Sprung from Einstein’s head

Science writer Jeremy Bernstein writes in a new paper:

Periodically I prepare an imaginary lecture the purpose of which is to remind philosophers of physics, and indeed some physicists, that the quantum theory had its origins in experiments. Unlike general relativity which seems to have sprung from Einstein’s head, the quantum theory was a response to experiment. Even de Broglie’s conjecture that particles had also a wave-like nature was influenced by how this notion could be used to explain the quantization of the radii of the Bohr orbits. The experiment driven theoretical developments of the quantum theory began with Planck and have continued ever since.

General relativity sprung from Einstein’s head? One of the persistent myths that I debunk in my book is that Einstein created relativity out of pure thought, with any input from experiment. Einstein himself promoted this myth in his later years, and paradigm shift philosophers have made it the centerpiece of bogus theories about how science works.

Usually the myth is told about the special relativity of 1905, as Einstein's biographers acknowledge that he relied heavily on others for general relativity.

The term general relativity means (special, spacetime, electromagnetic) relativity applied to gravity. It is called general because it is nonlinear. The first breakthru was in 1905, when Poincare discovered the space-time metric, proposed a Lorentz-invariant theory of gravity, and explained how gravity could propagate at the speed of light and still be consistent with solar system observations. A couple of years later he announced that he had figured out how to use relativity to partially explain an anomaly in Mercury's orbit.

Einstein's biggest breakthru was to deduce in 1907 that gravity had an apparent effect on clocks.

We know from Einstein's letters that he spent several years trying (off and on) to extend Poincare's work on Mercury. Others helped him on the problem. He also wanted to explain the deflection of starlight. His next big breakthru was in 1915 when he showed how Grossmann's 1913 relativity equations could be used to explain the Mercury anomaly. When Hilbert gave another derivation of Grossmann's equations in 1915, Einstein became convinced that those equations must be right. Einstein's famous general relativity paper was published in 1916, with an acknowledgement to Grossmann, but no mention of Poincare or Hilbert.

Thus relativity had its origin in experiments, just like quantum mechanics.

Update: A new paper on Einstein the Stubborn: Correspondence between Einstein and Levi-Civita has explained the correspondence between Einstein and Levi-Civita and Hilbert in 1914-16. The letters mostly consisted of Levi-Civita and Hilbert trying to convince Einstein of errors in his general relativity papers. Grossmann had introduced covariant equations in 1913, but Einstein did not accept them, and gave fallacious arguments for non-covariant equations. Einstein finally admitted in 1916 to Hilbert, "The error you found in my paper of 1914 has now become completely clear to me".

No quantum probabilities needed

Here is how probabilities arise in quantum mechanics.

The core of the theory is an algebra of observables. These include position coordiates, momentum, energy, spin, electric charge, and anything else that is measurable as a real variable.

The key fact is that the observables do not commute. That is, the position X and the momentum P have the property that XP is not equal to PX. They differ by h-bar, a small quantity called Planck's constant.

This is not so radical, as many everyday observables also have this property that observations depend on the order that they are performed. For example, poll questions:

Sometimes the very order of the questions can have an impact on the results. Often that impact is intentional; sometimes it is not. The impact of order can often be subtle.

During troubled economic times, for example, if people are asked what they think of the economy before they are asked their opinion of the president, the presidential popularity rating will probably be lower than if you had reversed the order of the questions. And in good economic times, the opposite is true.

For more, see Why Question Order Changes Poll Results.

To observe a system, we need a representation of the observables on a Hilbert space of possible system states. That means that a vector ψ represents the state of the system, that an observable A acts on ψ to give a new state Aψ, and that two vectors ψ₁ and ψ₂ can be combined to get a number <ψ₁|ψ₂>. The latter is like an ordinary dot product and gives 0 when the vectors are orthogonal.

If an observable A is measured is measured on a system state ψ, the expected value is <ψ|Aψ>, also written <ψ|A|ψ>. It is a real number.

