Hope for quantum information

Physicist Adam Frank writes in the NY Times:

Given its importance, many of us in the physics community expected the event to earn this year’s Nobel Prize in Physics. Instead, the award went to achievements in a field far less well known and vastly less expensive: quantum information. ... It could well usher in a radical new era of technology, one that makes today’s fastest computers look like hand-cranked adding machines.

All of our computers today depend on quantum information, so new research is great, but it is not going to do what Frank says.

He tries to summarize the Interpretations of quantum mechanics:

Take the superposition debate. One camp claims that a deeper level of reality lies hidden beneath all the quantum weirdness. Once the so-called hidden variables controlling reality are exposed, they say, the strangeness of superposition will evaporate.

Another camp claims that superposition shows us that potential realities matter just as much as the single, fully manifested one we experience. But what collapses the potential electrons in their two locations into the one electron we actually see? According to this interpretation, it is the very act of looking; the measurement process collapses an ethereal world of potentials into the one real world we experience.

And a third major camp argues that particles can be two places at once only because the universe itself splits into parallel realities at the moment of measurement, one universe for each particle location — and thus an infinite number of ever splitting parallel versions of the universe (and us) are all evolving alongside one another. ...

Soon at least one interpretation, the most common sense version of hidden variables, was completely ruled out.

The hidden variable interpretation has been ruled out by the quantum mechanics textbooks since about 1930. Einstein, Bohm, Bell, and a few others tried to ressurect the idea, but they were always proven wrong.

The third interpretation, many-words (MWI), has several serious defects. First, it postulates zillions of worlds with no observable consequences. Second, it does not make any computation or understanding of our world any easier. Third, it is philosophically self-defeating, like denying free will.

A quantum machine using no more than 300 qubits would be a million, trillion, trillion, trillion times faster than the most modern supercomputer.

Going even further is the seemingly science-fiction possibility of “quantum teleportation.” Based on experiments going on today with simple quantum systems, it is at least a theoretical possibility that one day objects could be reconstituted — beamed — across a space without ever crossing the distance.

This is fiction. No one has even made one scalable qubit. Even a 300-qubit quantum computer would only be faster on certain obscure search functions of limited utility. And no one has found any use for quantum teleportation.

Update: Greg Kuperberg writes in Slate:

Of course, I was thrilled that the Nobel Foundation recognized this field. However, I was dismayed to read in the press release that "a quantum computer of only 300 qubits could hold 2³°° values simultaneously." Actually, 300 qubits can't hold so many zillion values; it is a mathematical fact that 300 qubits can store only 300 bits. This press release is part of a larger pattern of breathless exaggerations. In the name of accessibility, many popular accounts take quantum computing to implausible levels of hype.

A comment says:

Basically, once we have a fully scaled up quantum computer we will have cures for all sorts of diseases(protein folding problems will be solved quickly), space travel and worm holes, teleportation advances, nuclear fusion. This will be the biggest technological revolution that the planet has ever seen. Believe it or not, that day is coming and soon 5-10 yrs.

No, I do not believe that day is coming in the 1000 years.

Debating Pythagoreanism

Here is a video debate:

Pythagoras thought he had discovered the key to universe: mathematics. Was Pythagoras right? Should we see mathematics as the ultimate character of the world or is this a limited vision?

As Peter Woit points out:

An interesting debate, but maybe they should have had some mathematicians involved…

Physicist Lee Smolin accepts Pythagoreanism, but rejects Max Tegmark's Mathematical universe hypothesis. He implies that most people agree with him.

My FQXi essay expresses a contrary view.

The video server was buggy, so I could only watch part of it. The arguments seemed weak to me.

