May 062024

A couple of months ago, I came across a nice paper, by Verma and Silk (of Silk damping fame, as he’s known to cosmologists), showing what would happen if we had a chance to view the “shadow” of a supermassive black hole as it is microlensed by an intervening smaller black hole along the line-of-sight.

It occurred to me that I have the means to model this. At first I thought I’d write a short paper. But there really is nothing new that I can add to what Verma and Silk said in their paper, other than a nice animation produced by my ray tracing code.

So here it is. A brief animation of a small black hole passing in front of the famous “shadow”.

Things are not exactly to scale, of course, but for what it’s worth, this video corresponds roughly to a 10,000 solar mass black hole passing through, halfway between us and Sagittarius A*.

 Posted by at 11:59 pm
May 052024

I finally saw last year’s blockbuster, Oppenheimer. Let’s just say that my reaction to the film is not exactly in the mainstream.

That is, Best Picture my ass.

I am okay with Murphy’s Best Actor. Downey Jr. was especially good, earning his Best Supporting Actor in a role that I can only describe as unpleasant, playing the main villain of the Oppenheimer story, Lewis Strauss.

An actual photo of the real Oppenheimer

But the film?

For starters, there’s the jumbled timeline.  I am deeply familiar with the Manhattan project, and reasonably familiar with Oppenheimer’s life, including the story of the humiliating revocation of his security clearance in the 1950s. Even so, I was confused: I had a hard time keeping track of what I was seeing.

Then, there are some of the portrayals. Teller was unrecognizable. Where was the famous limp? And what’s with the accent? Sometimes, no accent at all, sometimes an accent that, whatever it was, didn’t sound even remotely like Teller’s. For some of the other, well-known physicists, it was same thing: I’m glad the closed caption sometimes showed the name of the person talking, otherwise, I swear I would not have known that one of them was Szilard, for instance. And Groves? His portrayal by Matt Damon was more like a caricature than the real general.

And then there are the gratuitous sex scenes. I hope I don’t come across as a prude by mentioning this, but… was it really necessary? I mean, yes, I get it, their penetrating questions about Oppenheimer’s private life were metaphorically undressing him, but was it really necessary to assume that the audience is so dumb, they won’t “get it” unless you put Oppenheimer, stark naked, fucking his girlfriend right there in the chair in the conference room while he is being interrogated? Seriously, this was so over the top, I could not believe my eyes. My reaction was that they were trying to out-Kubrick Kubrick, but without the talent of Kubrick (and I am decidedly not a Kubrick fan.)

Then how about the conversations? Some of them, I swear, sounded like a bad AI (no, not GPT-4 or Claude 3, more like GPT-2 or compact versions of Llama) trying to recreate conversations between scientists. I don’t want to set an impossible standard here. How about just meeting the standard, say… of a sitcom? The Big Bang Theory and Young Sheldon are both more respectful of the science (and the intellectual quality of discussions between scientists) than this film.

And some of the scenes were just grossly inauthentic. Never mind misrepresenting the then-perceived significance of the Oppenheimer-Snyder paper on gravitational collapse (yes, it is significant, but no, the term “black hole” was not even coined until a quarter century later), what was that with that childish celebration when the print edition arrived? By then, Oppenheimer and his colleagues would have known for months that the paper was accepted. Oppenheimer would have seen, and corrected, the galley proofs. The fact that print copies of the journal would appear on the appointed date would have been neither a surprise nor news to anyone involved.

What about the things that were omitted from the film? And no, I am not talking about technical details, not even the massive role facilities other than Los Alamos played in the development of the bomb. How about Oppenheimer’s 1960 visit to Hiroshima? It could have offered some profound moments, perhaps even allowing the film to conclude in a way much more fitting than the stupid “burn the atmosphere” CGI.

And speaking of CGI… what’s with the Trinity explosion itself? I read somewhere that it was not CGI. I could tell… it felt cheap. A bit like the explosion of the planet Alderaan in the original Star Wars movie, before the remaster.

The film had some redeeming segments, especially in the final half hour, but even those were overplayed, like that final (as far as I know, wholly fictitious) conversation between Oppenheimer and Einstein. Certainly not enough to salvage the movie for me. The best part were the end credits, as the music score was decent (not sure about Best Original Score quality, but it was enjoyable).

All in all, between the two acclaimed blockbusters from last year, in my view, Barbie won hands down.

