Here is a belated picture of yesterday’s solar eclipse, taken by my friend David in New York City:
His equipment is (semi-)professional but the solar filter that he used wasn’t. Still, it is a heck of a lot better than anything I was able to see (or project with a makeshift pinhole camera). I suggested to him to obtain a quality solar filter by 2024. Who knows, we may meet in Watertown to watch totality.
I just came across an interesting slide.
It was part of a presentation by Bill Foster, a member of an endangered species in the United States Congress: a scientist turned politician. He gave a talk at the April meeting of the American Physical Society. This slide from his talk speaks for itself:
I don’t have data for Canada, other than a list of a grand total of 6 engineers serving in our federal House of Commons. That low number suggests that Canada’s Parliament would not be positioned too far from the U.S. Congress in this chart.
Is this a bad thing? I hesitate, because I note that totalitarian regimes tend to have many scientists among their leaders. Is it because scientists are more likely to prefer authoritarianism? Or more likely to serve autocrats? I don’t know. I do know that as a free citizen, I much prefer to be governed by a dysfunctional Congress or Parliament than by a totalitarian Politburo, regardless of the number of scientists in these bodies.
There is a brand new video on YouTube today, explaining the concept of the Solar Gravitational Telescope concept:
It really is very well done. Based in part on our paper with Slava Turyshev, it coherently explains how this concept would work and what the challenges are. Thank you, Jimiticus.
But the biggest challenge… this would be truly a generational effort. I am 54 this year. Assuming the project is greenlighted today and the spacecraft is ready for launch in ten years’ time… the earliest for useful data to be collected would be more than 40 years from now, when, unless I am exceptionally lucky with my health, I am either long dead already, or senile in my mid-90s.
Slava Turyshev and I just published a paper in Physical Review. It is a lengthy, quite technical paper about the wave-theoretical treatment of the solar gravitational telescope.
What, you say?
Well, simple: using the Sun as a gravitational telescope to image distant objects. Like other stars, the Sun bends light, too. Measuring this bending of light was, in fact, the crucial test carried out by Eddington during the 1919 solar eclipse, validating the predictions of general relativity and elevating Albert Einstein to the status of international science superstar.
The gravitational bending of light is very weak. Two rays, passing on opposite sides of the Sun, are bent very little. So little in fact, it takes some 550 astronomical units (AU; the distance between the Earth and the Sun) for the two rays to meet. But where they do, interesting things happen.
If you were floating in space at that distance, and there was a distant planet on the exact opposite side of the Sun, light from a relatively small section of that planet would form a so-called Einstein ring around the Sun. The light amplification would be tremendous; a factor of tens of billions, if not more.
But you have to be located very precisely at the right spot to image a particular spot on the exoplanet. How precisely? Well, that’s what we set out to figure out, based in part on the existing literature on the subject. (Short answer: it’s measured in tens of centimeters or less.)
In principle, a spacecraft at this distance, moving slowly in lateral directions to scan the image plane (which is several kilometers across), can obtain a detailed map of a distant planet. It is possible, in principle, to obtain a megapixel resolution image of a planet dozens of light years from here, though image reconstruction would be a task of considerable complexity, due in part to the fact that an exoplanet is a moving, changing target with variable illumination and possibly cloud cover.
Mind you, getting to 550 AU is costly. Our most distant spacecraft to date, Voyager 1, is just under 140 AU from the Sun, and it took that spacecraft 40 years to get there. That said, it is a feasible mission concept, but we must be very certain that we understand the physics thoroughly.
This is where our paper comes in: an attempt to derive detailed results about how light waves pass on both sides of the Sun and recombine along the focal line.
The bulk of the work in this paper is Slava’s, but I was proud to help. Part of my contribution was to provide a visualization of the qualitative behavior of the wavefront (described by a hypergeometric function):
In this image, a light wave, initially a plane wave, travels from left to right and it is deflected by a gravitational source at the center. If you squint just a little, you can actually see a concentric circular pattern overlaid on top of the distorted wavefront. The deflection of the wavefront and this spherical wave perturbation are both well described by an approximation. However, that approximation breaks down specifically in the region of interest, namely the focal line:
The top left of these plots show the approximation of the deflected wavefront; the top right, the (near) circular perturbation. Notice how both appear to diverge along the focal line: the half line between the center of the image and the right-hand side. The bottom right plot shows the combination of the two approximations; it is similar to the full solution, but not identical. The difference between the full solution and this approximation is shown in the bottom left plot.
