I got to know Charles “Chip” Sebens back in 2012, when he emailed to ask if he could spend the summer at Caltech. Chip is a graduate student in the philosophy department at the University of Michigan, and like many philosophers of physics, knows the technical background behind relativity and quantum mechanics very well. Chip had funding from NSF, and I like talking to philosophers, so I said why not?
We had an extremely productive summer, focusing on our different stances toward quantum mechanics. At the time I was a casual adherent of the Everett (many-worlds) formulation, but had never thought about it carefully. Chip was skeptical, in particular because he thought there were good reasons to believe that EQM should predict equal probabilities for being on any branch of the wave function, rather than the amplitude-squared probabilities of the real-world Born Rule. Fortunately, I won, although the reason I won was mostly because Chip figured out what was going on. We ended up writing a paper explaining why the Born Rule naturally emerges from EQM under some simple assumptions. Now I have graduated from being a casual adherent to a slightly more serious one.
But that doesn’t mean Everett is right, and it’s worth looking at other formulations. Chip was good enough to accept my request that he write a guest blog post about another approach that’s been in the news lately: a “Newtonian” or “Many-Interacting-Worlds” formulation of quantum mechanics, which he has helped to pioneer.
In Newtonian physics objects always have definite locations. They are never in two places at once. To determine how an object will move one simply needs to add up the various forces acting on it and from these calculate the object’s acceleration. This framework is generally taken to be inadequate for explaining the quantum behavior of subatomic particles like electrons and protons. We are told that quantum theory requires us to revise this classical picture of the world, but what picture of reality is supposed to take its place is unclear. There is little consensus on many foundational questions: Is quantum randomness fundamental or a result of our ignorance? Do electrons have well-defined properties before measurement? Is the Schrödinger equation always obeyed? Are there parallel universes?
Some of us feel that the theory is understood well enough to be getting on with. Even though we might not know what electrons are up to when no one is looking, we know how to apply the theory to make predictions for the results of experiments. Much progress has been made―observe the wonder of the standard model―without answering these foundational questions. Perhaps one day with insight gained from new physics we can return to these basic questions. I will call those with such a mindset the doers. Richard Feynman was a doer:
“It will be difficult. But the difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, ‘But how can it be like that?’ which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. I will not describe it in terms of an analogy with something familiar; I will simply describe it. … I think I can safely say that nobody understands quantum mechanics. … Do not keep saying to yourself, if you can possibly avoid it, ‘But how can it be like that?’ because you will get ‘down the drain’, into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.”
-Feynman, The Character of Physical Law (chapter 6, pg. 129)
In contrast to the doers, there are the dreamers. Dreamers, although they may often use the theory without worrying about its foundations, are unsatisfied with standard presentations of quantum mechanics. They want to know “how it can be like that” and have offered a variety of alternative ways of filling in the details. Doers denigrate the dreamers for being unproductive, getting lost “down the drain.” Dreamers criticize the doers for giving up on one of the central goals of physics, understanding nature, to focus exclusively on another, controlling it. But even by the lights of the doer’s primary mission―being able to make accurate predictions for a wide variety of experiments―there are reasons to dream:
“Suppose you have two theories, A and B, which look completely different psychologically, with different ideas in them and so on, but that all consequences that are computed from each are exactly the same, and both agree with experiment. … how are we going to decide which one is right? There is no way by science, because they both agree with experiment to the same extent. … However, for psychological reasons, in order to guess new theories, these two things may be very far from equivalent, because one gives a man different ideas from the other. By putting the theory in a certain kind of framework you get an idea of what to change. … Therefore psychologically we must keep all the theories in our heads, and every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics.”
