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.

Neal Stephenson on Leibniz, monads, and more

Posted in Uncategorized on September 9, 2014 by quantummoxie

I have finally gotten around to editing the videos from the workshop I ran with Dean Rickles last March. The first few have been posted on the workshop website and I’m going to slowly repost them here as well (in lieu of writing another blog post — trust me, Neal Stephenson is far more compelling than anything I could write). So, without further adieu, here is the estimable Neal Stephenson, recorded at Trinity College, Cambridge by yours truly back in March. Stay tuned for more.

CPT-symmetry and the nature of time

Posted in Uncategorized on June 18, 2014 by quantummoxie

Our follow-up to last summer’s PRL outlining a quantum resource theory for CPT-symmetry has hit the arXiv and been accepted for publication (without mods!) in PRA. We’ve got some further generalizations we’re starting to work on, but one of the things this work has crystallized in both my mind and many other people’s minds is that true “time-reversal” is really CPT-reversal. Nevertheless, there are still some pesky questions about time that persist, despite Ken Wharton’s argument that there’s really no funny business going on at all. Ken has tried to convince me to buy into the block universe explanation. I’m still not entirely sold on the idea, but I have come to believe that the problem of the nature of time as an “isolated” problem is less important than the relative nature time to space. In other words, I think the more important question that needs to be addressed is, why does the metric tensor that describes the universe have at least one negative eigenvalue, i.e. why is the sign of the time component always opposite to the sign of the spatial components in the metric?

Ken might answer that this is an artifact of our perception. For example, I might say that “normal” geometry, i.e. the Euclidean geometry of everyday life, doesn’t exhibit this feature. Ken might counter that that’s just a result of the fact that we perceive one of the four dimensions differently even though they’re all really the same. But that still leaves the question as to why we perceive that one dimension differently. It clearly is independent of the human mind since other species “perceive” time and time does appear to have some kind of preferred direction while space does not. Either way, the fact of the matter is that the metric tensor that describes the universe that we observe and measure has a negative eigenvalue, regardless of whether the space is flat or curved. We can’t magically force the metric to have only positive eigenvalues. Science is about describing what we can reliably measure with a healthy dose of Occam’s Razor thrown in for good measure. The simplest description of the universe’s geometry that matches experiment forces the presence of at least one negative eigenvalue in the metric tensor. Why? That’s the question that needs to be answered.

Progress on the Mach-Zehnder interferometer

Posted in Uncategorized on April 25, 2014 by quantummoxie

It has been an insanely busy 2014 for me. I spent nearly the entire month of March elsewhere, with the APS March Meeting in Denver and then the workshop Information and Interaction that I organized with Dean Rickles which turned out to be a resounding hit (videos will be posted soon — I need to get through the end of the semester first). At any rate, I did find a bit of time to delve into my Mach-Zehnder interferometer in recent weeks and am pleased to report that I have figured out one of the problems I was having. Sometimes it is helpful just to have someone around to bounce ideas off of, and my former student, Eric Holland, who works in superconducting qubits and returned to campus to give a talk, kindly obliged. Of the many problems I was having last year when trying to understand the basic interference pattern, one of the more perplexing was the fact that I seemed to only get an interference pattern for specific sizes of the central square of the interferometer. I am happy to report that this was just a relic of the fact that at certain sizes, the interferometer is more difficult to align. I was able to get a pattern for every size I tried when Eric was here (maybe MZIs only work when someone named Eric Holland is in the room?).

I discussed my general issues with Markus Aspelmeyer over dinner in Denver and he maintained that the classical pattern is a result of the fact that the beam widens as it propagates. Last year, I did the ray tracing for such a spreading beam and, faithfully keeping track of the phases and wavelengths, still couldn’t get the result I expected. I’m going to go back and retry it because Markus seemed fairly confident that this was the explanation. He pointed out that the coherence lengths for the lasers I work with should be very, very long and thus should not be an issue. At any rate, in order to do what I need to do eventually, this all means I will have to figure out how to collimate the beam.

Anyway, Eric and I did figure out that there are vibrational issues affecting the stability of the pattern which means next fall I’m going to have to get some students to develop a damping system for it. But progress has been made! Not bad for a theorist, eh?

Book Review: Beating the Odds: The Life and Times of E.A. Milne

Posted in Uncategorized on February 2, 2014 by quantummoxie

I have been meaning to post this review for quite some time and just haven’t gotten around to it until now. That should in no way reflect how I felt about the book (as you will see if you continue to read this post).

