Physics – Spinor Info

Saying clever things

Cats, Personal, Physics, Politics No Responses »

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…

My latest papers

Astronomy, Personal, Physics No Responses »

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.

More lensing

Astronomy, Personal, Physics No Responses »

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.

Gravitational lenses

Astronomy, Mathematics, Physics No Responses »

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.

Hungarian Nobels

Physics, Science No Responses »

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.

Falling antimatter

Physics No Responses »

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.

Moffat’s finite quantum field theory

Personal, Physics No Responses »

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 arxiv.org 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.

Look before you leap…

Personal, Physics No Responses »

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?

What we are up against with the SGL

Astronomy, Personal, Physics No Responses »

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?

Coulomb’s Memoirs

Physics No Responses »

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.

GPT-4 and physics

Cybernetics, Physics No Responses »

May 022023

Not exactly the greatest discovery, I know, but GPT-4 still managed to offer an impressive demonstration of its understanding of gravitational physics when I asked it to build a Newtonian homogeneous universe:

What distinguishes GPT-4 from its predecessor is not that its training dataset is larger, but that it has significantly improved reasoning capabilities, which is well demonstrated by this answer. GPT 3.5 and Claude have the same knowledge. But they cannot put the pieces together quite like this (although they, too, can do impressive things with appropriate human guidance, one step at a time.)

Another paper

Personal, Physics, Space No Responses »

Apr 202023

Another paper of ours, in all its 36-page glory, was accepted by Physical Review D and I am delighted.

One of the things we do in this paper is the use of symmetric trace-free tensors (STF) that allow us, among other things, to effect a rotation of spherical harmonic coefficients. This approach likely has many uses as a bit of practical math, beyond modeling gravitational fields.

Eye of the Sun

Film, Personal, Physics, Space No Responses »

Mar 222023

Students at the California State University, Northridge, are currently working on a short documentary film about our work on the Solar Gravitational Lens.

The project hopes to attract modest crowdfunding. They also produced a teaser trailer.

Of course I hope they succeed; our SGL work could use some good publicity.

No, the Earth’s core is not spinning backwards

Geology, Physics 1 Response »

Jan 262023

“Stop the presses! The Earth’s core stopped spinning! In fact it is now spinning backwards!”

Well, that’s pretty much how much of the popular press handled a recent article, published in Nature Geoscience, under the far less pretentious title, “Multidecadal variation of the Earth’s inner-core rotation”.

And indeed, the first half-sentence in the abstract says it all (emphasis mine): “Differential rotation of Earth’s inner core relative to the mantle“.

It’s not like the core stopped spinning. It’s just that the core is sometimes spinning slightly faster, sometimes spinning slightly slower than the mantle, an oscillatory pattern that has to do with the complex interaction between the two.

How much faster/slower? Don’t expect anything dramatic. At most a few degrees a year, but more likely, just a small fraction of a degree a year. So even if the ~70-year cycle (deduced by the authors of the recent article — there are other estimates) is valid, the core would only get ahead, or behind, the mantle by just a few degrees before it slows down or catches up again.

And this is what supposedly happened: the core was slowing down until a few years ago, its rotation came to be in sync with that of the mantle. Slowing down further, it’s now falling ever so slightly behind, only to catch up again, presumably, a few decades from now.

The way it is misleadingly presented in the media and the degree to which it is sensationalized demonstrate that we live in the era of hype.

Fusion breakthrough?

Physics No Responses »

Dec 122022

The National Ignition Facility has achieved a net power gain in its experimental fusion reactor. This is heralded as a major breakthrough.

Does this mean that in 50 years, we will have practical nuclear fusion power our world?

Oh wait. We were told exactly that some 50 years ago:

At the beginning of the 1950s, it seemed that success is not far away. But later, difficulties arose one after another […]
…
Unfortunately today there are still gigantic difficulties in the path towards utilizing this fabulously rich supply of energy […]
…
In fourteen countries of the world, more than two thousand engineers and scientists are laboring on working out different types of fusion devices.
…
To date, more than a hundred different models have been devised […]
…
Let us introduce only one group of these: the Soviet Tokamak devices, because around the world, these are the ones in which researchers have the most faith, viewing them as prototypes of future fusion power plants.
…
A year and a half ago, in an experiment carried out in collaboration between Soviet and English physicists, they directly measured the temperature and density of the plasma of Tokamak-3, and it became clear that the results were even better than indicated by prior measurements. To date, no other device could produce plasma of such quality.
…
When will the first fusion power plants be realized, when will the investigation of controlled nuclear fusion exit the constraints of laboratory experiments? According to Professor Igor Golovin, the world-renowned expert on thermonuclear research, it will be possible to develop Tokamak devices into electricity-producing equipment by the last decade of our century. L. Hirsch, one of the leading physicists of the American Atomic Energy Commission is a little more cautious. According to him the path from the first experiments to the worldwide spread of fusion power plants is longer, and we’re lucky if they will enter the world’s energy production market in fifty years.

