I have been fascinated by quantum weirdness ever since I first learned of it from my high school chemistry teacher, Mr. Quest (his real name), in about 1971. The story of quantum weirdness begins in 1801, when Thomas Young did the famous double slit experiment (discussed below) and interpreted it to mean that light behaves like waves. This was a big surprise at the time, since Sir Isaac Newton had shown that light behaves like particles. The physics of the 1800’s firmly established the wave nature of light. Then in the early 1900’s, Planck and Einstein re-established the particle nature of light. It turned out Isaac Newton and Thomas Young were both right-ish: light acts sometimes like particles and sometimes like waves, and both descriptions are needed to fully captures its behavior.
With the development of quantum mechanics in the 1920’s, things got much weirder. Unlike most theories in physics, quantum mechanics did not start with a picture of how the universe works, and then grow a mathematical formalism to make testable predictions based on that picture. For quirky historical reasons, quantum mechanics provides a mathematical formalism without an underlying explanation. It has been tested experimentally in as many ways as physicists can dream up and carry out and has proven to be at least as accurate as our best measurements, which over time have become astonishingly precise.
We are left with a laundry list of questions about what the theory means. What do the wave equations and the matrix elements actually represent? Do they reside in this universe or in some abstract mathematical space? Why does it permit and even demand complex numbers with both real and imaginary parts? How can the mutually exclusive particle-like and wave-like behaviors described by the equations and observed in experiments be reconciled? Why are predictions only probabilistic? How can identical conditions produce varying results? How and why does the wave function change abruptly and discontinuously when a measurement is made? How can separated but entangled parts be in instantaneous communication when physically distant from each other? What is the mechanism behind this nonlocality?
If you don’t understand half of that list of questions, don’t worry about it. The point is that physicists whose job it is to understand this stuff have been arguing for almost a century about the meaning behind the most accurate and successful theory in all of physics.
The double slit experiment works like this. If you shine light at a pair of closely spaced slits in an opaque material, you get a pattern of light on the wall behind the slits. If light were made of tiny pellets, you would expect two bands of light on the wall where the slits allowed pellets through. Instead, you get a series of light and dark bands. Each slit acts like a source of light waves. Where the peaks from one slit align with the peaks from the other, you get a bright band. Where the peaks from one align with the valleys from the other, you get a dark band. Multiple light and dark bands are strong evidence that light behaves as waves.
So far so good. Now dim the original light source to the point where you’re shooting photons one at a time and let them accumulate on the wall. You still get multiple bands, but now photons can’t be interacting with other photons. Each photon goes through both slits, interferes with itself, and over time many photons build up multiple bands. If you add a detector to determine which slit a photon went through, then it goes through one slit or the other. But if you don’t make it choose a slit, it goes through both. Very weird.
Incidentally, this strange behavior is not limited to massless photons. Electrons and even whole molecules will also form interference patterns after passing through double slits.
John Cramer [The Quantum Handshake, p. 7] describes the bizarre behavior of the quantum world with an analogy (which he formatted like a quote but with no citation):
As a fanciful example, consider the following analogy. Suppose that I were in Boston, and I went down to the docks and threw a beer bottle into the waters of Boston Harbor. The bottle disappeared, producing waves that spread out across the Atlantic Ocean in all directions from the entry point. Some of these waves traveled toward England and France and Spain and Western Africa and Eastern South America. In particular, some waves from the bottle traveled over the North Sea to the harbor of Copenhagen. Then the waves abruptly disappeared, and my beer bottle suddenly appeared in its original form on the Copenhagen dock. At the instant of its appearance, the waves traveling elsewhere around the Atlantic abruptly disappeared too [according to the Copenhagen interpretation]. In this scenario, my beer bottle has moved quantum mechanically from Boston to Copenhagen.