Incidentally, I reminded myself that I had an equally negative view of another famous blockbuster from ten years ago, Interstellar: crappy story, crappy science, a psychedelic scene that wanted to be a bit Kubrick-like but couldn’t quite make it (and I absolutely hated what Kubrick has done with the closing scenes of 2001: A Space Odyssey). What I didn’t realize until this moment is that both Interstellar and Oppenheimer were directed by the same Christopher Nolan. Guess that makes it official: I am no fan of Christopher Nolan! On the other hand, I suppose I am a fan of his younger brother: I liked Westworld, and I am beyond impressed by what he did with Fallout.

 Posted by at 11:27 pm
Apr 302024

One of the reasons why I find the sitcom, The Big Bang Theory, as well as its spinoff, Young Sheldon, enjoyable, is the fact that they respect the science.

That is to say, the science that we see pop up in the series from time to time is, well, it may be fictitious but not bogus. Not gobbledygook.

Here’s the latest example. In the most recent Young Sheldon episode, we see Sheldon’s first paper, published in the fictitious journal, “International Physics Review”.

The journal may be fictitious, but the format is not: It’s the standard Physical Review layout, pretty much. Looks quite legit!

The title actually makes sense. The Calabi-Yau manifold is a popular mathematical tool, used to deal with, or “compactify” the unwanted excess dimensions of 10-dimensional supersymmetric string theory.

The abstract cannot be read in full, but the words that are visible are not nonsense. OK, as far as I know there is no “Vail-Walker metric compactification”, but the fragments of text that we can read actually make sense, sort of: which is to say, the words are not randomly strung together, they actually form expressions that you might encounter in entirely legitimate physics texts.

I mean, usual Hollywood would have something like this Midjourney creation on a sheet of paper or a blackboard:

Midjourney’s response to the prompt, “A gentlecat physicist in front of a blackboard discussing the Schwarzschild metric”.

I mean, Midjourney draws lovely physicist cats, but it certainly knows nothing about the Schwarzschild solution. The creators of The Big Bang Theory do: If Sheldon Cooper talks about the Schwarzschild solution, you can bet that in the background, on the blackboard you’d see something like \(ds^2=(1-2GM/r)dt^2-(1-2GM/r)^{-1}dr^2-r^2d\theta^2-r^2\sin^2\theta d\phi^2.\)

 Posted by at 11:43 pm
Apr 232024

Despite working with them extensively for the past 18 months or so, our “little robot” friends continue to blow me away with their capabilities.

Take this: the other day I asked Claude opus 3 to create an N-body simulation example from scratch, in HTML + JavaScript, complete with the ability to record videos.

Here’s the result, after some very minor tweaks of the code produced by Claude, code that pretty much worked “out of the box”.

The code is simple, reasonably clean and elegant, and it works. As to what I think of our little robot friends’ ability to take a brief, casual description of such an application and produce working code on demand… What can I say? There’s an expression that I’ve been overusing lately, but it still feels the most appropriate reaction: Welcome to the future.

 Posted by at 6:11 pm
Apr 202024

So here is the thing. When you announce to the world your latest breakthrough in quantum computing, you might want to make sure first that the results cannot be replicated using hardware that is nearly half a century old, from the heyday of 8-bit personal computers.

Granted, the paper announcing this result was presented at a joke conference, but the paper itself is no joke: It’s actually quite well-written and the results appear credible.

I admit I loved this result because not only does it provide an example supporting my skepticism of sensationalist quantum computing claims, it also involves the computer that played a significant role in my early career, and which also happens to be the first computer that I proudly owned.

Of course the real point is that sensationalist coverage aside, apart from highly specialized, niche applications in which quantum computers basically play the role of specialized analog computers, the “quantum revolution” will not happen without scalable quantum computing, and scalable quantum computing will not happen without beating the threshold theorem. I am one of the skeptics: I strongly suspect that the threshold theorem will be shown to be a “no go” theorem. It is, of course, entirely possible that I am wrong about this, but in my mind, quantum computing is in the same league as fusion power: a technology that forever remains “just around the corner”.

 Posted by at 7:52 pm
Jan 242024

Someone sent me a link to a YouTube podcast, a segment from an interview with a physicist.

