This may clarify (or provoke) discussion of Moscow vs. Washington. It's interesting that
Carroll and Sebens use FPI and Sean says it increases his confidence in Everett's MWI.
But in his penultimate paragraph he essentially lays out an endorsement of Fuchs QBism,
which is generally seen as the instrumentalist alternative to MWI.
Brent
-------- Original Message --------
Subject: [New post] Why Probability in Quantum Mechanics is Given by the Wave Function
Squared
Date: Thu, 24 Jul 2014 15:21:04 +0000
From: Sean Carroll <donotre...@wordpress.com>
To: meeke...@verizon.net
WordPress.com
Sean Carroll posted: "One of the most profound and mysterious principles in all of physics
is the Born Rule, named after Max Born. In quantum mechanics, particles don't have
classical properties like "position" or "momentum"; rather, there is a wave function that
assigns a (co"
New post on *Sean Carroll*
<http://www.preposterousuniverse.com/blog/?author=4>
Why Probability in Quantum Mechanics is Given by the Wave Function Squared
<http://www.preposterousuniverse.com/blog/2014/07/24/why-probability-in-quantum-mechanics-is-given-by-the-wave-function-squared/>
by Sean Carroll <http://www.preposterousuniverse.com/blog/?author=4>
One of the most profound and mysterious principles in all of physics is the Born Rule
<http://en.wikipedia.org/wiki/Born_rule>, named after Max Born. In quantum mechanics
<http://www.preposterousuniverse.com/eternitytohere/quantum/>, particles don't have
classical properties like "position" or "momentum"; rather, there is a wave function
<http://en.wikipedia.org/wiki/Wave_function> that assigns a (complex) number, called the
"amplitude," to each possible measurement outcome. The Born Rule is then very simple: it
says that the probability of obtaining any possible measurement outcome is equal to the
square of the corresponding amplitude. (The wave function is just the set of all the
amplitudes.)
*Born Rule:* \mathrm{Probability}(x) = |\mathrm{amplitude}(x)|^2.
The Born Rule is certainly correct, as far as all of our experimental efforts have been
able to discern. But why? Born himself kind of stumbled onto his Rule. Here is an excerpt
from his 1926 paper
<http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Born_1926_statistical_interpretation.pdf>:
Born Rule
<http://www.preposterousuniverse.com/blog/wp-content/uploads/2014/07/bornrule.jpeg>
That's right. Born's paper was rejected at first, and when it was later accepted by
another journal, he didn't even get the Born Rule right. At first he said the probability
was equal to the amplitude, and only in an added footnote did he correct it to being the
amplitude squared. And a good thing, too, since amplitudes can be negative or even imaginary!
The status of the Born Rule depends greatly on one's preferred formulation of quantum
mechanics
<http://www.preposterousuniverse.com/blog/2014/05/29/quantum-mechanics-smackdown/>. When
we teach quantum mechanics to undergraduate physics majors, we generally give them a list
of postulates that goes something like this:
1. Quantum states are represented by wave functions, which are vectors in a
mathematical
space called Hilbert space <http://en.wikipedia.org/wiki/Hilbert_space>.
2. Wave functions evolve in time according to the Schrödinger equation
<http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation>.
3. The act of measuring a quantum system returns a number, known as the
eigenvalue
<http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors> of the quantity
being
measured.
4. The probability of getting any particular eigenvalue is equal to the square
of the
amplitude for that eigenvalue.
5. After the measurement is performed, the wave function "collapses" to a new
state in
which the wave function is localized precisely on the observed eigenvalue
(as opposed
to being in a superposition of many different possibilities).
It's an ungainly mess, we all agree. You see that the Born Rule is simply postulated right
there, as #4. Perhaps we can do better.
Of course we can do better, since "textbook quantum mechanics" is an embarrassment
<http://www.washingtonpost.com/blogs/wonkblog/wp/2013/02/07/quantum-mechanics-is-an-embarrassment/>.
There are other formulations, and you know that my own favorite is Everettian
("Many-Worlds") quantum mechanics
<http://www.preposterousuniverse.com/blog/2014/06/30/why-the-many-worlds-formulation-of-quantum-mechanics-is-probably-correct/>.
(I'm sorry I was too busy to contribute to the active comment thread on that post. On the
other hand, a vanishingly small percentage of the 200+ comments actually addressed the
point of the article, which was that the potential for many worlds is automatically there
in the wave function no matter what formulation you favor. Everett simply takes them
seriously, while alternatives need to go to extra efforts to erase them. As Ted Bunn
argues <http://blog.richmond.edu/physicsbunn/2014/06/30/many-worlds/>, Everett is just
"quantum mechanics," while collapse formulations should be called "disappearing-worlds
interpretations.")
Like the textbook formulation, Everettian quantum mechanics also comes with a list of
postulates. Here it is:
1. Quantum states are represented by wave functions, which are vectors in a
mathematical
space called Hilbert space.
2. Wave functions evolve in time according to the Schrödinger equation.
That's it! Quite a bit simpler -- and the two postulates are exactly the same as the first
two of the textbook approach. Everett, in other words, is claiming that all the weird
stuff about "measurement" and "wave function collapse" in the conventional way of thinking
about quantum mechanics isn't something we need to add on; it comes out automatically from
the formalism.
The trickiest thing to extract from the formalism is the Born Rule. That's what Charles
("Chip") Sebens <https://www.sites.google.com/site/csebens/> and I tackled in our recent
paper: Read more of this post
<http://www.preposterousuniverse.com/blog/2014/07/24/why-probability-in-quantum-mechanics-is-given-by-the-wave-function-squared/#more-12088>
*Sean Carroll <http://www.preposterousuniverse.com/blog/?author=4>* | July 24, 2014 at
8:19 am | Categories: arxiv
<http://www.preposterousuniverse.com/blog/?taxonomy=category&term=arxiv>, Philosophy
<http://www.preposterousuniverse.com/blog/?taxonomy=category&term=philosophy>, Science
<http://www.preposterousuniverse.com/blog/?taxonomy=category&term=science> | URL:
http://wp.me/p2WMeM-38Y
Comment
<http://www.preposterousuniverse.com/blog/2014/07/24/why-probability-in-quantum-mechanics-is-given-by-the-wave-function-squared/#respond>
See all comments
<http://www.preposterousuniverse.com/blog/2014/07/24/why-probability-in-quantum-mechanics-is-given-by-the-wave-function-squared/#comments>
Unsubscribe
<https://subscribe.wordpress.com/?key=a1ce795b5ed69b1da0629cff342548e7&email=meekerdb%40verizon.net&b=sC2%3DH1hEfToWz%25303-GQUd_j%3FRvaejPbFGMn%5DgZko5r-XC31t9>
to no longer receive posts from Sean Carroll.
Change your email settings at Manage Subscriptions
<https://subscribe.wordpress.com/?key=a1ce795b5ed69b1da0629cff342548e7&email=meekerdb%40verizon.net>.
*Trouble clicking?* Copy and paste this URL into your browser:
http://www.preposterousuniverse.com/blog/2014/07/24/why-probability-in-quantum-mechanics-is-given-by-the-wave-function-squared/
--
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 everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