And it gets even weirder and more inexplicable than that. “A violation of realism”: The future can change the past (quoted extensively below by permission) provides an excellent summary of the strange but experimentally verified predictions of quantum mechanics, leading up to a grand finale based on this scientific paper. Here’s the setup: there is a way to generate pairs of entangled photons that fly off in different (predictable) directions and are guaranteed to be polarized in opposite directions. The opposite-polarization guarantee is what we mean by “entangled”: if we measure the polarization direction of one, we automatically know the polarization direction of the other. There is also a way to sort photons (or light waves generally) by polarization direction, called a polarization beam splitter. We can arrange things so that one of our two entangled photons goes through a polarization beam splitter, and then through one slit if it’s polarized one way or through the other slit if it’s polarized the other way. The beam splitter doesn’t count as a measurement, because it relies solely on wave properties of transmission or reflection. Now, back to our two entangled photons with opposite polarization.
Let’s send one of these two photons through our polarization beamsplitter and double slit. We’ll call that photon Bert. Let’s let the other photon go somewhere else and call that one Ernie.
The first time we try this, we’ll let everything be. No measurements. Our Bert photons go through the beamsplitter and double slit one at a time, and we don’t measure them in any way except marking where they hit the wall. We don’t do anything at all with the Ernie photons, so it’s like they don’t even exist. If we keep doing that, as before, we get lots of stripes — an interference pattern — on that back wall that the Bert photons keep hitting. That’s because we didn’t know which way the Bert photons were polarized when they went through the slits, so they didn’t have to choose where they were until they hit the wall.
But now, what if we DO measure each Ernie photon’s polarization? Then we’ll know which way each Bert photon must have gone, without even measuring it. If we do that, this time we DON’T get an interference pattern. We get two stripes! That’s because we gained information about the Bert photons, thanks to Ernie, even though we didn’t touch the Bert photons in any way. We found out their polarizations, and therefore which way they went, just as we did when we put a detector by each slit.
That’s already pretty freakin’ weird, but now we’ve arrived at the main event. And that takes us to the Canary Islands!
An experiment was done using two locations in the Canary Islands, 89 miles (144 km) apart, on moonless nights.
And this sets the stage for the big experiment. We can still put each Bert photon through our little beamsplitter and double slit right here on La Palma, while each counterpart Ernie photon flies all the way over to Tenerife, 90 miles away, which takes about half a millisecond. That means we can’t measure Ernie’s polarization until well after Bert has already hit the back wall and “picked” a spot.
But let’s go one further. We won’t even DECIDE whether we want to measure Ernie’s polarization until AFTER Bert has already hit the wall. We’ll let a computer flip a coin. If it’s heads, we’ll measure Ernie’s polarization, but if it’s tails, we won’t. But the computer won’t flip the coin until Bert’s fate is decided, until he’s already hit the wall and therefore already had to decide where to focus himself.
Let’s do this a few thousand times, and we’ll look at the pattern our Bert photons make when we do measure Ernie and when we don’t. For example, let’s say we measured Ernie photons on tries #2, #5, #6, #8, etc. We can look at Bert photons #2, #5, #6, #8, etc. and see what pattern they end up making. Then, separately, we can look at the other Bert photons (#1, #3, #4, #7, etc.), and see what pattern they make.
But remember — each Bert photon had already hit the wall long before we even decided whether to measure the polarization of its matching Ernie photon or not.
So what happens?
When we look at Bert’s pattern for all the times we did measure Ernie (and therefore found out which way Bert went), we get two big fat stripes. No interference. And that’s because we gained information about them, via Ernie, in the future. When those Bert photons hit the wall, they couldn’t have “known” that we were going to measure Ernie, because we hadn’t even decided yet whether we were going to measure Ernie.
But when we didn’t measure Ernie, Bert gave us an interference pattern.
We would have gotten an interference pattern for ALL the Bert photons if we hadn’t measured any of the Ernie photons, but for some of them we did measure Ernie, and for those, AND ONLY THOSE, the interference pattern changed into a two-stripe pattern. Because of something that happened in the future.
I don’t mean to keep repeating this, but our measurement of Ernie changed what Bert had already done in the past, from the future.
You’re still waiting for the part about understanding quantum weirdness, right? It’s coming, I promise. I’m done setting up the weirdness to be understood. The rest is a piece of cake — just wave the right conceptual magic wand.
But first, back to my high school chemistry teacher. Mr. Quest introduced his students to the Copenhagen Interpretation of quantum mechanics, which goes more or less like this:
- The wave function of quantum mechanics is a mathematical representation of an observer’s knowledge of a quantum mechanical system, and changes when the knowledge changes. The wave function does not represent a physical object.