I didn’t like the interview. It was about string theory. My dislike is best illustrated by a point that was made by the speaker. He matter-of-factly noted that, well, math is weird, the sum of \(1 + 2 + 3 + …,\) ad infinitum, is \(-\tfrac{1}{12}.\)

This flawlessly illustrates what bothers me both about the state of theoretical physics and about the way it is presented to general audiences.

No, the sum of all positive integers is not \(-\tfrac{1}{12}.\) Not by a longshot. It is divergent. If you insist, you might say that it is infinite. Certainly not a negative rational number.

But where does this nonsense come from?

Well, there’s the famous Riemann zeta-function. For values of \(s>1,\) it is indeed defined as

$$\zeta(s)=\sum_{n=1}^\infty \frac{1}{n^s}.\tag{1}$$

It is a very interesting function, at the heart of some unresolved problems in mathematics.

But the case of \(s=-1\) (which is when the right-hand side of the equation used to define \(\zeta(s)\) corresponds to the sum of all positive integers) is not an unresolved problem. As it is often presented, it is little more than a dirty trick befitting a cheap stage magician, not a scientist.

That is to say, the above definition of \(\zeta(s),\) as I said, is valid only for \(s>1.\) However, the zeta-function has what is called its analytic continuation, which makes it possible to extend the definition for other values of \(s,\) including \(s=-1.\) This can be accomplished utilizing Riemann’s functional equation, \(\zeta(s)=2^s\pi^{s-1}\sin(\tfrac{1}{2}\pi s)\Gamma(1-s)\zeta(1-s).\) But the right-hand side of (1) in this case does not apply! That sum is valid only when it is convergent, which is to say (again), \(s>1.\)

A view of the Riemann zeta-function, from Wikipedia.

So no, the fact that \(\zeta(-1)=-\tfrac{1}{12}\) does not mean that the sum of all integers is \(-\tfrac{1}{12}.\) To suggest otherwise only to dazzle the audience is — looking for a polite term here that nonetheless accurately expresses my disapproval — well, it’s dishonest.

And perhaps unintentionally, it also shows the gap between robust physics and the kind of mathematical games like string theory that pretend to be physics, even though much of it is about mathematical artifacts in 10 dimensions, with at best a very tenuous connection to observable reality.

 Posted by at 10:48 pm
Jan 182024

I gave a brief invited talk today via Zoom, participating in a workshop on cosmological models, organized by Complutense University of Madrid, Spain.

The subject of my talk was John Moffat’s theory of gravitation, MOG/STVG, to which I made significant contributions myself over the past 18 years, in an on-going collaboration with John. Judging by the questions that followed my short presentation, I think it was reasonably well received.

The workshop was streamed live on YouTube, and the video is archived.


 Posted by at 9:25 pm
Dec 052023

Now that Roy Kerr’s paper on black holes and singularities is on arXiv, I am sure I’ll be asked about it again, just as I have been asked about it already on Quora.

Roy Kerr, of course, is one of the living legends of relativity theory. His axisymmetric solution, published in the year of my birth, was the first new solution in nearly half a century after Karl Schwarzschild published his famous solution for a spherically symmetric, static, vacuum spacetime. I hesitate to be critical of this manuscript since chances are that Kerr is right and I am wrong.

Kerr now argues that the singularity theorems are nonsense, and that his axisymmetric solution actually hides some nonsingular configuration of matter therein.

At a first glance, the paper seems well written and robust. Still… when I dug into it, there are a few things that caught my attention, and not in a right way. First, the paper takes argument with “singularity believers” using language that almost sounds like pseudoscience. Second, it has some weird factual errors. E.g., it asserts that black holes “as large as 100 billion solar masses have been observed by the James Webb Telescope” (not even close). Or, it describes the famous Oppenheimer-Snyder paper of 1939 as having “used linear, nineteenth century ideas on how matter behaves under extreme pressures” (actually, Oppenheimer and Snyder discuss the collapse of a “dust” solution with negligible pressure using the tools of general relativity with rigor). Kerr further criticizes the Oppenheimer-Snyder paper as attempting “to ‘prove’ that the ensuing metric is still singular”, even though that paper says nothing about the metric’s singularity, only that the collapsing star will eventually reach its “gravitational radius” (i.e., the Schwarzschild radius). Nonetheless, later Kerr doubles down by writing that “Oppenheimer and Snyder proved that the metric collapses to a point,” whereas the closest the actual Oppenheimer-Snyder paper comes to this is describing collapsing stars as stars “which cannot end in a stable stationary state”.

