Archive for May, 2015

Objective reality (and the return of this blog)

Posted in Uncategorized on May 19, 2015 by quantummoxie

It has been a really, really, really long time since I posted anything. I had plenty to say but just an insane amount of stuff going on. Well, maybe that’s not quite right. It’s partially right, anyway. But I also couldn’t bear the thought of sitting down and writing. I’m a bit of an obsessive compulsive when it comes to writing. I’m one of those people who obsesses over every word and I was obsessing over a lot of other stuff so the thought of doing so for the blog just didn’t appeal to me for awhile. But now that the semester has ended and I have some free time, here I am.

So what is it that has me so inspired as to start clicking away again? Objective reality. Yes, indeed, folks I get that worked up over objective reality. It’s been a theme running through my life of late. Or, rather, it’s the denial of objective reality by other people that has gotten me riled up. George Orwell wrote a lot about objective reality. 1984 was particularly notable in that regard. One could argue that the Enlightenment was about objective reality. In fact, that’s exactly what it was about.

But I don’t have the time or energy to unload about the assault on objective reality that is modern society. (Plus, this is ostensibly a science blog.) Instead, what I do plan to do is to discuss the nature of objective reality in physics. The two greatest theories of twentieth century physics – relativity and quantum mechanics – both include subjective elements. Let’s talk about relativity first.

Technically speaking, relativity didn’t begin with Einstein. It actually goes back to Galileo and Newton. But time was still absolute. Einstein showed that both space and time were relative, i.e. subjective. Notably, special (and general) relativity supposedly rid us of an absolute reference frame. This idea was then coopted by non-physicists (and even by some physicists) to mean that there is no objective reality. But is that necessarily true? In fact, relativity provides us with a mechanism by which two observers can agree. That’s the entire point of the Lorentz transformations. In fact, that’s the idea behind the famous Twin Paradox. People often mistakenly think that the paradox is that one twin is older than the other. That’s actually not the real paradox. In fact, there really isn’t a paradox at all. One twin really is younger than the other. But maybe I’m getting ahead of myself.

The typical description of the Twin Paradox begins with (duh) twins. Let’s call our twins Alice and Bob. One twin (let’s say Bob) hops on a spacecraft, accelerates to a relativistic speed and travels off toward a distant star. Later, Bob comes back. Now, according to a superficial understanding of relativity, Alice will think that Bob is younger because he was moving at a relativistic speed, i.e. close to the speed of light. And time slows down the closer one gets to the speed of light so Alice will think Bob is younger. But – and here’s the apparent paradox – in Bob’s reference frame, it’s actually Alice – and the entire observable universe, in fact – that moves off at a relativistic speed while Bob remains stationary since we are always stationary in our own reference frames. So shouldn’t Alice appear younger to Bob? After all, everything’s relative, right?

Not quite. There are two things to consider here. The first is that, proper time is measured along worldlines (world lines) in relativity. The person with the longer worldline measures the shorter amount of proper time. So if we consider this problem from the reference frame of, say, the sun, the worldlines (and associated events for this scenario) would appear as in this diagram where time is measured in years (y) and space (distance) is measured in light-years (y).

TwinParadox

Notice that Alice’s worldline just moves around and around the sun. Clearly Bob’s worldline is longer and hence he will be younger. This result is entirely objective because we stepped outside of the Alice-Bob system and observed it from a third reference frame. But what if we chose a fourth or a fifth reference frame? Could we not find one in which things looked the opposite? That brings us to the second thing we need to consider here.

There actually is something that is exactly the same in every inertial (i.e. non-accelerating) reference frame: the speed of light! This is not only an empirically provable result, it is one of the key axioms of special relativity. (As a cautionary note, special relativity only assumes that the speed of light should be a maximum speed; it does not predict an actual value for that speed.) So the speed of light is also an objective reality – it’s the same for everyone, everywhere! So the closer an object gets to the speed of light, the smaller the differences become between inertial reference frame observations of that object’s speed (with the exception of the object’s own frame in which it is always at rest). Thus, even if we switch to a fourth or a fifth inertial reference frame in order to observe Alice and Bob, because Bob is moving at highly relativistic speeds, we won’t see his worldline change much when we observe it in some other reference frame. Alice’s, on the other hand, might change dramatically. For example, we could be in a frame in which the solar system itself is moving at a relativistic speed in the +x direction. That would tilt Alice’s worldline quite a bit, but wouldn’t change Bob’s all that much (I encourage the interested reader to work out the details).

