interpretation

Are Parallel Universes Real?

esiegel — Wed, 25 Sep 2013 15:38:54 +0000

Are Parallel Universes Real?

Farnsworth: "There is it. The edge of the Universe!"
Fry: "Far out. So there's an infinite number of parallel Universes?"
Farnsworth: "No, just the two."
Fry: "Oh, well, I'm sure that's enough."
Bender: "I'm sick of parallel Bender lording his cowboy hat over me!" -Futurama

Our existence here in this Universe is something that we know is rare, special, beautiful, and full of wonder.

Image credit: Kelly Montgomery.

Some things happen with amazing regularity and predictability: the occurrence of days-and-nights, the tides, the seasons, the motion of the heavenly bodies, and so much more. The physical laws that govern the Universe are very, very well understood, and that understanding has helped us construct a rather comprehensive view of exactly what our observable Universe consists of, where it came from, and what it looks like.

And yet, it's not an entirely predictive system! Sure, laws like gravity are predictive and deterministic: in other words, if we knew the positions and momenta of all the particles, and had infinite computational power, we could figure out the properties of any particle an arbitrary amount of time into the future. (Or the past, for that matter.)

But then quantum physics came along.

Image credit: © Copyright CSIRO Australia 2004, via http://outreach.atnf.csiro.au/.

And it turns out that knowing the positions and momenta of particles -- even of every particle in the Universe -- isn't enough to determine the properties of that particle in the future. Give me an atom of Uranium, and sure, you know it will decay. But you can't predict when!

You can predict the probability that any particular Uranium nucleus will decay after a given amount of time, and you can -- if you get a large enough sample of Uranium -- predict some properties of the larger ensemble that the individual particles make up. But there is no way, regardless of what you do, to predict what any one particular particle will do. And the same quantum weirdness, or indeterminism, turns up in other system, such as firing a single photon at a screen with multiple openings in it.

Image credit: Robert Austin and Lyman Page / Princeton University.

Sure, if you fire enough photons, you can be confident in the pattern that will emerge, statistically. That's what quantum mechanics allows you to predict with great accuracy.

But if you are asking about the properties of one particular particle -- where it winds up, what path it took, etc. -- there is no way to know. This is one of the most mind-boggling, puzzling aspects of the quantum reality of our Universe.

And at the same time, remember, our Universe, our physical, observable Universe, is full of a huge amount of this stuff!

Image credit: NASA, ESA, R. Windhorst, S. Cohen, and M. Mechtley (ASU), R. O’Connell (UVa), P. McCarthy (Carnegie Obs), N. Hathi (UC Riverside), R. Ryan (UC Davis), & H. Yan (tOSU).

When you add everything up that we know of: photons, neutrinos, protons-and-neutrons (or quarks and gluons, if you want to go more fundamental), electrons, antimatter, and everything else, we know that there are at least some 10⁹⁰ particles in the observable Universe. The Universe has been around -- since the era of the Big Bang -- for some 13.8 billion years, or some 4 × 10¹⁷ seconds, or (if you prefer units of Planck time) about 8 × 10⁶⁰ units of Planck time.

Now think about all that time, and think about one particle. Any one you want, but just one.

Image credit: James Schombert of University of Oregon, via http://abyss.uoregon.edu/~js/.

How many times did that one particle experience a quantum interaction with another? How many times did its position or momentum change? How many times did one particular quantum possibility happen for that particle, and hence, not the other possibilities?

The answer, for each of these 10⁹⁰ particles, is a lot. Each time a nuclear reaction takes place inside a star -- something that happens maybe 10²⁰ times each second in our Sun alone -- a huge number of particles experience a quantum interaction. And if just one of these interactions had a different outcome, our Universe would be in a different quantum state than the one it's actually in.

Image credit: Jeff Miller, Ph.D. via Apologetics Press, from http://vnn.org/.

If just one randomly directional process -- like matter-antimatter annihilation -- had occurred in a slightly different direction, like it was off by 0.000000001°, our Universe would be different. If a single radioactive atom decayed just an attosecond later than it actually did, our Universe would be different.

And with all the particles interacting in all the ways they have over the Universe's history, you can make some calculations to try and determine how many of these quantum "decisions" have been made, and what the odds are that our Universe would exist with every quantum phenomenon shaking out exactly the way it has.

Well, the number of possibilities is somewhere around -- are you ready for a big number? -- 10^10⁹⁰!, which should be read as ten-to-the-((ten-to-the-ninety)-factorial). Which, unless you're a professional mathematician who specialized in number theory, is probably the biggest number you've ever seen or conceived of. (For comparison, I'm going to show you only 1000!, or 10³!, below.)

Image credit: Mohammad Shafieenia of http://www.codeproject.com/.

"So what," you might scoff! "A number can be as big as it wants, but if the Universe is infinite, then there are an infinite number of realizations that are just like this, and every quantum possibility can happen somewhere!"

Easy there. Those are some big assumptions. First off, there's an assumption underlying the idea that parallel Universes could be real, something that's glossed over by many-worlds interpretation enthusiasts.

Image credit: Wikipedia's comparison of interpretations of quantum mechanics.

You see, in quantum mechanics, we define a particle's properties by a wavefunction, and that function changes over time. Now, in some interpretations, that wavefunction isn't a real thing, with definite properties, that determines anything about that particle. Measurables are the real thing, and the wavefunction is just a calculational tool. But in other interpretations (like many-worlds), the wavefunction is really a real thing, and so every time a "quantum decision" can be made, every possibility happens somewhere, and what we experience as our Universe is simply a path being chosen.

Image credit: Christian Schirm of Wikimedia Commons.

Mathematically, these different interpretations yield the same measurable results. But if we want this latter interpretation -- the many-worlds one (with a huge number of parallel Universes and all) -- to be true, we need at least 10^10⁹⁰! Universes-worth of space, time, and matter for it to happen in.

And while there are some good arguments that we do, in fact, live in a multiverse, the leap to having that much Universe to work with is staggering. Let me explain.

Image credit: me.

You see, the Universe, in its very early history, underwent a period of cosmic inflation, where the Universe expanded exponentially. For a period of at least ~10^-30something seconds, this was what happened to set up the Big Bang.

There are some good arguments that inflation has been happening for a very long time (detailed here), which means that there could be 10^10⁹⁰! regions of spacetime identical (more-or-less) to our own.

Image credit: me.

But there's a huge leap between "at least 10^-30something seconds" and the "at least 10^10⁹⁰! seconds" (or years, or Planck units, or whatever; the units are unimportant at this level) that having real parallel Universes requires.

Now, this isn't to say it can't or doesn't happen, but it is a tremendous leap, and one that requires an inordinate extrapolation to make. We're still trying to figure out what came before inflation, how long it lasted, and whether there was a singularity or not to initiate it. Let's keep in mind how mind-bogglingly much one must assume if we want infinite parallel Universes to be real, and remember as we move forward in time through the Universe: some infinities are bigger than others. And that's what I have to say about the physics of parallel Universes!

esiegel Wed, 09/25/2013 - 11:38

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everett

Before we had direct observational evidence of the atom, many scientists scoffed at the idea that they existed, even if the calculations/theories of the times indicated that they did exist. They believed that science could not explain the reality of the situation and should only be used as a calculation tool. This is instrumentalism. This view should have been laughed at by other scientists of the time, but it wasn't, it was a mainstream view.

If our best explanations seem to indicate that X could be true about the world, then it should be taken seriously, and not just brushed off as a calculation tool. To not do, is a failure of imagination and inhibits further progress. The multiverse denial seems so anthropocentric.

Ethan: See position space and momentum space on wiki and note the reference to the Fourier transform. Then take a look at weak measurement work by Aephraim Steinberg and Jeff Lundeen et als. Note Jeff's semi-technical explanation where he says this:

"So what does this mean? We hope that the scientific community can now improve upon the Copenhagen Interpretation, and redefine the wavefunction so that it is no longer just a mathematical tool, but rather something that can be directly measured in the laboratory".

Think of the photon as a waveform in space, analagous to a seismic wave deep in the ground. It goes through both slits and interferes with itself. However when you detect it at one slit you perform a wavefunction-wavefunction interaction that operates akin to an optical Fourier transform. The photon is transformed into a dot at that slit so it goes through that slit only, and there is no interference. When you detect it on the screen you perform another wavefunction-wavefunction interaction that again operates akin to an optical Fourier transform. Hence you get a dot on the screen. No magic, no mystery, and no multiple universe is required.

Yeah, it seems like a perfect example of an argument from incredulity to me. Besides, I don't know of any a priori reason to assume that all 10^10^90! or so universes would have had to exist from the beginning, rather than being spawned at each possible interaction.

FWIW, I am kind of a fan of many-worlds, but I do acknowledge that there's essentially no evidence for it, and it may not even be possible to collect any evidence in principle, so I wouldn't be upset if some other interpretation turned out to be correct, or at least many-worlds were disproved. In some regards, I'd actually be rather relieved.