- When we gain information about the location or state of a quantum, the wave function disappears instantaneously everywhere due to the change in our knowledge.
- One should focus on the observable quantities of a system and avoid asking questions about aspects that are not subject to measurement. If you want to know what quantum theory has to say, “shut up and calculate.” (This meme is attributed to Prof. N. David Mermin of Cornell University, in a 1989 Physics Today article critical of the Copenhagen Interpretation.)
- The quantum mechanical description of nature is probabilistic and random. Identical conditions can produce varying outcomes.
- It is postulated, and found experimentally, that the probability of an event is the absolute square of the amplitude of the wave function related to it. (This is called the Born Rule, after Max Born.)
As I recall, Mr. Quest mentioned that Albert Einstein never bought this viewpoint, but that’s an argument Einstein didn’t win. I got the impression Mr. Quest was on Einstein’s side. In any case, he certainly didn’t convince me that this explains how the universe operates. The first point above is particularly troublesome, leading to endless fruitless philosophical discussions. What exactly is an observer? Does it have to be a sapient ape? Why isn’t Schroedinger’s cat an observer of its own fate? If we define a physicist to be part of a quantum mechanical system, does he cease to be an observer and enter into a superposition of possible states? Does knowledge of a quantum mechanical system have to be actual, or do we include potential knowledge? And so on.
Besides, when an electron in its particle aspect interacts with a photon in its particle aspect, say by absorbing or emitting it, don’t the electron and the photon necessarily observe each other? Their interaction gives them both properties such as location, momentum, and so on, defined within the limits imposed by the Heisenberg Uncertainty Principle. In other words, it meets all the requirements of a quantum observation, aside from an excuse for making the wave function disappear instantaneously everywhere.
No, I can’t believe the Copenhagen interpretation represents what the universe is up to behind the scenes. The part about mathematically representing the knowledge of a real or hypothetical observer is ridiculous, and the part about not asking awkward questions is an embarrassment. That’s no way to run a universe.
I had a good friend in Junior High School, with whom I am still in occasional communication by email. We share a number of interests, including quantum weirdness. I will refer to him here by his initials, WWIII. In the fall of 2012, he developed a breathless enthusiasm for the writings of David Deutsch and his many-worlds interpretation of quantum mechanics. In this interpretation, everything that can possibly happen, does happen in some universe. All possible outcomes are realized, and time is perpetually branching into an uncountably infinite number of universes to accommodate them all. This is intended to resolve some paradoxes of quantum theory and eliminate the need for wave functions to instantaneously collapse. WWIII had a copy of Deutsch’s first book (The Fabric of Reality) shipped to me, and urged me to at least read the first two chapters. I dutifully did so. Here’s part of my response to my friend WWIII:
My first reaction was, I'm not convinced… The many universes theory avoids having to even talk about wave/particle duality and what Einstein called "spooky action at a distance." But the price is very high -- instead, every photon (etc.) in the universe has to follow every path it could possibly follow, all but one of them in new-born universes other than the one we inhabit, spawning a near-infinite thicket of universes in every direction every zeptosecond. And somehow the universe we experience is randomly selected from among that continuous dense fog of possibilities and shadow-particles. It seems to me a very brute-force, profligate, inelegant approach, uglier than the problem it tries to avoid.
WWIII’s response was polite enough, but I understood it to really mean something like “Okay Mr. Smartypants, then how do YOU think the universe works?” I took up the challenge by reading what Wikipedia had to say about Interpretations of quantum mechanics. It lists and compares more than a dozen. I read and thought, followed links and read more. To my way of thinking there was a clear winner: John Cramer’s Transactional Interpretation. When it was published in 2016, I bought Cramer’s book, The Quantum Handshake, and (in 2016 after I retired from my mechanical engineering job) read it cover to cover. It is not an easy read, and it uses some mathematical notation to make its meaning clear to physicists, but I was able to slog through it with good comprehension, and I thought it time and effort well spent. A handy summary by Cramer in the form of presentation slides can be found here.