Now let’s turn to quantum mechanics. There are two somewhat related reasons that objective reality is questioned in quantum mechanics. First, as is well-known, standard (i.e. non-weak) measurements disturb the system being measured. As such, one could legitimately ask if we can ever truly know the state of a system since merely looking at it disturbs it. Second, measurement results in quantum mechanics depend on the context within which they are measured, a phenomenon known as contextuality. So, as an example, consider a sequence of three Stern-Gerlach devices. For those who are unfamiliar with such devices, they measure the spin angular momentum of a particle (in this case, a spin-1/2 particle) along a particular axis. The result of the measurement shows the particle to either be aligned or anti-aligned with the given axis. As shown in the following figure, whether it comes out of the top or bottom of a device, determines whether it is aligned or anti-aligned respectively.

SmallFig

The classical (neo-realist) assumption is that when we measure the spin along a particular axis, that result should be the same in any subsequent measurement on that axis regardless of any intermediate measurements (and assuming there are no other external interactions that affect the system in the interim). So, in other words, if A and C represent the same axis, one would expect that, for the figure shown above, the particle should exit from the top (+) of the last device. But this doesn’t happen in quantum systems. The outcome probabilities for a given spin measurement depend solely on the angle between the axis of the current measuring device and the axis of the device immediately preceding the current one. In the example shown, that means that the probabilities associated with where the particle will exit the last device, only depend on the angle between the second and third devices. Thus it doesn’t matter if A and C are the same axis since the first device is irrelevant to the outcome. In other words, it would seem that the result is entirely subjective since it is context-dependent.

But hang on a second. Sure, the spin measurement may be dependent on the context, but the actual nature of the particle never changes. For example, if you send a stream of electrons into such a sequence of devices you never see stream of protons coming out. It just doesn’t happen. So even though, for example, we may not know a state fully, since measurement results depend on context and since the act of measurement disturbs the system, there are certain things about systems that we do know with absolute certainty. These are things that everyone will agree on. They represent an objective reality.

The fact is, that’s precisely the point of science: it is a method whereby people can come to an agreement about an objective reality. We fully expect that an electron, when observed in New York, will be an electron when observed in Tokyo. We rely on that fact. And that’s one of the great lessons of relativity: the laws of physics must be the same in every inertial reference frame. We literally (not figuratively!) cannot imagine a universe in which they weren’t.

That brings me to my final point of this post. Supposedly, some QBists deny the existence of an objective reality. I’ve never actually gotten into a deep, philosophical discussion about reality with any of them. But I do know Carl Caves, Rüdiger Schack, and Chris Fuchs (the progenitors of QBism). Given some of the things Carl has said over the years in random conversations here and there, I would find it difficult to believe that he really didn’t believe in some kind of objective reality (and I plan to ask him the next time I talk to him). Rüdiger gave a talk at a workshop I hosted last year (and I should finish editing his video soon in case you are interested), but I don’t recall anything he said as suggesting there truly isn’t an objective reality. Again, maybe I’ll pester him about it at some point. At any rate, that leaves Chris. I know that Chris has had to defend QBism against charges that it is solipsistic. He swears it isn’t. However, in my mind, a truly solipsistic argument is the only legitimate counter to claims of an objective reality since it can’t really be refuted, e.g. if you told me that I existed solely in your imagination, I would have absolutely no way to disprove that to you (even your death wouldn’t disprove it to you since you would be dead). Even so, I don’t think QBism necessarily requires the denial of an objective reality. Either way, I plan to pester Chris about this as well.

So that, in a nutshell, is why I think people are mistaken when they claim that physics somehow denies the existence of an objective reality. Quite the opposite, I say: physics requires it.