I am not reading this as multi-universe denial, as much as "Before we go off whole hog, let's get some questions answered, because this is a big one!"

Mike,

That is correct. You see, the recognition that the Universe went through a period of cosmic inflation coupled with our understanding of quantum field theory leads us to the conclusion that even though our little corner of the Universe has stopped inflating, inflation has been happening in most places for the last 13.8 billion years, and who-knows-how-long before that.

http://scienceblogs.com/startswithabang/2011/10/28/why-we-think-theres-…

But you think there's a big difference between 10^-33 seconds and 13.8 billion years? Try the difference between either of those numbers and 10^((10^90)!), and you'll be thinking in exclamation points, too!

The problem is with referring to each one as a "real parallel universe". That's just a visualization, at least relative to Everett's original idea. There's one universe, which exists in a superposition of multiple states. I've seen other articles about the idea talk about violating conservation of energy when "creating" these other universes and I just facepalm, because that's not what this interpretation actually says. (Thank you for not going there.) There aren't a whole lot of universes, there are a whole lot of terms in the wave function that describes the universe. And in exchange, you get locality and determinism. This way of describing it is surely less interesting to sci-fi authors (though one could still imagine a technobabble explanation for "traveling between universes" - it could even use the word "phase" in a semi-accurate way!) but if you can grok the math, it makes a lot more sense. (And note that the little math needed to use bra-ket notation is all you'd really need.) Looking at it like that, I actually find it vastly simpler than any other interpretation.

Multiple universes is fun and very syfy to consider. However, such thoughts still describe the issue in three dimensional terms. What are the other dimensions that the mathematics suggest are there? Even the terms "what" and "there" rely on 3D ideas.
If we can conceptualize other dimensions, and consider the properties they offer, and the effect of the 4 we normally deal with, we might begin to understand quantum issues as intersections, wave functions as descriptions of reality and not just tools.
No analytical support? Einstein et al conceived of much of what we know long before they had the tools to confirm it. Creative thinking, consistency of argument and a recognition that current ideas are inadequate.

When Sean Carroll describes the Many Worlds interpretation, he describes it more like BenHead does. There aren't many parallel universes, there's just a single universe described by a single wave function which evolves according the the Schrodinger equation and that's it. "Many worlds" just comes from the fact that we are part of that wave function, too, and the various outcomes for us exist in a superposition just like it does for everything else, and what "I" am is just one of those possibilities which is why, subjectively, it looks like wave functions collapse.

He's made the "brief intro to QM" chapter of one of his books available online and it goes into the Many Worlds interpretation. Here's a linky:
http://preposterousuniverse.com/eternitytohere/quantum/

After reading that the Many Worlds interpretation made a lot more sense to me, and now I think it has a lot to recommend it.

It does still have the unnerving property there are 10^whatever other "me"s that exist just as much as I do. But not in the same sense as "parallel universes".

Jim:

"What" and "there" are well-defined valid terms for any arbitrary dimensionality. A "dimension" is an axis of measurement, and "there" is a position; in N-dimensional space "there" is defined by N values. Additional dimensions may be nigh-impossible to visualize, but it's trivial to conceptualize and there's lots of math already dealing with it and theories that incorporate that math. I don't think any of them have solved the fundamental interpretation issues with QM.

Not to say that a specific idea which includes extra dimensions couldn't solve the issue, but I don't think it's as easy as postulating a greater than 3+1 dimensional space.

BTW, seeing that "Turbo C++ IDE" window was a real blast from the past. :)

Just for a little clarification, the many-worlds-interpretation doesn't require that parallel universes are real. The parallel Universes are -- in a conservative MWI view -- a visualization of what the wavefunction creates.

But there are people who are putting together the huge amount of Universe-space created via eternal inflation and the MWI to argue that parallel Universes are real, and that for every quantum realization that occurs in our Universe, there exists a real parallel Universe where everything that ever occurred in our Universe occurred over there, except for that one difference.

That is what I've been talking about here; commenters BenHead and CB are correct that the MWI does not necessitate these real, infinite parallel Universes.

What eternal inflation? We can envisage an early universe where energy density was very high, much as it is down near a black hole where gravitational time dilation is high. So if the universe expands even at some sedate pace, any observers within that universe would assert that the expansion was extremely rapid. Like inflation. And we have no evidence that this occurred in only one region. So all this multiverse stuff is a speculation riding a hypothesis on top of a conjecture. It isn't science, it's pseudoscience. It's woo. But people sure do love their woo.

Well the other quantum possibilities encoded in the wave function would be as "real" as I am (and I think I'm pretty real).

But I think I understand your clarification about combining it with eternal inflation -- the idea is that they're really *parallel*, as in taking place in a separate inflation bubble that happened to exactly match the quantum state of ours up to some point of divergence, and with infinitely many such bubbles every quantum event will be the point of divergence between ours and some other bubble.

Is that correct?

Seems to me that by assuming that once a quantum event occurs differently in the two universes that they now diverge entirely after taking on a specific state, this is more Copenhagen + eternal inflation. If it was Many Worlds, each inflation bubble that started with the exact same quantum state would evolve the same way, each containing all the possibilities. Which makes me feel like I'm not understanding.

In any case, thanks Ethan.

Darn. When I said "we have no evidence that this occurred in only one region" I should have said "we have no evidence that this occurred in more than one region".

I think you're underestimating the necessary universes by a few orders of magnitude, Ethan. Each of those parallel universes would have their own evolution, and unless we somehow assume ours is special, then each of them would need that huge number of parallel universes itself, right? And so on...

When I read your columns, Ethan, I always regret that I did not get my degree in astrophysics. So fascinating!

it could possible be true due to quantum mechanics and string theory which states there a 7 dimensions instead of 4 as we thought of in the past. This is due to Einstein General relativity and quantum mechanics so there could be other dimensions that we can explore and see the laws of physics even govern them as they do in our 4 dimensional universe.

I honestly don't see the issue with the number being so big. The question is a process one: do we have scientific evidence or theory which predicts there is a process for universe-splitting or universe-formation at quantum events. If the answer is "yes," then whatever number of universes you end up with is just the natural outcome. If the answer is "no," then you don't have any reason to expect any of them.

Its sort of like compound interest or evolution. Non-experts are are constantly surprised/amazed at the amount of total change those processes can produce in a significant time too. Again though, it's just a question of whether you have a reasonable mechanism. If you do, then you ought to accept any counter-intuitive result you might get out of cranking that mechanism.

So, what happens to the law of conservation of mass-energy? Every particle change creates, from nothing, an entire new universe having all of the dark and barionic matter of the first. Just doesn't pass the test of common sense.

Does quantum computing offer any ability to exclude or favor any of the interpretations on offer? Some authors I've read have argued that if we're successful in building quantum computers this proves the reality of many-worlds (This was in In Search of the Multiverse, but I think David Deutsch has said similar things).

Um, the wave function evolves in a Hilbert space of undetermined dimensions. _Not_ our three- (or four-) dimensional physical space (or spacetime.) So yeah, there's extra dimensions to move around in. But they're more like the temperature-dimension or the momentum-dimension.

Ah, I see this has already been covered. My apologies. That'll teach me to skim ;-)

CB and marcel - thanks for the feedback
I first began to think of other dimensions when I followed the Herculean effort at CERN to drill deeper and deeper. Instead of trying to breach the vault door directly, mightn't one simply walk around the edge of the facade and unlock the vault from the inside?
My favorite idea for another dimension relates to human perception. Some call it a sixth sense, others intuition. I have no idea what causes this, but haven't you known people who seem to have insights that others lack? Like they can see into the future, or have an understanding of a person or situation that is remarkable. Are they more "in tune" with another dimension and able to better adapt to our 3+1?

Many worlds?

How many papers have the phrase "many worlds" in their title
- 17 papers published in 2013 on the Philosophy of Science preprint online data base
- 1 paper published in 2013 on the arXiv (e.g. physics) preprint online data base

As I suspected. The "many worlds" idea seems not to make much difference to physics and astronomy either experimental or theoretical. There are very few even thought experiment differences between the many worlds interpretation and other quantum mechanics interpretations. But the many worlds idea is very important philosophically.