Never mind, let’s ignore these issues as they may not be relevant to Kerr’s argument after all. His main argument is basically that Penrose and Hawking deduced the necessary presence of singularities from the existence of light rays of finite affine length; i.e., light rays that, in some sense, terminate (presumably at the singularity). Kerr says that no, the ring singularity inside a Kerr black hole, for instance, may just be an idealized substitute for a rotating neutron star.

Now Kerr has an interesting point here. Take the Schwarzschild metric. It is a vacuum solution of general relativity, but it also accurately describes the gravitational field outside any static, spherically symmetric distribution of matter in the vacuum. So a Schwarzschild solution does not imply an event horizon or a singularity: they can be replaced by an extended, gravitating body that has no singularities whatsoever so long as the radius of the body is greater than the Schwarzschild radius associated with its mass. The gravitational field of the Earth is also well described by Schwarzschild outside the Earth. So in my reading, the crucial question Kerr raises is this: Is it possible that once we introduce matter inside the event horizon of a Kerr black hole, perhaps that can eliminate the interior Cauchy horizon or, at the very least, the ring singularity that it hides?

I don’t think that is the case, and here is why. Between the two horizons of a Kerr black hole, the “radial” coordinate is now the timelike coordinate, with the future pointing “inward”, i.e., towards the Cauchy horizon. That means that particles of matter do not have trajectories that would allow them to avoid the Cauchy horizon; no matter what path they follow, they will reach that horizon in finite proper time.

Inside the Cauchy horizon, anything goes, since closed timelike curves exist. So presumably, it might even be possible for particles of matter to travel back and forth between the past and the future, never hitting the ring singularity. But that’s not what Kerr is suggesting in his paper; he’s not talking about acausal worldlines inside the Cauchy horizon, but some “nonsingular interior star”. I don’t see how to make sense of that suggestion, because I don’t see how a stationary configuration of matter could exist inside the inner horizon. Wobbling back-and-forth between yesterday and tomorrow in a closed timelike loop is not a stationary configuration!

For these reasons, even as I am painfully aware that I am arguing with a Roy Kerr so there’s a darn good chance that he’s right and I’m spouting nonsense, I must say that I remain unconvinced by his paper. The language he uses (e.g., describing the business of singularities as “dogma”) is not helping either. Also, his description of the interior of the rotating black hole sounds a bit off; to use his own words, “nineteenth century” reasoning, much more so than the Oppenheimer-Snyder paper that he criticizes.

 Posted by at 7:31 pm
Dec 022023

I just came across a quote attributed to Einstein: “If I had foreseen Hiroshima and Nagasaki, I would have torn up my formula in 1905.

The problem with this quote is that it is utter nonsense, and not something Einstein likely would have said, ever.

An image of Einstein that is just as real as some of the quotes attributed to him. Courtesy of Midjourney.

The “formula” of mass-energy equivalence simply states that an object’s resistance to motion (its inertia) is proportional to its energy-content. That is all. Yes, I know that in the popular imagination, \(E=mc^2\) is frequently associated with the nuclear age. But that’s nonsense. \(E=mc^2\) is not about “converting” anything into anything. Mass-energy is mass-energy, and it is conserved. Whether it is in the form of the nuclear binding energy of a uranium atom (or for that matter, the chemical binding energy of carbon atoms in a fireplace log) or in the form of the kinetic energy of photons released by a nuclear or chemical reaction has absolutely nothing to do with \(E=mc^2\): the formula does not explain nuclear fission any more than it explains the chemical reactions that govern the burning of wood.

But then, what about this quote, which appears in a number of reliable places, including Wikiquotes?

It is attributed to a book published by a William Hermanns, who supposedly interviewed Einstein on a number of occasions between the late 1920s and Einstein’s death in 1955.

The person appears real. I found, in Google’s archive, the May 2, 1955 issue of Life, which includes a personal recollection of one of Life’s own editors, William Miller, of his very last visit to Einstein, when he actually met William Hermanns.

Hermanns’s book, Einstein and the Poet: In Search of the Cosmic Man, is also real: In fact, it even has a Kindle edition.

But… how much of it is true?

Considering that Hermanns has an exceptional biography (which one can read on a Web site dedicated to his life) it is more than a bit odd that the only references to his name in Wikipedia are Einstein-related. Yet his name does not appear in notable Einstein biographies, including Abraham Pais’s definitive scientific biography, or Walter Isaacson’s exceptionally good Einstein bio.