To give an idea of the philosophical ideas of the speakers, here is Peter Hacker:

Peter Hacker is one of the most powerful contemporary exponents of the linguistic-therapeutic approach to philosophy pioneered by Ludwig Wittgenstein. In this approach, the words and concepts used by the language community are taken as given, and the role of philosophy is to resolve or dissolve philosophical problems by giving an overview of the uses of these words and the structural relationships between these concepts. Philosophical inquiry is therefore very different from scientific inquiry, and Hacker maintains accordingly that there is a sharp dividing line between the two: "Philosophy is not a contribution to human knowledge, but to human understanding"

And Hilary Lawson:

Lawson's theory 'Closure' proposes that the human condition is to find ourselves on the cusp of openness and closure. The world is open and we, along with other living organisms, are able to apprehend and make sense of it through the process of closure. The theory, described by Don Cupitt as the first attempt to offer a non-realist metaphysics[10] shifts the focus of philosophy away from language and towards an exploration of the relationship between openness and closure. An important element of the theory of closure is its own self-referential character.

I am sure these guys do not have anything serious to say about math or science.

Copenhagen more coherent than many-worlds

Cosmologist Sean M. Carroll writes:

For a long time, quantum mechanics could be treated as a black box. You had an atomic nucleus sitting their quietly, not really deviating from your classical intuition, and then some quantum magic would occur, and now you have several decay products flying away. The remoteness of the quantum effects themselves is what has enabled physicists to get away for so long using quantum mechanics without really understanding it. (Thereby enabling such monstrosities as the “Copenhagen interpretation” of quantum mechanics, and its unholy offspring “shut up and calculate.”) ...

The objection to Copenhagen is just that it’s completely incoherent. It imagines a distinct “classical” realm, doesn’t tell you what’s in that realm and what’s truly quantum, doesn’t explain when wave functions collapse, etc. The Born Rule isn’t “explained” at all — it’s just postulated. And the Uncertainty Principle is exactly the same in MWI as it is in Copenhagen, so I’m not sure what the distinction is there.

MWI has its own issues, certainly, as do all other known versions of QM. But at least it’s well-defined, whereas Copenhagen is kind of a joke.

No, the Copenhagen interpretation is not a joke. It is a lot more coherent than the Many-worlds interpretation (MWI).

Copenhagen does not postulate the Born rule, but at least it explains the probabilities. The MWI does not explain probabilities at all, and has no experimental evidence for it.

The core of the problem is that Niels Bohr was a positivist while Carroll subscribes to this view:

The basic scientific assumption is that there is exists a complete and coherent description of how the world works. ... Given what we know about the universe, there seems to be no reason to invoke God as part of this description.

This view lead Carroll to believe in zillions of unobesrvable alternate universes and all sorts of other bizarre hypotheses, but he refuses to accept a scientific explanation that he regards as incomplete.

There is no reason to accept MWI.

A recent essay asks, Has Science Established that the Cosmos is Physically Comprehensible? The answer is no.

Science is all about testing hypotheses, and not leaping to unverifiable conclusions just because you pursue a more complete and coherent description of how the world works. I say Carroll has a very wrong idea of science. That is why he subscribes to string theory and other nonsense.

Albert Einstein's Methodology

Galina Weinstein has posted a paper on Albert Einstein's Methodology. She details how Einstein needed his friends for his most famous papers, but he refused to give them the credit they deserved. He wrote:

I am now occupied exclusively with the gravitational problem, and believe that I can overcome all difficulties with the help of a local mathematician friend. But one thing is certain, never before in my life have I troubled myself over anything so much, and that I have gained great respect for mathematics, whose more subtle parts I considered until now, in my ignorance, as pure luxury! ...

With this task in mind, in 1912, I was looking for my old student friend Marcel Grossmann, who had meanwhile become a professor of mathematics in the Swiss Federal Polytechnic institute. He was immediately caught in the fire, even though he had as a real mathematician a somewhat skeptical attitude towards physics. ...

He looked through the literature, and soon discovered that the particular implied mathematical problem was already solved by Riemann, Ricci and Levi-Civita. ...

Grossman will never claim to be considered a co-discoverer. He only helped in guiding me through the mathematical literature, but contributed nothing of substance to the results.

