Many-worlds Interpretation

[ma1ic3]

Interesting article about quantum computing that mentions the many-worlds interpretation. I've never heard of this before. What would the Copenhagen interpretation be?

From: http://www.newscientist.com/channel/opinion/mg19225811.800-lone-voices-special-at-play-in-the-multiverse.html

"Say we decide to factorise a 10,000-digit integer, the product of two very large primes. That number cannot be expressed as a product of factors by any conceivable classical computer. Even if you took all the matter in the observable universe and turned it into a computer and then ran that computer for the age of the universe, it wouldn't come close to scratching the surface of factorising that number. But a quantum computer could factorise that easily in seconds or minutes. How can that happen?

Anyone who isn't a solipsist has to say the answer was produced by some physical process. We know there isn't enough computing power in this universe to obtain the answer, so something more is going on than what we can directly see. At that point, logically, we have already accepted the many-worlds structure. The way the quantum computer works is: the universe differentiates itself into multiple universes and each one performs a different sub-computation. The number of sub-computations is vastly more than the number of atoms in the visible universe. Then they pool their results to get the answer. Anyone who denies the existence of parallel universes has to explain how the factorisation process works."

[Paul C. Anagnostopoulos]

http://en.wikipedia.org/wiki/Many_worlds

http://en.wikipedia.org/wiki/Copenhagen_Interpretation


~~ Paul

[andyandy]

i would explain the many world interpretation - but i've already done it in another universe, and i don't want to repeat myself :D

[nimzov]

A series of video lectures by David Deutsch on quantum computing.

http://www.quiprocone.org/Protected/DD_lectures.htm

nimzo

[Squishua]

Interesting article about quantum computing that mentions the many-worlds interpretation.
Let's wait until they actually figure out a way to construct a "quantum computer" before we go hypothesizing on what we can infer from them.

AFAIK, there is no way, even in principle, to construct such a beast, let alone be able to get some kind of working input-output with it. Mr. Deutsch would probably qualify for the JREF's $million if he could actually produce such a device.

Castles in the sky....

-Squish

[Unnamed]

Let's wait until they actually figure out a way to construct a "quantum computer" before we go hypothesizing on what we can infer from them.

AFAIK, there is no way, even in principle, to construct such a beast, let alone be able to get some kind of working input-output with it. Mr. Deutsch would probably qualify for the JREF's $million if he could actually produce such a device.
How do you call the device that IBM used to factor the number 15 (http://domino.research.ibm.com/comm/pr.nsf/pages/news.20011219_quantum.html) using a quantum algorithm?

[Squishua]

How do you call the device that IBM used to factor the number 15 (http://domino.research.ibm.com/comm/pr.nsf/pages/news.20011219_quantum.html) using a quantum algorithm?
Sorry, I should have clarified that I was refering to a quantum computer that could do anything practical. 7 qbits is a hell of a long way from the computational power necessary to do a prime factorization of a 10,000 digit number.

-Squish

[Unnamed]

Sorry, I should have clarified that I was refering to a quantum computer that could do anything practical. 7 qbits is a hell of a long way from the computational power necessary to do a prime factorization of a 10,000 digit number.
Then we are in agreement. Short of an overwhelming scientific breakthrough, I don't expect to see one built in my life (quite like fusion power).

But the only million dollars for which it would qualify would be those from the Nobel committee.

[jmercer]

Sorry, I should have clarified that I was refering to a quantum computer that could do anything practical. 7 qbits is a hell of a long way from the computational power necessary to do a prime factorization of a 10,000 digit number.

-Squish

Then we are in agreement. Short of an overwhelming scientific breakthrough, I don't expect to see one built in my life (quite like fusion power).



You may be wrong about how long it will be before a useful quantum computer is built. Quantum encryption - both key and actual data - are a reality today; it's conceivable that a quantum processor (albeit a highly-specialized one!) may exist within a decade or two. I know for a fact that Intel and IBM are pursuing this in a non-pure-research fashion. :)

Time will tell.