When I read the few pages of Hermanns’s book that are available as a Kindle preview, I grow even more suspicious. For instance, according to Hermanns, already in 1927 Einstein was “marked by Nazis as ‘Enemy number One of the Nation,’ and the object of at least seven plots to take his life.” News to me.

But then, Hermanns goes on to quote Einstein who supposedly said, “When I was about five, my father gave me a compass as a toy. I wanted to find out why the needle never deviated […] When I asked my uncle, an engineer, he immediately proceeded to teach me some fundamentals of algebra, with this advice: ‘What you don’t know, call x, then hunt til you find what it is.’ From that time on, I have called everything I didn’t know x, especially magnetism.

As I asked ChatGPT just moments ago, can you imagine Einstein saying these words, in 1927, to a stranger who just visited him?

Long story short, I don’t know what to think. Based on what I have read, I do not believe Hermanns’s accounts of his conversations with Einstein are credible. At the very least, they must be severely distorted versions of Einstein’s words, probably deeply colored, warped by Hermanns’s imagination. For what it’s worth, ChatGPT concurs: “The lack of independent verification and recognition in authoritative sources casts doubt on the accuracy and credibility of his accounts. Your reservations about accepting Hermanns’ narratives as factual are well-founded.”

 Posted by at 11:32 pm
Nov 302023

This morning, like pretty much every morning, there was an invitation in my inbox to submit a paper to a journal that I never heard of previously.

Though the unsolicited e-mail by itself is often an indication that the journal is bogus, predatory, I try to be fair and give them the benefit of the doubt, especially if the invitation is from a journal that is actually related to my fields of study. (All too often, it is not; I’ve received plenty of invitations from “journals” in the medical, social, biological, etc., sciences, subjects on which I have no professional expertise.)

So what are the signs that I am looking for? Well, I check what they published recently. That’s usually a good indication of what to expect from a journal. So when I read a title that says, say, “Using black holes as rechargeable batteries and nuclear reactors,” I kind of know what to expect.

Oh wait. That particular paper appears to have been accepted for publication by Physical Review D.

Seriously, what is the world of physics coming to? What is the world of scientific publishing, by and large, coming to? Am I being unfair? Just to be sure, I fed the full text of the paper on black hole batteries to GPT-4 Turbo and asked the AI to assess it as a reviewer:

 Posted by at 11:06 am
Nov 082023

Sometimes it feels… so pretentious.

Here I am, saying all sorts of clever things in my blog. I once declared blogs to be write-only media, my way of shouting at the world without the world saying anything in return, but that kind of ceased being true when I decided, eons ago, to share my blog posts on social media, where a few friends at least reacted occasionally.

So who do I think I am, proclaiming my wisdom to the world, really?

For instance, a few days ago I thought I’d blog about the first precision clock arriving in America centuries ago, and promptly failing, leading to a better understanding of how the gravitational acceleration on the surface of the Earth may change with geographic location. But is there anything I can add to the subject other than what’s in the article I am citing?

Or take this report from earlier today, about Singapore’s Prime Minister expressing very much the same concerns that I have about the world experiencing a moment of danger not unlike the moments before the Great War. OK, so I blog about it. Is there anything I can add other than, hey, look, I am ever so clever, even Singapore’s PM shares my views!?

I suppose I feel most comfortable blogging about my actual research or my work. These are subjects that I can address with some competence.

Or maybe just blog about cats. They know how to be wise and silent, after all.

Meanwhile, in the world of humans…

F-15s strike weapons facility in Syria

By Lauren C. Williams and Jennifer Hlad

ABOARD A MILITARY PLANE—Two U.S. F-15 fighter jets attacked a weapons storage facility in eastern Syria on Wednesday, in what Defense Secretary Lloyd Austin called a “precision self-defense strike” in response “to a series of attacks against U.S. personnel in Iraq and Syria by the [Iranian Islamic Revolutionary Guard Corps]-Quds Force” and related groups.

So I must now follow my cats’ example and resist the urge to blog about how the US and Iran might already be at war…

 Posted by at 9:51 pm
Nov 012023

A few minutes ago, I checked Google News on my phone and lo and behold, there was a link to Universe Today, a new article discussing my latest manuscript on multiple gravitational lenses.