-Feynman, The Character of Physical Law (chapter 7, pg. 168)
In the spirit of finding alternative versions of quantum mechanics―whether they agree exactly or only approximately on experimental consequences―let me describe an exciting new option which has recently been proposed by Hall, Deckert, and Wiseman (in Physical Review X) and myself (forthcoming in Philosophy of Science), receiving media attention in: Nature, New Scientist, Cosmos, Huffington Post, Huffington Post Blog, FQXi podcast… Somewhat similar ideas have been put forward by Böstrom, Schiff and Poirier, and Tipler. The new approach seeks to take seriously quantum theory’s hydrodynamic formulation which was developed by Erwin Madelung in the 1920s. Although the proposal is distinct from the many-worlds interpretation, it also involves the postulation of parallel universes. The proposed multiverse picture is not the quantum mechanics of college textbooks, but just because the theory looks so “completely different psychologically” it might aid the development of new physics or new calculational techniques (even if this radical picture of reality ultimately turns out to be incorrect).
Let’s begin with an entirely reasonable question a dreamer might ask about quantum mechanics.
“I understand water waves and sound waves. These waves are made of particles. A sound wave is a compression wave that results from particles of air bunching up in certain regions and vacating other. Waves play a central role in quantum mechanics. Is it possible to understand these waves as being made of some things?”
There are a variety of reasons to think the answer is no, but they can be overcome. In quantum mechanics, the state of a system is described by a wave function Ψ. Consider a single particle in the famous double-slit experiment. In this experiment the one particle initially passes through both slits (in its quantum way) and then at the end is observed hitting somewhere on a screen. The state of the particle is described by a wave function which assigns a complex number to each point in space at each time. The wave function is initially centered on the two slits. Then, as the particle approaches the detection screen, an interference pattern emerges; the particle behaves like a wave.
There’s a problem with thinking of the wave as made of something: the wave function assigns strange complex numbers to points in space instead of familiar real numbers. This can be resolved by focusing on |Ψ|2, the squared amplitude of the wave function, which is always a positive real number.
We normally think of |Ψ|2 as giving the probability of finding the particle somewhere. But, to entertain the dreamer’s idea about quantum waves, let’s instead think of |Ψ|2 as giving a density of particles. Whereas figure 2 is normally interpreted as showing the evolution of the probability distribution for a single particle, instead understand it as showing the distribution of a large number of particles: initially bunched up at the two slits and later spread out in bands at the detector (figure 3). Although I won’t go into the details here, we can actually understand the way that wave changes in time as resulting from interactions between these particles, from the particles pushing each other around. The Schrödinger equation, which is normally used to describe the way the wave function changes, is then viewed as consequence of this interaction.
In solving the problem about complex numbers, we’ve created two new problems: How can there really be a large number of particles if we only ever see one show up on the detector at the end? If |Ψ|2 is now telling us about densities and not probabilities, what does it have to do with probabilities?
Removing a simplification in the standard story will help. Instead of focusing on the wave function of a single particle, let’s consider all particles at once. To describe the state of a collection of particles it turns out we can’t just give each particle its own wave function. This would miss out on an important feature of quantum mechanics: entanglement. The state of one particle may be inextricably linked to the state of another. Instead of having a wave function for each particle, a single universal wave function describes the collection of particles.
The universal wave function takes as input a position for each particle as well as the time. The position of a single particle is given by a point in familiar three dimensional space. The positions of all particles can be given by a single point in a very high dimensional space, configuration space: the first three dimensions of configuration space give the position of particle 1, the next three give the position of particle 2, etc. The universal wave function Ψ assigns a complex number to each point of configuration space at each time. |Ψ|2 then assigns a positive real number to each point of configuration space (at each time). Can we understand this as a density of some things?
A single point in configuration space specifies the locations of all particles, a way all things might be arranged, a way the world might be. If there is only one world, then only one point in configuration space is special: it accurately captures where all the particles are. If there are many worlds, then many points in configuration space are special: each accurately captures where the particles are in some world. We could describe how densely packed these special points are, which regions of configuration space contain many worlds and which regions contain few. We can understand |Ψ|2 as giving the density of worlds in configuration space. This might seem radical, but it is the natural extension of the answer to the dreamer’s question depicted in figure 3.
Now that we have moved to a theory with many worlds, the first problem above can be answered: The reason that we only see one particle hit the detector in the double-slit experiment is that only one of the particles in figure 3 is in our world. When the particles hit the detection screen at the end we only see our own. The rest of the particles, though not part of our world, do interact with ours. They are responsible for the swerves in our particle’s trajectory. (Because of this feature, Hall, Deckert, and Wiseman have coined the name “Many Interacting Worlds” for the approach.)
