Apr 062021
 

World, please say hello to Freddy.

Freddy has been with us for more than two years now. He is a very funny cat. Strong-willed, to be sure; he might even bite you if he disapproves of your behavior. (No, he has not bitten off any fingers or earlobes yet.) And he likes… green peas. Or kernels of corn. And like one of our past kitties, Pipacs, Freddy also stole a freshly cooked potato from the kitchen not too long ago.

Last but not least, I should mention that his favorite toys are small pompoms. We have many of those, on account of my wife’s knitting. So I have a box of pompoms right here, next to my desk. Freddy often shows up here and, after carefully sniffing the pompoms, selects one, takes it from the box, puts it down on the floor and sits down proudly next to it, quietly meowing a few times. That is my cue to pick up the pompom and throw it down the stairs, with Freddy sprinting after it. Often, he then spends a good half hour playing with that pompom.

He also occasionally plays with his somewhat larger buddy, Rufus. I suppose Rufus looks just like a big gray-and-white pompom…

 Posted by at 9:33 pm
Apr 052021
 

My success story of the day involves two cups.

A few days ago, I heard my wife grumbling loudly in the kitchen. I went downstairs to see what was wrong. She showed me a pair of cups, a teacup, inside which there was one of our brand new espresso cups.

And when I say inside, I mean wedged inside. Firmly and utterly stuck, quite impossible to remove.

We tried to separate them using force, but they wouldn’t budge. We obviously didn’t want to break either cup. Not that they are terribly expensive but the teacup, well, we’re quite fond of these teacups and as for the espresso cup, it was brand new, I only just purchased the set off Amazon a few days earlier.

Force failed to do the trick so we tried to be clever. Use some oil to make it slick? Nope. Dishwasher detergent? That didn’t work either. I tried holding the outer cup, upside down, under hot water in the hope that thermal expansion might loosen the smaller cup inside; nope.

Nonetheless we thought that a temperature difference might help, so we filled the cups with water and put them in the freezer. Once the water was frozen solid, we took them out and placed them in a pot of boiling water. Again, the hope was that the high heat would cause the larger cup to expand, while the ice keeps the smaller cup cold, allowing it to fall out. Nope.

After this experiment failed for the third time earlier this afternoon, I sat down with the cups in hand and once again, tried brute force. The outer cup was still quite hot to the touch, the inner cup still quite cold and this may have helped; suddenly, I felt them budge, and after one more pull, they were separated, completely undamaged.

I was… absolutely delighted. Later I remarked to my wife that we humans are creatures of simple pleasures. Never mind the animations I completed just today using gravitational lenses of arbitrary shape. Never mind the work I am doing on another project on payment processor integration, or yet another project involving Microsoft Teams. (Yes, I multitask. Virtual desktops can be quite handy.) All of that is fun, sure, but it’s having been able to separate these poor cups without breaking or damaging them that really made my day.

 Posted by at 9:33 pm
Apr 042021
 

You know, I am beginning to sympathize with all those Trumpists, Fake News afficionados, anti-vaxxers, flat Earthers and the like.

The other day, I commented on a post concerning the 34 Ottawa area pharmacies that are designated as AstraZeneca vaccination sites by Doug Ford’s government.

I disagreed that this was a political decision, despite the fact that I didn’t vote for Mr. Ford, and that, in fact, I voted for the MPP in question who raised this issue in the first place. I suggested that we should leave such hyperpartisan politicking to our American friends. Last but not least, I was able to find some mapping data from StatCan and from a Twitter post (which I can no longer find — thanks for nothing, Facebook!) that, when overlaid, showed that the vaccination sites roughly correspond to the population density map of the Ottawa region.

Facebook, unfortunately, concluded that my post goes against their community guidelines as spam, despite the fact that (I swear!) I was not trying to sell any Russian brides, fake PPE, dubious cryptocurrency investment schemes, or steal anyone’s social insurance number.

None of it ever stopped Facebook from delivering Trumpist garbage, genuine Fake News, anti-vaxxer nonsense, even flat Earth propaganda to my account.