I also helped with working out evil-looking things like a series approximation of the confluent hypergeometric function using so-called Pochhammer symbols and Stirling numbers. It was fun!
To make a long story short, although it involved some frustratingly long hours at a time when I was already incredibly busy, it was fun, educational, and rewarding, as we gave birth to a 39-page monster (43 pages on the arXiv) with over 300 equations. Hopefully just one of many contributions that, eventually (dare I hope that it will happen within my lifetime?) may result in a mission that will provide us with a detailed image of a distant, life-bearing cousin of the Earth.
Donald Trump, Demagogue-in-Chief of America the Greatest, now took his proud nation to new heights: America joined forces with the ever-so-enlightened, wonderful regime of Bashar al-Assad in Syria, along with Central America’s Daniel Ortega in Nicaragua, announcing that his nation will withdraw from the Paris Climate Agreement.
Americans must be so proud. Gone are the days of Obama leading from behind… instead, their orange-skinned leader is now proudly leading them behind.
To be honest, I don’t mind it too much. I always wondered just how effective the Paris agreement was going to be anyway. And it’s not like Ottawa’s climate is too hot… nor do I have any children to worry about, so why should I care if we leave behind a messed up world when my generation dies?
The only thing that bothers me about this is the, well, stubborn anti-intellectualism and outright, blatant stupidity. Not just the Deceiver-in-Chief’s, mind you. A few hours ago I witnessed a brief debate between a CNN anchor and Rand Paul about the nature and origin of the current climate change and its comparison to past climate events. Talk about the blind leading the sightless…
I am watching the morning news and it’s all about numbers. Some good, some not so good, some really bad. Here are a few, in descending order:
I thought of turning these bullet points into a numbered list, but that would have been too confusing.
I am no photo artist, and my best camera is, well, my phone. That’s it.
Even so, a few minutes ago I felt compelled to take a couple of photographs. We are a few minutes away from sunset and a big storm just began. Then I looked out my window and I found the building across the street brighter than the sky above.
The light came from the other side of the sky. The Sun was not visible but the sky in that direction was bright enough to light things up.
Photographs (especially, photographs taken with a phone) really don’t do these sights justice. The contrasts were amazing.
Recently, I answered a question on Quora on the possibility that we live in a computer simulation.
Apparently, this is a hot topic. The other day, there was an essay on it by Sabine Hossenfelder.
I agree with Sabine’s main conclusion, as well as her point that “the programmer did it” is no explanation at all: it is just a modern version of mythology.
I also share her frustration, for instance, when she reacts to the nonsense from Stephen Wolfram about a “whole civilization” “down at the Planck scale”.
Sabine makes a point that discretization of spacetime might conflict with special relativity. I wonder if the folks behind doubly special relativity might be inclined to offer a thought or two on this topic.
In any case, I have another reason why I believe we cannot possibly live in a computer simulation.
My argument hinges on an unproven conjecture: My assumption that scalable quantum computing is really not possible because of the threshold theorem. Most supporters of quantum computing believe, of course, that the threshold theorem is precisely what makes quantum computing possible: if an error-correcting quantum computer reaches a certain threshold, it can emulate an arbitrary precision quantum computer accurately.
But I think this is precisely why the threshold will never be reached. One of these days, someone will prove a beautiful theorem that no large-scale quantum computer will ever be able to operate above the threshold, hence scalable quantum computing is just not possible.
Now what does this have to do with us living in a simulation? Countless experiments show that we live in a fundamentally quantum world. Contrary to popular belief (and many misguided popularizations) it does not mean a discretization at the quantum level. What it does mean is that even otherwise discrete quantities (e.g., the two spin states of an electron) turn into continuum variables (the phase of the wavefunction).