The Transactional Interpretation of Quantum Mechanics (TIQM) goes like this. The quantum wave function actually has two solutions: one where waves travel forward through time, and one where waves travel backward, arriving before they set out. Physics students are generally taught to discard the time-reversed solution as non-physical and in violation of causality. But now that we have experiments that appear to violate causality, perhaps we can put it to explanatory use.
Consider our light source, which at the quantum level might be a bound electron in an excited state that wants to emit a photon’s worth of light. This electron is the emitter, looking for an absorber. Think of the quantum wave function as an offer to transmit a quantum. This “offer wave” spreads out, attenuating as it spreads, encountering various potential absorbers after various lengths of time. The potential absorbers respond by sending time-reversed waves, called “confirmation waves” but better thought of as offers to receive a photon. The confirmation waves all arrive at the emitter at the moment the offer wave was sent out, thanks to time reversal. One of these is accepted as the successful bidder. The offer wave and the winning confirmation wave form a standing wave and reinforce each other “until the strength of the space-time standing wave that thus develops is sufficient in strength to transfer a quantum of energy and momentum from the emitter to the absorber, completing the transaction.” [Cramer, p. 63].
In other words, the emitter sends out an offer of a photon, and the absorber sends a mirror-image (technically, complex conjugate) offer to take delivery, back the timeline. The probability of a deal being struck is the amplitude of the offer wave times the amplitude of the confirmation wave, as found experimentally. This is equivalent to the squared amplitude postulated by the Born Rule, which no longer needs to be a postulate since this result arises naturally from the interpretation.
From the point of view of the emitter, all possible absorbers are instantly visible, and it can choose one (or none) of them. And there is no longer any need for the quantum wave function to disappear instantly everywhere once a particle is transmitted. The offer wave can continue to propagate through spacetime, and potential absorbers can keep sending back confirmation waves to no effect. The universe must be just packed with unrequited quantum offers.
One of the weaknesses of the Copenhagen Interpretation is the way it answers this question: at what point does the universe commit to a quantum-scale event? It answers in a way that threatens to leave poor Mr. Schroedinger’s cat in a most unsatisfactory superposition of alive and not-alive states. The Transactional Interpretation gives a much cleaner (though chronologically convoluted) answer: the commitment to emit a quantum and the commitment to absorb a quantum are tightly coupled, and commitment occurs throughout the time interval between the two.
The Transactional Interpretation changes nothing in the mathematics of quantum mechanics, except to add back a piece that has long been discarded and ignored. It’s just a different way to tell the story of what the math means. It may be necessary to add one rule, which Cramer calls “hierarchy”, stating that confirmation offers coming from the shortest spacetime distances are considered first. That way, once an offer is accepted and a quantum is transmitted, the subsequent evolution of the universe can unambiguously include the effects of relocating a quantum. I think the jury is still out on the need for and precise formulation of this hierarchy rule.
The way I see it, the universe is serious about enforcing its conservation laws. Quanta are the currency in which it does its accounting, and quantum mechanics is the enforcement mechanism. Relocating even a single quantum requires a delivery receipt and prior approval, to make sure that all conserved quantities and characteristics are in fact conserved.
And while I’m at it, I should note that the Transactional Interpretation changes the way I think of the quantum-scale universe in another respect. We tend to think of the quantum world as being made up of tiny pellets, but particles are ephemeral and mostly illusory. An electron bound to an atomic nucleus is not a little charged pellet whizzing around, it is a standing wave that encodes the probability of finding a tiny pellet if we look for one with fine enough tools. In this case the “offer wave” is not so much an offer to go somewhere as an offer to be somewhere. Think of particles as nodes in a space-time network, connected by the straight (technically geodesic) lines through space and time where offer waves and confirmation waves reinforce each other. A “quantum transaction” is not the emission or absorption of a quantum, it is the emission and the absorption and most of all the wave functions that join and coordinate them through space and time. That’s where the stuff of the universe resides, mostly or perhaps entirely. If it turns out that space and time are emergent properties rather than fundamental, surely the network of “quantum transactions”, representing the quantum-by-quantum evolution of the universe, must be what they emerge from.
Now, let’s return to the Canary Islands, and see how that mind-blowing experiment looks through the Transactional Interpretation. The narrative necessarily zig-zags back and forth in time. Bear with me.
