Poincare and Einstein on Mass-Energy Equivalence

Einstein's most famous equation is E = mc². Supposedly it created the Atomic Age.

New article:

Poincare and Einstein on Mass-Energy Equivalence: A Modern Perspective on their 1900 and 1905 Papers
Patrick Moylan

Both Poincaré in his 1900 Festschrift paper \cite{Poincare} and Einstein in his 1905 \textsl{Annalen der Physik} article \cite{Einstein} were led to $E=mc^2$ by considering electromagnetic processes taking place in vacuo. Poincaré's treatment is based on a generalization of the law of conservation of momentum to include radiation. Einstein's analysis relies solely on energy conservation and the relativity principle together with certain assumptions, which have served as the source of criticism of the paper beginning with Max Planck in 1907. We show that these objections raised by Planck and others can be traced back to Einstein's failure to make use of momentum considerations. Relevance of our findings to a proper understanding of Ives' criticism of Einstein's paper is pointed out.

Planck criticized Einstein's derivation in 1907. Various Einstein biographers and idolizers have attempted to support Einstein, but his 1905 work was inferior to what Poincare did in 1900.

Einstein never believed that an atomic bomb was possible, until Szilard and others convinced him around 1940.

Einstein never cites the Poincare 1900 paper, or the Hasenoehrl 1904 and 1905 papers on the subject. For Einstein's derivation to work, he needs radiation to have momentum, but never mentions it.

So how did Einstein do it? The obvious possibilities are: (1) he made a blunder, and just happened to get the right answer; (2) he read the Poincare and Hasenoerhl papers, and learned about radiation momentum from them; or (3) he rediscovered radiation momentum on his own, but did not think it was important enough to mention.

Considering that Einstein spent his whole life concealing and lying about his sources, the obvious conclusion is (2). His most famous relativity papers do not cite any sources, even though they directly build on the work of others. He spent his whole life pretending that he did not know about Poincare's work.

There is a myth that Einstein worked in isolation and obscurity, but that is not true. He was very well read on current Physics, and often wrote reviews of current research papers. The above paper says:

After all, it is hard to imagine that Einstein, at the time he wrote his paper, was not aware of Poincar ́e’s Festchrift article, which was one of the most important and widely read physics papers of that time [41], and it seems almost certain he would have been aware of Hasen ̈ohrl’s papers published some months before in the same journal to which he submitted his first two relativity papers [28].

Before his death, someone finally confronted Einstein with the fact that Poincare had published all of his relativity ideas beforehand, and Einstein had no response.

The above paper does a good job of explaining the mental gymnastics that the Einstein idolizers have done to defend him.

Many-worlds is not an Interpretation

Scott Aaronson, a quantum mechanics (QM) and quantum computer (QC) expert, writes:

There’s no such thing as a “many worlds theorem.” Many worlds is an interpretation. There’s a genuine case for it but the case is philosophical, and remains argued about by people who understand everything there is to know about the subject. ...

No, many-worlders and non-many-worlders make exactly the same predictions for what QCs will and won’t be able to do. That’s why many worlds is an “interpretation,” rather than a competing empirical theory!

I challenged him on this, and he replied:

I’m aware of all of this. The hardcore many-worlders think that non-many-worlders have a nonsense theory from which one shouldn’t be able to make predictions at all, and the hardcore Copenhagenists, QBists, etc. think exactly the same of many-worlders. Nevertheless, they do make the same predictions, regardless of whether they should! 🙂

At least, they do to whatever extent they accept the empirical recipe of QM. People who deny the empirical recipe are (I’d say) neither many-worlders nor Copenhagenists nor QBists nor etc., but believers in a rival physical theory (whether or not they have clear ideas about what the rival theory is).

And as for the QC skeptics who accept QM, but believe some yet-to-be-discovered principle “censors” or “screens off” scalable QC? I’d hope that even they could still make the same conditional predictions: “yes, if it weren’t for our yet-to-be-discovered principle, then this is how a QC would operate, and this is the class of problems it could solve in polynomial time.”

: The I no longer agree with calling many-worlds an "interpretation". It would be if they accepted the empirical recipe of QM, but they don't.

The empirical recipe gives unique outcomes to experiments, but the many-worlders deny that. David Deutsch is a many-worlder, and he says a QC would prove the parallel universes.