This is precisely what makes a quantum computer powerful: like an analog computer, it can perform certain algorithms more effectively than a digital computer, because whereas a digital computer operates on the countable set of discrete digits, a quantum or analog computer operates with the uncountable infinite of states offered by continuum variables.
Of course a conventional analog computer is very inaccurate, so nobody seriously proposed that one could ever be used to factor 1000-digit numbers.
This quantum world in which we live, with its richer structure, can be simulated only inefficiently using a digital computer. If that weren’t the case, we could use a digital computer to simulate a quantum computer and get on with it. But this means that if the world is a simulation, it cannot be a simulation running on a digital computer. The computer that runs the world has to be a quantum computer.
But if quantum computers do not exist… well, then they cannot simulate the world, can they?
Two further points about this argument. First, it is purely mathematical: I am offering a mathematical line of reasoning that no quantum universe can be a simulated universe. It is not a limitation of technology, but a (presumed) mathematical truth.
Second, the counterargument has often been proposed that perhaps the simulation is set up so that we do not get to see the discrepancies caused by inefficient simulation. I.e., the programmer cheats and erases the glitches from our simulated minds. But I don’t see how that could work either. For this to work, the algorithms employed by the simulation must anticipate not only all the possible ways in which we could ascertain the true nature of the world, but also assess all consequences of altering our state of mind. I think it quickly becomes evident that this really cannot be done without, well, simulating the world correctly, which is what we were trying to avoid… so no, I do not think it is possible.
Of course if tomorrow, someone announces that they cracked the threshold theorem and full-scale, scalable quantum computing is now reality, my argument goes down the drain. But frankly, I do not expect that to happen.
Chemistry is weird. Even in inorganic chemistry, there are some really strange compounds. There is, for instance, phosphotungstic acid: \({\rm H}_3{\rm P}{\rm W}_{12}{\rm O}_{40}\). Never heard of it until today.
And then there is this one (if it exists at all):
Somebody posted this on Google+. They wanted to know what its properties are. And now, so do I. There are a few tungsten compounds listed in online databases, but this is not one of them. Does it even exist? I don’t know. For some reason, I expect it to have properties not unlike those of tungsten carbide, but I could be completely off the mark.
A short while ago, I turned on a computer. Like several of my other computers, this one is also configured to display a weather widget on the desktop. Here is what it showed:
If only it were true! Alas, the reason for this overly optimistic weather report had to do with the fact that the computer in question has last been turned on more than four months ago, back in September. In reality, this is what our weather is like right now:
And even that is a significant improvement over the −21°C that greeted me early in the morning.
Yup, this is Canada.
Enough blogging about politics. It’s time to think about physics. Been a while since I last did that.
A Facebook post by Sabine Hossenfelder made me look at this recent paper by Josset et al. Indeed, the post inspired me to create a meme:
The paper in question contemplates the possibility that “dark energy”, i.e., the mysterious factor that leads to the observed accelerating expansion of the cosmos, is in fact due to a violation of energy conservation.
Sounds kooky, right? Except that the violation that the authors consider is a very specific one.
Take Einstein’s field equation,
$$R_{\mu\nu}-\tfrac{1}{2}Rg_{\mu\nu}+\Lambda g_{\mu\nu}=8\pi GT_{\mu\nu},$$
and subtract from it a quarter of its trace times the metric. The trace of the left-hand side is \(-R+4\Lambda\), the right-hand side is \(8\pi GT\), so we get
$$R_{\mu\nu}-\tfrac{1}{4}Rg_{\mu\nu}=8\pi G(T_{\mu\nu}-\tfrac{1}{4}Tg_{\mu\nu}).$$
Same equation? Not quite. For starters, the cosmological constant \(\Lambda\) is gone. Furthermore, this equation is manifestly trace-free: its trace is \(0=0\). This theory, which was incidentally considered already almost a century ago by Einstein, is called trace-free or unimodular gravity. It is called unimodular gravity because it can be derived from the Einstein-Hilbert Lagrangian by imposing the constraint \(\sqrt{-g}=1\), i.e., that the volume element is constant and not subject to variation.