Title: Beating the Odds: The Life and Times of E.A. Milne 

Author: Meg Weston Smith (Foreword by Roger Penrose)

Publisher: Imperial College Press, 2013

Let me begin by saying that I am very privileged to actually know Meg Weston Smith personally. I am forever indebted to her for her kindness and hospitality in welcoming my wife, my then-eighteen-month-old son (now 13 years old!), and me into her home many years ago when I was doing research for my PhD. Over the years she provided numerous bits of information on Milne and his relationship to Eddington that proved to be immensely helpful (not to mention fascinating). E.A. Milne was her father and I know just how long she has been working on this project which was started as a way to learn more about him (he died at the age of 54 when Meg was just 17).

At points poignant and at points heart-breaking, but wholly inspirational, the story of Edward Arthur Milne is one of striking success in the face of seemingly insurmountable odds. Twice widowed before the age of 50 (both times to suicide) and hampered by progressive Parkinsonism as a result of contracting encephalitis lethargica during the outbreak that swept around the world in the early 1920s, he persevered and became one of the giants of 20th century astrophysics, cosmology, and mathematics. While known primarily for his work in astrophysics, he made seminal contributions to ballistics during both World Wars, during the second of which his house was destroyed by a German V-1 launched in retaliation for the D-Day invasions. I suppose there is some dark irony in that fact.

Also less-well-known is the fact that Milne was the first to suggest that light signals be used to standardize time measurements. This, of course, is exactly how the SI unit of time – the second – is presently defined. The present definition is not quite what Milne had envisioned. In fact the present definition of the meter is actually closer to his original idea. Nevertheless, special relativity implies that the second could easily be defined in similar terms. Tom Moore has an excellent derivation of the Minkowski metric using light clocks in his book Six Ideas That Shaped Physics, Unit R: The Laws of Physics are Frame-independent. Milne originally received a great deal of criticism for this idea. Max Born referred to Milne’s light signals (used to measure time) as “weird inventions.” Of course, Milne got the last laugh.

Part of Milne’s problem was that he held some unconventional views that were unfortunately seized upon by Herbert Dingle who never missed an opportunity to publicly ridicule them. It may seem strange in retrospect that Dingle, who strongly opposed special relativity because it was grounded in theory and not experiment (though has nevertheless been repeatedly experimentally verified), should actually be taken seriously, but one must realize that these were very early days in modern physics, before the cosmic microwave background radiation was discovered, before dark matter and dark energy, before string theory and loop quantum gravity. Like Eddington, with whom Milne had a close friendship but strong professional disagreement, it may be that Milne was ahead of his time. Some of Milne’s ideas are enjoying a bit of a renaissance, though in somewhat altered form. In my own work on CPT-symmetry I have begun to wonder if there might actually be more than one sense of time, as Milne had suggested.

It should be said that Milne was, first and foremost, a mathematician and was thus very strongly grounded in theory as driven by mathematics. This also squarely put him in the camp of what I like to call the “deductivists” whose standard-bearer at that time was Eddington. The deductivists put a priority on theoretical and mathematical derivations. Einstein himself was essentially a deductivist in that he famously said, in response to a question posed to him when Eddington’s results turned out to match his theory, that any experiment that disagreed with relativity would simply be wrong. Today, Milne, Eddington, and Einstein would not actually be considered all that radical. Max Tegmark, for instance, firmly believes that the universe is entirely mathematical. I would think that Milne would find something of a kindred spirit in Max.

At any rate, all of these thoughts were prompted by my (relatively) recent reading of Meg’s wonderful book. I highly recommend it to anyone with an interest in the history of science or even just in history itself. It is not technical and so does not require any mathematics background to read. The book itself is deeply personal and yet wholly accessible. It is a terrific homage to a father who sincerely tried his best to provide for his family and to serve his country, college (Wadham), and students, all while contributing a wealth of ground-breaking and enduring ideas to applied mathematics.

Science and Religion

Posted in Uncategorized on January 24, 2014 by quantummoxie

I’m wading into shaky waters by posting this, but it arose out of several conversations I have had recently. In one, when discussing global warming with a skeptic, I found myself having to defend science against charges that it is a religion. In the second, when discussing randomness (actually, the recent death of John Dobson which then led to other discussions), I was confronted with the odd claim that, unlike other religions that are based on mere faith, Christianity is an evidentiary faith. The latter is an interesting tactic; it would seem that in an attempt to combat science (or certain tenets of science), some people have taken to co-opting the language of science (while, whether they realize it or not, changing the meaning of that language). Clearly, “evidential” and “faith” are antonymic words. According to Webster’s Ninth New Collegiate Dictionary (which I was required to use for a deductive logic class in college because it contains word origins), evidence is something that furnishes proof. Conversely, Webster’s defines faith as a firm belief in something for which there is no proof (emphasis mine).