I guess I am the skeptic who accepts QM, but believes some yet-to-be-discovered principle “censors” or “screens off” scalable QC. Scott has become a many-worlder, so he would probably also say I must believe in some yet-to-be-discovered principle that collapses the wave function.

This is not exactly my view. I am a positivist, and do not believe in yet-to-be-discovered principles. I accept what Scott calls "the empirical recipe of QM". How could I not? It works amazingly well.

I am skeptical about scalable QC.

I am also skeptical about intelligent life on other planets. Not because I believe in a yet-to-be-discovered principle. It just seems unlikely to me.

Scott's main point is to attack Kaku's new book on quantum supremacy, which I also attacked on May 6.

How Einstein's Quantum Realism was First Rebutted

I did not know that the 1935 Einstein EPR paper was rebutted before Bohr:

It must be observed that Bohr article was not the first response to EPR appearing in print in the physical review. Arthur E. Ruark in a very short paper focused on the previous quotation of EPR and developed the strongly positivist conclusion (iii):

This [EPR] conclusion is directly opposed to the view held by many theoreticians, that a physical property of a given system has reality only when it is actually measured, and that wave mechanics gives a faithful and complete description of all that we can learn from measurements.

That is correct.

The above paper makes a silly argument that Einstein and Bohr were both wrong. It says:

Of course this was just the beginning of the story: In 1964 John Bell, based on EPR work, discovered his famous theorem ([3], chap. 2) firmly establishing that quantum mechanics (irrespectively of being complete or incomplete) must be nonlocal.

No, this is false. Quantum mechanics is local. The 2022 Nobel Prize went to Bell theorem experiments, and the citation conspicuously avoided saying that QM is nonlocal.

Nazis Attacked Einstein's Jewish Science

Philip Ball wrote a 2014 book on Nazi Physics, and a chapter was excerpted in SciAm.

Anti-Semitism did not just deprive German physics of some of its most valuable researchers. It also threatened to prescribe what kind of physics one could and could not do. For Nazi ideology was not merely a question of who should be allowed to live and work freely in the German state—like a virus, it worked its way into the very fabric of intellectual life. Shortly after the boycott of Jewish businesses at the start of April 1933, the Nazified German Students Association declared that literature should be cleansed of the “un-German spirit”, resulting on 10 May in the ritualistic burning of tens of thousands of books marred by Jewish intellectualism. These included works by Sigmund Freud, Bertolt Brecht, Karl Marx, Stefan Zweig and Walter Benjamin: books full of corrupt, unthinkable ideas. Into some of these pyres, baying students threw the books of Albert Einstein.

I am skeptical about this. Books by Freud and Marx are indeed full of corrupt ideas that the Germans were better off without. Germany was at risk of a Marxist revolution like Russia's.

Einstein's books were irrelevant by the time the Nazis came to power. Relativity had been written into the textbooks by then.

Here is how he trashes a couple of Nobel Prize winners.

The fact is that Lenard was a rather unremarkable man: an excellent experimental scientist in his heyday, but of limited intellectual depth, and emotionally and imaginatively stunted. When circumstances contrived to carry him further than his talents should have permitted, he was forced to attribute his shortcomings to the deceptions and foolishness of others. This combination of prestige and deluded self-image is invariably poisonous. ...

Like Lenard, Stark was an experimentalist befuddled by the mathematical complexity that had recently entered physics. He was another extreme nationalist whose right-wing views had been hardened by the First World War. He too felt that Einstein had stolen his ideas, this time over the quantum-mechanical description of light-driven chemical reactions. (Stark never in fact fully accepted quantum theory, even though an understanding of the “Stark effect” depended on it.) And being a mediocrity who struck lucky, he found himself being passed over for academic appointments to which he was convinced he had the best claim.

Einstein never fully accepted quantum theory either, and was also befuddled by mathematical complexity.

The stories are interesting, but in the end, the Nazis did not have much influence on Physics:

But the truth was that, while the dispute rumbled on through the late 1930s, the Nazis tightened their grip on German science regard­less. In some disciplines, such as chemistry, scientists fell into line in short order. In a few, such as anthropology and medicine, the collu­sion of some researchers had horrific consequences. Physics was another matter: just docile enough for its lapses, evasions and occa­sional defiance to be tolerated. The physicists were errant children: grumbling, arguing among themselves, slow to obey and somewhat lazy in their compliance, but in the final analysis obliging and dutiful enough. If they lacked ideological fervour, the Nazis were pragmatic enough to turn a blind eye.