So dear Facebook… You played an instrumental part in turning America into a lunatic asylum, you played an instrumental part in helping the January 6 insurrection happen, you continue to play an instrumental part in radicalizing America and the world, you continue to let Putin’s trolls and China’s agents provocateurs own you, not to mention losing the personal data of more than 500 million of us… but you censor my post as spam because of your broken algorithms? Forgive the strong language but please, just fuck off.

I wonder if this blog post survives on Facebook or gets censored as well…

 Posted by at 8:15 pm
Apr 032021
 

My beautiful wife is getting really good at this.

She just made this kalach (kalács), Hungarian style braided sweetbread/eggbread, on account of Easter.

It is absolutely yummy for breakfast. Might work for lunch and dinner, too, if you ask me.

Yes, it has raisins in it. I love kalach with raisins.

 Posted by at 1:05 pm
Mar 272021
 

Courtesy of Radio Free Europe, here are some images (yes, do click on the link for the full experience) of the city of my birth, Budapest, in ways you may never have seen before, superimposing images from 1945 and the present.

It is incredible, what this beautiful city went through during that war. (Reminder to those who blame Stalin for the destruction: It was Hungary that declared war on the Soviet Union using a bombing that might have been staged, and which in any case was minor, as a pretext.)

The city is beautiful again. I visited just over a year ago, literally days before the world shut down on account of the COVID-19 pandemic. Whatever my thoughts about Hungarian politics and attitudes, it was a very pleasant trip with many pleasant encounters.

And looking at these horrific images of past devastation, I was reminded that even though I have not lived there since 1986, it remains the city where I was born and grew up: most places I recognized at a glance, in both the “before” and the “after” photos. Only Ottawa comes close as a place that I know this intimately.

 Posted by at 3:22 pm
Mar 272021
 

Bald eagles have a fearsome reputation as predators of the sky. They also symbolize the great United States of America.

Canada geese? Not so fearsome. They are best known for pooping a lot. (If you ever walked through an Ottawa park after it was visited by a flock of geese, you know what I am talking about.)

Yet just like the country that they are named after, these geese are not so timid after all. Here is a recent series of images (and if you search online, you see that this by no means is an exception) captured by a PEI photographer of a Canada goose, fighting off a bald eagle:

Reader’s Digest version: The eagle remained hungry that day.

 Posted by at 12:03 am
Mar 262021
 

Courtesy of The New Yorker, we now know the history of Lawyer Cat, otherwise known (as we now know) as Eldest Mouse.

 Posted by at 2:49 pm
Mar 262021
 

So I learned today that J. K. Rowling writes hate-filled drivel on Twitter (her last post is from December 4 but never mind), and that forgiving Einstein for being a man of his times when he wrote about the white and Chinese races in the 1920s is the same as forgiving the Nazis.

Makes me sympathize more than ever with Principal Skinner.

This intolerant cultural orthodoxy that is promoted by virtue signaling champions of progressive tolerance not only fails to protect those who actually need it most (last time I checked, capitalizing Black has not reduced violence against black people, introducing a multitude of made-up pronouns has not eliminated transphobia, and preaching against white supremacist mathematics education—yes, this really is a thing!—has not brought potable drinking water or meaningful jobs to indigenous communities here in Canada), it also creates a backlash by feeding the trolls who promote actual racism and hate.

Here is a recent example: a tweet by the Mayor of London and the reaction. The tweet said, in part, “There’s no good reason why 65% of people working in science and engineering should be white men.” In one of the responses, we read “Fixing it? That deems it to be broken, in an 85% white country I would have expected the white % to be higher.”

The commenter obviously doesn’t know how to use a calculator, otherwise he would have pondered how 42.5% (assuming half of that white 85% are males) of the population can have 65% of the science and engineering jobs, whereas the remaining 57.5% gets only 35%. Which means that if you’re a white man, you have a 2.5 times better chance to get a job in science and engineering. But aside from the obvious innumeracy, there is this greater problem: by his careless choice of words, the Mayor of London may have made things worse.