These are all quotes (my translations) from a 1972 Hungarian-language educational children’s publication, “Boys’ Almanac 1973”.

As I express my (probably uninformed) skepticism concerning practical fusion power generation, I note that in the deep interior of the Sun, under gravitational confinement due to the combined mass of more than 300,000 Earths, fusion progresses at the leisurely rate of a few hundred watts per cubic meter. (The power output of a well-maintained industrial compost pile.) For practical power generation, we need something that is at least a million times that, a few hundred megawatts per cubic meter… and we don’t have 300,000 Earths for gravitational confinement.

Of course I’d be delighted if they proved me wrong.

Priests and philosophers

Personal, Physics No Responses »

Nov 072022

Every so often, I am presented with questions about physics that go beyond physics: philosophical questions of an existential nature, such as the reasons why the universe has certain properties, or the meaning of existence in light of the far future.

I usually evade such questions by pointing out that they represent the domain of priests or philosophers, not physicists. I do not mean this disparagingly; rather, it is a recognition of the fact that physics is about how the universe works, not why, nor what it all means for us humans.

Yesterday, I came across a wonderful 1915 painting by Russian avant-garde painter Lyubov Popova, entitled Portrait of a Philosopher:

What can I say? This painting sums up how I feel perfectly.

Bloggables

Personal, Physics, Politics No Responses »

Oct 242022

There are only about six days left of the month of October and I have not yet written anything in this blog of mine this month. I wonder why.

Ran out of topics? Not really, but…

… When it comes to politics, what can I say that hasn’t been said before? That the murderous mess in Ukraine remains as horrifying as ever, carrying with it the threat of escalation each and every day? That it may already be the opening battle of WW3?

Or should I lament how the new American radical right — masquerading as conservatives, but in reality anti-democratic, illiberal authoritarianists who are busy dismantling the core institutions of the American republic — is on the verge of gaining control of both houses of Congress?

Do I feel like commenting on what has been a foregone conclusion for months, Xi “Winnie-the-pooh” Jinping anointing himself dictator for life in the Middle Kingdom, ruining the chances of continuing liberalization in that great country, also gravely harming their flourishing economy?

Or should I comment on the fact that prevalent climate denialism notwithstanding, for the first time in the 35 years that I’ve lived in Ottawa, Canada, our air conditioner came online in the last week of October because the house was getting too hot in this near summerlike heat wave?

Naw. I should stick to physics. Trouble is, apart from the fact that I still feel quite unproductive, having battled a cold/flu/COVID (frankly, I don’t care what it was, I just want to recover fully) my physics time is still consumed with wrapping up a few lose ends of our Solar Gravitational Lens study, now that the NIAC Phase III effort has formally come to a close.

Still, there are a few physics topics that I am eager to revisit. And it’s a nice form of escapism from the “real” world, which is becoming more surreal each and every day.

Purple spiders in physics

Physics No Responses »

Sep 282022

I don’t always agree with Sabine Hossenfelder but every once in a while, she hits the nail spot on.

Case in point: Her article, published in The Guardian on September 26, about the state of particle physics.

Imagine going to a zoology conference, she says, where a researcher discusses a hypothesis (complete with a computer-generated 3D model) of a 12-legged purple spider living in the Arctic. Probably doesn’t exist but still, how about proposing a mission to the Arctic to search for one? After all, a null result also contains valuable data. Or how about a flying earthworm that lives in caves? Martian octopuses, anyone?

Zoology conferences do not usually discuss such imaginary monsters but, Sabine argues (and she is spot on) this is pretty much what particle physics conferences are like: “invent new particles for which there is no evidence, publish papers about them, write more papers about these particles’ properties, and demand the hypothesis be experimentally tested”. Worse yet, real money is being spent (wasted might be a better word) on carrying out such experiments.

She points out that while it is true that good science is falsifiable, the opposite isn’t always the case: Just because something is falsifiable does not make it good science.

And not just particle physics, I hasten to add. How about cosmology and gravitation? Discussions about what may or may not have happened during the Planck epoch? Exploring exotic spacetime topologies, often in dimensions other than four? And let me not even mention quantum computing or fusion energy…

Perhaps I am a born skeptic lacking imagination, but to me, these are all 12-legged purple Arctic spiders. The science we actually know and have the ability to confirm are general relativity in a spacetime that is by and large the perturbed Minkowski metric; and the Standard Model of particle physics, extended with a neutrino mass mixing matrix. These are the things that work. Not perfectly, mind you. General relativity needs “dark matter” (name aside, we don’t know what it is except that it has a dust equation of state) and “dark energy” (again, it has a name but beyond that, we don’t know what it is beyond its equation of state) to account for galaxy dynamics and cosmic evolution. The Hubble tension, the discrepancy between values of the Hubble parameter measured using different methods, is real. Observations by the James Webb space telescope suggest that we do not understand the “dark ages”, the first few hundred million years after the surface of last scattering (i.e., the epoch when the cosmic microwave background radiation was produced), well. Massive neutrinos invite the question about the apparent absence right-handed neutrinos.

