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.

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 as 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.

Not for the first time, I am reading a paper that discusses the dark matter paradigm and its alternatives.

Except that it doesn’t. Discuss the alternatives, that is. It discusses the one alternative every schoolchild interested in the sciences knows about (and one that, incidentally, doesn’t really work) while ignoring the rest.

This one alternative is Mordehai Milgrom’s MOND, or MOdified Newtonian Dynamics, and its generalization, TeVeS (Tensor-Vector-Scalar theory) by the late Jacob Bekenstein.

Unfortunately, too many people think that MOND is the only game in town, or that even if it isn’t, it is somehow representative of its alternatives. But it is not.

In particular, I find it tremendously annoying when people confuse MOND with Moffat’s MOG (MOdified Gravity, also MOffat Gravity). Or when similarly, they confuse TeVeS with STVG (Scalar-tensor-Vector Gravity), which is the relativistic theory behind the MOG phenomenology.

So how do they differ?

MOND is a phenomenological postulate concerning a minimum acceleration. It modifies Newton’s second law: Instead of $$F = ma$$, we have $$F = m\mu(a/a_0)a$$, where $$\mu(x)$$ is a function that satisfies $$\mu(x)\to 1$$ for $$x\gg 1$$, and $$\mu(x)\to x$$ for $$x\ll 1$$. A good example would be $$\mu(x)=1/(1+1/x)$$. The magnitude of the MOND acceleration is $$a_0={\cal O}(10^{-10})~{\rm m}/{\rm s}$$.

The problem with MOND is that in this form, it violates even basic conservation laws. It is not a theory: it is just a phenomenological formula designed to explain the anomalous rotation curves of spiral galaxies.

MOND was made more respectable by Jacob Bekenstein, who constructed a relativistic field theory of gravity that approximately reproduces the MOND acceleration law in the non-relativistic limit. The theory incorporates a unit 4-vector field and a scalar field. It also has the characteristics of a bimetric theory, in that a “physical metric” is constructed from the true metric and the vector field, and this physical metric determines the behavior of ordinary matter.

In contrast, MOG is essentially a Yukawa theory of gravity in the weak field approximation, with two twists. The first twist is that in MOG, attractive gravity is stronger than Newton’s or Einstein’s; however, at a finite range, it is counteracted by a repulsive force, so the gravitational acceleration is in fact given by $$a = GM[1+\alpha-\alpha(1+\mu r)e^{-\mu r}]$$, where $$\alpha$$ determines the strength of attractive gravity ($$\alpha=0$$ means Newtonian gravity) and $$\mu$$ is the range of the vector force. (Typically, $$\alpha={\cal O}(1)$$, $$\mu^{-1}={\cal O}(10)~{\rm kpc}$$.) The second twist is that the strength of attractive gravity and the range of the repulsive force are both variable, i.e., dynamical (though possibly algebraically related) degrees of freedom. And unlike MOND, for which a relativistic theory was constructed after-the-fact, MOG is derived from a relativistic field theory. It, too, includes a vector field and one or two scalar fields, but the vector field is not a unit vector field, and there is no additional, “physical metric”.

In short, there is not even a superficial resemblance between the two theories. Moreover, unlike MOND, MOG has a reasonably good track record dealing with things other than galaxies: this includes globular clusters (for which MOND has to invoke the nebulous “external field effect”), cluster of galaxies (including the famous Bullet Cluster, seen by some as incontrovertible proof that dark matter exists) and cosmology (for which MOND requires something like 2 eV neutrinos to be able to fit the data.)

 MOG and the acoustic power spectrum. Calculated using $$\Omega_M=0.3$$, $$\Omega_b=0.035$$, $$H_0=71~{\rm km}/{\rm s}/{\rm Mpc}$$. Also shown are the raw Wilkinson Microwave Anisotropy Probe (WMAP) three-year data set (light blue), binned averages with horizontal and vertical error bars provided by the WMAP project (red) and data from the Boomerang experiment (green). From arXiv:1104.2957.

There are many issues with MOG, to be sure. Personally, I have never been satisfied with the way we treated the scalar field so far, and I’d really like to be able to derive a proper linearized version of the theory in which the scalar field, too, is accommodated as a first-class citizen. How MOG stands up to scrutiny in light of precision solar system data at the PPN level is also an open question.

But to see MOG completely ignored in the literature, and see MOND used essentially as a straw man supposedly representing all attempts at creating a modified gravity alternative to dark matter… that is very disheartening.

In the fourth volume of the Hitchhiker’s Guide to the Galaxy “trilogy”, we learn that just before the Earth was about to be destroyed by the Vogons to make way for a new interstellar bypass, the whales left. They left behind a simple parting message: “So long and thanks for all the fish.”

Which makes me feel rather alarmed now that I am learning that hundreds of North Atlantic right whales went missing. I hope it’s not a bad sign.

This is an eerie anniversary.

Thirty years ago today, reactor 4 of the Chernobyl nuclear power plant blew to smithereens.

It’s really hard to assign blame.

Was it the designers who came up with a reactor design that was fundamentally unstable at low power?

Was it the bureaucrats who, in the secretive Soviet polie state, made it hard if not impossible for operators at one facility to learn from incidents elsewhere?