No matter how knowledgeable and observant you are, you cannot know precisely where every single particle in the universe is located. Put another way, you don’t know where our world is located in configuration space. Since the regions of configuration space where |Ψ|2 is large have more worlds in them and more people like you wondering which world they’re in, you should expect to be in a region of configuration space where|Ψ|2 is large. (Aside: this strategy of counting each copy of oneself as equally likely is not so plausible in the old many-worlds interpretation.) Thus the connection between |Ψ|2 and probability is not a fundamental postulate of the theory, but a result of proper reasoning given this picture of reality.
There is of course much more to the story than what’s been said here. One particularly intriguing consequence of the new approach is that the three sentence characterization of Newtonian physics with which this post began is met. In that sense, this theory makes quantum mechanics look like classical physics. For this reason, in my paper I gave the theory the name “Newtonian Quantum Mechanics.”
I never liked Everett’s interpretation, especially since it was explicitly formulated to avoid the “objectionable” involvement of the observer. However, since the “solution” was to avoid collapse of the wave function altogether by making every unobserved outcome actual somewhere else, it seems bizarre to take these quarantined-by-definition outcomes and let them interact…
John D: Another off the wall interpretation which also draws on weak measurement for support is Shan Gao’s – which is interesting…
@trivialknot; True, that is what I hear about the math. I think you math guys use the term “Non-Trivial”. The non-linearity bifurcation of the load vs. deflection making a saw-tooth pattern with the fit points on a log curve would be no fun to try to describe. It would be strange that a natural mechanical classical effect could not be described but I guess and think of others that can not be describe.
There is a video on youtube where Feynman gives an introductory lecture on photons and electrons that is fairly old. In it, he insist that particles are actually particles and not waves. One thing that stroke me as awfully peculiar is that he stated the recent theories developed where consistent with relativistic spacetime. I thought that strange because relativity and quantum mechanics are supposed to be incompatible theories.
Then he went on to describe the calculation with simple Feynman diagrams. He then said that the probability vectors of the particles are actually all of the possible vectors that the particle could have, as if they where reflected from every single point they possibly could have.
I couldn’t help but think that it was ingenious. Why didn’t I think of that? It made me wonder if he had just been leading everyone on that he didn’t understand it, but he just didn’t care to fully explain it to everyone. It had me convinced that was the closest we could get to a final theory to describe particle behavior. It just turns out that the averages of these vectors are the same if you just consider two points as if you consider all of them.
Another strange thing was that he said that model could work to describe all classical behavior. It would work just as well to describe anything else. In a way, it seems like the Standard Model just beats around the bush. It doesn’t describe the circumstances exactly, but it is a model that judges that behavior indirectly.
There was a four part lecture, I think most of the information I mention is in the third and forth lecture. I may have not described it in a correct manner. See for yourself.
https://www.youtube.com/watch?v=eLQ2atfqk2c
Is it forbidden that imaginary numbers can have a physical meaning or be used in such a manner? Why is the complex number aspect of the wave function so difficult for people to physically comprehend? I guess it’s not, but nobody wants to speculate and get reamed for it. You would first have to speculatively declare things about the quantum nature of spacetime. Or likely that there is a relativistic manner to spacetime just as there is for everything else. But I’m just a student. We’ll just have to wait for the pioneers at Waterloo to come through with an answer for us. Until then.
From a quantum gravity perspective the many worlds intepretation is analogous to a multiple interval intepretation.Each phi squared corresponds to an interval.Each interval corresponds to a quantized volume of space-time.So an elementary particle can exist in multiple super imposed spacetimes.
Sean,
With regards to falsifiability and how it doesn’t matter to you as long as your theory is explanatory, I have an unfalsifiable but explanatory theory that explains the cosmological constant: God created the universe in such a way as to have life (and eventually us) evolve. There you go. It’s explanatory, but unfalsifiable.
What do you think?