An actual lab measured value may not match the expected value exactly. Real numbers never match exactly in the lab, with quantum mechanics or any other scientific theory. The standard deviation, or sigma, is also an observable with an expected value. Thus, the mechanics might say that a particle will be observed at a distance of 5.24 ± .03 meters. Then a measurement is likely to be between 5.21 and 5.27.

So quantum mechanics make probabilistic predictions in the sense that it gives a range of likely outcomes for measurements. But every other branch of science does something similar, and this is not why quantum mechanics is said to be probabilistic.

Quantum mechanics is said to be probabilistic because is predicts probabilities. Here is how. Suppose that the observable A is a yes-no (boolean) observable, such as asking whether an electron is in a particular region of space. Yes means 1, no means 0, and no other values are observed. Then the expected value <ψ|A|ψ> will be in the range [0,1]. If the value is 1, then you can be sure of a yes, and if the value is 0, then you can be sure of a no. If the value is in between, then it can be interpreted as a probability of a yes. This interpretation is called the Born rule. Max Born suggested it as one possibility in a 1926 paper footnote, and got a Nobel prize for it in 1954.

Probabilities do not play an essential role here. Testing the Born rule is just a special case of testing an expected value of an observable, where the observable is a yes-no variable. An experiment does not really say whether there is any genuine randomness. It just says that if the expected value of a yes-no observable is 0.65, and you do 100 experiments, then you should get about 65 yes outcomes.

It is better to just say that quantum mechanics predicts the expected values of observables. That is what the formulas really do, and that is how the theory is tested. The Born rule adds an interpretation in the case of a yes-no observable. But that interpretation is just metaphysical fluff. There is no experimental test for it. The tests are just for the expected values, and not for the probabilities.

Thus I do not believe that it is either necessary or very useful to talk about probabilities in quantum mechanics. I guess you could say that the probability gives a way of understanding that the same experiment does not give the same outcome every time, but it does not give any more quantitatively useful info. This understanding is nothing special because every other branch of science also has variation in experimental outcomes.

My view here is a minority view. I have not seen anyone else express it this way. The textbooks usually say that ψ is a probability density or amplitude. But ψ is complex-valued or maybe even spinor-valued, and it requires some computation to get a probability. It is not a probability. That computation is precisely the expectation value described above. Sometimes the textbooks admit that the quantum probabilities require special interpretation because they can be negative. I say that negative probabilities are not probabilities and that the probabilities are no more essential to quantum mechanics than to any other physical theory that does real number computations.

I reader asks what quantum interpretation this is. It is similar to the ensemble interpretation, without the probabilities.

Quantum mysteries disentangled

I just stumbled across a video on The Quantum Conspiracy: What Popularizers of QM Don't Want you to know. It was a Google Tech Talk January 6, 2011 Presented by Ron Garret. His paper is Quantum Mysteries Disentangled.

It is an explanation of some of the mysteries of quantum mechanics, by a non-physicist. He has a slightly unconventional view that I did not find totally persuasive. But I do agree with him that physicists present the subject as more mysterious than it really is, as if there is a conspiracy to confuse you.

A reader sends the 1997 paper, Quantum Mechanics of Measurement, N. J. Cerf, C. Adami, for more details on Garret's view.

Pushed over the quantum edge

Scott Aaronson offered $100,000 (and then reneged) for disproving scalable quantum computing, and added:

Besides Gil and Robert Alicki, other notable QC skeptics include Leonid Levin (of Cook-Levin Theorem fame), Oded Goldreich, Gerard ‘t Hooft (the Nobel physicist), Stephen Wolfram, and Ed Fredkin (well, he actually believes P=BQP). Besides them, my experience has been that there’s also a significantly larger group of physicists, chemists, and computer scientists who agree with the anti-QC sentiments but haven’t articulated them in print (there were even a few who angrily accosted me after department colloquia to accuse me of peddling lies!) If you read the comment threads on Gil’s blog, you’ll see lots of contributions from two more skeptics, both of whom played large roles in “pushing me over the edge” to make this bet: Roger Schlafly (author of a book called “How Einstein Ruined Physics”) and Craig Feinstein (author of numerous wrong P!=NP proofs).