We give our light source (call it Big Bird) a quick zap, and it starts sending out a stream of quantum wave-function waves offering a pair of polarization-entangled photons. Part of the wave passes through our beam splitter and both of our double slits, interacts with itself in a way that gives it spatially distributed amplitude ripples, and then smacks into an opaque screen, where it interacts with a zillion spots that could potentially absorb a photon (call all those spots Bert). They send confirmation waves back in time, telling Big Bird, “Pick me! Pick me!” (Actually, the confirmation wave includes a full dating profile, but there’s no need to clutter this account with that quite yet.) But the offer is for two photons, the confirmation wave offers are for one photon, and this is an all-or-nothing deal, so the conservation laws are not satisfied, and nothing happens “right away”. We’ll leave Bert in limbo here, and get back to him later. (And earlier.)
Meanwhile, another part of the offer wave passes through a hole in the wall of our lab, and heads across the ocean to our other lab 89 miles away. Almost half a million nanoseconds later, it gets there and interacts with one of two detectors, depending on a virtual coin flip while it was traveling. If it’s Detector A, a bunch of confirmation waves go back through time and space (from Ernie, say) to Big Bird, saying “Pick me! I can take a photon, and I don’t care how it’s polarized.” Now, by which I mean back at time zero, Big Bird has confirmation waves that meet all the conservation-law requirements. Then Bert comes out of limbo, a pair of photons (with no particular polarization) are launched, and the transfer is consummated with Bert’s position consistent with a diffraction pattern.
Or, if the coin came up the other way, the offer wave interacts with Detector B, and Ernie sends back confirmation waves that say “Pick me! I can take a photon, but I need it to have a well-defined polarization.” Now Big Bird reviews the dating profiles provided by the Bert candidates, which includes information about how each would respond to a horizontally polarized photon, a vertically polarized photon, a circularly polarized photon, a photon of undesignated polarization, and so on. The confirmation wave also provides feedback on any physicists’ tricks along the route.
So this time Big Bird picks a specific Bert and a specific Ernie consistent with photons of defined polarization. The bargain is struck with quantum-wave handshakes, and consummated with the transfer of photons. Bert’s photon lands in one of the two areas where polarized photons are most likely to land - that is to say, one of the potential Berts in those two areas is selected as the winning bidder.
And what do the photons think of all this? They literally don’t have time to think! Einstein taught us that the experience of time slows down as speeds increase, going to zero at the speed of light. So photons don’t experience time. For them, being emitted by Big Bird and being absorbed by Bert or Ernie are simultaneous. But that’s relativity weirdness, not quantum weirdness.
So when does the universe commit to the transfer of two quanta? Not until all of the emission and absorption end points and conditions are known. Reality gets negotiated over a time interval, and then time can run smoothly forward from start to predetermined finish of a quantum transaction.
I wouldn’t have guessed that time works exactly this way, but I never really understood how time works anyhow. And who am I to argue with the universe about it?
And what about the causality disaster that physicists expected time-reversed waves to cause? Cramer devotes a significant portion of his book to thought experiments aimed at using time-reversed waves to transmit information faster than light (or time). He comes up empty -- there appears to be no way to accomplish it. By which we are all greatly relieved. Apparently, time reversal can only be used to enforce laws, not to break them. The universe is very clever that way.
Go outside on a clear dark night and look at the stars. The middle star of Orion’s belt, for example, is 1340 light-years away. Or find the Andromeda galaxy if you can, about 2.5 million light-years away. In one sense, the light you see has been on its way to you for all those years. In another sense, the light detectors in your eyes detected offer waves and sent confirmation waves back through all those years. Some of the offers turned out to have expired, but others were still valid, and your retina struck a deal with some bit of hot stellar material in the distant past to receive a photon. The universe just delivered on that deal. From your retina’s perspective, it just now solicited photons and the response was immediate. From the point of view of the photons, the star might as well have hand-delivered them to your retina — for them the trip took no time at all. Even with your eyes closed, starlight faintly illuminates your skin, thanks to a cross-time quantum dialogue. And that is how you are connected to distant parts of the cosmos.
And that’s how I understand quantum weirdness.