"The reason for adopting the MWI is that it avoids the collapse of the quantum wave. (Other non-collapse theories are not better than MWI for various reasons, e.g., nonlocality of Bohmian mechanics; and the disadvantage of all of them is that they have some additional structure.)... The MWI is a deterministic theory for a physical Universe and it explains why a world appears to be indeterministic for human observers... However, THE ADVANTAGE OF THE MWI IS THAT IT ALLOWS US TO VIEW QUANTUM MECHANICS AS A COMPLETE AND CONSISTENT PHYSICAL THEORY which agrees with all experimental results obtained to date." date.http://plato.stanford.edu/entries/qm-manyworlds/

But is quantum mechanics "a complete and consistent theory" yet?
A few typical quotes suggest NOT if you include gravity.
"general relativity and quantum field theory are outright incompatible... there is no way to a peaceful coexistence; a shoot out is inevitable."
"The 21st century has thus inherited a fundamental crisis in physics, viz., the incompatibility of general relativity and quantum physics!"
"I would like to suggest that it is possible that quantum mechanics fails for large distances and large objects. Now, mind you, I do not say that quantum mechanics does fail at large distances, I only say that it is not inconsistent with what we do know. If this failure of quantum mechanics is connected with gravity, we might speculatively expect this to happen for masses such that GM2/~c = 1, of M near 10^−5 grams, which corresponds to some 1018 particles ” - Feynman (1957)

Also INTERPRETATION OF MANY WORLD INTERPRETATION VARIES DEPENDING UPON WHICH PHYSICIST YOU READ.

The importance of the MWI, for me, is that it is a current example that illustrates how important philosophical assumptions are to current physics. Physicists seldom will admit that philosophy plays any role in their theories. (e.g. "As a theory relevant to the origin of the universe, the Big Bang has significant bearing on religion and philosophy. As a result, it has become one of the liveliest areas in the discourse between science and religion. Some believe the Big Bang implies a creation, while others argue that Big Bang cosmology makes the notion of a creator superfluous." wikipedia

Why is there a problem with the wavefunction collapsing? Maybe that's what is happening (in as much as the model of the thing is the thing itself).

"But is quantum mechanics “a complete and consistent theory” yet?"

Again, it depends on what you're going to want for making the assessment of being complete and consistent.

Its successes, especially in areas where they were consequential results of the model but not a prediction or pre-requisite for it shows it's to that extent complete.

And consistent with what?

F=ma can be proved from "first principles" from the wave equation of QM (if you assume the Newtonian result is the "expectation value" result.

So it's consistent with classical mechanics.

Then again, you can point to places where it's inconsistent with other theories and where it doesn't apply (even if only because QMing a cat is a silly thing to find out if it purrs: ask a vet).

So the answer is yes and no.

One reason why science isn't interesting to the Jenny Housecoats of the world but religion "seems" "better": it's damn certain in its answers, and doesn't publicly waver.

So, what happens to the law of conservation of mass-energy?

Maybe it puts a limit on the types of universes out there - i.e., they must have net zero energy - but it certainly doesn't limit the amount. Ten-to-the-((ten-to-the-ninety)-factorial) times [universe which has zero net energy] is still zero net energy.* You could also have a bunch of net-positive and net-negative universes that balance out to meta-net-zero.

But that is a curious and possibly informative question. If we hypothesize that all of those ten-to-the-((ten-to-the-ninety)-factorial) universes must, like ours, have a net zero energy, does that allow us to derive some understanding of what those universes must be like? Or does having the same net energy as our universe mathematically follow from QM (same number of particles and strength of gravity, just with the bits arranged differently), and thus not really tell us anything?

*Like ours. AIUI, according to how cosmologists and physicists count, our universe has a net energy balance of 0 because the 'negative' energy of gravity matches all the other energy and mass in the universe. In fact, this observation is the reason why Hawking came out a few years back and said that the universe could come from nothing.

, so mass and energy can be conserved no matter how many universes there are.

I could never understand the logic or rational for Many Worlds interpretation.

Multiverse from inflation does allow for similar universes. But that is not the same as Many Worlds. Yes.. if there are enough unique bubble universes, there is a chance that in one of them everything happened in just the right way to make another me with everything being the same except i won a lottery. But that's irrelevant to anything physics says about this universe.

Like I said in the beginning, I could never understand MW. Would like for someone to explain what it really means for a "function" to be physically real. I just don't understand what that means. No more than I understand "truth" to be physically real.

Where is that function? Is it big? Small? How much does it weight? Does it like pizza?

But it gets worse, because it's not that there are many universes. No.. you have our universe.. that goes on it's merry way, then I choose to wear red socks, and whoala.. a whole universe appears "somewhere" that has to replicate my universe exactly, just with i.e. green socks. Eghm... seriously? Appear from what, where, how? By what energy and cause? etc...

So ok.. forget that one. Let's look at it in a different way. They say we have a physically real function... So there it is, this "wave function" that is somewhere..., and in it is everything that has happened, happens, and will happen. It hasn't been made. It's without cause. It "knows" everything. And everything that happens "under" it has no more say in it than anything else. It does as it wills. In a way this sounds like a notion of deity. Except now you know it's useless to pray to it 'cause math says there is no "prayer" value in the function...

I took it to extreme, but no more than I feel MW camp has taken "randomness" to extreme.

"Would like for someone to explain what it really means for a “function” to be physically real. I just don’t understand what that means. No more than I understand “truth” to be physically real."

I've used this one many times, but again.

Evanescent waves.

Simplifying the maths for an E-M wave you can, instead of using sin/cos for the amplitudes of the electric and magnetic fields, you can keep a single *complex value* amplitude and have it rotate and the real part gives you the real (observed) electric field strength. The change of this gives you the magnetic field strength.

HOWEVER, using a complex number on the 19C maths used to describe total internal reflection there's an imaginary part that extends beyond the medium reflected in the original direction of travel. This decays exponentially and is entirely imaginary (as in it's a value multiplied by the square root of -1, there is no real part of the complex number).

HOWEVER, again according to that maths, if you put another refracting medium in this "evanescent" field, you will get the creation of a new EM field with a strength equal to the size of the imaginary vector of the evanescent wave at that distance from the totally reflected surface.

This was only a mathematical trick to make it easier to do the figures.

But when placing a refracting medium close to another one which had a wave being totally reflected internally to that medium, you got light coming out of the first medium, unlit by anything else.

A function that appears to be totally real: EM fields of a photon being a single-valued complex number rotating through i-r number space.

I think it's possible that the probability wave is more real than the classical particle since this helps describe the two-slit experiment in the case of limited numbers of discrete quanta entering the experiment and being individually measured.

It is also to some extend realised inthe lamb shift, where the probability of the electron acts as if it were an equivalent fraction of an electron with an equivalent fraction of an electronic charge and interferes with itself and the remainder of the atom. I.e. the electron is "smeared out" throughout the QM probability distribution of the electron in its shell.

This also explains why this electron isn't giving off massive amounts of synchrotron radiation: it's not moving at all: the wavefunction is stationary.

In a two-slit experiment, the probability field means that the probability of an event resulting in detection reflects the diffraction pattern in a wave-like experiment and the scattered beam in a particle-like experiment. Both types change the probability wave. Neither make the "electron" "know" that it's in a different experiment in-flight.

Maybe one way to change this would be to have a wavelike/particlelike experiment set up that can be changed as to what it's meant to detect quicker than the transit time from emission to detection locations for the particle/wave, then swap between them and see if the pattern changes.

Maybe it wouldn't help at all. I've not yet managed to work out what the consequence that would happen under any model of what "reality" "really is" and therefore make this experiment capable of eliminating a view or not.

This, however, doesn't require a MW view. Just that the wavefuntion is more "real" than the quanta that is detected.

Although "just" is a rather small word compared to what it means.

Rather like "In order to fly, you just have to throw yourself at the ground and miss".

Sinisia @27:

Multiverse from inflation does allow for similar universes. But that is not the same as Many Worlds.

Isn't it the same sort of mechanism though? In the first case, you've got a set of QM principles that allows universes to form. The probability of allowed events never happing is infinitely small, so we can reasonably expect them to happen.

In the latter case, we've got a set of QM rules that appear to allow wavefunctions to collapse in many different ways. Since its allowed....[repeat above logic]

Hawking and Mlodinow's Grand Design hints at this (but doesn't cover it...gripe gripe gripe). In the book, they point out first that QM allows our present to have many possible futures. Then, secondly, they point out that QM allows our present to have many possible pasts. Okay. That leads very naturally to a discussion I wish they had included (but didn't): are there therefore many presents? Seems odd to think that the QM multiverse has an infinite number of futures, a lesser but still infinite number of pasts, but necks down to a single universe at each instant of the present. If Hawking is right about past and future, why should we think such a neck exists?

Sinisa:

Yeah it's always troublesome trying to think of math as "real" rather than as a description of reality. Even if unintuitive implications of that math end up being borne out by reality, like evanescent waves, you could just take it to mean the math was an even better description of reality than you thought (but not necessarily perfect). So let's just set that aside.

What Many Worlds is saying is that the wave function isn't just a description of the state of a quantum system prior to its "collapse" into a single classical state, but rather a description of reality at all times. What appears to be "collapse" is really just the measurement apparatus and the system being measured becoming entangled so only certain subsets of their states are consistent. An electron exists as a superposition of all possible locations. When the apparatus measures an electron "there", then only states of the electron where it is "there" are consistent. Yet because the measurement apparatus is itself a quantum system, it also exists as a superposition of every possible ("electron measured there", "electron is there") state.