Unimodular gravity has some interesting properties. Most notably, it no longer implies the conservation law \(\nabla_\mu T^{\mu\nu}=0\).
On the other hand, \(\nabla_\mu(R^{\mu\nu}-\tfrac{1}{2}Rg^{\mu\nu})=0\) still holds, thus the gradient of the new field equation yields
$$\nabla_\mu(\tfrac{1}{4}Rg^{\mu\nu})=8\pi G\nabla_\mu(T^{\mu\nu}-\tfrac{1}{4}Tg^{\mu\nu}).$$
So what happens if \(T_{\mu\nu}\) is conserved? Then we get
$$\nabla_\mu(\tfrac{1}{4}Rg^{\mu\nu})=-8\pi G\nabla_\mu(\tfrac{1}{4}Tg^{\mu\nu}),$$
which implies the existence of the conserved quantity \(\hat{\Lambda}=\tfrac{1}{4}(R+8\pi GT)\).
Using this quantity to eliminate \(T\) from the unimodular field equation, we obtain
$$R_{\mu\nu}-\tfrac{1}{2}Rg_{\mu\nu}+\hat{\Lambda} g_{\mu\nu}=8\pi GT_{\mu\nu}.$$
This is Einstein’s original field equation, but now \(\hat{\Lambda}\) is no longer a cosmological constant; it is now an integration constant that arises from a conservation law.
The vacuum solutions of unimodular gravity are the same as those of general relativity. But what about matter solutions? It appears that if we separately impose the conservation law \(\nabla_\mu T^{\mu\nu}\), we pretty much get back general relativity. What we gain is a different origin, or explanation, of the cosmological constant.
On the other hand, if we do not impose the conservation law for matter, things get interesting. In this case, we end up with an effective cosmological term that’s no longer constant. And it is this term that is the subject of the paper by Josset et al.
That being said, a term that is time-varying in the case of a homogeneous and isotropic universe surely acquires a dependence on spatial coordinates in a nonhomogeneous environment. In particular, the nonconservation of \(T_{\mu\nu}\) should lead to testable deviations in certain Parameterized Post-Newtonian (PPN) parameters. There are some reasonably stringent limits on these parameters (notably, the parameters \(\alpha_3\) and \(\zeta_i\) in the notation used by Clifford Will in the 1993 revision of his book, Theory and experiment in gravitational physics) and I wonder if Josset et al. might already be in violation of these limits.
So here is another thing I don’t expect to see from Donald Trump: Publishing an article in the highly respected multidisciplinary journal Science.
His predecessor, the still sitting Barack Obama did just that: his article about “The irreversible momentum of clean energy” was published yesterday, January 13, 2017. In it, he makes the case that economic growth does not depend on energy-related emissions, and that combating climate change does not require accepting lower growth or a reduced standard of living.
Once again, I feel compelled to use the same image and same words that I have been using for many years, to wish all my family, all my friends, indeed everyone on the good Earth a very merry Christmas: the words of the astronauts of Apollo 8.
I know, I know, it’s the same thing every year. But there really aren’t any better words. Just imagine: three human beings, for the first time in human history, far from the Earth, in orbit around another celestial body. And back on Earth, one of the most troubled years in recent history: 1968. So on Christmas Eve, with about a billion people listening—a full one quarter of the Earth’s population at the time—they greeted us Earthlings with the opening passages from the Book of Genesis, the common creation mythology of several major religions.
And then Frank Borman ended the broadcast with words that are as appropriate today as we are heading towards more troubled times as they were back then: “And from the crew of Apollo 8, we close with good night, good luck, a Merry Christmas – and God bless all of you, all of you on the good Earth.”
I have been so busy this week, I forgot to blog about our latest Maxima release, 5.39. Nothing spectacular, just incremental improvements over 5.38; for me, this was a big milestone though as this was the first time that I used a CentOS platform to prepare the release. (Which, incidentally, is why I haven’t done this months ago.)
And SourceForge, kindly enough, once again designated Maxima as one of the site’s Projects of the Week.
Hey, I am getting famous again!
