I will think about it. Not sure I see a big the difference with
Everett, but I need to look to the original papers.
Bruno
On 17 Dec 2014, at 05:01, meekerdb wrote:
This may be a step toward Bruno's idea taken from the other
(Aristotelean) side.
Brent
-------- Original Message --------
New post on Sean Carroll
Guest Post: Chip Sebens on the Many-Interacting-Worlds Approach to
Quantum Mechanics
by Sean Carroll
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.
Figure 1: The evolution of Ψ with the amount of color proportional
to the amplitude (a.k.a. magnitude) and the hue indicating the phase
of Ψ.
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.
Figure 2: The evolution of |Ψ|2.
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.)
Figure 4: The evolution of particles in figure 3 with the particle
that lives in our world highlighted.
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.”
Sean Carroll | December 16, 2014 at 3:02 pm | Categories: Guest
Post, Philosophy, Science | URL: http://wp.me/p2WMeM-3cq
Comment See all comments
Unsubscribe to no longer receive posts from Sean Carroll.
Change your email settings at Manage Subscriptions.
Trouble clicking? Copy and paste this URL into your browser:
http://www.preposterousuniverse.com/blog/2014/12/16/guest-post-chip-sebens-on-the-many-interacting-worlds-approach-to-quantum-mechanics/
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