I am not sure what the Jewish Science was. By the time the Nazis came to power, Einstein was determinist, Communist, Zionist, quantum-denier, and pursuer of bogus unified field theory. He was not doing any real science anymore.

And yet Nazi attempts to cancel Einstein seem trivial by modern standards. The Ball SciAm article gives this example:

In 1942 Sommerfeld was about to publish some lectures on physics when he received a letter from Heisenberg saying (as Rudolf Peierls later recalled it) that “a political adviser and close friend of mine, also a physicist, would like to call to your attention certain guidelines which are now in use, that is, we note, the publisher noticed that you mentioned Einstein’s name four times in your lectures, and we wondered if you couldn’t get by with mentioning him a little less often?” Sommerfeld complied, retaining just one of the references. “I must mention him once”, his conscience obliged him to write back. Peierls adds that “after the war the names were quickly put back in”.

So the number of Einstein citations was changed from 4 to 1, and back to 4. Nowadays, scientists are canceled for ideological reasons all the time, and Einstein is cited about 1000 times more than he deserves.

Droste Discovered the Schwarzschild Metric

The Schwarzschild metric is famous for describing a black hole in general relativity. It was discovered in 1915 immediately after publication of the field equations by Einstein and Hilbert, although the significance of black holes was only figured out much later.

I recently learned that this metric was independently discovered by a student of Lorentz.

From a 2002 paper:

Johannes Droste’s “Field of a single center in Einstein’s theory of gravitation, and the motion of a particle in that field.” It is a remarkable paper, arguably one of the most remarkable in the annals of general relativity and yet, although the paper is known to historians of science, practitioners of relativity themselves have been almost universally unaware of its existence for nearly a century, and no mention of it appears in any standard text. ...

We know little about Johannes Droste. From what we do know (see the biographical note), Einstein’s theory of gravitation was the subject of his Ph.D. thesis. As he tells us in the introduction to the current paper, he had been working on the equations of motion in general relativity as early as 1913 after Einstein published a preliminary version of the field equations.

The birth of Newtonian gravity is considered to be the central force law, although the field equations came much later. For general relativity, the birth is considered to be the field equations, not the central force law.

I am not sure why. The Schwarzschild-Droste metric is the analog of the central force law. It is what you want for celestial orbits. Einstein and Grossmann published an "Entwurf" theory in 1913, saying Ricci = 0 in empty space. Einstein retracted this in subsequent papers, but it is apparently what Droste used to figure out the correct central force law.

If Einstein had never met Hilbert in 1915, and they never published their field equations, we still might have had the essence of the theory from Droste's work. Probably Lorentz contributed also.

Kaku Plugs Quantum Supremacy

Here is a new interview of Michio Kaku on Quantum Supremacy:

Theoretical physicist Michio Kaku discusses his new book, Quantum Supremacy: How the Quantum Computer Revolution Will Change Everything. He explores how quantum computing may eventually illuminate the deepest mysteries of science and solve some of humanity’s biggest problems, like global warming, world hunger, and incurable disease.

From Peter Woit's blog:

Out of interest, why is there no public effort by physicists to counter the relentless nonsense coming from Kaku?

I know that there is a LOT of hype and inaccurate information in pop Sci books and science magazines, but Kaku seems to be responsible for a disproportionately large share of the garbage! ...

That’s a good question, one I’ve asked people over the years. On the string theory front, Kaku has been writing misleading popular books on the topic for over 35 years. Most string theorists agree, at least privately, that what he writes and says has become increasingly inaccurate and increasingly embarrassing. They generally however make the argument: “dealing with this is not my responsibility, there’s loads of misleading stuff out there about science. And, maybe it will have a positive effect, getting young people and the public interested in this kind of science, going on to read better books.” ...

As for his nonsense about quantum computing, there’s so much promotional bullshit going on that it’s understandable that anyone wanting to do something about this has no particular reason to start with Kaku.

Woit also recommend this rambling video on string theory lied to us and now science communication is hard. Yes, I think that the credibility of all physicists is diminished by crackpot claims going unrebutted.

In Defense of Merit in Science

Biology professor Jerry Coyne writes:

In the end, we’re grateful that our paper will be published. But how sad it is that the simple and fundamental principle undergirding all of science—that the best ideas and technologies should be the ones we adopt—is seen these days as “controversial.”