For the second time, Quora decided to feature one of my answers on their Forbes blog site. This one was in response to the question, “Is Theoretical physics a waste of resources”? I used the example of Maxwell’s prediction of electromagnetic waves to turn the question into a rhetorical one.
Forbes used a stock Getty image of some physicists in front of a blackboard to illustrate the blog post. Here, allow me to use the image of a bona fide blackboard, one from the Perimeter Institute, containing a few of the field equations of MOG/STVG, during one of our discussions with John Moffat.
Anyhow, I feel honored. Thank you Quora.
Of course, I never know how people read my answers. Just tonight, I received a mouthful in the form of hate mail from a sarcasm-challenged defender of the US space program who thought that in my answer about astronauts supposedly having two shadows on the Moon, I was actually promoting some conspiracy theory. Duh.
Some people call squirrels furry rats. Yet they are cute.
Cute enough, it seems, for people to feed them donuts. Or was this donut stolen?
A moment in a squirrel’s life, caught by my wife earlier today with her cell phone camera.
Not sure how I landed on this page (maybe I was reading too many gloomy assessments of the post-Brexit world?) but here it is anyway: An incredible collection of dioramas by artist Lori Nix, titled The City, depicting a post-apocalyptic world:
A world without humans. Scary visions. Real life examples exist, of course, in places like abandoned sections of Detroit or the Zone around Chernobyl, to name just a couple of prominent ones.
Recently, someone on Quora asked where one would place a time capsule to survive a trillion years. Yes, a trillion. Ambitious, isn’t it? Meanwhile, we have yet to learn how to build things that survive a mere thousand years or less. There is nothing, absolutely nothing that humans constructed, or can construct, that will survive in any recognizable form for a trillion years, be it on the Earth, in space, or on another planet.
Alexander Fleming discovered Penicillin in 1928. He received the Nobel prize for his discovery in 1945.
A Facebook friend shared his Nobel lecture. Particularly, the following quote:
“The time may come when penicillin can be bought by anyone in the shops. Then there is the danger that the ignorant man may easily underdose himself and by exposing his microbes to non-lethal quantities of the drug make them resistant. Here is a hypothetical illustration. Mr. X. has a sore throat. He buys some penicillin and gives himself, not enough to kill the streptococci but enough to educate them to resist penicillin. He then infects his wife. Mrs. X gets pneumonia and is treated with penicillin. As the streptococci are now resistant to penicillin the treatment fails. Mrs. X dies. Who is primarily responsible for Mrs. X’s death? Why Mr. X whose negligent use of penicillin changed the nature of the microbe. Moral: If you use penicillin, use enough.”
Fleming thus foresaw the dangers of emerging antibiotic resistance. Too bad the world failed to listen. Now, a growing number of people die from once treatable (e.g., post-operative) infections because the evolution of bacteria outpaced our ability to develop new antibiotics.
The Crafoord prize is a prestigious prize administered by the Swedish academy of sciences. Not as prestigious as the Nobel, it is still a highly respectable prize that comes with a respectable sum of money.
This way, one of the recipients was Roy Kerr, known for his solution of rotating black holes.
Several people were invited to give talks, including Roy Kerr’s colleague David Wiltshire. Wiltshire began his talk by mentioning the role of a young John Moffat in inspiring Kerr to study the rotating solution, but he also acknowledged Moffat’s more recent work, in which I also played a role, his Scalar-Tensor-Vector (STVG) modified gravity theory, aka MOG.
All too often, MOG is ignored, dismissed or confused with other theories. It was very good to see a rare, notable exception from that rule.
This morning, Quora surprised me with this:
Say what?
I have written a grand total of three Quora answers related to the Quran (or Koran, which is the spelling I prefer). Two of these were just quoting St. Augustine of Hippo, an early Christian saint who advised Christians not to confuse the Book of Genesis with science; the third was about a poll from a few years back that showed that in the United States, atheists/agnostics know more about religion than religious folk from any denomination.
As to string theory, I try to avoid the topic because I don’t know enough about it. Still, 15 of my answers on related topics (particle physics, cosmology) were apparently also categorized under the String Theory label.
But I fail to see how my contributions make me an expert on either Islam or String Theory.