What Many Worlds is asking you to believe is "real" is superposition and entanglement. It's asking you to believe that quantum systems subject to these phenomenon aren't just tiny collections of particles we study in a lab, but everything. Including the apparatus, and also -- now here's the tough part -- including you.

You are not a classical observer who makes quantum systems start behaving classically when you look at them. You are a quantum system that exists as a superposition of all valid states. However because you are heavily entangled with everything around you, those valid states for you correlate heavily with specific subsets of valid states for the rest of the universe. So each of the possible "you"s sees only that subset of consistent valid states for the universe, which is why the world mostly looks classical and why wave functions appear to "collapse".

The key point for me to make here is that there are no spontaneously generated universes -- the "many worlds" are really just subsets of the valid states of the universe as described by the wave function that all exist in a superposition. No Conservation of Energy problem. No new information is created, or for that matter destroyed. Unlike in Copenhagen, in Many Worlds quantum mechanics is (in principle) completely reversible.

A universal wave function that defines all possibilities in the universe shouldn't on its own strike you as odd. It is in this sense precisely the same as the set of classical laws of physics plus the state of everything in the universe, from which one could calculate all future (and past) states.

"" Multiverse from inflation does allow for similar universes. But that is not the same as Many Worlds."

Isn’t it the same sort of mechanism though?"

No, not really.

Multiverses do not start out (or get chosen from) states that are in one universe progressing.

The MWI in its broadest and most colloquial sense is saying that the possibility produces another world where the alternative outcome was the one chosen.

The "solution" this gives is that which universe you perceive as real is the one of those many possible outcomes that came out true.

I.e. you're about to roll a dice. Six universes come into being from that point where one universe rolls a 1, another has a 2, and so on.

When you, the observer, notice that the answer that came up was 5, the universes stay, but your continuing consciousness has been placed into the universe that rolled a 5.

Those other universes, in the most common use of MWI, continue to exist, since the result of the "random" dice roll was never random, only which one you happened to follow on to was random.

Multiverses were abandoned because no causality from this one can ever reach it, even to the extent of "The value of the constant G is 6.7x10^-11". Or anything else.

Unless some physical laws are required for a universe to "survive" (three space dimensions, for example, may be an absolute requisite for a universe that can survive more than a plank time).

It never linked, never was, never will be, to a universe that had you, or any particle, force, wave or propagation that you will find in this universe, past, present or future.

@CB

am not sure I understand MW the way I do. It's not about believing that we are all QM systems or that we as observers are QM entangled as well. I understand that and agree.

If we move it from electron cloud to two slit.. the way I understand MW (and as ethan writes as well)... there IS physicaly REAL universe parallel to this where the particle passes through the other slit. and so on for every interaction... or the cat. just because the math says there's a 50/50 odds that's dead or alive, the moment you open the box there isn't a new universe getting created where the cat dies... yet it seems to me that MW is arguing precisely that

p.s. sorry first sentence should be: "... the way YOU do."

p.p.s.

" in Many Worlds quantum mechanics is (in principle) completely reversible."

well, how does this reconcile with uncertainty or entropy rise?

Quantumly, (cromulent new word!) entropy is just the difficulty of getting the same state back. Colliding two billiard balls back to their original location goes from having one force (the initial cueing) that was done any old how, to having to have two forces putting the two balls back in their original places and, rather than be any old way, they have to be precisely reversed.

If in the meantime, one or other (or both) had hit another ball, the reversal would require more forces in the right direction to cause the reversal.

And, stochastically, there are many more "wrong" ways to get the balls moving back (but not to precisely the same location) than there are "right" ones, leaving the scene as it found it.

MWI has many more worlds where you don't go back to where you started but if you could navigate precisely, you may be able to find one.

I don't really know it helps, though.

think I'll end here because it's hard to keep track :) anyways the math is same, regardless of interpretation. and as long as we get same results, i guess it's ok to believe anything :)

Sinisa: "well, how does [MWI implying QM is reversible] reconcile with uncertainty or entropy rise?"

Same way as all the other laws of physics which are completely reversible. :) In principle if you could reverse the motion of every particle in a (classic ideal) gas resulting from mixing a hot and cold gas you could get it to return to its original state of two separate resevoirs In practice the odds of this happening spontaneously are infinitesimal, and therefore (at a macroscopic statistical level) entropy always rises.

"there IS physicaly REAL universe parallel to this where the particle passes through the other slit. "

Absent path information, the particle passes through both slits. Do you believe that is physically real? MWI asks you to believe that it is.

All that happens then is when you detect the path, then the detector becomes correlated (entangled) with the particle and each of the two possibilities of detection are not compatible with the opposite possibility of path.

Both paths still occur, though. Just now the superposition includes the correlated state of the detector. And then you, as you say either "Ah-ha! It went through slit A!" or "Ah-ha! It went through slit B!" Those two possibilities exist in a superposition, as do their further evolutions. But the "you" that saw it go through slit A cannot see anything about the "you" that saw it go through slit B because those states are no longer compatible.

So instead of viewing it as every interaction forking a new universe, you can look at it as every interaction causing a subset of the universe (which is all states allowed in the wave function) becoming invisible to you.

I'll leave this link here again as it explains it much better than I can:
http://preposterousuniverse.com/eternitytohere/quantum/

I'll finish by saying that while MWI has grown on me (not having an point of arbitrary irreversibility being part of why), I don't really "believe" it. Frankly I don't "believe" any interpretation of QM, and use Copenhagen as my mental model because it's simpler to conceptualize. I and my macroscopic experimental apparatus are classical observers and when quantum superpositions are observed they collapse and all the possibilities that I didn't observe cease to exist. Simple!

Consider that measurement will realise the answer of a quantum superposition. That doesn't have to be you looking at it either, it can just be something that can change if the superposition were in one state but not in any of the others.

Yes, the _last_ thing I want to do is imply that "observation" implies "observer" implies "human sentience" -- the pun-based "logic" that results in all kinds of woo. Observation is measurement is anything that's state will correlate with the state of the thing being measured, whether that's intentional or not (one of the ways this is made practically clear is by the difficulty designers of quantum computers have *not* measuring the state).

@CB #43: I think you (i.e., all of us physicists) have to be a bit careful when you say "anything." Generically, if you have something which couples to (correlates) "with the state of the thing being measured," what you end up with is an entangled quantum system.

In order to reduce or avoid that entanglement, and end up with a "classical measurement," what you need is a coupling which not only "correlates with the state of the thing being measured", but also acts as a projection operator, picking out one of the eigenstates of the system (by "picking", I mean a la the Born rule).

This turns out to be much harder, philosophically. In practical terms, what we have observed so far (pun entirely intended :-) ) is that you need something which couples to the environment, or to anything with a large number of stochastic degrees of freedom. That something acts as a projection operator, or to diagonalize the density matrix, or to "collapse the wavefunction," or whatever particular terminology you like this week.

There have been some really cool papers over the past decade or so, which have quantified this. For example, coupling an atom in a superposition to a microwave cavity, and measuring, for example, the time it takes the atom to end up in one of the two eigenstates as a function of how many photons are in the cavity. It's not instantaneous, and the time varies inversely with a power of the cavity population.

It's quite impossible to imagine about another universe 'cause we are bought up to believe that our earth is the only one that has air water and oxygen but I do believe in parallel universe because of all of my friends amazing facts and information and a lots of images

Amazing or what? Just amazing. God's Nature is amazing.

re #46: I thank you. It's some of my best work. I'm working on Nature v 2.0, using what I learned in creating this one.

Shaping up to be great!

Interference of Independent Photon Beams: The Pfleegor-Mandel Experiment

drorzel — Fri, 19 Nov 2010 09:38:04 +0000

Interference of Independent Photon Beams: The Pfleegor-Mandel Experiment

Earlier this week, I talked about the technical requirements for taking a picture of an interference pattern from two independent lasers, and mentioned in passing that a 1967 experiment by Pfleegor and Mandel had already shown the interference effect. Their experiment was clever enough to deserve the ResearchBlogging Q&A treatment, though, so here we go:

OK, so why is this really old experiment worth talking about? What did they do? They demonstrated interference between two completely independent lasers, showing that when they overlapped the beams, the overlap region contained a pattern of bright and dark spots characteristic of interference.

How did they do that in 1967? What did they use, photographic plates? No, they used photomultiplier tubes, that produce an electrical pulse when a single photon falls on them.

But a PMT only detects photons in a single position. How did they make a picture out of that? They didn't, because they found a clever way to arrange it so they didn't need to. Here's a schematic of their apparatus:

All right, what are we looking at? In the upper left, you see a diagram showing the optical layout. They start with two independent lasers, and split off a small part of the light from each to go to a detector that monitors the frequency difference between the two lasers, and only turns on the detector system when the lasers are close enough in frequency to produce a good interference pattern.

Wait a minute. These are lasers, aren't they a single frequency? They are, but the frequency wanders around a little bit, just enough to change the interference pattern a little. As a precaution, they only look for the pattern at times when both lasers have wandered into the same basic range.