I knew that this was in the works, as the author approached me with some questions earlier in the day, but I didn’t expect it to appear this quickly, and, well, seeing it on my phone like this was a nice surprise.

Had the author asked, I’d have happily granted permission to use one of my generated images or animations involving multiple lenses.

Meanwhile, my paper on a four-satellite configuration used to detect deviations from Newtonian gravity was published by Astrophysics and Space Science, one of the Nature journals. I am officially permitted (in fact, encouraged) by Springer to share the link to an online read-only version of the published paper.

 Posted by at 1:25 am
Oct 122023

I’m doing more work on gravitational lensing. In particular, the little ray tracing model that I developed can now use actual astronomical images as sources. Here’s a projection of a nice spiral galaxy as it would be seen through a pair of non-coplanar, imperfectly lined up lenses:

Somehow, I suspect, no astronomer would recognize (at least not without a spectral analysis) that these are four images of the same rather nice-looking galaxy, NGC-4414:

These lensing examples also demonstrate how difficult it is to reconstruct either the original view, or the mass distribution of the lens itself, when all we see is something like the first image above.

 Posted by at 9:35 pm
Oct 082023

I am simulating gravitational lenses, ray tracing the diffracted light.

With multiple lenses, the results can be absolutely fascinating. Here’s a case of four lenses, three static, a fourth lens transiting in front of the other three, with the light source a fuzzy sphere in the background.

I can’t stop looking at this animation. It almost feels… organic. Yet the math behind it is just high school math, a bit of geometry and trigonometry, nothing more.

NB: This post has been edited with an updated, physically more accurate animation.

 Posted by at 5:35 pm
Oct 052023

I don’t know much about attosecond light pulses but my wife and I did note that one of the recipients of this year’s physics prize was a physicist who studied just a year ahead of Ildiko at ELTE (Eötvös University). She doesn’t recall if she ever bumped into Ferenc Krausz, though.

And of course one of the recipients of the Nobel prize in physiology or medicine was Katalin Kariko, for her groundbreaking work in mRNA vaccines. Well-deserved indeed! I actually know (a little bit) more about mRNA vaccines than about attosecond physics, which might seem odd, considering that physics is my home turf, and organic chemistry is like an alien landscape. But the generation of ultrashort photon pulses is a very specialized field of study, to which I never paid much attention.

Anyhow, Kariko and Krausz are now added to that long list of scientists who were born, and studied in, Hungary, but who eventually ended up abroad, where they did the bulk of the work that earned them this recognition.

 Posted by at 7:03 pm
Sep 292023

OK, not exactly a surprising result but still, a fantastic experimental achievement: Yes, Virginia, antimatter falls downward.

Why is this important? Well, we kind of knew that it was inevitable. I mean, if antimatter were to fall upward, it’d have meant that our entire understanding of gravitation is wrong. That even our understanding of special relativity is probably wrong.

So it was a rather safe bet that antimatter follows the same geodesics as normal matter and falls downward.

But physics, lest we forget it, is ultimately not about erudite speculation. It is about experiment and observation.

And this amazing experiment achieved the almost impossible: it observed antihydrogen atoms in a vertical vacuum chamber at cryogenic temperatures and, as expected, most of those hydrogen atoms ended up at the bottom.

 Posted by at 12:33 am
Sep 162023

My friend John Moffat has a finite quantum field theory that, I think, deserves more attention than it gets.

The theory is nonlocal (then again, so is quantum physics to begin with). However, it does not violate causality. So its nonlocality is a mathematical curiosity, not a physical impossibility.

The essence of the theory is present in the form of its “nonlocal field operator”. Given, e.g., a scalar field in the form \(\phi(x),\) the field is transformed as

$$\tilde\phi(x)=\int d^4x’f(x-x’)\phi(x’).$$

Now if we just used the Dirac delta-function \(f(x-x’)=\delta^4(x-x’),\) we’d get back \(\phi(x).\) But what if we use some other function, the only restriction being that \(f(x)\) must be an entire function, which is to say, unambiguously defined without poles or singularities over the entire complex plane?

