because the experimenter at the positron has no idea whether the electron has been measured yet. All he knows is his positron is spin-down. The only way this “spooky action at a distance” information is revealed is when the two experimenters travel (causally) to each other to compare data.

While we physicists certainly don’t have all the answers when it comes to quantum mechanics, the facts as we know them now more strongly support a random Universe than a deterministic one. Given that particles lack absolute states, it’s impossible to claim they will evolve identically, and therefore the future progress of all particles was not inevitably set in motion after the moments of the Big Bang.

After this question was first posed and considered I reported on some objections to my answer. If you haven’t already read those posts, I encourage you to do so now. Put briefly, both Marcus and Andre contend that particles must follow the immutable laws of physics. They argue (sensibly it would seem) that two identical worlds following identical laws must wind up in the same place. In this post I will defend that A) we cannot predict where those worlds will wind up, and in tomorrow’s B) even if we could, the results would be indeterminate.

ON PREDICTABILITY

My argument is that Universes starting from identical initial conditions will have different outcomes. I want to make very clear that his statement has nothing to do with our ability to predict those outcomes.

For instance, if we knew the position, velocity, temperature, etc. of every particle in the Universe at a given point in time, it might be reasonable to conclude that with perfect knowledge of the laws of physics, we could predict the outcome of the system. Of course, such computational ability would require resources greater than the Universe could provide. For example, if you built a computer that could run such a simulation, the simulation would have to take into consideration all parts of the Universe including the computer itself. It would have to have perfect knowledge about how the computer would evolve and how it would find the answer that it has yet to find”¦such a computer would also need at least as many atoms for computation as exist in the rest of Universe (to account for each particle), which is, of course, impossible.

The moral of the story is that regardless of whether or not the Universe evolves deterministically, no entity in that Universe could predict its outcome. That said, let’s agree to decouple the notions of predictability and outcome. For the sake of this discussion, I don’t care whether or not an outcome is predictable. My claim is that starting from identical initial conditions the outcomes themselves will not be the same. Tomorrow, I’ll explain why in greater detail.

My postulation that identical Universes will evolve differently has engendered some discussion, most of which disagrees with my answer. I want to highlight two points of contention. The first concerns the distinction between outcomes and their predictability. Marcus Geduld writes:

You rephrased the question as “What you are asking is if you take an infinite number of Universes all starting from exactly the same initial condition, will they all evolve in identical ways?” And you answered no.

Why not? How can you be so sure?

I feel like there was a very subtle slippage in meaning in your (otherwise) fantastic answer. I see this same slippage a lot, in Scientific and Philosophical discussions, so it’s very possible (likely) that I’m the one who is slipping. But I’ll go ahead and explain my objection, anyway.

There’s a difference between what we can predict and what winds up happening. I agree we can’t make PREDICTIONS about whether universe A will behave identically with universe B, given the same initial conditions”¦event X at time will be identical in both universes. However, we can’t predict X in either universe. If we could predict it in A, we COULD predict it in B. But we can’t predict it in A.

A second contributor, Andre Parsa, tells me I’m flat out wrong. He answers the question of whether the future of all particles was set after the Big Bang by writing:

Yes. The result or apparent behavior of a system is the sum of its past. This comes out of several points including:

• A system in physics, in the broadest sense of the term is the sum of states of its parts, and whatever rules govern those parts. Basically all matter, in the specific states of energy each individual smallest part is in and whatever rules govern all possible interaction this smallest part may have with other parts in the system.
• The issue of “quantum mechanical uncertainty” has nothing to do with this. The “uncertainty” of the concept is that we are unable to obtain absolute knowledge of particles in a quantum system (at the quantum level), in other words, to know in what state the particle is in. But each particle does have its own absolute state, a position and velocity etc. The mistake in using it here is that concept only explains that humans cannot measure these values because we affect them when we do, if we leave the particle alone, it has an actual and concrete state. Radiation may be released at rather random points in time from a mass, but is released at a concrete time nonetheless. Radioactivity is not random it only difficult to measure this is a concept chemists understand not physicists.

To me, the first critique can be answered with a clarification while the second assumes a philosophy I don’t believe best fits the data physicists currently possess. In future posts I will use our knowledge of the weird and wacky quantum mechanical wavefunction to justify my answer of “No, the Universe’s future is not locked in stone.”

This question was posed on the website Quora, a human-driven question/answer service similar to that of Yahoo! Answers and Aardvark. Every respondent but me answered “Yes.” I wanted to include here why the answer is:

No. What you are asking is whether an infinite number of Universes starting from exactly the same initial conditions will evolve in identical ways. The answer is no.

The reason is quantum mechanical uncertainty. Quantum mechanics teaches us that at the atomic level we cannot have absolute knowledge of a system. For instance, we cannot know exactly where a particle is or exactly how quickly it’s moving. We can only know the probability of, say, electrons being in a particular position. This means if 1000 scientists measured the positions of electrons in 1000 initially identical systems they would get 1000 different answers. This is often referred to as the Heisenberg uncertainty principle.

For a very simple example of how this stops the Universe from being absolutely predictable, consider the Schrödinger’s cat thought experiment in which a cat is placed in a box along with some radioactive material. Radioactive materials decay, releasing particles as they do, but we cannot predict exactly when a decay particle will be emitted. In this thought experiment, we rig the decay material to trigger a can of cyanide which will kill the cat. Since identical boxes will release radioactive particles at different random times, in some Universes the cat is alive at time and in others it is dead.

If you are compelled by this argument, then you must conclude that the future is not yet written. However, this fact alone does not imply that human beings have free will. If you view human actions as being driven by the immutable laws of physics subject to external stimuli and the internal workings of the human brain (which are dependent on factors such as genetics and acquired knowledge), then all beings may lack the ability to steer their own destinies. But because of quantum mechanics, those destinies would not be predetermined.