OK, so they've got two lasers. Then what? Then they take the two independent lasers and steer them together with mirrors, and overlap them with a small angle between the two. This should produce an interference pattern with a spacing between bright and dark fringes that depends on the angle between the beams. They put this pattern onto a specially made detector.

Yeah, that's the whole question. How does that work, when they just have PMT's as detectors? The detector they used (inspired by a Dr. Neil Isenor, who gets a footnote of thanks but not an author credit) is shown in the inset at the lower right. It's an array of small glass plates, cut like little prisms, with a thickness equal to roughly half of the spacing between one bright spot and the next in the expected interference pattern. The odd-numbered prisms-- first, third, fifth, etc.-- direct light falling on them to one PMT, while the even-numbered prisms-- second, fourth, sixth, etc.-- direct light hitting them to another PMT. When the light falls on the stack in just the right way, the bright spots in the pattern will fall on the odd-numbered prisms while the dark spots fall on the even-numbered prisms, so one detector will detect lots of photons, while the other sees almost nothing.

Yeah, but how do they get the pattern to line up? I mean, you said that the problem with this measurement is that the pattern changes position randomly all the time. That's the really clever part. They don't need to have a stable interference pattern, and they don't need to have the pattern line up precisely with one set of prisms. All they have to do is look at correlations between the detector signals.

You see, if the pattern falls with the bright spots on one set of prisms, one detector will get all the photons, while the other gets none. If you shift the pattern so the bright spots are on the other set, then the second detector gets all the light, and the first one gets none. Which shows that the signals from the two detectors should be anti-correlated-- when one gets a lot of light, the other gets very little.

But if you shift the pattern only halfway, then they each get half of the photons. True, but that's only true in a tiny range. Most of the time, one detector will get more photons than the other. That means that, statistically, you expect that any smallish sample of the count data will show a significant imbalance between the two. That's the thing they look for in the data.

And that worked? Yes. They have a table in the paper showing the counts on each detector for 25 different trials lasting 20 microseconds each. The average number of counts per detector over the whole sample was pretty close-- 5.08 for one and 4.40 for the other-- but the individual trials almost all show a significantly greater number on one detector than the other. The correlation coefficient between the two count rates is negative, as you would expect from an interference pattern falling on the detector.

I don't know, dude. It's not science without graphs. Isn't there a graph you could show? Ask, and ye shall receive:

This shows the correlation coefficient (plotted with negative numbers being up) as a function of the ratio of the thickness of the prisms L to the expected fringe spacing l. When the thickness is equal to the spacing, so that if one bright spot falls on an odd-numbered prism, the next bright spot will fall on the next odd-numbered prism, they see a maximum in the negative correlation, which drops off as the fringes get either closer together or farther apart. The lines in the graph are the predictions of a simple model of the expected statistics, for different values of the number of pairs of prisms illuminated. Their data agree very nicely with something between 2 and 3 pairs illuminated.

OK, so their detector shows an interference pattern between photons from two different lasers. How does that work, exactly? Do the two photons bounce off each other, or something? That's the other cool thing about this experiment. Before they sent the beams onto the detectors, they used big filters to knock the intensity way down. They used big enough filters that there was only one photon (on average) in the apparatus at any given time. They got around 10 photons per 20 microsecond data run, which gives an average spacing between photons of 2 microseconds, which corresponds to a spatial separation of about 2000 feet (the speed of light being very nearly one foot per nanosecond).

This large spacing means that this isn't an interference caused by two simultaneously arriving photons, but rather a single photon arriving and somehow knowing that it needs to form an interference pattern, even though it can only have come from one laser.

OK, that's just weird. How do you explain that? The key issue here is that you have no way of knowing for sure which laser the photon came from. That's what allows you to see interference. When they block one laser or the other, so that they know for sure which laser the photon came from, the interference goes away.

Yeah, but what's interfering? I mean, a photon can't really come from two places at once, can it? That's the tricky bit. They have a wonderfully deadpan way of putting this: "In terms of photons, the experiment raises one or two interesting questions of interpretation."

That's an understatement. Exactly.

There are two ways you can go with this. One is to view it as an interference created by the detection process. That's the language they use: "It seems better to associate the interference with the detection process itself, in the sense that the localization of a photon at the detector makes it intrinsically uncertain from which of the two sources it came." This is a little toward the Copenhagen side of things, interpretation-wise, though it could also be a little Bohmian. It says that the observed pattern is something to do with the detectors-- that configuring the detectors the way they did creates a situation in which the only possible outcome is an interference pattern.

Another way of putting it would be to use the language of field theory. That is, the photons we talk about as particles are really excitations of a mode of the electromagnetic field having a specific wavelength and direction. The interference pattern you see is an interference between two modes of the field, meaning that one photon coming in to the detector is necessarily an excitation of a field mode that contains the interference pattern within it.

In either case, the important thing here is that the photons are not strictly particles in the classical sense. There's something nonlocal about them, that allows an interference pattern to be produced even when you have only one photon, but aren't certain of its place of origin.

That's, um, really odd. Yes, yes it is. Which is why this experiment didn't go in the book-- it's a little too strange and requires a little too much hand-waving to explain. But it's a very cool experiment, and an impressive display of ingenuity.

Pfleegor, R., & Mandel, L. (1967). Interference of Independent Photon Beams Physical Review, 159 (5), 1084-1088 DOI: 10.1103/PhysRev.159.1084

drorzel Fri, 11/19/2010 - 04:38

Tags

* brain explodes *

Very cool man. Keep on blogging great stuff like this!

Yes, what Ted said. And, what Andrew said too.
Still, if you accept Young's Double slit experiment with single photons - and you have to , because that's what happens - then this is perfectly logical. Sometimes you have to accept what happens, without knowing the how or why.

Brad

So, the multiverse concept has new universes branching out from each quantum decision. In the case of two possible sources for the photon could this represent a merging of two universes?

In a double slit experiment I can sort of accept that you wave your hands and say the particle 'takes both ways'. And if you accept that I can accept that the amplitude is calculated as the sum of amplitudes for going through either slit.

In this two-laser case, 'taking both ways' seems harder to accept. How is the prob. amplitude calculated in this case?

(confused)

Excellent post.

I'm speculating that the wave from the laser is in a sense in effect even when there is momentarily no particle there, thus conveying to the actual particle that there is something there to interact with.
Which may be utter nonsense. I am not a particle physicist, I just like reading about it.

It's like the first time a friend explained how a correlation spectrometer worked. My reaction was, "That makes no sense at all." "Welcome to quantum mechanics."

Really nice commentary, especially the penultimate two paragraphs which summarize the position in language of QFT. Personally, I think it is time that introductory textbooks stopped distinguishing between so-called 'quasi-particles', like phonons and excitons, and 'real' particles which all occur as (fairly localised) excitations of some quantum field. Why is it that people are happy to accept creation, annihilation and non-local scattering processes for particles arising as quantised lattice vibrations but have a problem accepting essentially the same behaviour for electrons or photons? Is it really any more odd than the behaviour predicted by classical mechanics? It's just what happens, and we should get used to it.

Ok I've got a question because I still don't completely understand the setup. How is this any different from a single light source, two slits, and when you place a detector one one slit the interference pattern weakens? Basically, I'm asking, is the laser prevented from shining through the other slit? Because if that is true then it is super cool.

And one more question - so is the end result a interference pattern of two single slit patterns added on top of each other? Or a double slit pattern? Or something else? (or is there any difference? Sorry, I'm not good enough to understand the graph:P)

Bohemian Mechanical Rhapsody

drorzel — Fri, 14 May 2010 09:36:58 +0000

Bohemian Mechanical Rhapsody

Blame Bryan O'Sullivan for this-- after his comment about misreading "Bohmian Mechanics" as "Bohemian Mechanics," I couldn't get this silly idea out of my head. And this is the result.

I like to think that this was Brian May's first draft (he does have a Ph.D. in astrophysics, after all), before Freddie Mercury got hold of it:

Is this the real life?

Is this just fantasy?

Do objects have real states

Or just probabilities?

