Do Black Holes have Singularities?

New paper:

There is no proof that black holes contain singularities when they are generated by real physical bodies. Roger Penrose claimed sixty years ago that trapped surfaces inevitably lead to light rays of finite affine length (FALL's). Penrose and Stephen Hawking then asserted that these must end in actual singularities. When they could not prove this they decreed it to be self evident. It is shown that there are counterexamples through every point in the Kerr metric. These are asymptotic to at least one event horizon and do not end in singularities.

It is by the same Kerr who found the general relativity solution for rotating black holes.

I will have to read this. It is hard to believe that everyone exaggerated the Penrose Hawking singularity theorems.

Why we use the Lebesgue Integral

Non-mathematicians are often baffled at why mathematicians seek generalizations and abstractions, and often think that the abstractions can have no practical purpose.

Here is an example. The Riemann integral appears to suffice for any function of practical interest, and yet mathematicians insist on defining a Lebesgue integral to handle a wider variety of cases.

Andrew D. Lewis writes:

Should we fly in the Lebesgue-designed airplane? -- The correct defence of the Lebesgue integral

It is well-known that the Lebesgue integral generalises the Riemann integral. However, as is also well-known but less frequently well-explained, this generalisation alone is not the reason why the Lebesgue integral is important and needs to be a part of the arsenal of any mathematician, pure or applied. ...

The title of this paper is a reference to the well-known quote of the applied mathematician and engineer Richard W. Hamming (1915–1998):

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.

The paper goes on to explain this very well. In particular, it shows why the Riemann integral is not good enough. In short, the Lebesgue integral makes L^p(R) complete normed vector spaces. If a sequence appears to converge, then it really does converge to a function in the space. This allows the use of limits in Fourier analysis, differential equations, and other areas of analysis.

Deriving Lorentz Metric from Electromagnetism

New paper:

Chen, Lu and Read, James (2023) Is the metric signature really electromagnetic in origin?

The paper is interesting, but the 4-metric signature +++- is mainly a consequence of causality, be it electromagnetic or anything else.

Causality requires that events only affect nearby events. If spacetime were Euclidean, with metric signature ++++, then an event could be close to an event outside its light cone. Affecting that nearby event would mean going faster than light. Action at a distance.

Electromagnetic effects do not go faster than light. You need the non-euclidean geometry of a +++- signature metric. Once you accept all that, Maxwell's electromagnetism is one of the simplest possible field theories, compatible with the geometry.

Harvard/MIT claims Quantum Error Correction

Scott Aaronson announces:

The biggest talk at Q2B this year was yesterday’s announcement, by a Harvard/MIT/QuEra team led by Misha Lukin and Vlad Vuletic, to have demonstrated “useful” quantum error-correction, for some definition of “useful,” in neutral atoms (see here for the Nature paper). To drill down a bit into what they did:

They ran experiments with up to 280 physical qubits, which simulated up to 48 logical qubits. ...

They don’t claim to have demonstrated quantum supremacy with their logical qubits—i.e., nothing that’s too hard to simulate using a classical computer.

Assuming the result stands, I think it’s plausibly the top experimental quantum computing advance of 2023 (coming in just under the deadline!). We clearly still have a long way to go until “actually useful” fault-tolerant QC, which might require thousands of logical qubits and millions of logical gates. But this is already beyond what I expected to be done this year, and (to use the AI doomers’ lingo) it “moves my timelines forward” for quantum fault-tolerance. It should now be possible, among other milestones, to perform the first demonstrations of Shor’s factoring algorithm with logically encoded qubits (though still to factor tiny numbers, of course). I’m slightly curious to see how Gil Kalai and the other quantum computing skeptics wiggle their way out now, though I’m absolutely certain they’ll find a way! Anyway, huge congratulations to the Harvard/MIT/QuEra team for their achievement.

What, is it my job to critique these experiments? He says "assuming the result stands", so he is not so sure himself. This is all I know.

IBM may soon have one Logical Qubit

SciAm reports:

IBM has unveiled the first quantum computer with more than 1,000 qubits — the equivalent of the digital bits in an ordinary computer. But the company says it will now shift gears and focus on making its machines more error-resistant rather than larger.