Setting aside this linguistic pretzel, one of the claims in the discussion that grew out of Dobson’s death was actually a continuation of another one I had had with the same group of individuals (some believers, some not) last year: whether there is true randomness in the universe. One of the people in the discussion argued that since God knows the outcome of every single process and since God created the universe, there thus can be no random processes in the universe. (He then went on to say he does not reject any type of science despite having rejected evolution as it applies to humans in at least one discussion.)

My response to that is this: I have no problem with anyone believing that God or the Divine or whatever knows all and for him/her/it/them there is no randomness. The fact of the matter is that none of us as human beings can and will ever achieve the status of God and thus be able to know everything. We live in the here and now, in an empirical world that, for whatever the reason (God, randomness, etc.), is possessed of certain patterns that are somehow comprehensible to us via deductive and inductive logic. Science is concerned with the here and now. It is concerned with what we can know. Legitimate science is always supported by evidence which means empirical data and the rules of formal logic. Religion didn’t discover insulin and penicillin. It didn’t invent automobiles and televisions. If you want to believe that God has helped guide these discoveries, I have absolutely no problem with that. But that is a question that is beyond science.

Now, by saying that there is no randomness or chance because God knows all (and therefore rejecting, for example, evolution), one either is suggesting that we can achieve God-like status or that a mere faith in God is all we need to understand seemingly random processes. But a faith in God isn’t going to suddenly allow someone to predict the outcomes of die rolls in a game of craps or to suddenly understand how to get around the uncertainty principle. Science makes incredibly accurate predictions and models as it is. Nevertheless, there are God-fearing scientists out there (e.g. John Polkinghorne). But it’s not like they have been any more successful than anyone else at figuring out how to predict games of craps or getting around the uncertainty principle.

And that is precisely the point. The aim of science is to make sense of the real world in which we live, to understand (or “model” as best we can) how it works, and, to some extent, improve our lives in this real world since, for better or for worse, it is the one we inhabit at this moment. Whatever individual scientists may say, science really says nothing about actual reality (at least in the philosophical sense). But that was never its point. It’s purpose is to comprehend the world around us, the world we inhabit right here, right now.

Science is a profoundly human endeavor. Certainly its results are, to some extent, objective in the sense that a scientist from China and a scientist from France can agree on the result of an experiment even if they don’t speak the same verbal language (mathematics is, in some sense, the language of science, and mathematics is universal). But science is still human. It describes the state of our knowledge about the world around us and, sometimes, the limitations of that knowledge itself. If someone wants to believe that everything we perceive every day of our lives is an illusion, that’s fine. Maybe it is, maybe it isn’t. But that doesn’t help humanity make practical advances to better our lives and the lives of others. It doesn’t help us make accurate predictions about anything. Like it or not, we rely on certain things being consistent in our lives — the Sun coming up every morning, stuff not suddenly “falling” up, the fact that you won’t wake up tomorrow morning on Mars. Science extends the scope of reliability. When science talks about randomness, it has something very specific in mind that must, in some sense, produce reliably predictable results because that is what science does. Period.

And that is the crux of my response to the person who made the accusation that science was a religion (intimating in his accusation that religion is inherently a lot of hogwash, an idea David Albert nicely put to rest two years ago in his review of Lawrence Krauss’ book). Science produces reliably predictable results that are self-consistent and follow the basic rules of formal logic. If it’s a religion, then it’s the only one that can make future predictions about physical systems with anything more than 50% accuracy.

So people can believe what they want about how the world really works, but don’t tell me, when something that is quantifiably verifiable, i.e. offers up results that can be agreed upon across cultures and across times, that those same methods are wrong. My response will be: can you give me a method that is better and that I — and humanity itself — can rely on to be consistently correct and predictable every single time? If religion were the answer to that question, science never would have arisen to begin with.

FQXi live blogging

Posted in Uncategorized on January 8, 2014 by quantummoxie

I’ve got some live blogging happening over at the FQXi site from the FQXi conference. One post is up and the next will be coming out today sometime.

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