Modified from a note I wrote the authors:
I have a comment concerning the issue of the constraint on the worlds needed to get the approximation to work. It’s essentially that the phase varies smoothly among neighboring worlds. You wonder if somehow that emerges in the high-N limit, although the theory is not intended to describe quite that limit. Perhaps the easy (too easy?) answer is anthropic. Pick any world not in some smooth-phase patch and nothing is coherent enough to support observers. In this case, since you already need the enormous ensemble of worlds, we’re not cheating by using anthropic post-selection.
My question: You say that you’ll be able to show how non-locality (Bell violations) arises indirectly via the interaction with other worlds, which is local in configuration space but not in ordinary real space. It would be nice to see that argument, but I’ll assume for now it works out. The question then is: what constrains the within-world interaction to be local in real space? That raises all sorts of fuzzy trains of thought, best deferred for now.
Finally, a cultural note. For many years we’ve been aware that Bohm could be taken just as easily in MW form. In fact, the idea of a swarm of world-dots on those trajectories went part way toward solving the probability problem. (You’ve probably heard people quip that Bohm is “Many Worlds in drag.”) The whole issue of the asymmetric dualism with the wave was not helped by that. You guys had the idea to dispense with the wave and let the swarm itself replace its role. (Many Worlds with repulsion, not drag.) I hope you understand it’s a high compliment to say that Huxley’s reaction to Darwin crossed my mind, “How extremely stupid not to have thought of that.”
so from a total layperson… and not very bright one at that (but who does at least understand the Dunning-Krueger effect 🙂 )
would the many worlds explanation in any way account for dark energy, in that when all those other universe dimensions branch off from the one we find ourselves in every time a particle has other paths to take, that somehow reacts with our world?
also, doesn’t the many worlds explanation account for paradoxes in time-travel? for example the going back in time and stepping on a butterfly scenario… forget the butterfly, as soon as you are back in time, and the universe is splitting over and over due all the options for particles, the likelihood of you managing to remain in the exact universe out of all the splitting ones seems impossible regardless, so as soon as you appear back in time (through wormhole or however) you are guaranteed to be in or move into a parallel universe and so anything you do isn’t to “your” universe anyway..?
sorry if all this is really basic from your point of view, I have a feeling I’m working with my interpretations of analogies designed to be understood by people who understand the math anyway 🙂
anyway, keep up the great work Sean! I love your videos, and I love learning more from you 🙂
Logicophilosophicus: thanks, I saw http://fqxi.org/community/forum/topic/1381 and http://arxiv.org/abs/1108.1187 but wasn’t keen.
Imants: if there was something akin to an optical Fourier transform happening when a photon is detected, the dual slit experiment wouldn’t be at all mysterious.
Brt: imaginary numbers are associated with real-world rotation, see things like this.
JohnD:
Re: Your reply to Brt: The use of imaginary numbers in the Schrodinger equation implies just one thing: a coupled two equations. As simple as that. There was a guy from Hong Kong who had a paper (of all places) at arXiv. I should like to locate it, should you want me to do so. [It used to be on my desktop for a while, and I knew, precisely for that reason, that I should forget its details when the time was ripe for me to throw around a note or two.]
Cool. Not in a mood to think a lot right now, but will get back some indefinite time in future.
Bye and best,
–Ajit
I would regard it as an evidence that I have not been taken seriously should I not be downvoted at this blog also for this reply.
[E&OE]
‘EPR program: a local interpretation of QM’
http://arxiv.org/abs/1412.5612
“Wave particle duality is described as the compound system of point particle plus accompanying wave (in the æther). “
@Physics Guy
I know you didn’t mean it seriously, but for me the God hypothesis raises more questions than it explains. One way that I like to put it: an incomprehensible entity of unknown origin and unknown means of operation has no explanatory value (in the absence of any reliable, positive evidence of its existence). Another way: saying, “I don’t know how or why it happened” and saying “God did it” convey the same information. The multiverse hypotheses also raise further questions but have origins and operations which are based on existing theoretical models for empirical observations.
@trivialknot: Thanks for the explanations. They added a lot to what would have otherwise been an interesting but largely incomprehensible (due to lack of fine details) post.
We want to understand everything, I get it.