They had to publish their paper in the Journal of Controversial Ideas. More mainstream journals rejected the paper with comments like “the concept of merit ... has been widely and legitimately attacked as hollow.”

I do think that the XX century will be a high-water mark for science. We will never see another century with so many exciting scientific advances. Our civilization is in decline.

Cosmology of a Communist

Here is a new paper:

The Cosmology of David Bohm: Scientific and Theological Significance

We discuss David Bohm's dual contributions as a physicist and thinker. First, de Grijs introduces Bohm's universe, with an emphasis on the physical quest that led Bohm to the elaboration of an original cosmology at the nexus of science and philosophy. Next, Costache takes his cue from de Grijs' explorations by highlighting the affinity between Bohm's scientific cosmology and patristic ideas that are central to the Orthodox worldview. It is our hope that this approach will stir the interest of Bohm scholars in the Orthodox worldview and also lead Orthodox theologians to nurture an appreciation for Bohm's cosmology.

David Bohm has a cult following.

The paper does not mention that he was a Communist, and those philosophical ideas are outgrowth of his Marxist and Communist ideas. He was a student of J.R. Oppenheimer, and refused to testify before Congress. Because of his Communist activities, he fled the USA.

Among physicists, he is mainly known for a nonlocal hidden variable theory. His followers call it "causal", but it is the opposite of causal. Local theories are causal. Bohm's theory had action-at-a-distance, where events cannot be attributed to causal influences. It generates a lot of research papaers, but no one uses it for any practical work.

Bohm is dead, but there is an Irish organization that tries to keep his mystical ideas alive.

I am not trying to cancel a scientist for his terrible political views. His contributions to Physics are wildly exaggerated for reasons that are not political. At least I don't think that they are political. I am not sure why he has a cult following. Maybe it is partly political, I don't know. I am just pointing out the shortcomings of his Physics, and his politics.

How geometry created modern physics

Here is an elementary new lecture:

How geometry created modern physics – with Yang-Hui He

The Royal Institution

2,019 views Apr 13, 2023 THE ROYAL INSTITUTION

What's the story behind the five axioms of Euclidean geometry - and how is post-Euclidean geometry linked to modern physics?

From geometry’s classical beginnings, via the Renaissance and the Enlightenment, to the present day, Yang-Hui He takes us on a journey through time and space, culminating in our understanding of spacetime itself. In the 19th century, mathematicians such as Carl Gauss and Bernhard Riemann considered what would happen if we relaxed Euclid’s axioms. The result was the explosion of post-Euclidean geometry, which paved the way for Einstein’s theory of relativity and the birth of modern physics.

Here is the Q & A.

It is a nice expository lecture. It makes me wonder if modern Physics would have even been created, if not for Euclid's Elements. He says it is the most read book ever written, next to the Bible.

Historically, I wonder who first realized that XX century Physics was so dependent on geometry. Surely Hermann Weyl understood it a century ago. Einstein did not accept it, and particle physicists of the 1960s were slow to accept it.

Eventually the theorists were taken over by string theorists who want to do everything with geometry.

Logical Implications of Strict Physicalism

Here is a new 5-minute podcast on Stephen Barr - What is Human Mind in a Theistic World?.

The guest argues that if you want to be a strict physicalist, then you are forced into the many-worlds interpretation, with infinitely many copies of you.

Normally I would say that he is using bad Physics to justify his spiritual beliefs, but there are many respected atheist physicists who say the same thing.

I may be in the minority, but I say that strict physicalism means just believing in what is physically observable, and that rules out many-worlds. Believing in unobservable parallel universes and many copies of yourself is just another spiritual/religious belief, about like believing in the Bible. Believe in it if you want, but do not pretend that it is scientific, or logical, or strictly physical. It is not.

Yudowsky Says Shut AI Down Now

Top rationalist Guru Eliezer Yudowsky writes in Time magazine:

This 6-month moratorium would be better than no moratorium. I have respect for everyone who stepped up and signed it. It’s an improvement on the margin. ...

Many researchers steeped in these issues, including myself, expect that the most likely result of building a superhumanly smart AI, under anything remotely like the current circumstances, is that literally everyone on Earth will die. Not as in “maybe possibly some remote chance,” but as in “that is the obvious thing that would happen.” It’s not that you can’t, in principle, survive creating something much smarter than you; it’s that it would require precision and preparation and new scientific insights, and probably not having AI systems composed of giant inscrutable arrays of fractional numbers. ...