So a lot of important scientists are skeptical about quantum computing (see also here), and they do not necessarily say so on the record. But a few negative blog comments, and he goes ballistic!

Craig criticized it in comments here, and I did on this blog and here.

Quantum computing is one of those subjects that academic scientists are not supposed to criticize because it gets a lot of govt grant funding. It frequently makes extravagent promises about a new computer paradigm, and computers that will outperform all current computers. None of its promises have ever been realized, and there is no likelihood that they ever will. I am glad that I have provoked Scott into defending his position, but his offer is meaningless because he has defined it in a way so that he will never have to pay.

Scott is entitled to his opinion, of course. But we ought to understand that he is doing abstract analyses of hypothetical computers that do not exist in the real world, and are probably contrary to the laws of physics.

Scott argues in IEEE Spectrum:

I study quantum computing at MIT. Recently, on my blog, I offered a $100 000 reward for a demonstration, convincing to me, that scalable quantum computing is impossible in the physical world. The award is entirely at my discretion; ...

Most of the skeptics say that they have no problem with quantum mechanics itself (it is, after all, the best-confirmed physical theory of all time); it's only scalable quantum computers that they object to. To date, though, no one really knows how you can have quantum mechanics without the possibility of quantum fault-tolerance. So as I see it, the burden falls on the skeptics to give an alternative account of what's going on that would predict the impossibility of scalable QC.

I think that is a strange view. Quantum mechanics is the best explanation we have of what is going on. It just does not imply scalable QC, and all attempts at scalable QC have failed.

Quantum computing not like Martian trip

Computer scientist Scott Aaronson argues for quantum computing:

I became interested in quantum computing because of a simple trilemma: either (i) the Extended Church-Turing Thesis is false, (ii) quantum mechanics is false, or (iii) factoring is in classical polynomial time. As I put it in my dissertation, all three possibilities seem like wild, crackpot speculations, but at least one of them is true! The question of which will remain until it’s answered. ...

Yeah, alright. So I ought to amend (ii) from “quantum mechanics is false” to “current low-energy physical theories are wrong.”

He adds:

No, if you accept quantum mechanics, the burden is on you to explain why a computer couldn’t be built that takes advantage of the phenomena of superposition, interference, and entanglement that have been the entire core of quantum mechanics, verified over and over, since 1926.

Believing quantum mechanics but not accepting the possibility of QC is somewhat like believing Newtonian physics but not accepting the possibility of humans traveling to Mars.

I accept quantum mechanics, but not quantum computing. It is just not true that quantum computing follows from the quantum mechanics of 1926. I guess Aaronson tried to show that in his papers cited below and failed. So he claims that somehow the burden is on someone else to show the opposite.

The Mars analogy is ridiculous. The feasibility of a Mars trip is an easy extrapolation from the Moon trip. But there is no demonstrated feasibility of quantum computing.

Scott Aaronson replies:

Sure, it’s easy to understand the impossibility of quantum computing, in exactly the same way it’s easy to understand how the earth can be resting on a giant turtle. The key is not to ask what the turtle’s standing on, and likewise, not to ask what the flaw is in our current understanding of quantum mechanics that makes QC impossible. All sorts of scientific problems can be quickly cleared up this way, once we learn to stop asking annoying followup questions and embrace doofosity!

The problem with quantum computing is that it does not follow from any established scientific theory, there is no observational evidence for it, and it leads to implausible outcomes. There are a lot of such speculative concepts in physics, and we ordinarily reject them. Examples are time travel, Maxwell's demon, tachyons, and wormholes. Quantum computing is like the giant turtle, and the burden on its proponents should be to show some good reason for believing in such a far-fetched concept.