And yes, we are very much in the blind concerning these issues. Nature has not yet provided hints and we are not smart enough to figure out the answers entirely on our own. But how is that an excuse for inventing 12-legged spiders?

I think it isn’t.

A silly idea that didn’t get me anywhere

Physics No Responses »

Sep 012022

A few days ago I had a silly thought about the metric tensor of general relativity.

This tensor is usually assumed to be symmetric, on account of the fact that even if it has an antisymmetric part, $g_{[\mu\nu]}dx^\mu dx^\nu$ will be identically zero anyway.

But then, nothing constrains $g_{\mu\nu}$ to be symmetric. Such a constraint should normally appear, in the Lagrangian formalism of the theory, as a Lagrange-multiplier. What if we add just such a Lagrange-multiplier to the Einstein-Hilbert Lagrangian of general relativity?

That is, let’s write the action of general relativity in the form,

$$S_{\rm G} = \int~d^4x\sqrt{-g}(R – 2\Lambda + \lambda^{[\mu\nu]}g_{\mu\nu}),$$

where we introduced the Lagrange-multiplier $\lambda^{[\mu\nu]}$ in the form of a fully antisymmetric tensor. We know that

$$\lambda^{[\mu\nu]}g_{\mu\nu}=\lambda^{[\mu\nu]}(g_{(\mu\nu)}+g_{[\mu\nu]})=\lambda^{[\mu\nu]}g_{[\mu\nu]},$$

since the product of an antisymmetric and a symmetric tensor is identically zero. Therefore, variation with respect to $\lambda^{[\mu\nu]}$ yields $g_{[\mu\nu]}=0,$ which is what we want.

But what about variation with respect to $g_{\mu\nu}?$ The Lagrange-multipliers represent new (non-dynamic) degrees of freedom. Indeed, in the corresponding Euler-Lagrange equation, we end up with new terms:

$$\frac{\partial}{\partial g_{\alpha\beta}}(\sqrt{-g}\lambda^{[\mu\nu]}g_{[\mu\nu]})=
\frac{1}{2}g^{\alpha\beta}\sqrt{-g}\lambda^{[\mu\nu]}g_{[\mu\nu]}+\sqrt{-g}\lambda^{[\mu\nu]}(\delta^\alpha_\mu\delta^\beta_\nu-\delta^\alpha_\nu\delta^\beta_\mu)=2\sqrt{-g}\lambda^{[\mu\nu]}=0.$$

But this just leads to the trivial equation, $\lambda^{[\mu\nu]}=0,$ for the Lagrange-multipliers. In other words, we get back General Relativity, just the way we were supposed to.

So in the end, we gain nothing. My silly thought was just that, a silly exercise in pedantry that added nothing to the theory, just showed what we already knew, namely that the antisymmetric part of the metric tensor contributes nothing.

Now if we were to add a dynamical term involving the antisymmetric part, that would be different of course. Then we’d end up with either Einstein’s attempt at a unified field theory (with the antisymmetric part corresponding to electromagnetism) or Moffat’s nonsymmetric gravitational theory. But that’s a whole different game.

Differentiation

Mathematics, Personal, Physics No Responses »

May 252022

From time to time, I promise myself not to respond again to e-mails from strangers, asking me to comment on their research, view their paper, offer thoughts.

Yet from time to time, when the person seems respectable, the research genuine, I do respond. Most of the time, in vain.

Like the other day. Long story short, someone basically proved, as part of a lengthier derivation, that general relativity is always unimodular. This is of course manifestly untrue, but I was wondering where their seemingly reasonable derivation went awry.

Eventually I spotted it. Without getting bogged down in the details, what they did was essentially equivalent to proving that second derivatives do not exist:

$$\frac{d^2f}{dx^2} = \frac{d}{dx}\frac{df}{dx} = \frac{df}{dx}\frac{d}{df}\frac{df}{dx} = \frac{df}{dx}\frac{d}{dx}\frac{df}{df} = \frac{df}{dx}\frac{d1}{dx} = 0.$$

Of course second derivatives do exist, so you might wonder what’s happening here. The sleight of hand happens after the third equal sign: swapping differentiation with respect to two independent variables is permitted, but $x$ and $f$ are not independent and therefore, this step is illegal.

I pointed this out, and received a mildly abusive comment in response questioning the quality of my mathematics education. Oh well. Maybe I will learn some wisdom and refrain from responding to strangers in the future.

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