We are not ready. We are not on track to be significantly readier in the foreseeable future. If we go ahead on this everyone will die, including children who did not choose this and did not do anything wrong.

Shut it down.

He goes on to tell about how his partner sent him an email about a little girl losing her first tooth.

Maybe I am stupid, but I did not get the point of this little anecdote at all. Is this partner his wife, or a business partner? Is the girl their daughter? What is the big deal about the tooth? Why did he have to tell us he got persmission to tell this story? Maybe someone can explain it to me.

His concern is that super-intelligent bots will take over the world, and not be aligned with human values.

My fear is that lizard people have are already taking over the world, and they do not have my values.

I couldgive examples but I try to keep my political opinions off of this blog. I refer to this essay by physicist Lawrence M. Krauss:

Astrobiology: The Rise and Fall of a Nascent Science

Premature claims, distorted results, and ‘decolonizing’ the search for extraterrestrial intelligence. ...

The once-great science magazine, Scientific American, which has degenerated in recent years as social justice concerns have taken priority over science, published an article entitled “Cultural Bias Distorts the Search for Alien Life” (“‘Decolonizing’ the search for extraterrestrial intelligence (SETI) could boost its chances of success, says science historian Rebecca Charbonneau”).

Okay, no one cares about Astrobiology anyway, but more important sciences are being ruined.

How to Avoid Giving an Opinion on New Research

Physicist turned philosopher Sean M. Carroll posted his monthly podcast rant.

He gives this excuse for ignoring a surprising research paper:

So, when you have a claim in a scientific paper that goes entirely against everything the reader might have expected to be true, it is your job as the author to do two things. ...

So, when I read a paper like this, I'm looking for an acknowledgement that here's what you might expect and here's why we are different. And then, the other thing of course is that, that latter part here is why your expectations are not going to come true in this particular case. Here is why your intuitions are off. And I didn't see that in these papers. [chuckle] ...

0:22:02.7 SC: I'll give you a completely other... And the second example I do with great trepidation, 'cause I don't want to tar people with bad associations, but it sticks in my mind, The Bell Curve. Remember The Bell Curve? You know that book, Charles Murray and James Herrnstein from the '80s, and it came out in the '80s and it was talking about a distribution of IQ etcetera, and what the implications of that are for public policy. And I'm not an expert in this stuff and I was just a college student when it came out, but you know, I'm curious, it was a big deal when it came out. People are still talking about it today. And so, one of the... I didn't read the whole book by any stretch of the imagination, but I did look at it.

0:22:42.2 SC: I opened it and paged through. Again, to do this judgment, is this worth my time? Right? That's the question. And one of the very first questions I asked myself was, you know, look, there have been a lot of claims over the years that I can do science and show that some people, some racial groups are dumber than others, right? And these claims have a very bad history of being bad science badly done, because people wanted the results to be true, because it's a bunch of white people saying that black people are dumb. Usually, historically, that's what it's been. And these historical examples have been used to justify some terribly racist things. So, when a book comes along in the 1980s, which purports to be super duper modern and scientific, but yet reaching conclusions that are very similar to conclusions that have been reached a hundred years ago by pseudoscientific nonsense people, what I'm looking for is, once again, an acknowledgement.

0:23:45.8 SC: You might worry that this is just pseudoscientific racism, because that's been... We've had a long history of pseudoscientific racism and here is why we are not that. So, when you open The Bell Curve, you do not find that discussion. In fact, you find that they cite some of the pseudoscientific racism of the past approvingly. And at that point. I said, meh, this is not really gonna be worth my time.

It is true that the field of Psychology has a history of bad science badly done. Many textbook results could not be replicated, when done more carefully.

But IQ research has held up better than all the other areas of psychology. And the research is not necessarily what people wanted to be true. It says that Jews and Chinese are smarter, on average, in studies done by people who are not Jewish or Chinese. Blacks have done studies also.

Perhaps research was used to justify some terribly racist things, but denying the research was also used to justify racist things.

This whole example was to justify dismissing a paper on black holes!

The main point of the Bell Curve book was not about race. It was that spending on social programs will not raise IQ, so the money could be better spent on other goals. Rejecting that point has led to policies like No Child Left Behind, a big failure. More people should have read the book.