Our brains evolved to solve problems magnificently in the scale of millimeters to kilometers in 3 spatial dimensions and in seconds to years in linear time. There is no guarantee that the intuition we have evolved will be sufficient to fully understand everything at all scales. I hope it does, but maybe not.
Do the trajectories of individual versions of the electron in the swarm shown in figures 3 and 4 match up with trajectories for electrons in Bohmian mechanics, or are they different?
@JimV
“The multiverse hypotheses also raise further questions but have origins and operations which are based on existing theoretical models for empirical observations.”
Ah…you seem to imply that string theory and/or inflation predict a multiverse. Please explain to me how one may use string theory and/or inflation to calculate our value of the cosmological constant, along with every other parameter for our universe and what equation “decides” how the laws and parameters for each universe are chosen.
Once you successfully do that, you can claim that string theory/inflation are more explanatory than saying that God did it with lifeforms in mind.
Merry Christmas, Sean!
Merry Christmas to everyone!!!
Interesting perspective, Chip. The story could get more intricate once branes, CTCs, and tachyons come into play. The particles usually discussed are brane configurations from the perspective of M-theory, and the general prescription for quantization of branes isn’t yet rigorous. In transforming brane configurations (e.g., extremal black holes), one has more than unitary transformations at her disposal, such as conformal and quasiconformal transformations. At present time, it is possible to assign an entangled qubit interpretation to some of the brane configurations and semi-rigorously study their associated worldvolume structure. You might want to look into this to expand your proposal. See papers by Michael Duff (who was at UMich for quite some time) and his team on arxiv.
Happy Birthday, Jesus! It’s Christmas! Yaaay!
I’m surprised to see “the God hypothesis” even mentioned but it is not true that it isn’t falsifiable! Such a claim is a straw man attack! A more nuanced view of it begins by noting that infinity, omniscience, omnipotence, etc coupled with human experience of such things as value and manifest moral choice have logical consequences. From these something of what would be the “purposes of God” can be derived and some of their implications can be tested. For example knowing what we know about cosmology now we can infer that the following two statements are true:
1. There are likely billions of planets inhabited by morally capable beings
2. There will never be an alien invasion of earth.
#2 is testable.
This is the whole subject of my book “Why This Universe? God, Cosmology, Consciousness, and Free Will” Amazon Kindle 2014. There is much more to “God did it” than that statement.
The state of the art is that *contextuality* characterizes quantum mechanics more than entanglement (there are many good videos at PIRSA). Entanglement can be gotten from a restricted-classical-information theory. How does your interpretation handle contextuality?
Taken from http://arxiv.org/abs/1412.7544
“For my work on the Optimal Argument for the Existence of God and related
philosophical and theological ideas, I am indebted to conversations with David Albert,
Michael Almeida, Luke Barnes, John Barrow, Nicholas Beale, Andrew Briggs,
Peter Bussey, Bernard Carr, Sean Carroll,…”
Sean, do you have anything to explain to us?
By the way thank you trivialknot for taking some time to respond to my comments on Everett. I’m not convinced concerning conservation of energy perhaps because I do not understand where the splitting stops!
“There’s a problem with thinking of the wave as made of something: the wave function assigns strange complex numbers to points in space instead of familiar real numbers. This can be resolved by focusing on |Ψ|2, the squared amplitude of the wave function, which is always a positive real number.”
So in your view, complex-valued wave functions are too “strange” to actually exist, but concocting a panopoly of parallel universes out of a derived probability density function, “which is always a positive real number”, is a simpler, more Occam-worthy alternative? Really, if that’s all you’ve got (beside “Anthropic Landscape” speculations) to justify favoring Star Trek physics over Bohmian Mechanics, then I’ll leave you to your unfalsifiable fantasies.
As an interested layman the Many Worlds hypothesis intrigued me, but as time goes on I have come to detest it and similar ideas. Too much like Deepak Chopra to be brutally honest. I’ll pop back later when there’s some verifiable experimentation to be done.
Hey, the upvoting and downvoting has disappeared. Good. I think it sucks. I mean, science does not progress by popular vote. Instead it progresses because some guy is right, and all the other guys aren’t.