Open your eyes

Look up to the skies and see

Studying quantum (poor boy), I need no sympathy

Because I'm easy come, easy go

A little psi, little rho

No interpretation ever really matters to me, to me

Mama, just killed a cat

'Least I think I might've did

Won't know 'til I lift the lid

Local realism was fun

But now I've gone and thrown it all away

Mama, ooo

Didn't mean to make you cry

If I'm incoherent this time tomorrow

Calculate, calculate, as if nothing really matters

Too late, my state's collapsed

Sends shivers down my spine

Decohering all the time

Goodbye determinism- you've got to go

Gotta leave you all behind for random chance

Einstein, ooo - (anyway the wind blows)

God should not play dice

I sometimes wish I'd never read Born at all

I see a little silhouetto of a psi

Scaramouche, scaramouche will you do the fandango

Action at a distance, very very spooky to me

Gallileo, Gallileo,

Gallileo, Gallileo,

Gallileo where'd you go? I don't know (oh, oh, oh)

I'm just a physicist, nobody loves me

No information has speeds more than c

Spare all our brains from non-locality

Easy come easy go - will you let me go

Bell's theorem! No - we will not let you go

let him go

Bell's theorem! We will not let you go

let him clone

No cloning! We will not let you clone

let me go

Will not let you go

let me go (never)

Never let you go

let me go

Never let me go - ooo

No, no, no, no, no, no, no

Oh mama mia, mama mia, mama mia let me go

Heisenberg has a matrix put aside for me

for me

for meeeeeee

So you think you can stone me and spit in my eye

And then decohere me and collapse my psi

Oh baby - can't do this to me baby

Just gotta get out - just gotta get right outta here

Ooh yeah, ooh yeah

Nothing really exists

When no-one can see

Nothing really exists - nothing really matters to me

Anyway the wind blows...

If you want a reminder of the tune, and a better parody than I'm capable of, look here:

A few of the more obscure jokes explained for the less geeky:

"Psi" is the Greek letter ψ, traditionally used for the wavefunction in quantum mechanics. "Rho" is the greek letter ρ, used for the "density matrix," which is another way of expressing quantum states.
"Born" is a reference to Max Born, who was the originator of the interpretation of wavefunctions in probabilistic terms.
"Bell's Theorem" shows that quantum states have to be non-local; that is, that measurements at one position can affect measurements at another position instantaneously, rather than being limited to transmission at the speed of light c.
The "No-Cloning Theorem" by Bill Wootters and Woijciech Zurek shows that it is impossible to make an exact duplicate of an unknown quantum state.
One of the earliest versions of quantum theory was "matrix mechanics," developed by Werner Heisenberg (of the Heisenberg Uncertainty Principle).

And, just for kicks, the original:

drorzel Fri, 05/14/2010 - 05:36

Tags

Quick Impressions of Bohmian Mechanics

drorzel — Thu, 13 May 2010 10:03:27 +0000

Quick Impressions of Bohmian Mechanics

I get asked my opinion of Bohmian mechanics a fair bit, despite the fact that I know very little about it. This came up again recently, so I got some suggested reading from Matt Leifer, on the grounds that I ought to learn something about it if I'm going to keep being asked about it. One of his links led to the Bohmian Mechanics collaboration, where they helpfully provide a page of pre-prints that you can download. Among these was a link to the Bohmian Mechanics entry in the Stanford Encyclopedia of Philosophy, which seemed like a good place to start as it would be a) free, and b) aimed at a non-physics audience, which is a plus, given the cold I have at the moment, which isn't doing much for my clarity of thought.

It turns out I had read some of this before, and my immediate reaction now was the same as my reaction then, namely "It's a miracle you can type while balancing that chip on your shoulder." The introduction is fairly neutral, but as you go down through the article, there are a bunch of little shots at "orthodox quantum theory" which have the cumulative effect of making me start to wonder if the author is actually a crank-- in the previous read (while I was writing How to Teach Physics to Your Dog), I actually gave up after a quick skim for just this reason. As the author is one of the authorities Matt recommended, I read it more carefully this time out, and what follows are some quick impressions based on reading through the article. I would not begin to claim that I have gained any deep understanding, and I'll look at some more physics-oriented resources next (maybe the textbook Matt mentioned, though the freely available front matter had the same shoulder-chip issue noted above), but this is, as the title suggests, the stuff I thought of immediately.

The short version, above the fold to serve as both teaser and attention conservation notice is two items: 1) In many ways, this sounds like an unholy union between Einstein and Heisenberg, and 2) I still don't see the point.

Quick summary fo the summary article: Bohmian mechanics is a version of quantum theory which considers two objects of equal importance: A wavefunction, which evolves according to the usual Schrödinger Equation, and a particle with definite position and velocity, which evolve according to a "guiding equation" which depends on the wavefunction. If you prefer something that looks more like classical Hamiltonian mechanics, you can express things in terms of a "quantum potential," and replace the "guiding equation" with a more typical force-type equation.

Every particle considered thus has a definite position and momentum at all times, unlike the situation usually presented in the orthodox quantum theory. If you know the initial position and momentum of a particle with sufficient accuracy, you can thus calculate a perfectly normal classical trajectory for it, with the wavefunction "guiding" the particle along the trajectory. The outcome of many repeated measurements is determined using the "quantum equilibrium hypothesis," which appears to consist of assigning initial positions and momenta that are randomly distributed in much the same way that the positions and momenta of particles in the canonical gas-in-a-box are randomly distributed according to a Maxwell-Boltzmann distribution in statistical mechanics or thermodynamics. The end result is a distribution of final positions that looks exactly like the probability distribution you get from the Born rule in the regular quantum theory, namely the squared norm of the wavefunction at the position of the detectors.

The bulk of the article consists of applying this basic formalism to a variety of quantum examples, and talking about how it a) reproduces all the measured effects of quantum theory while b) maintaining a definite position and velocity for every particle at all times.

General Comments:

- The "unholy union between Einstein and Heisenberg" comment above would probably be taken as an insult by everyone involved, but the presentation in the article make it sound like it's combining key features of both of their approaches. The Einstein part is obvious, with the well-defined particle properties at all times. the Heisenberg part comes from the insistence on considering measurement apparatus, for example when they describe the key processes at the end of section 4:

This demonstrates that all claims to the effect that the predictions of quantum theory are incompatible with the existence of hidden variables, with an underlying deterministic model in which quantum randomness arises from averaging over ignorance, are wrong. For Bohmian mechanics provides us with just such a model: For any quantum experiment we merely take as the relevant Bohmian system the combined system that includes the system upon which the experiment is performed as well as all the measuring instruments and other devices used in performing the experiment (together with all other systems with which these have significant interaction over the course of the experiment). The "hidden variables" model is then obtained by regarding the initial configuration of this big system as random in the usual quantum mechanical way, with distribution given by |Ï|2. The initial configuration is then transformed, via the guiding equation for the big system, into the final configuration at the conclusion of the experiment. It then follows that this final configuration of the big system, including in particular the orientation of instrument pointers, will also be distributed in the quantum mechanical way, so that this deterministic Bohmian model yields the usual quantum predictions for the results of the experiment.

This doesn't go to the Heisenbergian extreme of stating that measurement outcomes are the only reality, but it does keep some of the same primacy of measurement, albeit in a hidden way. Rather than having interaction with the measurement apparatus determine a previously indeterminate state, the configuration of the measurement apparatus determines the shape of the wavefunction, which then guides the particles along a particular trajectory.

A lot of time is spent denying the importance of the act of measurement, but it seems to me that this is just pushed back a step. I'm not sure there's as much difference between "measuring the state determines the state" and "the configuration of the measurement apparatus determines the evolution of the definite state" as the author clearly wants me to think.

- There are some claims that strike me as... let's say "inflated in their phrasing." For example, in the paragraph before the one quoted above, the list of virtues of their formulation begins:

First, it makes sense for particles with spin -- and all the apparently paradoxical quantum phenomena associated with spin are, in fact, thereby accounted for by Bohmian mechanics without further ado.

That sounds pretty interesting-- if Bohmian mechanics explains spin, that would be really cool. So I read down to the section on spin, which starts with:

We thus might naturally wonder how Bohmian mechanics manages to cope with spin. But this question has already been answered here. Bohmian mechanics makes sense for particles with spin, i.e., for particles whose wave functions are spinor-valued.

This is anticlimactic, to say the least. Bohmian mechanics makes sense of spin because it works with spinor-valued wavefunctions. Yeah, well, so does orthodox quantum theory-- in fact, I'm teaching an upper-level quantum mechanics course right now that started off with spinor-valued wavefunctions on day one. I'm not seeing the huge gain, here. It's not like the Bohm approach explains the existence of spin, and I can perfectly well formulate the Schrödinger equation in a way that takes spinor-valued functions in a more orthodox theory. Color me unimpressed.

- If I'm not mistaken, every pro-Bohm quote in the article is taken from one book by John Bell. Which makes me wonder why I'm reading this, rather than just reading Bell's book...

- The article tries to walk a weird line between brushing off non-locality/ contextuality as not that big a deal:

However, to understand contextuality from the perspective of Bohmian mechanics is to appreciate that almost nothing needs to be explained. Consider an operator A that commutes with operators B and C (which however don't commute with each other). What is often called the "result for A" in an experiment for "measuring A together with B" usually disagrees with the "result for A" in an experiment for "measuring A together with C" because, even if everything else is the same, these experiments are different and different experiments usually have different results. The misleading reference to measurement, with the associated naive realism about operators, makes contextuality seem more than it is.

(note the shot at "naive" realism, and also the primacy of measurement), while also suggesting that it's a virtue of the theory. This is a little weird.