[Squishua]

You may be wrong about how long it will be before a useful quantum computer is built.
Yes, the time frame is likely never

The computational power of a quantum CPU, assuming one could be constructed, would be negated by decoherence caused by the input/output interface. Enormous amounts of qbits must be used for error correction.

From Wikipedia:
For [prime factoring] a 1000 bit number, this implies a need for 10^12 to 10^18 qubits. Fabrication and control of this large number of qubits is non-trivial for any of the proposed designs.

The devil is in the details.

-Squish

[l0rca]

The article seems to be assuming our universe isn't infinite for its computing example.

[wipeout]

Interesting article about quantum computing that mentions the many-worlds interpretation. I've never heard of this before. What would the Copenhagen interpretation be?

The short version is that Copenhagen will always either repeat the final physical predictions of the much-expanded many-worlds interpretation that is decoherence theory or else it's screwing something up. The reason is that many-worlds and the later decoherence work follow quantum mechanics to the letter while Copenhagen tries to avoid that and ends in paradoxes. However, nobody needs to take any "worlds" of many-worlds other than our own as being real and wiser physicists don't do that. It could come back to bite people like Deutsch if an addition to the theory showed only one possible "world" becomes real.

[Squishua]

The article seems to be assuming our universe isn't infinite for its computing example.
The article is assuming that the amount of matter in the universe isn't infinite.

This view is shared by most physicists and cosmologists.

-Squish

[l0rca]

The article is assuming that the amount of matter in the universe isn't infinite.

That's what I meant.

This view is shared by most physicists and cosmologists.

Last I was here, there was an argument about this. I think the view on this has changed in the last few years, actually.

[Squishua]

Last I was here, there was an argument about this. I think the view on this has changed in the last few years, actually.
Hmm. I may need to update my references!

-Squish

[Zygar]

Last I was here, there was an argument about this. I think the view on this has changed in the last few years, actually.

I think they are referring to the amount of matter that was used for the Dark Matter/Dark Energy calculations. Effectively the amount of observable matter in the observable universe.

[baron]

I'm no expert on quantum computers but I'm pretty sure it's incorrect to say they rely on the many worlds hypothesis. AFAIK they work by exploiting the state potentiality of bits of information, and one of the possible explanations for how this works is the many worlds hypothesis. The other plausible explanation is the waveform collapse scenario, which essentially says that nothing exists in a definite form unless witnessed by a conscious observer.

Correct me if I'm wrong; as I say quantum computers aren't my strong point and it's too late to Google :)

[Ben Tilly]

The short version is that Copenhagen will always either repeat the final physical predictions of the much-expanded many-worlds interpretation that is decoherence theory or else it's screwing something up. The reason is that many-worlds and the later decoherence work follow quantum mechanics to the letter while Copenhagen tries to avoid that and ends in paradoxes. However, nobody needs to take any "worlds" of many-worlds other than our own as being real and wiser physicists don't do that. It could come back to bite people like Deutsch if an addition to the theory showed only one possible "world" becomes real.

http://www.hedweb.com/manworld.htm#believes

This strongly suggests that "wiser physicists" do not include people like Hawking and Feynman.

Anyways the long and short of it is that, to the extent that quantum mechanics accurately describes the observer as well as the observed, many worlds is true. Even if a future theory replaces quantum mechanics, that statement will be true. Either you postulate that quantum mechanics breaks down before describing large complex systems like human beings, or else the many worlds hypothesis provides an accurate explanation of why we observe a "collapse".

Cheers,
Ben

[Ziggurat]

Anyone who isn't a solipsist has to say the answer was produced by some physical process.

Yes.

We know there isn't enough computing power in this universe to obtain the answer, so something more is going on than what we can directly see.

Wrong. We know that classical algorithms cannot compute the answer with the resources available in the universe. But quantum computers do not use classical algorithms, and the limits of classical algorithms need not (and do not) apply.

At that point, logically, we have already accepted the many-worlds structure.

Maybe this guy has, but there is absolutely no requirement that the rest of us do so.