And unlike Principal Skinner’s dilemma, this should have been easy to fix. Just say, “There’s no good reason why only 35% of the people working in science and engineering should be women or come from a non-white background” and right there, he’d have avoided feeding the trolls who promote the idea, ever so popular among frustrated, unsuccessful white men, that they are the victims here of identity politics. More careful words would have helped keeping the focus on the second part of the message, which describes genuine action to address the problem in a constructive, dare I say progressive way: “So far we’ve helped 10,000 young Londoners learn these subjects so they can follow their dreams.”

So how about if we stop vilifying J. K. Rowling* and others who do not flawlessly conform to the ideals of some narrow-minded progressive orthodoxy, stop condemning historical figures who lived decades or centuries ago for having failed to live up to the standards of the present, end “cancel culture” and instead start supporting policies that actually help those in need, even if it means sacrifices such as (gasp!) higher taxes?

Naw, why bother. It’s so much easier to just condemn people as racist misowhatever somethingophobes. Makes you feel good!


*Since I wrote this blog entry, I also learned that Rowling is an anti-Semite. How do we know? Why, those gold-loving goblin bankers in Harry Potter, with their obviously Jewish appearance, hooked noses and all.

I kid you not.

 Posted by at 2:13 pm
Mar 242021
 

For more than a day now, I’ve been watching the news about a giant container ship that is blocking the Suez Canal. Supposedly it now “partially refloated”, whatever that means.

In the process, I learned about vesselfinder.com, a Web site that tracks ships on the high seas, much like sites like flightradar24.com track airplanes. Here it is, a real-time snapshot of this stuck vessel:

I have no idea though why the ship is given the name “EVER GIVEN” here. Its actual name, written on the side of the ship in giant block letters, appears to be “EVERGREEN”. (Or not. I’ve since learned that EVERGREEN is the name of the company, not the ship.) And yes, it does block the canal in spectacular fashion.

Given the importance of this shipping route, I wonder why this is not bigger news than it appears to be. Is it perhaps because the general expectation is that the problem will be resolved shortly, causing no more than minor delays in some shipments? I hope.

 Posted by at 11:59 am
Mar 192021
 

I remembered something today. A set of playing cards.

I never had a card deck like this but some of my grade school classmates did. This was the (very) early 1970s in communist Hungary. It was through these cards that I first learned of the existence of luxury sports cars, supercars like Ferrari, racecars like Lotus.

It was cards like these:

These were not some imports from the decadent West. Not subtle imperialist propaganda. These cards were produced by the state-owned Playing Card Factory (yes, that was the name of the company!) and they were much coveted by many 7-year olds. Like me.

But now that I think back, it makes me wonder: Exactly what were they thinking? I mean, this was a bleeping communist dictatorship (of the goulash variety, but still). What on Earth did they think they were doing, these self-appointed masters of agitprop, poisoning our young, impressionable minds with such blatant Western consumerist propaganda?

Ah, the sweet irony.

 Posted by at 9:28 pm
Mar 162021
 

Somebody just reminded me: Back in 1982-83 a friend of mine and I had an idea and I even spent some time building a simple simulator of it in PASCAL. (This was back in the days when a 699-line piece of PASCAL code was a huuuuge program!)

So it went like this: Operative memory (RAM) and processor are separate entities in a conventional computer. This means that before a computer can do anything, it needs to fetch data from RAM, then after it’s done with that data, it needs to put it back into RAM. The processor can only hold a small amount of data in its internal registers.

This remains true even today; sure, modern processors have a lot of on-chip cache but conceptually, it is still separate RAM, it’s just very fast memory that is also physically closer to the processor core, requiring less time to fetch or store data.

But what if we abandon this concept and do away with the processor altogether? What if instead we make the bytes themselves “smart”?

That is to say what if, instead of dumb storage elements that can only be used to store data, we have active storage elements that are minimalist processors themselves, capable of performing simple operations but, much more importantly, capable of sending data to any other storage element in the system?

