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Quan­tum Mechanics

TagLast edit: 10 Feb 2021 18:30 UTC by Yoav Ravid

Quantum Mechanics: the bad news: our ordinary world is made out of weird, fuzzy, unpredictable stuff. The good news: the weird, fuzzy, unpredictable stuff is made out of unfamiliar but perfectly sensible math.

Related Pages: Physics, Decoherence, Many-worlds interpretation, Configuration space,Egan’s Law, Timeless Physics

The biggest conceptual difference between the world of quantum mechanics and the physical world at the level we typically interact with is that it’s much harder to specify the state of a system. Classical systems like a bowling ball or a planet have well-defined positions and velocity, and the state of such a system can be completely specified by just those two quantities. Quantities like position and velocity are called vectors, and in a 3-dimensional world a vector has component along each of the 3 dimensions. The state of a classical point particle can thus be given by just 6 numbers.

In quantum mechanics, particles don’t have both a well-defined position and velocity, and as a consequence, the vector that describes a quantum system can’t be expressed in just 3 dimensions. In general, there is no upper limit on the number of dimensions a quantum system can have, and so while the state of our bowling ball exists in two 3D spaces (one for position and one for velocity), a quantum system, in general, exists in a space that’s similar to the 3D space we’re used to, but with an infinite number of dimensions. This space is called Hilbert space. In order to be able to write down answers without using infinite numbers, quantum systems are usually mapped to other “spaces” like the 3D position and velocity spaces that we mentioned before. But information can be lost in this mapping, the same way a low-resolution photograph won’t fully capture a 3-dimensional object. As a consequence of the lossy nature of this transformation, instead of the position of a quantum particle we instead get a distribution of possible positions. This is why quantum mechanics is often described as random or unpredictable.

Actually, quantum mechanics is perfectly predictable in Hilbert space. The only difficulty is that we don’t live in Hilbert space, and while we have meter sticks and interferometers for making measurements in 3D space, we don’t have any equipment for measuring Hilbert space directly. As a consequence, we have to make guesses about quantum systems based on what we see in 3D space. This is made even more difficult by the fact that once you measure a quantum system, it doesn’t have the same distribution of possible positions it did before you measured it, so you can’t sample repeatedly from the same distribution. Because we can’t measure Hilbert space, the detailed dynamics of how exactly Hilbert space maps to real space, and what exactly happens in Hilbert space when you measure a system are still a matter of speculation and debate. People here have generally favored Hugh Everett’s many-worlds interpretation over others.

In spite of that, quantum mechanics is a mature field, and even if there’s some uncertainty about what the results might imply, actually doing quantum mechanics is not terribly difficult for single-particle systems. From a practical standpoint, the evolution of the state of the system (also called the wave function or the state vector) is governed by differential equations the same way it is in classical physics. In quantum mechanics, this equation is called Schrödinger equation and most of practical quantum mechanics is concerned with solving this equation for different sets of boundary conditions, and in trying to find a “space” in which the quantum system can be expressed and solved most easily. Systems of more than one particle are considerably trickier because the state vector has to be mapped into multiple different 3D spaces at the same time.

External Links

Mangled Worlds

Resources

Con­figu­ra­tions and Amplitude

Eliezer Yudkowsky11 Apr 2008 3:14 UTC
47 points
390 comments10 min readLW link

I’m still mys­tified by the Born rule

So8res4 Mar 2021 2:35 UTC
74 points
42 comments10 min readLW link

Distinct Configurations

Eliezer Yudkowsky12 Apr 2008 4:42 UTC
49 points
23 comments6 min readLW link

De­co­her­ence is Simple

Eliezer Yudkowsky6 May 2008 7:44 UTC
50 points
61 comments11 min readLW link

De­co­her­ence is Falsifi­able and Testable

Eliezer Yudkowsky7 May 2008 7:54 UTC
37 points
40 comments9 min readLW link

Liv­ing in Many Worlds

Eliezer Yudkowsky5 Jun 2008 2:24 UTC
47 points
79 comments5 min readLW link

Quan­tum Non-Realism

Eliezer Yudkowsky8 May 2008 5:27 UTC
37 points
37 comments8 min readLW link

If Many-Wor­lds Had Come First

Eliezer Yudkowsky10 May 2008 7:43 UTC
73 points
181 comments9 min readLW link

[Question] Are the Born prob­a­bil­ities re­ally that mys­te­ri­ous?

Adele Lopez2 Mar 2021 3:08 UTC
43 points
13 comments1 min readLW link

[Question] What am I miss­ing? (quan­tum physics)

kithpendragon21 Aug 2020 12:39 UTC
10 points
11 comments1 min readLW link

Quan­tum Explanations

Eliezer Yudkowsky9 Apr 2008 8:15 UTC
64 points
58 comments6 min readLW link

Many Wor­lds, One Best Guess

Eliezer Yudkowsky11 May 2008 8:32 UTC
31 points
79 comments13 min readLW link

Joint Configurations

Eliezer Yudkowsky11 Apr 2008 5:00 UTC
50 points
40 comments4 min readLW link

Col­lapse Postulates

Eliezer Yudkowsky9 May 2008 7:49 UTC
41 points
64 comments3 min readLW link

Where Philos­o­phy Meets Science

Eliezer Yudkowsky12 Apr 2008 21:21 UTC
37 points
22 comments4 min readLW link

Quan­tum Joint Con­figu­ra­tion ar­ti­cle: need help from physicists

mwengler22 Dec 2010 18:32 UTC
25 points
10 comments2 min readLW link

Quan­tum Me­chan­ics, Noth­ing to do with Consciousness

Donald Hobson26 Nov 2018 18:59 UTC
10 points
27 comments3 min readLW link

Quan­tum im­mor­tal­ity: Is de­cline of mea­sure com­pen­sated by merg­ing timelines?

avturchin11 Dec 2018 19:39 UTC
9 points
8 comments2 min readLW link

Quan­tum the­ory can­not con­sis­tently de­scribe the use of itself

avturchin20 Sep 2018 22:04 UTC
7 points
16 comments1 min readLW link
(foundations.ethz.ch)

The Con­scious Sorites Paradox

Eliezer Yudkowsky28 Apr 2008 2:58 UTC
11 points
41 comments5 min readLW link

Rel­a­tive Con­figu­ra­tion Space

Eliezer Yudkowsky26 May 2008 9:25 UTC
16 points
22 comments8 min readLW link

Why I Pre­fer the Copen­hagen In­ter­pre­ta­tion(s)

dadadarren31 Oct 2020 21:06 UTC
5 points
44 comments4 min readLW link
(www.sleepingbeautyproblem.com)

[Question] Is “phys­i­cal non­de­ter­minism” a mean­ingful con­cept?

Liron16 Jun 2019 15:55 UTC
23 points
15 comments1 min readLW link

Im­pli­ca­tions of Quan­tum Com­put­ing for Ar­tifi­cial In­tel­li­gence Align­ment Research

22 Aug 2019 10:33 UTC
16 points
2 comments13 min readLW link