Space is not digital

The current SciAm asks is space digital?

Craig Hogan believes that the world is fuzzy. This is not a metaphor. Hogan, a physicist at the University of Chicago and director of the Fermilab Particle Astrophysics Center near Batavia, Ill., thinks that if we were to peer down at the tiniest subdivisions of space and time, we would find a universe filled with an intrinsic jitter, the busy hum of static. This hum comes not from particles bouncing in and out of being or other kinds of quantum froth that physicists have argued about in the past. Rather Hogan’s noise would come about if space was not, as we have long assumed, smooth and continuous, a glassy backdrop to the dance of fields and particles. Hogan’s noise arises if space is made of chunks. Blocks. Bits. Hogan’s noise would imply that the universe is digital.

The experiment is a variant of the Michelson–Morley experiment that was so crucial for the discovery of special relativity. Another variant is LIGO, which tries to detect gravity waves from another galaxy.

Philosophers commonly say that it was silly for physicists to repeat the Michelson-Morley experiment so many times in so many different ways in the early 20th century, because Einstein deduced relativity from pure thought. I guess they think of relativity as a believe system that is independent of empirical evidence. They are wrong about the origin of relativity, as I explain in my book.

I do think that the belief in digital space is strange and unwarranted. These new experiments are very unlikely to find any evidence for it. Contrary to some beliefs, quantum mechanics does not require digital space.

The impossibility of quantum computers

A blog is debating whether quantum computers are the perpetual motion machines of the 21st century:

Gil Kalai and Aram Harrow are world experts on mathematical frameworks for quantum computation. They hold opposing opinions on whether or not quantum computers are possible. ...

Are quantum computers feasible? Or are their underlying models defeated by some fundamental physical laws? ...

As an aside, let me briefly say why I tend to regard universal quantum computers as unrealistic. An explanation for why universal quantum computers are unrealistic may require some change in physics theory of quantum decoherence. On the other hand, universal quantum computers will be physical devices that are able to simulate arbitrary quantum evolutions, where the word “simulate” is understood in the strong sense that the computer will actually create an identical quantum state to the state created by the evolution it simulates, and the word “arbitrary” is understood in the strong sense that it applies to every quantum evolution we can imagine as long as it obeys the rules of quantum mechanics. As such, quantum computers propose a major change in physical reality.

The perpetual motion analogy is a good one. Quantum computer research keep claiming progress, but it is like the progress of free energy researchers. Yes, they may find some slight gain in efficiency, but the research says nothing toward showing that the goal is attainable.

It is just not true that the skeptics of quantum computing are really skeptics of quantum mechanics. All of quantum mechanics can be true without quantum computers.

Update: Physicist Scott Aaronson is betting that Quantum Computing is possible:

I hereby offer $100,000 for a demonstration, convincing to me, that scalable QC is impossible in the physical world.

... Whether Bigfoot exists is a question about the contingent history of evolution on Earth. By contrast, whether scalable QC is possible is a question about the laws of physics. It’s entirely conceivable that future developments in physics would conflict with scalable QC in the same way relativity conflicts with faster-than-light communication and the Second Law conflicts with perpetuum mobiles. It’s such a development in physics that I’m offering $100k for.

I am not sure about this distinction. The post has four conjectures that are consistent with quantum mechanics and all of the experimental evidence, but make quantum computers impossible. The Second law of thermodynamics was demonstrated by people trying to build perpetual motion machines. We do have other arguments for it, but I doubt that they would cause someone to pay off a $100k bet.

Update: Aaronson now argues "that the burden is on the QC skeptics to answer" how quantum computing is impossible, based on his 2003 paper and his PhD thesis. This opinion seems bizarre to me, considering that quantum computing is contrary to every experiment that has even been done, but I guess that I will have to study his paper. Unfortunately, he has already reneged on his $100k offer.