The massive number of required interconnection between storage elements may appear like a show-stopper but here, we can borrow a century-old concept from telephony: the switch. Instead of sending data directly, how about having a crossbar-like interconnect? Its capacity will be finite, of course, but that would work fine so long as most storage elements are not trying to send data at the same time. And possibly (though it can induce a performance penalty) we could have a hierarchical system: again, that’s the way large telephone networks function, with local switches serving smaller geographic areas but interconnected into a regional, national, or nowadays global telephone network.

Well, that was almost 40 years ago. It was a fun idea to explore in software even though we never knew how it might be implemented in hardware. One lesson I learned is that programming such a manifestly parallel computer is very difficult. Instead of thinking about a sequence of operations, you have to think about a sequence of states for the system as a whole. Perhaps this, more than any technical issue, is the real show-stopper; sure, programming can be automated using appropriate tools, compilers and whatnot, but that just might negate any efficiency such a parallel architecture may offer.

Then again, similar ideas have resurfaced in the decades since, sometimes on the network level as massively parallel networks of computers are used in place of conventional supercomputers.


Gotta love the Y2K bug in the header, by the way. Except that it isn’t. Rather, it’s an implementation difference: I believe the PDP-11 PASCAL that we were using represented a date in the format dd-mm-yyyy, as opposed to dd-MMM-yyyy that is used by this modern Pascal-to-C translator. As I only allocated 10 characters to hold the date in my original code, the final digit is omitted. As for the letters "H J" that appear on top, that was just the VT-100 escape sequence to clear the screen, but with the high bit set on ESC for some reason. I am sure it made sense on the terminals that we were using back in 1982, but xterm just prints the characters.

 Posted by at 12:54 pm
Mar 152021
 

The cartoon series The Simpsons is into its 32nd season this year. It has been picked up for at least another two seasons by Fox.

The Simpsons depicts a “typical” American family of five: Homer the breadwinner, with only a high-school diploma, holding a dead-end but secure job as a safety inspector at the Springfield Nuclear Plant, Marge the housewife, mother of three children and the three kids, two of them school-age, one still a toddler. The Simpsons live in a detached house in a suburb and own two cars. They are not rich, but they do have disposable income: Homer spends his evenings gulping down beer as Moe’s Tavern, Marge never seems to have a problem paying for groceries.

In other words, The Simpsons live the American dream: a comfortable North American middle class lifestyle from a single income.

A dream that, as lamented in a recent opinion article in The Atlantic, is no longer attainable.

This, I think, really explains it all. The polarization of American politics. The emergence of extremism. The appeal of slogans like “Make America Great Again”. The “we have nothing to lose” attitude that led many to vote for Trump, despite their misgivings.

And it is by no means a US-only phenomenon. Income inequality may not be as bad in Canada as it is in the US, but the middle class is not doing spectacularly well here either. Europe, too, is not heading in the right direction.

Lest we forget the lessons of history, this is precisely what provides fertile ground for totalitarian ideologies like fascism and communism. When liberal democracy fails to deliver on society’s most basic promise, the ability to provide a life as good as, but preferably better than your own for your children, people turn to other ideas. That was just as true a century ago as it is today.

 Posted by at 10:52 pm
Mar 142021
 

The next in our series of papers describing the extended gravitational lens (extended, that is, in that we are no longer treating the lensing object as a gravitational monopole) is now out, on arXiv.

Here’s one of my favorite images from the paper, which superimposes the boundary of the quadrupole caustic (an astroid curve) onto a 3D plot showing the amplitude of the gravitational lens’s point-spread function.

I was having lots of fun working on this paper. It was, needless to say, a lot of work.

 Posted by at 9:18 pm
Mar 142021
 

I am reading about Heino Falcke.

Dr. Falcke is a scientist. He is the leader of the Event Horizon Telescope project, the first successful attempt to image the event horizon (actually, the shadow of the photon sphere cast on the accretion disk background) of a black hole.

