Re: [New post] Why Probability in Quantum Mechanics is Given by the Wave Function Squared
Thanks for posting, Brent. Fine topics to dig into when one takes the time. And if we never take the time for these things, how can we ever expect to derive proper energetic eigenvalues for hydrogen like stuff in the wave we're surfing on, independent of distracting deadlines? The hard answer nobody wants to face is: we don't. And the result is we die as lesser men. For only idiots wait for the right wave, blinking in the sun. A proper surfer of the fundamental just goes when it's time, surfs that one right wave, and simultaneously leaves the idiots waiting for the wave in his wake... forever. Timeless cojones. Not even a contest. The gender ghost haunts this statement mumbling something about exclusion, but I just destroyed it before it could finish the sentence. No time for vain attention sinks or these kinds of silly ghosts. They will be crushed as they have dangerous property of propagating tedious boredom broadcast waves, a highly contagious, prevalent, virulent disease of our time. We shouldn't engage this nonsense; just kill it, walk away, and not bother to even contemplate looking back. The wave pushes forward regardless, and laughs at time's ridiculous routines and dead lines. Born (squared tude) again. PGC On Thu, Jul 24, 2014 at 8:24 PM, meekerdb meeke...@verizon.net wrote: On 7/24/2014 11:09 AM, David Nyman wrote: On 24 July 2014 18:40, meekerdb meeke...@verizon.net wrote: 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, could you possibly summarise what you see as the essential distinction between the CS and Fuchs alternatives for dummies? I'd need to study CS's paper a little, I just read Sean's blog summary. But Fuch's quantum Bayesianism says that the collapse of the wave function is just like the collapse of a classical probability distribution when we learn the value of the random variable. It's purely epistemic. It's a sort of instrumentalism. Brent -- 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. -- 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.
Re: [New post] Why Probability in Quantum Mechanics is Given by the Wave Function Squared
On 24 Jul 2014, at 19:40, meekerdb wrote: 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. The universal machine does that too. Eventually all mode of existence are psychological, as you can guess by interpreting physics as the inside view of the arithmetical FPI undetermined machine. The observable (roughly the []p p ( p) hypostases (with p sigma_1) are mental, or machine self- referencial modalities. We just don't know yet if those dreams glue enough to determine a multiverse or a multi-multiverse, has filtered from what at the start his a giant web of (machine) dreams emulated in arithmetic. Nice post. I like Born, even when wrong. I appreciate the Born- Einstein dialog. Nice way to call the Copenhagen theory: the theory of disappearing universes, it is already closer to the brain filtration of realities, or consciousness differentiation. Bruno 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 + From: Sean Carroll donotre...@wordpress.com To: meeke...@verizon.net New post on Sean Carroll Why Probability in Quantum Mechanics is Given by the Wave Function Squared by Sean Carroll 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 (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: 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: 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 wasequal 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. When we teach quantum mechanics to undergraduate physics majors, we generally give them a list of postulates that goes something like this: Quantum states are represented by wave functions, which are vectors in a mathematical space called Hilbert space. Wave functions evolve in time according to the Schrödinger equation. The act of measuring a quantum system returns a number, known as the eigenvalue of the quantity being measured. The probability of getting any particular eigenvalue is equal to the square of the amplitude for that eigenvalue. 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. There are other formulations, and you know that my own favorite is Everettian (Many-Worlds) quantum mechanics. (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, 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: Quantum states are represented by wave functions, which are vectors in a mathematical space called Hilbert space. Wave functions evolve in time according to the Schrödinger equation. That's it! Quite a bit simpler -- and the two
Re: [New post] Why Probability in Quantum Mechanics is Given by the Wave Function Squared
On 24 Jul 2014, at 20:24, meekerdb wrote: On 7/24/2014 11:09 AM, David Nyman wrote: On 24 July 2014 18:40, meekerdb meeke...@verizon.net wrote: 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, could you possibly summarise what you see as the essential distinction between the CS and Fuchs alternatives for dummies? I'd need to study CS's paper a little, I just read Sean's blog summary. But Fuch's quantum Bayesianism says that the collapse of the wave function is just like the collapse of a classical probability distribution when we learn the value of the random variable. It's purely epistemic. It's a sort of instrumentalism. It would be purely epistemic if it made not the universe disappearing. But why postulate universe(s) at the start? We know only that there are person(s), and some agreements on 0, 1, 2, 3, ... Bruno Brent -- 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. 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 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.
Fwd: [New post] Why Probability in Quantum Mechanics is Given by the Wave Function Squared
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 +
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
Re: [New post] Why Probability in Quantum Mechanics is Given by the Wave Function Squared
On 24 July 2014 18:40, meekerdb meeke...@verizon.net wrote: 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, could you possibly summarise what you see as the essential distinction between the CS and Fuchs alternatives for dummies? David -- 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.
Re: [New post] Why Probability in Quantum Mechanics is Given by the Wave Function Squared
On 7/24/2014 11:09 AM, David Nyman wrote: On 24 July 2014 18:40, meekerdb meeke...@verizon.net mailto:meeke...@verizon.net wrote: 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, could you possibly summarise what you see as the essential distinction between the CS and Fuchs alternatives for dummies? I'd need to study CS's paper a little, I just read Sean's blog summary. But Fuch's quantum Bayesianism says that the collapse of the wave function is just like the collapse of a classical probability distribution when we learn the value of the random variable. It's purely epistemic. It's a sort of instrumentalism. Brent -- 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.