The way the quantum computer works is: the universe differentiates itself into multiple universes and each one performs a different sub-computation.

That's only if you accept the multiple-universe assumption. Alternatively, the quantum computer is initialized with a wave function which is in a superposition state, and so just like a violin vibrates at multiple frequencies, each component of the superposition will evolve in time on its own, allowing multiple simultaneous calculations using the same resources.

Then they pool their results to get the answer. Anyone who denies the existence of parallel universes has to explain how the factorisation process works."

Uh, NO. The whole point about the various "interpretations" of quantum mechanics is that the theory itself does not differentiate between them. If quantum computers offered a way to differentiate between them, then that would mean that quantum computation added some fundamentally new physics, and it would be at the absolute CENTER of modern physics, rather than just one more specialty among so many. This guy has far too inflated an opinion of his own work.

[ma1ic3]

Thanx for the input everyone.


This guy has far too inflated an opinion of his own work.


I was suspecting that.

[Rob Lister]

So, so far we're up to factoring a two digit number using Quantum Computers.

Just 9998 digits to go before we prove the many world theory?

I ask in honesty. I don't know Quantum from Quantis, but to surmise that because one can construct a quantum computer to factor a two digit number is a far cry from one that can factor a 10000 digit number.

[Myriad]

The analogy with conventional computers might be leading Deutsch to unjustified over-optimistic conclusions. The idea of easy scalability is so universal at all levels of computer science, theoretical as well as practical, that it tends to get taken for granted. If you can etch one logic gate on a chip, you can etch an array of ten million logic gates on a chip. If a program performs an operation three times (and the code is written with good "style"), it's trivially easy to modify it to perform the operation three million times. The same algorithm that factors a two-digit number can factor a 10,000-digit number. (It might take way longer than the age of the universe to run, but you can be certain it works.) And so forth.

If quantum computing shared that aspect of conventional computing, then surely getting the first few qbits to work was the hard part, and scaling it up to gigaqbits is just a matter of patient engineering and efficient mass-production.

But instead, quantum computing might be dealing with hardware design for which (if certain ideas about decoherence are valid) some fundamental aspect of causality fights against your attempts to scale it up. This is unfamiliar territory to say the least.

The whole point about the various "interpretations" of quantum mechanics is that the theory itself does not differentiate between them. If quantum computers offered a way to differentiate between them, then that would mean that quantum computation added some fundamentally new physics, and it would be at the absolute CENTER of modern physics, rather than just one more specialty among so many.

Because it's worth repeating.

Respectfully,
Myriad

[Unnamed]

http://www.hedweb.com/manworld.htm#believes

Anyways the long and short of it is that, to the extent that quantum mechanics accurately describes the observer as well as the observed, many worlds is true. Even if a future theory replaces quantum mechanics, that statement will be true.
The whole point about the various "interpretations" of quantum mechanics is that the theory itself does not differentiate between them. If quantum computers offered a way to differentiate between them, then that would mean that quantum computation added some fundamentally new physics [...]
This part of that Everett FAQ linked by Ben proposes a way to differentiate the interpretations:

What unique predictions does many-worlds make? (http://www.hedweb.com/manworld.htm#unique)


[note: edited for length]
Many-worlds makes at least three predictions, two of them unique: about linearity, quantum gravity and reversible quantum computers.

Assuming that we have a reversible machine intelligence to hand then the experiment consists of the machine making three reversible measurements of the spin of an electron (or polarisation of a photon). (1) First it measures the spin along the z-axis. (2) Second it measures the spin along the x-axis and records either spin "left" or spin "right" and notes this in its memory. The machine now reverses the entire x-axis measurement - including reversibly erasing its memory of the second measurement. (3) Third the machine takes a spin measurement along the z-axis.

According to the Copenhagen interpretation the original (1) and final (3) z-axis spin measurements have only a 50% chance of agreeing because the intervention of the x-axis measurement by the conscious observer (the machine) caused the collapse of the electron's wavefunction. According to many-worlds the first and third measurements will always agree. Hence when the machine reversed the second measurement these two worlds merged back together, restoring the original state of the electron 100% of the time.

