# Many Worlds Interpretation

1. Aug 11, 2006

### Riposte

I recently learned about the Many Worlds Interpretation of quantum mechanics from another post on this forum. Unfortunately, the post became more of an argument about whether some experiment had or hadn't proven this interpretation to be true, and there wasn't a whole lot of information on what MWI was. Does anyone have any suggestions on where to find more information?

From what I have read on it, I like the idea of a wavefunction which evolves solely according to Schroedinger's equation and does not collapse during observations. However, I was under the impression that the Copenhagen interpretation's collapse of the wavefunction was a necessary outcome of experiments. If an electron is observed to be at a particular location, then one femtosecond later, if observed again, it will not have strayed far. Measurements repeated in very quick succession, return nearly the same value for the electron's location. Is that true?

If so, then I don't see how the MWI can work. Let's say one observation of the electron finds it in an unlikely location. If the wavefunction did not collapse and still obeys Schroedinger's law, then a second observation is likely to find it in an entirely different spot.

If I'm wrong and the quickly taken electron measurements do not need to be consistent, then why was the wavefront collapse added to the Copenhagen interpretation?

2. Aug 11, 2006

### Hurkyl

Staff Emeritus
In MWI, measurements don't happen in the absolute sense; instead a measurement is simply entangling a "measuring device" with the system being "measured".

So, in your thought experiment, you began with two independent systems:
(1) Your electron, which is in a superposition of being in a "likely spot" and an "unlikely spot"
(2) Your measuring device.

Then after the experiment, the systems have been entangled, and are in a superposition of the two states:
(A) Your electron is in a likely spot and your measuring device says the electron was in a likely spot.
(B) Your electron is in an unlikely spot and your measuring device says the electron was in an unlikely spot.

If you had another measuring device and repeated the measurement, then you'd get the superposition of
(A) Your electron is in a likely spot and both measuring devices say the electron was in a likely spot.
(B) Your electron is in an unlikely spot and both measuring devices say the electron was in an unlikely spot.

and so forth.

3. Aug 11, 2006

### lalbatros

Riposte,

I like it too.
Specially as it is a direct consequence of the interaction (entanglement) between a microscopic object and a macroscopic object. No need for more! No need for science fiction!

(See Landau & Lifchits, Quantum Mechanics Chap 1, §7)

Michel

Last edited: Aug 12, 2006
4. Aug 11, 2006

### BoTemp

I'm of the same mindset as Riposte on MWI v Copenhagen. I can accept a non-deterministic future, but I have difficulty accepting a non-deterministic past. But that's just me.

Does anyone know of mathematical explorations of MWI? My understanding is that at the mathematical level, interpretations aren't relevant, so maybe that's a dumb question. What I am looking for is work showing how QM reduces to CM as particle number (or mass, or something else) becomes large. Mainly particle number, as an entanglement of a large number of particles would be a a description of macroscopic reality. Shining a light on a baseball to see where it is is a measurement.

5. Aug 12, 2006

### lalbatros

BoTemp,

The transition from QM to CM is explained in many books.
I can mention "Quantum by E. Elbaz, Springer".
It starts with an overview on classical mechanics: Lagrange, Hamilton, least action, Hamilton-Jacobi.
If I remember well "Messiah" is also a good reference on that.
You could also read about optics: the transition from physical optics to geometrical optics and the Maupertuis principle.

The transition from QM to CM is not really related to the number of particles.
The transition occurs when the limit $\hbar \rightarrow 0$ becomes a good approximation for the system considered. For example, this is the case for the electron in an hydrogen atom for high 'n' states, called the Rydberg states. A classical picture of the motion emerges then.

You can learn the essential by yourself. Refresh on the least action principle in CM.
Then work out this "exercice":
start from the Schrödinger equation $$\newcommand{\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } }i \hbar \pd{\Psi}{t}{} =- \frac{\hbar^2}{2 m} \ \pd{\Psi}{x}{2} + V \Psi$$

assume $$\Psi = e^{\frac{i}{\hbar} S}$$, S is the "action"

make this subtitution and get a partial differential equation for S

observe what happen if $\hbar \rightarrow 0$

in this limit, the equation you get is the "Jacobi" equation from CM

the physical interpretation is very interresting
it explains -in a sense- the origin of the least action principle in CM

the term neglected in the classical limit is called the quantum potential
it sustains the "random" of QM: it couples the probability to the motion !!
this is the start point for the Bohm point of view on QM​

I think with all these keywords above, you will easily find anything you need from the web.
Also, read Feynmann once more!

Enjoy,

Michel

PS:
Note also another book: From Classical to Quantum Mechanics that makes the reverse journey.
This book goes from particular to more general, like history.

Last edited: Aug 12, 2006
6. Aug 13, 2006

### selfAdjoint

Staff Emeritus
Albert Messiah's Quantum Mechanics is now available as a cheap Dover reprint

7. Aug 13, 2006

### Schrodinger's Dog

Thanks for that I checked it out on Amazon, apparently it's good as reference but terrible as first source for the material

And I was going to buy that too? Any thoughts?