Was it the engineers at Chernobyl who, concerned about the consequences of a total loss of power at the station, tried to test a procedure that would have kept control systems and the all-important coolant pumps running using waste heat during an emergency shutdown, while the Diesel generators kicked in?

Was it the Kiev electricity network operator who asked Chernobyl to keep reactor 4 online for a little longer, thus pushing the planned test into the late night?

Was it the control room operator who ultimately pushed the button that initiated an emergency shutdown?

And the list continues. Many of the people we could blame didn’t stick around long enough: they died, after participating in often heroic efforts to avert an even greater disaster, and receiving lethal doses of radiation.

Some lived. This photo shows Arkady Uskov, who suffered severe radiation burns 30 years ago as he helped save colleagues. He, along with a few other people, recently revisited the control room of reactor 4, and were photographed there by Radio Free Europe. (Sadly, the photos are badly mislabeled by someone who didn’t know that “Arcadia Uskova” would be the name of a female; or, in this case, the genitive case of the male name Arkady Uskov. Thus I also cannot tell if “Oleksandr Cheranov”, whose name I cannot find anywhere else in the literature of Chernobyl, was a real person or just another RFE misprint.)

Surprisingly, the control room, which looks like a set of props from a Cold War era science fiction movie, is still partially alive. The lit panels, I suspect, must be either part of the monitoring effort or communications equipment.

It must have been an uncanny feeling for these aging engineers to be back at the scene, 30 years later, contemplating what took place that night.

Incidentally, nuclear power remains by far the safest in the world. Per unit of energy produced, it is dozens of times safer than hydroelectricity; a hundred times safer than natural gas; and a whopping four thousand times safer than coal. And yes, this includes the additional approximately 4,000 premature deaths (UN estimate) as a result of Chernobyl’s fallout. Nor was Chernobyl the deadliest accident related to power generation; that title belongs to China’s Banqiao Dam, the failure of which claimed 171,000 lives back in 1975.

This beautiful image is a frame capture of the latest SpaceX first stage rocket, moments after its successful landing on the drone ship Of Course I Still Love You (yes, that really is the drone ship’s name) last night:

The landing was a little sloppy. I mean, look how far off-center the rocket happens to stand.

Still… I am seriously beginning to believe that Elon Musk may accomplish his ultimate goal within my lifetime: the beginning of the human colonization of Mars.

To live long enough to see the first human set foot on Mars… now that’s a dream worth living for.

This was the view from my window late last night, before I went to sleep:

Now this is a perfectly normal way for our street to appear, say, in January… but April 7?

Really, people, if the rest of the world doesn’t care, I am all for global warming.

Sometime last year, I foolishly volunteered to manage new releases of the Maxima computer algebra system (CAS).

For the past several weeks, I’ve been promising to do my first release, but I kept putting it off as I had other, more pressing work obligations.

Well, not anymore… today, I finally found the time, after brushing up on the Git version management system, and managed to put together a release, 5.38.0.

Maxima is beautiful and incredibly powerful. I have been working on its tensor algebra packages for the past 15 years or so. As far as I know, Maxima is the only general purpose CAS that can derive the field equations of a Lagrangian field theory; for instance, it can derive Einstein’s field equations from the Einstein-Hilbert Lagrangian.

I use Maxima a lot for tensor algebra, though I admit that when it comes to integration, differential equations or plotting, I prefer Maple. Maple’s ODE/PDE solvers are unbeatable. But when it comes to tensor algebra, or just as a generic on-screen symbolic calculator, Maxima wins hands down. I prefer to use its command-line version: Nothing fancy, just ASCII art, but very snappy, very responsive, and does exactly what I want it to do.

So then, Maxima 5.38.0: Say hi to the world. World, this is the latest version of the oldest (nearly half a century old) continuously maintained CAS in existence.

Until recently, this used to be one of my favorite deep space images:

It is a frozen lake in the Ruach Planitia region of Neptune’s Moon Triton: an incredibly distant, dark and desolate world.

OK, the image is still one of my favorites, but on my list of favorites, it’s just been taken over by this one:

That, ladies and gentlemen, is a large (about 30 km) frozen lake (most likely frozen nitrogen), in the Sputnik Planum region of the planet Pluto.

Who would have thought that Pluto, the recently demoted ex-planet, a frozen world at the edge of the solar system, would have such complex climate and such a fascinating geological history?

Wow.

I was watching the news this morning. Including the weather. And then I double-checked my calendar, wondering if I perhaps became delusional: Is this really March, or is it still January?

Then again, tonight supposedly it’ll get even colder.

Here is a spectacular photograph of the Moon made last night by my good friend David Ada-Winter in light-polluted New Jersey:

David explains: “I took this picture of the Moon using the so-called Sunny 16 rule, the essence of which is the following: On a clear day, with an aperture of 16, the exposition time must be the reciprocal of the ISO value. In the case of this picture, the ISO was 200, so the exposition time was 1/200 with an aperture of 16. In front of my telescopic lens, I also used a doubler that extended the focal length to 800 mm. The picture itself was made with the Canon Rebel t2i camera, which has a crop factor of 1.6, allowing the Moon to appear even larger in the image.”

Apparently, David’s wife disapproves of his pricey hobby. I’m tempted to remind her that other men of David’s age often acquire even pricier hobbies, which usually involve brightly colored sports cars and lightly clad ladies…