For years, IBM has been following a quantum-computing road map that roughly doubled the number of qubits every year. The chip unveiled on 4 December, called Condor, has 1,121 superconducting qubits arranged in a honeycomb pattern. ...

Researchers have generally said that state-of-the-art error-correction techniques will require more than 1,000 physical qubits for each logical qubit. A machine that can do useful computations would then need to have millions of physical qubits. ...

A new IBM road map on the its quantum research unveiled today sees it reaching useful computations — such as simulating the workings of catalyst molecules — by decade’s end.

Okay, one logical qubit, as soon as IBM gets that error correction figured out. And something useful by the year 2029.

Philosophy of Quantum Mechanics

David Wallace writes Philosophy of Quantum Mechanics:

This is a general introduction to and review of the philosophy of quantum mechanics, aimed at readers with a physics background and assuming no prior exposure to philosophy. It is a draft version of an article to appear in the Oxford Research Encyclopedia of Physics.

He summarizes the interpretations, and concludes:

Among physicists, the (more operationalist versions of the) probability-based approach, and the Everett interpretation, are roughly as popular as one another, with different sub-communities having different preferences. (The modificatory strategies are much less popular among physicists, although they are probably the most common choice among philosophers of physics.) But more popular than either is the ‘shut-up-and-calculate’ approach [167]: the view that we should not worry about these issues and should get on with applying quantum mechanics to concrete problems.

In its place, there is much to be said for ‘shut up and calculate’. Not everyone needs to be interested in the interpretation of quantum mechanics; insofar as a physicist working on, say, solar neutrinos or superfluidity can apply the quantum formalism without caring about its interpretation, they should go right ahead — just as a biochemist may be able to ignore quantum mechanics entirely, or a behavioral ecologist may be able to ignore biochemistry.

There is some overlap here. The theory described in textbooks could be called probability-based, or shut up and calculate.

Wallace has sympathies to Everett many-worlds, but admits:

More productive criticisms4 of the Everett interpretation have mostly fallen into two classes, known collectively as the ‘preferred basis problem’ and the ‘probability problem’. ...

It is fairly widely accepted that decoherence provides a solution to the preferred-basis problem. ...

The probability problem remains largely intact when decoherence is considered, and has been the main locus of controversy about the Everett in- terpretation in 21st-century discussions.

I am coming around to the view that there are really just two interpretations: QM with and without the probabilities. With the probabilities, you can make predictions and do experiments. Without, you get many-worlds, and a lot of philosophers and physicists love it, but I don't see what it has to do with the real world.

Carroll has new course on Many Worlds

Physicist Sean M. Carroll announces a new course:

The Many Hidden Worlds of Quantum Mechanics

One universe is not enough. Learn about the Many-Worlds Interpretation of quantum mechanics in this exciting course taught by a renowned expert. ...

Professor Carroll explains how quantum mechanics predicts the existence of a large number of universes parallel to our own. ...

Use the concepts developed in the course so far to learn how physicist Hugh Everett arrived at a bold new approach to quantum mechanics. Called the Many-Worlds Interpretation, it holds that the wave function represents reality and evolves smoothly into multiple distinct worlds when a quantum measurement takes place. Contrast Everett’s straightforward idea with the opaque Copenhagen Interpretation. ...

Many-Worlds theorist David Deutsch helped pioneer quantum computing, which he argues is an outgrowth on the Many-Worlds Interpretation. ...

By contrast, Many-Worlds is deterministic. We can derive an understanding of probability by thinking about where we are in the quantum wave function. ...

Many-Worlds and competing theories on the foundations of quantum mechanics may seem essential for our understanding of reality, but they were long ignored by no-nonsense practicing physicists. Close the course by witnessing how the tide is turning, as it becomes increasingly clear that the foundational issues are likely the key to unlocking the outstanding mysteries of the cosmos.

This is all nonsense. There is no practical value to Many-Worlds, or to the other "competing theories" he presents. They do not even make sense has scientific theories. This course is crackpot stuff.

I have posted many times with details on why Many-worlds is nonsense. Carroll giving a course on this is like giving a course on Astrology. The students should be warned that they will not learn anything worthwhile.

His Thanksgiving post was a plug for his latest book, saying that he is thankful for quanta.