It's especially weird given the section on Lorentz invariance, where the author admits that "Lorentz invariant nonlocality would remain somewhat enigmatic." That's an understatement.

There's a brief suggestion of an approach that views Lorentz invariance as a statistical property of measurements rather than a fundamental symmetry of space-time, an approach which would seem likely to make a few heads explode (though perhaps fertile ground for SF writers looking to hand-wave FTL), but it's skipped over pretty quickly, which is understandable given the awkwardness of the topic.

- As I said above the fold, I still don't quite see the point. That is, I understand that it's a theory with definite particle properties at all times, but if at the end of the day, you're still going to calculate the probabilities of the outcomes of your measurements using the same old Born rule, I don't see how you've gained anything. Other than a warm sense of philosophical satisfaction at having retained definite particle properties, which combined with a dollar will get you a candy bar.

Which is not to say that there might not be something out there to be gained from this approach. It may be that some future Bohmian version of quantum field theory will produce predictions that differ sharply from the orthodox quantum theory, in ways that will be experimentally testable, or even useful. (Again, the notion of putting Lorentz invariance on the same statistical footing as the Second Law of Thermodynamics seems like an interesting place to look for this sort of thing. And, as a bonus, it would make some heads explode.) Absent that, though, it seems like just another meta-theory, albeit one with more unique mathematical apparatus than Many-Worlds or Copenhagen.

So there's my semi-demi-hemi-informed first thoughts on taking a more serious look at the theory. I may poke through that textbook a little to see if there's anything interesting in the mathematical details, but at the moment, I have a little catching up to do after spending the last couple of days in an illness-induced fog.

drorzel Thu, 05/13/2010 - 06:03

Tags

Thanks for looking into Bohmian Mechanics.

But I can't believe that article is giving an accurate description of BM, because it sounds kinda dumb.

It seems like a bunch of hoops to jump through to reform standard theory in a package so you can say "This demonstrates that all claims to the effect that the predictions of quantum theory are incompatible with the existence of hidden variables, with an underlying deterministic model in which quantum randomness arises from averaging over ignorance, are wrong." But that's not a point anyone would argue: the issue to get at is "non-local hidden variables".

Bohmian mechanics seems to me to be one of those things (like Ilya Prigogine, or Hestenes' geometric algebra, or Ron Paul) which has a legion of intensely loyal supporters on the internet who like to oversell its virtues and seem kind of cultish, in a way that's really off-putting.

Here's a couple of links that may be more useful for you, as they use the Bohmian approach for the best reason of all--it makes the calculations more tractable:

http://pubs.acs.org/doi/abs/10.1021/jp055889q

http://k2.chem.uh.edu/preprints/draft-bittner.pdf
(The latter is an invited review chapter for Applied Bohmian Dynamics, Xavier Oriols and Jordi Mompart, Eds.)

One of the problems with science on the internet is demonstrated by the fact that Bohmian mechanics, an extremely old subject whose community of practitioners consists of maybe two dozen people worldwide, is attracting more attention than whole fields which actually have new and interesting things going on all the time. Hey, there are Iron-based superconductors, a fact we did not know about until recently, isnât it more interesting to talk about something new?

(Anything that does not incorporate QFT and all its predictions, many of them follow from combination of Lorentz invariance and QM, will not make heads explode, it will make shoulders shrug).

As I said above the fold, I still don't quite see the point. That is, I understand that it's a theory with definite particle properties at all times, but if at the end of the day, you're still going to calculate the probabilities of the outcomes of your measurements using the same old Born rule, I don't see how you've gained anything. Other than a warm sense of philosophical satisfaction at having retained definite particle properties, which combined with a dollar will get you a candy bar.

I dunno. What do you want out of life, man?

An interpretation can do one of two things. Either it can agree with all of the predictions of quantum mechanics (in which case of course you will still use the Born rule et. al.) or it can make a different prediction. If it is the former then people complain that it offers nothing over standard quantum mechanics and if it is the latter then people complain because it disagrees with quantum mechanics, so it must be wrong. The same objection is true of many-worlds, i.e. you still use the Born rule (providing you can make sense of why you should), but you didn't raise that as an objection against it.

In fact, Bohmian mechanics does make predictions that differ from quantum theory if we drop the equilibrium hypothesis -- something it makes sense to do in BM but not in standard QM. If we do that then we have to argue that there is an approach to equilibrium similar to that in statistical mechanics and we have to investigate the possibilities of observing nonequilibrium states. This is what Valentini's work is all about and that's why I suggested you should take a look at it as well.

In some sense BM has the best of both worlds in that we can say it agrees with QM completely if we happen to be in equilibrium, but it does offer the possibility of divergent physics as well.

What I found most surprising in your summary was the lack of mention of the fact that Bohmian mechanics solves the measurement problem, i.e. there is no ambiguity about whether the pointer on a measurement device is actually pointing to a particular outcome or not. This, after all, is the main point of any realist interpretation of quantum theory and nobody would take it even a little bit seriously if it didn't do that. The theory that results does have quite a few quirky features, as you point out, but we know from various no-go theorems that any hidden variable theory HAS to have many of those features, e.g. dependence of the outcome on configuration of the measurement apparatus follows from Kochen-Specker, lack of fundamental Lorentz invariance follows from Bell, etc. Therefore, I don't think these arguments are big drawbacks of the theory, since, if you are a realist, then you still have to solve the measurement problem in some way. (If you are not a realist then I am not quite sure why you would be worrying about interpretations in the first pace). The only semi-coherently-worked-out way of doing this that doesn't fall afoul of no-go results is many worlds, the virtues of which have been discussed already on this blog.

Regarding the chip on the shoulder thing, this is fairly common amongst realist foundations of QM types of a certain age. What you have to remember is that studying foundations from the '60s to the '80s was regarded as a pretty cranky pursuit. Most physicists believed that Bell's theorem had ruled out ALL hidden variable theories, without the crucial qualifier of LOCAL that we would use today. Hell, most physicists still believed that von Neumann had conclusively ruled out hidden variables. Very few people had actually read Bell's papers in any detail. Therefore, if you were working on things like Bohmian mechanics at that time then you had a pretty huge battle on your hands. Tenure, publication in journals and conference invites were not easy to come by for the would be quantum realist (and the situation is only a tiny bit better today). So yes, Goldstein (who wrote the article) probably does have a huge chip on his shoulder, and rightly so considering that through most of his career the physics community has been making it quite clear to him that they think his work is a load of old crap.

Since the combative attitude is so common in the foundations community, I think one needs to tune it out and try to judge the work on its merits. Fortunately, I find that younger foundations researchers don't have this attitude so often (or at least they don't have it yet).

Regarding the preponderance of Bell quotes, this is also fairly common in realist papers of a certain stripe. This is because Bell was one of the clearest thinkers there has ever been in the foundations of quantum theory and was a vociferous supporter of this type of realism. It is really difficult to state the arguments more clearly than he did. Therefore, yes you should be reading "Speakable and Unspeakable..." and so should anyone else who wants to have an informed opinion on foundations. That said, I do agree that the tendency to continuously quote the "gospel according to Bell" can get a bit grating after a while.

The only thing that bugs me as much as it bugs you about the article is the whole "naive realism about operators" shtick. If I were into accusing people of being naive, I could equally accuse the Bohmians of being "naive realists about wavefunctions". There can actually be good reasons for being realist about operators, especially if your realism is tempered by a good dollop of operationalism, which mine is. I'm not saying I completely buy operationalist approaches either, but the phrase "naive realism about operators" does tend to imply that there is no way of being realist about them that is non-naive.

And (as Lubos-Colbert would say) that's the memo.

I was disappointed that my misreading of the title as "Bohemian mechanics" wasn't borne out by the body. Perhaps you could write a followup about the influence of a relaxed scruffiness and gentle irony on 20th-century theories of physics.

Moshe: One of the problems with science on the internet is demonstrated by the fact that Bohmian mechanics, an extremely old subject whose community of practitioners consists of maybe two dozen people worldwide, is attracting more attention than whole fields which actually have new and interesting things going on all the time. Hey, there are Iron-based superconductors, a fact we did not know about until recently, isnât it more interesting to talk about something new?

As I said, people keep asking me about it. If people start asking me about iron-based superconductors, a subject I know even less about than quantum foundations, I will go learn something about iron-based superconductors. Lord knows, I'd be happy to find people who want to talk about something other than quantum interpretations and high-energy theory, but I'm stuck with the Internet we have, not the Internet I would like to have.

Anything that does not incorporate QFT and all its predictions, many of them follow from combination of Lorentz invariance and QM, will not make heads explode, it will make shoulders shrug

I was implicitly assuming that some future Bohmian field theory would match the predictions of QFT that have been experimentally confirmed. Otherwise, it would be pretty pointless.