8. Aug 16, 2006

### nrqed

So decoherence is totally irrelevant in MWI?

I thought that one might have to consider instead a tensor product

$$( |el-A> + |el-B>) \otimes (|md-A> + |md-B>) = |el-A> |md-A> +|el-A> |md-B>+|el-B> |md-A>+|el-B> |md-B>$$
where |el-A> = |electron in spot A>, |md-A> = |measuring device indicating elctron in spot A> , etc.

And I thought that decoherence was explaining the extremely rapid dampening out of the "cross terms" |el-A> |md-B> and |el-B> |md-A>.

I am probably mixing apples and oranges. Sorry.
So my questions are: am I understanding decoherence right? and does decoherence play any role in MWI?

9. Aug 16, 2006

### lalbatros

nrqed,

My feeling is that in the MWI society, to be polite, you should not pronounce the word "decoherence".

But you may use its (de facto) synonym: entanglement.

I concede, that MWI really is a comfortable luxury theory.
Life indeed becomes very simple: you can calculate and pretend not to "shut up"!
You have as many universe as you may want to talk about and explain anything.
But you don't predict anything more that simple "algebraic" QM.

Is this wealthy explanation affordable for common sense?

Michel

Postscriptum:
MWI is indeed a "simple" theory.
Maybe it is also a counter-exemple to the principle of simplicity.
It is simple to imagine a wealth of platonic universes, increasing beyond limits the number of degree of freedom in the explanations without bringing any new result. It would be better to reduce the degrees of freedom!
Simplicity doesn't necessarily make sense!
I would like to know why the world behaves as if MWI was true!

Last edited: Aug 17, 2006
10. Aug 16, 2006

### Hurkyl

Staff Emeritus
I thought it was still important? Anyways, my impression is that it works like this.

First, consider an isolated system. Say, a qubit whose basis states are |0> and |1>.

You have an interaction T that performs the following transformation on your qubit. (ignoring constant factors)

T|0> = (|0> + |1>)
T|1> = (|0> - |1>)

Then, if you prepared the superposition |0> + |1>, then applied your interaction, you get:

T(|0> + |1>) = |0>

the amplitudes for |1> have interfered and cancelled out. Life is great!

But suppose the system is not isolated. When we prepare our superposition, we really have something like:

(|0> + |1>)|e>

where |e> denotes some environment state. Then, before we're ready, the environment interacts with our qubit (decoherence) giving us:

|0>|e'> + |1>|e''>

Then, when we try applying T, we get:

|0>(|e'> + |e''>) + |1>(|e'> - |e''>)

Lo and behold, decoherence has spoiled our superposition, and the amplitudes for |1> don't cancel out!

If we leave the environment out of the analysis, and just focus on our qubit, then it can be described as follows: we started with our qubit in a superposition

|0> + |1>

and then decoherence had spoiled it, turning it into the statistical mixture

50% chance of being in |0>
50% chance of being in |1>

I think that's a good description of what happens to the density matrices -- but if you're looking at the state vectors that's not right.

11. Aug 17, 2006

### lalbatros

Hurkyl

Note that pure states can also be described by a density matrix.

The discussion -apparently- is "what to do when projecting a density matrix on a lower-dimensional space".
This starts with the density matrix of a pure-state but entangled system.
We want to "view" it as a density matrix of the initial (usually small) system.
The end result, everybody will agree, is not a pure state or 'pure' density matrix.
And the rule comes from the measurement postulate.
(Would another rule be even conceivable?)

Michel

12. Aug 17, 2006

### kvantti

This is not true. See this for example.

This is not true either. See this.

Because quantum theory is, as shown by Deutsch, a local theory when viewed from the Heisenberg picture and it merely appears to be non-local if viewed from the Schrödinger picture.

By the way for all of you who have questions concerning the MWI, please see The Everett FAQ by Michael Clive Price.

PS. Here is the link to the Wikipedia article about the subject.

Last edited: Aug 17, 2006
13. Aug 17, 2006

### lalbatros

kvantti,

After reading carefully your references as well a watching the Deutsch videos, I am sorry to say that there is not 1 bit of prediction that MWI can add to known experimental facts. (but for this I would have to buy such a huge amount of bits for the additional MWI reality!)

I only realised that the MWI is a very convenient way to brush off any discussion, which is similar to the "shut up and calculate". This is so because it is a way to formulate the essential difficulty of QM that is quite easy to visualize, like a science fiction cartoon. This essential difficulty can be traced back to the "quantum potential" in the Bohm viewpoint.

Now, to balance my opinion, I must say that I would not be reluctant at all to speak the MWI language. I do really think it is convenient. But I cannot see any new physics or any new progress in it.

Is that no good news? Finally it leaves the challenge totally open for those who like taking it.