Only by accepting the existence of the other Everett-worlds is this 100% restoration explicable.

[wipeout]

http://www.hedweb.com/manworld.htm#believes

This strongly suggests that "wiser physicists" do not include people like Hawking and Feynman.

Not necesarily. Gell-Mann and Feynman were in very close agreement on quantum mechanics and Gell-Mann gets included as a many-worlds believer when that is not what he believes at all. He believes in Everett's approach but not all the well-known associations.

Everett's approach leads to many possible past/present/future decohering histories of the universe (the "worlds" of many-worlds) but you can remain agnostic as to the reality of the worlds other than our own and also allow that some addition to the theory could show that only some worlds or only one world occurs.

It may be that, like Gell-Mann, when Hawking says he supports Everett's approach, people misinterpret that to mean he believes in many-worlds, all equally real, when he might not mean that as well.

[Ziggurat]

Assuming that we have a reversible machine intelligence to hand then the experiment consists of the machine making three reversible measurements of the spin of an electron (or polarisation of a photon).

Your source defined a necessary condition for reversibility, but it didn't actually define reversibility. But let me note that a Stern-Gerlach apparatus does, in fact, rely upon a reversible process.

(1) First it measures the spin along the z-axis. (2) Second it measures the spin along the x-axis and records either spin "left" or spin "right" and notes this in its memory. The machine now reverses the entire x-axis measurement - including reversibly erasing its memory of the second measurement. (3) Third the machine takes a spin measurement along the z-axis.

According to the Copenhagen interpretation the original (1) and final (3) z-axis spin measurements have only a 50% chance of agreeing because the intervention of the x-axis measurement by the conscious observer (the machine) caused the collapse of the electron's wavefunction.

You can already do this experiment, by putting multiple Stern-Gerlach apparati in sequence and at angles. In fact, exactly this experiment has probably already been done. And the answer WILL be that the first and third measurements will only show 50% correlation.

According to many-worlds the first and third measurements will always agree.

Contrary to the opinion expressed here, you can construct a many-worlds "theory" in which the first and third measurements do not, in fact, agree with each other 100% of the time. Once again, that's what the whole fuss is about: quantum mechanics tells you quite definitively and unambiguously that there will only be a 50% agreement between the first and third measurements, and the various interpretations remain only interpretations because they do NOT make differing predictions. The only way they ever WILL make different predictions is if some fundamentally new physics comes along. Nonlinearity of the wave function (one of the other methods noted) would qualify as fundamentally new physics.

[Ben Tilly]

Not necesarily. Gell-Mann and Feynman were in very close agreement on quantum mechanics and Gell-Mann gets included as a many-worlds believer when that is not what he believes at all. He believes in Everett's approach but not all the well-known associations.

Everett's approach leads to many possible past/present/future decohering histories of the universe (the "worlds" of many-worlds) but you can remain agnostic as to the reality of the worlds other than our own and also allow that some addition to the theory could show that only some worlds or only one world occurs.

It may be that, like Gell-Mann, when Hawking says he supports Everett's approach, people misinterpret that to mean he believes in many-worlds, all equally real, when he might not mean that as well.

I believe that Hawking really does believe in many-worlds, all equally real.

As for Feynman, he is quoted in that FAQ as saying that Everett's approach is how you have to model the collapse process. Which logically leads to many worlds. But whether those other worlds are truly real is a philosophical question. Given Feynman's well-known antipathy to philosophical questions, I doubt he'd particularly care to have any conversation on that topic.

But let me add John Baez as a fairly well-known physicist who is a very vocal advocate of many worlds.

Cheers,
Ben

[CurtC]

I've heard it said that quantum computers (will) steal processing power from those other universes. All I have to say is, those a**holes in other universes better not be stealing any of my processing power!

Or maybe they already are. Would be a bitch to go to all the trouble to make a large-scale quantum computer only to find out that other worlds had already used up their own processing power plus some of ours.