Well, then, assuming again that \(f(x)\) is an entire function, we can integrate iteratively in parts, until we arrive at an expression in the form,

$$\tilde\phi(x)={\cal F}(\partial_x)\phi(x),$$

where \({\cal F}(\partial_x)\) is a derivative operator, typically some power series in the form \(\lambda_i\partial_x^i\), acting on \(\phi(x).\)

Why is this good for us? Because this field redefinition can suppress high-energy divergences in the theory, essentially doing away with the need for renormalization, which, of course, is a Big Claim indeed but I think John’s theory works.

John’s first substantive papers on this topic were titled Finite quantum field theory based on superspin fields (J. W. Moffat, Phys. Rev. D 39, 12 (1989)) and Finite nonlocal gauge field theory (J. W. Moffat, Phys. Rev. D 41, 4 (1990)). Unfortunately these papers predate so only the paywalled versions are available. They are beautiful papers that deserve more recognition. More recently, John wrote another paper on the subject, collaborating with a student. One of these days, I’m hoping to spend some time myself working a bit on John’s theory because I believe it has merit: The theory appears to remain causal despite the nonlocal operator, and by doing away with the need for renormalization, it makes canonical quantization almost trivially possible. I keep wondering if there is, perhaps, a catch after all, but if that’s the case, I have yet to find it.

 Posted by at 1:37 pm
Sep 122023

I gave a talk on the Solar Gravitational Lens in Montreal back in July, using the above title.

Video of the talk is now available online, courtesy of the Interstellar Research Group.

I just listened to it myself and I didn’t cringe too much hearing my own voice or watching myself, which is probably a good sign?

 Posted by at 12:31 am
May 232023

In the last several years, we worked out most of the details about the Solar Gravitational Lens. How it forms images. How its optical qualities are affected by the inherent spherical aberration of a gravitational lens. How the images are further blurred by deviations of the lens from perfect spherical symmetry. How the solar corona contributes huge amounts of noise and how it can be controlled when the image is reconstructed. How the observing spacecraft would need to be navigated in order to maintain precise positions within the image projected by the SGL.

But one problem remained unaddressed: The target itself. Specifically, the fact that the target planet that we might be observing is not standing still. If it is like the Earth, it spins around its axis once every so many hours. And as it orbits its host star, its illumination changes as a result.

In other words, this is not what we are up against, much as we’d prefer the exoplanet to play nice and remain motionless and fully illuminated at all times.

Rather, what we are against is this:

Imaging such a moving target is hard. Integration times must be short in order to avoid motion blur. And image reconstruction must take into account how specific surface features are mapped onto the image plane. An image plane that, as we recall, we sample one “pixel” at a time, as the projected image of the exoplanet is several kilometers wide. It is traversed by the observing spacecraft that, looking back at the Sun, measures the brightness of the Einstein ring surrounding the Sun, and reconstructs the image from this information.

This is a hard problem. I think it is doable, but this may be the toughest challenge yet.

Oh, and did I mention that (not shown in the simulation) the exoplanet may also have varying cloud cover? Not to mention that, unlike this visual simulation, a real exoplanet may not be a Lambertian reflector, but rather, different parts (oceans vs. continents, mountain ranges vs. plains, deserts vs. forests) may have very different optical properties, varying values of specularity or even more complex optical behavior?

 Posted by at 12:06 am
May 052023

I got sent a link about an interesting, newly published book on the memoirs of Charles-Augustin de Coulomb. He was, of course, the French officer, engineer and physicist most famous for the Coulomb law that characterizes the electrostatic interaction.

As I occasionally receive e-mails from strangers about their self-published tomes or tomes published through vanity publishers of questionable credibility, I have come to the habit of dismissing such e-mails without paying them much attention. I am glad I paid more attention this time because this book is interesting, valuable, and genuine.

It is available as a matter of fact as a free PDF download from the authors but hey, I just bought the paperback. It was for some reason deeply discounted on Amazon Canada, so with free Prime shipping, all I am paying is the princely sum of $3.15. These days when even “cheap” paperback novels often cost 20 bucks if not more, how could I resist?

Of course it also helped that I looked at the PDF. I am sure the book has flaws (all books do) but it looks like a serious scholarly publication delivering real value to physicists and science historians both.

In fact, it is fascinating to see how modern, how advanced scientific thinking was already evident more than a quarter millennium ago. It makes me appreciate even more just how much of our collective human effort was needed to get from these early experiments to the present era of ubiquitous computer networks running amazing software that now mimics human intelligence, all powered by the same electricity that Coulomb was exploring.

 Posted by at 9:46 pm