She writes about his refusal to credit another long-time friend:

During a visit by Besso to Einstein in 1913 they both tried to solve the Einstein-Grossmann field equations to find the perihelion advance of Mercury. The theory predicted a wrong perihelion advance.

Towards the end of 1915 Einstein abandoned the Einstein-Grossmann theory, and with his new General Theory of Relativity got the correct precession so quickly because he was able to apply the methods he had already worked out two years earlier with Besso. Einstein did not mention Besso, probably because he still considered him as a sounding board; this as opposed to his other friend, Grossmann, who was his active partner since 1912 in creating the Einstein-Grossmann theory.

This is not quite right, as this "correct precession" was derived from Grossmann's 1913 equation that empty space is Ricci-flat. The Mercury precession is regarded as Einstein's most original contribution to general relativity, but only because he refused to credit his friends.

She also explains how Einstein used words to exaggerate the originality of his work:

Alberto Martínez asks in his latest book Kinematics, "Was the formulation of the special theory of relativity a discovery [Entdeckung] or an invention [Erfindung]? Nowadays, many writers call it a 'discovery'. But throughout his life, Einstein emphasized the importance of invention, when characterizing his theoretical
contribution."

Yes, I think that most people would say that non-Euclidean geometry, and its application to relativity, was a discovery, not an invention. Einstein did not discover or invent it. He was a big egomaniac to claim all the credit that he did.

Cold water on quantum hype

Charlie Bennett writes:

Throwing cold water on the Quantum Internet

The most common misconception about entanglement is that it can be used to communicate—transmit information from a sender to a receiver—perhaps even instantaneously. In fact it cannot communicate at all, except when assisted by a classical or quantum channel, neither of which communicate faster than the speed of light. So a future Internet will need wires, radio links, optical fibers, or other kinds of communications links, mostly classical, but also including a few quantum channels.

How soon before the quantum internet could arrive?
I don’t think there will ever be an all-quantum or mostly-quantum internet. Quantum cryptographic systems are already in use in a few places, and I think can fairly be said to have proven potential for improving cybersecurity. Within a few decades I think there will be practical large-scale quantum computers, which will be used to solve some problems intractable on any present or foreseeable classical computer, but they will not replace classical computers for most problems. I think the Internet as a whole will continue to consist mostly of classical computers, communications links, and data storage devices.

He is right that there will never be a quantum internet, but it is not true that quantum cryptographic systems have proven potential for improving cybersecurity. Nobody has ever shown that quantum cryptography has any cybersecurity value at all.

I do not believe that we will see practical large-scale quantum computers either. Others disagree with me, but we are still waiting for a proof of concept that any such computers are possible.

Update: Some are buying into the hype:

Jeff Bezos has put money into a robot factory worker, a 10,000 year clock and private car service. And he’s not done yet.

Bezos Expeditions and In-Q-Tel, the venture arm of the CIA, announced Thursday a $30 million investment in D-Wave Systems, a Vancouver-based company that develops quantum-computing applications.

D-Wave Systems integrates computer science and physics discoveries with new-age computational processes. It’s focused on solving “optimization” problems, like finding out the most efficient delivery routes or how protein atoms interact with drug compounds. Some say the technology is more efficient than classical computing.

D-Wave does not have the qubit computer that everyone wants. I guess they somehow convinced Bezos that they can do some useful computations anyway.

Update: Soott Aaronson writes:

D-Wave still hasn’t demonstrated 2-qubit entanglement, which I see as one of the non-negotiable “sanity checks” for scalable quantum computing. ... Keep in mind that D-Wave has now spent ~$100 million and ~10 years of effort on a highly-optimized, special-purpose computer for solving one specific optimization problem.

Selling paradigm shifts

From Non Sequitur.

Reality: Is everything made of numbers?

