I’m two-thirds through my second Paul Halpern book this month. Earlier I read his book about cosmology, Edge of the Universe: A Voyage to the Cosmic Horizon and Beyond (2012), which was okay. Now I’m reading The Quantum Labyrinth: How Richard Feynman and John Wheeler Revolutionized Time and Reality (2017), which I’m enjoying a bit more. In part because cosmology has changed more since 2012 than quantum physics has since 2017. (Arguably, the latter hasn’t changed much since the 1960s.)
I wrote about Halpern’s book, Einstein’s Dice and Schrödinger’s Cat (2015), last year. As the title implies, it focuses on two great names from physics. Quantum Labyrinth (as its title also implies) also focuses on two great physics names.
I’m not normally much into history; my other interests don’t leave time for it. Rather to my surprise, though, I’ve found the two Halpern books quite engaging (the cosmology one less so). It may be that my long-time interest in quantum physics (since before quarks) makes me more interested in its evolution.
Lately I’ve been studying quantum math, so my interest and focus has been stronger than usual. (Somewhat like baseball or fiction, it offers an escape from what’s become an angry, polarized, very tribal world. On the flip side, theoretical physics, like philosophy, can spiral in on itself and get lost in fantasy and mathematics.)
I don’t know that I’ll review either of the recent books. Halpern is easy and enjoyable to read; I would recommend his books to anyone with an interest in fairly entry-level accounts. (He’s written on diverse topics.) I didn’t write much about his Einstein and Schrödinger book, either. I just don’t have much to say other than “well-done and very accessible.”
As to the matter at hand, a rumination about wavefunction collapse, it’s inspired by the bit in Quantum Labyrinth about the perceived issues with it — specifically with regard to the Schrödinger equation.
That equation describes how a quantum system evolves over time in a strictly continuous and linear fashion. When such a system interacts with another quantum system, this causes an abrupt and non-linear jump (a “collapse”) in the function, and there is (currently) no math describing it.
Some physicists have a major problem with this. For many the problem is so serious that it’s a central motivating factor for embracing the Many Worlds Interpretation of quantum mechanics because of its central tenet: “No Collapse!”
It’s true that exactly what happens during an interaction is currently a gap in our understanding. It’s also true that it seems to involve some of the harder-to-swallow aspects of quantum mechanics (such as randomness and non-locality).
Yet I have always wondered what the big deal is. Despite everything I’ve learned (so far), nothing has illuminated exactly why it’s such a big deal. In contrast, I see many reasons why it’s not.
Firstly, quantum mechanics is, at best, an incomplete theory. It’s even barely possible that it’s a wrong theory, although it’s hard to imagine that a theory with such explanatory and predictive power would be completely wrong.
The most obvious aspect of its incompleteness is its conflict with our theory of gravity, our other “best” theory. That isn’t the only gap, though. There is much we don’t understand about how the quantum world works. (Including to what extent the classical world can be said to be quantum.)
That interpretations of quantum mechanics math even exist demonstrates just how big is the gap in our understanding. None of our other sciences have this issue of having to interpret what apparently successful mathematics means. Usually the math derives from the physical meaning.
So point #1 is that, given these big gaps, worrying that “collapse” is without explanation seems premature. We just don’t understand it, yet.
Secondly, “collapse” involves apparent true randomness and apparent non-locality, two possibly true aspects of reality that some find hard to accept. (I’m not only fine with them, I rather like living in a universe that has them as features.)
Shine a photon at a screen, and nothing we know tells us which electron in the screen will absorb the photon. It appears to be truly random. We have no idea why a given electron will absorb the photon, even after the fact. Knowing which electron still doesn’t tell us why.
All the other electrons might have absorbed the photon, and when they don’t, it seems something — probability, possibility, a pilot wave, something — that was there suddenly, instantly, isn’t. Something non-local seems to occur.
Certainly if one resists randomness or non-locality, “collapse” is a challenge.
Point #2, though, is that many experiments demonstrate this quantum non-locality, and all the experiments demonstrate the random nature of QM. These as yet mysterious, non-intuitive, hard-to-swallow aspects appear experimentally and thus, at least in our reality, have to be taken as factual. As such, their appearance in “collapse” is almost a given, not a problem.
Thirdly, the Schrödinger equation itself is both incomplete and inadequate. That it doesn’t completely describe reality isn’t at all surprising.
The equation isn’t relativistic, so right off the bat it only works in a single frame of reference. (Quantum field theory is the relativistic formulation of quantum mechanics.)
More importantly it doesn’t describe particle creation or annihilation, so it has no way to describe the situation above of an electron absorbing a photon. Neither can it describe the light source that emitted the photon.
Creation and annihilation are “collapse” events, and they lie completely outside the Schrödinger equation’s ability to describe.
On the other hand, something like a particle passing through a Stern-Gerlach device in a spin measurement experiences a sudden change in its wavefunction but isn’t absorbed until it’s somehow detected. (Or not! The silver atoms first used weren’t absorbed by their target (glass), but just built up to a visible clump.)
Finally, I see some analogy between classical equations and quantum ones.
Consider the classical equations that describe a thrown baseball or orbiting planet. They predict where the ball or planet will go. As with the Schrödinger equation, these equations describe the evolution of the object.
What they don’t do is describe the baseball hitting a passing pigeon or the planet being hit by a giant asteroid. Or any of myriad other possibilities.
These possibilities can be described, but only by adding on to the existing math.
So likewise quantum evolutions. The “collapse” is always due to some interaction that is “unexpected” from the point of view of the evolving quantum system.
No doubt this can be described by adding to the existing math. Once we understand what the existing math even means and what’s really going on when it comes to quantum systems.
Bottom line, “collapse” is, I agree, currently unexplained and mysterious, but since QM is also currently unexplained and mysterious, I don’t see what the big deal is.
Stay collapsed, my friends! Go forth and spread beauty and light.