Michel

Postscriptum
Can we seriously think that small linearities could help in any way making an advantage for the MWI? Would then other interpretation fall speechless? I could bet Michael Clive Price don't believe it anymore. Guess how many papers have been published on the NLSE, most without reference to the MWI.

Last edited: Aug 17, 2006
14. Aug 17, 2006

### kvantti

Apparently you didn't read this.

It is also a really convenient way to explain quantum physics as a local theory, which it actually is, as shown by Deutsch (and Tipler - see the end of the post).

Yes, and this is mostly due to physicists affraid of other physicists marking them as "crackpots". The poll in 1988 indicates that 58% of the 72 leading physicists at that time believed in many worlds interpretation. With the rise of string theory nowadays, I don't believe that the perceantage has decreased.

You are, ofcourse, free to believe in any interpretation; it is a matter of taste. But then again, the interpretation should be local. Here is a paper by Frank Tipler who has come to the same conclusion as Deutsch: quantum physics must be local:

"Thus, experiments confirming "nonlocality" are actually confirming the MWI."

15. Aug 17, 2006

### setAI

for the last decade David Deutsch's amazing work has firmly established the MWI as the only tenable interpretation of QM- the incredible success of his work and the work of those in quantum computer science has now made the MWI nearly universally accepted by the professional physics community- http://www.edge.org/3rd_culture/prize05/prize05_index.html however- this is a public physics forum- and given the socio-dynamics of forums it is inevitable that naysayers will still dispute the evidence as well as the consensus from the experts who actually understand the field and perform/publish experiments- and of course those of us who agree with their conclusions

"The quantum theory of parallel universes is not the problem, it is the solution. It is not some troublesome, optional interpretation emerging from arcane theoretical considerations. It is the explanation—the only one that is tenable—of a remarkable and counter-intuitive reality"
~David Deutsch

“The MWI is trivially true!” Steven Hawking

Last edited: Aug 17, 2006
16. Aug 17, 2006

### Hurkyl

Staff Emeritus
First off, it makes a silly mistake. It is impossible to compare the results of (1) and (3).

Secondly, ignoring that silly mistake, this experiment cannot distinguish between MWI and Copenhagen.

If the result of the experiment ostensibly agrees with MWI, the Copenhagenist just says "There's proof that your `machine intelligence' cannot collapse a wavefunction".

If the result of the experiment ostensibly agrees with Copenhagen, then MWIist just says "Decoherence happened, which spoiled the interference."

Stop making such ridiculous statements.

Your reference doesn't even come close to anything resembling support for your claim. :grumpy: Stop making such ridiculous statements.

And, of course, it is inevitable that there will be closed-minded people who cannot see any of the problems with their beliefs and arguments.

Interesting, the only reference on Google of SH saying exactly that in a post by you in another thread on PF.

Both of you have such extremely biased positions -- I actually like the MW interpretation, but your posts are just so ridiculous that I have to reject them.

Last edited: Aug 17, 2006
17. Aug 18, 2006

### lalbatros

" MWI and calculate ! " is the latest school in QM interpretation.

Fortunately, QM teaching all around the world do focus on what matters the most: the known physics, the maths behind and the their subtile and beautiful fit.

Interpretations, like dreams, can contribute only as far as they turn out as new operational theories. There is still plenty of room for fruitful interpretations. I dream of three ways to investigate:
the nature of space-time -again-,
the nature of vacuum fluctuations,
Information Theory​
I am very interrested to know about other tracks to go forward.

Michel

18. Aug 20, 2006

### Farsight

I thought we'd knocked all this stuff on the head back in another thread.

19. Aug 20, 2006

### Maaneli

Mwi

The reason for the MWI's popularity among quantum information theorists and philosophers of physics are a few fold. First, the Many Worlds interpretation is exactly that: an interpretation. There is no significant modification of the mathematical formalism of standard QM such as Schrodinger's equation. The state vector is interpreted not as a probabilistic superposition of states with a probabilistic collapse of the wave packet. Rather, all the possible consistent states of the measured system and the measuring apparatus are present in a real physical quantum superposition. This superposition of consistent state combinations of different systems is called an entangled state. With this interpretation, MWI actually removes the probabilistic projection postulates for the state vector and thus is distinctly simpler than Copenhagen. All this arises out of a single change in the interpretation of quantum superposition, and without any nonlinear mathematical modifications as in other formulations.

Secondly, measurement processes in MWI incorporate Zurek's quantum decoherence theory which is also widely considered among physicsts to be the resolution to the measurement problem.

Third, MWI is the only alternative to the Copenhagen formulation that is completely consistent with relativistic quantum field theory. Bohmian mechanics, stochastic mechanics, GRW, etc. are all still nonrelativistic in their formulation.

And of course, for physicists like Deustch, the potential for quantum computation faster than any classical computer.

20. Aug 21, 2006

### Hurkyl

Staff Emeritus
Don't forget the relational QM interpretation!

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