Amanda Gefter writes in the current NewScientist:

How is it possible that mathematics "knows" about Higgs particles or any other feature of physical reality? "Maybe it's because math is reality," says physicist Brian Greene of Columbia University, New York. Perhaps if we dig deep enough, we would find that physical objects like tables and chairs are ultimately not made of particles or strings, but of numbers.

"These are very difficult issues," says philosopher of science James Ladyman of the University of Bristol, UK, "but it might be less misleading to say that the universe is made of maths than to say it is made of matter."

Difficult indeed. What does it mean to say that the universe is "made of mathematics"? An obvious starting point is to ask what mathematics is made of. The late physicist John Wheeler said that the "basis of all mathematics is 0 = 0". All mathematical structures can be derived from something called "the empty set", the set that contains no elements. Say this set corresponds to zero; you can then define the number 1 as the set that contains only the empty set, 2 as the set containing the sets corresponding to 0 and 1, and so on. Keep nesting the nothingness like invisible Russian dolls and eventually all of mathematics appears. Mathematician Ian Stewart of the University of Warwick, UK, calls this "the dreadful secret of mathematics: it's all based on nothing" (New Scientist, 19 November 2011, p 44). Reality may come down to mathematics, but mathematics comes down to nothing at all.

That may be the ultimate clue to existence - after all, a universe made of nothing doesn't require an explanation. Indeed, mathematical structures don't seem to require a physical origin at all. "A dodecahedron was never created," says Max Tegmark of the Massachusetts Institute of Technology. "To be created, something first has to not exist in space or time and then exist." A dodecahedron doesn't exist in space or time at all, he says - it exists independently of them. "Space and time themselves are contained within larger mathematical structures," he adds. These structures just exist; they can't be created or destroyed.

That raises a big question: why is the universe only made of some of the available mathematics? "There's a lot of math out there," Greene says. "Today only a tiny sliver of it has a realisation in the physical world. Pull any math book off the shelf and most of the equations in it don't correspond to any physical object or physical process."

It is true that seemingly arcane and unphysical mathematics does, sometimes, turn out to correspond to the real world. Imaginary numbers, for instance, were once considered totally deserving of their name, but are now used to describe the behaviour of elementary particles; non-Euclidean geometry eventually showed up as gravity. Even so, these phenomena represent a tiny slice of all the mathematics out there.

Not so fast, says Tegmark. "I believe that physical existence and mathematical existence are the same, so any structure that exists mathematically is also real," he says.

So what about the mathematics our universe doesn't use? "Other mathematical structures correspond to other universes," Tegmark says. He calls this the "level 4 multiverse", and it is far stranger than the multiverses that cosmologists often discuss. Their common-or-garden multiverses are governed by the same basic mathematical rules as our universe, but Tegmark's level 4 multiverse operates with completely different mathematics.

All of this sounds bizarre, but the hypothesis that physical reality is fundamentally mathematical has passed every test. "If physics hits a roadblock at which point it turns out that it's impossible to proceed, we might find that nature can't be captured mathematically," Tegmark says. "But it's really remarkable that that hasn't happened. Galileo said that the book of nature was written in the language of mathematics - and that was 400 years ago."

If reality isn't, at bottom, mathematics, what is it? "Maybe someday we'll encounter an alien civilisation and we'll show them what we've discovered about the universe," Greene says. "They'll say, 'Ah, math. We tried that. It only takes you so far. Here's the real thing.' What would that be? It's hard to imagine. Our understanding of fundamental reality is at an early stage."

My FQXi essay argues that reality, at bottom is not mathematics. I say that Tegmark is wrong in the most extreme way. There is no real object that is also a mathematical structure. Not even an electron or a photon.

This is the last week for the public rating of the FQXi essays. My essay has consistently been in the top 10 on the community rating.

Tegmark says, "we might find that nature can't be captured mathematically," but I say that has already happened with quantum mechanics. Niels Bohr said:

It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature.

Everything we call real is made of things that cannot be regarded as real.

I think that Bohr was saying that observations about nature can be described mathematically, but nature itself cannot be captured mathematically.