Carroll exhibits a peculiar closed-mindedness. He believes in parallel universes, but refuses to read evidence for group differences in humans.

Update: Here is a Jordan Peterson video clip explaining why IQ is important, and why no one wants to talk about it.

I am not blaming Carroll for not wanting to talk about it. I am blaming him for using it as an example of something that scientists should disregard.

Pythagorean Theorem Proof is not so New

MSN reports:

The Pythagorean Theorem — discovered by the Greek mathematician Pythagoras in the 6th century BCE — is a cornerstone of mathematics. Simply stated as a² + b² = c², the theorem posits that the sum of the two shortest sides of a right triangle (a² and b²) is equal to that triangle’s longest side (c²). For centuries, this idea has been proven by some of history’s greatest minds, such as Albert Einstein, U.S. President James Garfield (of all people), and even Pythagoras himself.

In fact, there have been hundreds of proofs of the Pythagoras’ groundbreaking theorem, but almost none of them — if not none at all — have independently proved it using trigonometry. That’s because the fundamentals of the theorem are what the entire field of trigonometry is built on, and so, the thinking goes that to use trigonometry to prove the theorem is to employ what’s called “circular reasoning.” It’s essentially using the Pythagorean Theorem to prove the Pythagorean Theorem.

Some mathematicians argue that using trigonometry to independently prove the theorem is actually impossible, including Elisha Loomis, whose book on the topic (originally published almost a century ago) states that “there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem.”

No, this is ridiculous. There are lots of trignonometric proofs.

Here is one.

sin α = a / c
cos α = b / c
Area = ab/2 = c²(.5 sin α cos α)

This means that the area of any right triangle is given by the square of the hypotenuse, multipled by a trigonometric function of the angles.

Now drop a perpendicular from C to c, dividing the triangle into two smaller similar triangles. The area of the big triangle equals the sum of the areas of the two smaller ones. The big one has hypotenuse c, while the smaller ones have hypotenuses a and b. Thus a² + b² = c², after dividing by that common trigonometric factor. The factor is the same for all three triangles, because the angles are the same.

This uses trigonometry, but does not use the identity (sin²α + cos²α = 1).

The supposed new proof is much more complicated, and uses limits.

Witten Defends String Theory in Interview

Here is a newly-released video on Edward Witten - What are Breakthroughs in Science?.

Of course Witten says that String Theory and M-Theory are the big breakthroughs. He says that M originally stood for "membranes", because a colleague thought that it was a membrane theory, but Witten was skeptical so he abbreviated it to M. He coysishly pretended it stood for Magical or Matrix. If it turned out to be a membrane theory, he would claim credit.

He admits that string theory could never accommodate parity violation, so it was always inconsistent with the Standard Model.

He defends the Landscape and his inability to predict anything from his theories by saying that gravity theory does not predict the length of the Martian year. Also he says his critics do not suggest a competing theory.

Wow, he cannot admit that he is really a mathematician wannabe who happens to like studying the mathematical structures of theories with no physical significance.

Grover's Algorithm may be a Dud

Grover's algorithm is supposed to be one of the great theoretical accomplishments of quantum computers, along with Shor's algorithm.

Now a new paper argues Grover's Algorithm Offers No Quantum Advantage

Scott Aaronson is not impressed:

I haven’t yet read that paper carefully, but have discussed it with some students and colleagues. My current impression is that it’s a mishmash of

(1) well-known observations about the difficulty of seeing a Grover speedup in practice given the overhead of quantum fault-tolerance, and

(2) a completely absurd argument about the Grover problem being “classically solvable with 1 query,” which would of course violate a known lower bound (what they mean is, in a model where you effectively get explicit access to the oracle function … in which case, we’re no longer talking about query complexity at all, and 0 queries suffice! 🙂 )

I don't know. This paper seems devastating to me, if it is right.

Grover's Algorithm is supposed to let you search N items with only &sqrt;N steps, using a quantum computer.

It is usually described as searching a database. But a relational database usually has an index that allows searching in log(N) steps, much faster than the quantum computer.

Quantum computers are supposed to do it without an index. It seems like magic. Useless magic.

Update: Scott Aaronson refutes the new paper here and here. He agrees with this:

Since the current practical infeasibility is well-known, I assumed the paper was observing something fundamental. It was not.

Okay, not news. Everybody already knew Grover's algorithm was a dud.