Matt: In fact, Bohmian mechanics does make predictions that differ from quantum theory if we drop the equilibrium hypothesis -- something it makes sense to do in BM but not in standard QM. If we do that then we have to argue that there is an approach to equilibrium similar to that in statistical mechanics and we have to investigate the possibilities of observing nonequilibrium states. This is what Valentini's work is all about and that's why I suggested you should take a look at it as well.

This is, of course, the obvious weakness in reading about it via the Stanford Encyclopedia of Philosophy rather than more physics-oriented sources-- you get a limited presentation of relatively established stuff. I'll look for Valentini's stuff next.

In some sense BM has the best of both worlds in that we can say it agrees with QM completely if we happen to be in equilibrium, but it does offer the possibility of divergent physics as well.

That is a selling point, I agree. Though the QFT comments above are an important check on anything-- there are some pretty tight experimental constraints imposed by things like the Lamb shift and the electron g-factor, and I think I'd want to see those matched before spending too much time.

I thought that was implicit in the definite particle states business.

Anyway, yes, it solves the solvable bit of the measurement problem, which is to say "Why do we see only one outcome?" The other question-- "Why did this particular realization of this experiment give this exact result?" is sort of pushed back to the equilibrium hypothesis. which, to be fair, is arguably better than any of the other theories.

Oh, absolutely.
It's a vicious cycle-- if you work on something that sounds crank-ish, you get defensive about being seen as a crank, and that defensiveness is also characteristic of cranks. Lather, rinse, repeat.

Still, it's off-putting, especially without an independent way to assess the credibility of the author.

Well, that's pretty much Einstein in a nutshell, isn't it?

My immediate reaction to "Bohemian Mechanics" is more "Scaramouche, Scaramouche, can you do the fandango?" Which doesn't really lead anywhere good...

Yeah, OK, we agree on the basic point (including BTW the too much HET part, and not always the most solid part of HET either). My short experience with blogging also indicates that once you start talking about the bread and butter of what is going on in your field, people tend to drift off. Still, I feel the need to clarify what is the relative weight of various things, so outsiders donât get this absurdly skewed view. It is hard to do though, at least without being disparaging (as my rant above probably demonstrates).

I tried to teach a graduate course on it, for what it's worth. See here.

If it helps, I don't have a chip on my shoulder. I just think this stuff is quite fun.

If Bohmian QM can calculate a normal trajectory, why not simulate it in the lab with upsized particles and guiding waves? With today's technology, it is possible to guide objects according to any calculated law, with the help of radiofrequency or e-m fields. This would help to settle interpretational issues experimentally.

So... stupid question: Is momentum conserved in Bohmian mechanics?

It seems to me that the Bohm idea is full of problems. Just off top of my head: if every particle has definite position and velocity then why the residual energy of motion "due to the uncertainty principle." How does tunneling of the "real particles" occur? How about decay in general, why that distribution if a real clockworkey mechanism in there? The latter would have a time structure and not be genuine Poisson style decay? Then maybe handling delayed choice experiments, Renninger null, non-interactive redistribution (blockage in an interferometer leg) etc. How does this pilot wave interact with things? And so on.

I'm glad to see Mike Towler weigh in here. Consider him the world's expert on the subject, Chad. Being a modest Englishmen, he will of course deny this. That's fine. Name a better expert then, Mike.

I started a page on Towler, here, in early March, in which I also reference Robert Wyatt's excellent text, Quantum Hydrodynamics. It seems that BM or PWT has many other uses besides Foundational Physics, notably, as a teaching tool in Fluid Dynamics.

Now, if could just tie all of this together with quark-gluon plasma and black hole thermodynamics, hmm, ....

I just wanted to point out that there are several versions of Bohmian theory that reproduce QFT. My favorite is one that uses a particle ontology for fermions and a field ontology for bosonic fields due to Samuel Colin. None of these theories are fundamentally Lorentz invariant -- they can't be due to Bell's theorem -- but they are Lorentz invariant at the operational level provided the equilibrium hypothesis holds. Therefore, you can still use all your favorite Lorentz invariant techniques, just as you can still use the Born rule in nonrelativistic QM. At the fundamental level there is a preferred reference frame, which might admittedly seem distasteful, but the only way you are going to be able to get around that in a hidden variable theory is to make radical changes to the ontology, e.g. relational or retrocausal variables, and no one has made much sense of these to date.

Regarding nonequilibrium, I agree that current experiments provide extremely tight constraints. However, you can say the same thing about almost any proposed modification of QM. In fact, whenever someone proposes an modification of QM, it almost always gets tested fairly quickly in tabletop optical systems. This is fairly pointless because we already know that optical systems obey QM to extremely high precision. If the modifications hold anywhere then it has to be under fairly extreme conditions where current physics has not been tested experimentally. Nonequilibrium has an advantage over other proposed modification schemes in that its effects are expected to wash out very quickly so observing precise QM in the lab does not rule out nonequilibrium in the early universe for example. This is the sort of thing that Valentini is proposing.

Neil B: The answer to your first question is that the mass times the velocity of the Bohmian trajectory is not the same as the momentum you would obtain from measuring the usual momentum operator. Both are also uncertain due to the equilibrium hypothesis, but the measured momentum gets some of its uncertainty from the uncertain position of the measuring device as well. To answer the rest of your questions, you can prove that BM reproduces the predictions of QM exactly, so there is no problem explaining any of these experiments. It is true that in order to do so the Bohmian trajectories have to behave very weirdly compared to our intuitions about how trajectories should behave. For example, the Bohmian trajectory of a stationary state is stationary, so electrons orbiting an atom aren't actually orbiting at all according to Bohm. Trajectories also behave weridly in interferometers, Stern-Gerlach and the like, but basically you're going to have to have weird trajectories in order to reproduce QM rather than classical physics.

Note to self: I need to stop writing so many long comments defending Bohmian mechanics on other peoples' blogs. People will get the wrong idea.

Bottom line: Bohmian mechanics is probably not true as far as I am concerned. However, it is the most coherently worked out realist interpretation of QM and, as such, it is an incredibly useful foil for all sorts of foundational ideas. In particular, it is a first class b*****t detector. Next time you find yourself writing something like "QM implies that a particle can be in two places at once" or "instead of going through one slit or the other, a quantum particle goes through BOTH slits", ask yourself whether this is true in Bohmian mechanics. If not, then it is not really quantum mechanics that implies these things, but quantum mecahnics combined with some unspoken Copenhagenish assumptions that may turn out to be false in the long run.

Matt, if you are still paying attention...typically physical theories have many mathematical formulations, all of which are exactly equivalent, but employ different fiduciary objects (by which I mean those who do not correspond to results of measurements). QM has path integrals and operators on Hilbert spaces, wavefunctions or density operators. In QFT this only gets worse, for example you have bosonization, which means the exact same theory can be formulated in terms of bosons or in terms of Fermions. In other example you see that the dimensionality of spacetime, or the type of fields you have is also description-dependent. So, life is complicated when you look at complicated physical systems, and I am not sure what are the rules to determine the ontological status of those different objects. Is the idea getting a pretty picture, or is there something more systematic involved?

Or, when Clifford (and myself) are struggling to find an answer to a fairly similar question in quantum gravity, in

http://asymptotia.com/2010/05/11/but-is-it-real-part-one/comment-page-1…

is there a set of criteria we can use to reach an intersubjective conclusion?

QM is just weird, period. To agree with what the voltmeter says, the weirdness has to be there. Bohmian stuff to me takes all the weirdness and lops it into a very weird potential. You can do QM as JUST a statistical theory, albeit with negative probabilities. The weirdness has to be there, and it can be smeared around in the math so its harder to notice, or it can be balled up like a dust bunny in the corner of the room, but its got to be there.

See full response at http://www.mythiclogos.com/blog/?p=38. It was a little too long for a comment.

As a realist, basically, I want clearly formulated theories that apply outside physics labs. I like BM, but other alternatives are fine (they do exist) as long as they give a clear ontology, i.e., the contact with reality.

The Dirac equation, hence spin, can be derived from Bohmian notions (http://jostylr.com/thesis.pdf, chapter 3 )

Measurements appear only when discussing experiments. The theory itself is not concerned with measurements. Note that BM allows one to talk about and do experiments that measure the position of the particle incorrectly, but do measure the position observable. Hence the quote about "naive realism about operators"; they do not necessarily correspond to an underlying reality. One needs to prove that they do, when they do. And one needs an underlying theory to do that.

BM forms a very clear starting point for extending theories and can be used to easily extend QM to many places where standard quantization has issues such as general manifolds.

But really, I just want a story that minimizes "ridiculous, but true". And that is BM. It is simple and it is the closest to my sense of reality of all the theories that I have seen.

I think that the simple macroscopic fluid-dynamics related experiments that demonstrated behavior analogous to observations on the quantum level are largely responsible for the resurgence in the popularity of the brogile-bohm theory. But I wouldn't worry about it, since the internet search trends for terms like "bohmian mechanics" are stagnant.

You can say what you will, but many-worlds is as crack pot as it gets. Is it cool, yes. Is it real...not a chance.