One of the Event Horizon Telescope participating facilities, at Pico Veleta

Dr. Falcke also happens to be religious. A lay pastor, no less, in the Protestant Church in the Netherlands.

He represents yet another example of how faith and the sciences need not be in conflict.

I happen to be nonreligious. I even mock religion (not the religious! Never!) occasionally when I talk about “imaginary friends”, “sky daddy” or the “Flying Spaghetti Monster”. My mockery is not intended to hurt: rather, this truly is how I feel about these supernatural concepts, as surreal, outlandish flights of fancy, fairy tales, nothing more.

Yet I think I understand how faith can also give strength to people. Offer motivation. Fill their lives with meaning.

It has been invariably my experience that the company of a person of faith who is open-minded and capable of critical thinking is much preferable to that of a dogmatic atheist.

In any case, while I may not have much respect for the supernatural aspects of religion, I certainly take no issue with the basic tenets of Christianity, such as loving thy neighbor or not committing murder. If the core message of religion is to try to be a decent human being, well, I don’t need to believe in imaginary friends to accept and fully embrace these principles.

This always reminds me how the best description of Christianity I ever came across came from a devoted atheist, the late Douglas Adams (of Hitchhiker’s Guide to the Galaxy fame): “And then, one Thursday, nearly two thousand years after one man had been nailed to a tree for saying how great it would be to be nice to people for a change […]”

 Posted by at 6:38 pm
Mar 142021
 

Because I’ve been asked a lot about this lately, I thought I’d also share my own take on this calculation in my blog.

Gravitoelectromagnetism (or gravitomagnetism, even gravimagnetism) is the name given to a formalism that shows how weak gravitational fields can be viewed as analogous to electromagnetic fields and how, in particular, the motion of a test particle is governed by equations that are similar to the equations of the electromagnetic Lorentz-force, with gravitational equivalents of the electric and magnetic vector potentials.

Bottom line: no, gravitoelectromagnetism does not explain the anomalous rotation curves of spiral galaxies. The effect is several orders of magnitude too small. Nor is the concept saved by the realization that spacetime is not asymptotically flat, so the boundary conditions must change. That effect, too, is much too small, at least five orders of magnitude too small in fact to be noticeable.

To sketch the key details, the radial acceleration on a test particle due to gravitoelectromagnetism in circular orbit around a spinning body is given roughly by

$$a=-\frac{4G}{c^2}\frac{Jv}{r^3},$$

where \(r\) is the orbital speed of the test particle. When we plug in the numbers for the solar system and the Milky Way, \(r\sim 8~{\rm kpc}\) and \(J\sim 10^{67}~{\rm J}\cdot{\rm s}\), we get

$$a\sim 4\times 10^{-16}~{\rm m}{\rm s}^2.$$

This is roughly 400,000 times smaller than the centrifugal acceleration of the solar system in its orbit around the Milky Way, which is \(\sim 1.6\times 10^{-10}~{\rm m}/{\rm s}^2.\)

Taking into account that our universe is not flat, i.e., deviations from the flat spacetime metric approach unity at the comoving distance of \(\sim 15~{\rm Gpc},\) only introduces a similarly small contribution on the scale of a galaxy, of \({\cal O}(10^{-6})\) at \(\sim 15~{\rm kpc}.\)

A more detailed version of this calculation is available on my Web site.

 Posted by at 1:14 pm
Mar 062021
 

I just came across this painting on Twitter.

I find it poignantly beautiful. According to the description by the artist, Antony John, the cow in the painting is old, on her last pregnancy, as she stares outside at a late winter Southwestern Ontario landscape. The equipment in the room may appear scary but it is nothing sinister. It is used to help with difficult pregnancies; the artist also intended it as a metaphor representing the inexorable pull of time.

I fell in love with this painting the moment I saw it.

 Posted by at 5:20 pm
Mar 012021
 

Now it is time for me to be bold and contrarian. And for a change, write about physics in my blog.

From time to time, even noted physicists express their opinion in public that we do not understand quantum physics. In the professional literature, they write about the “measurement problem”; in public, they continue to muse about the meaning of measurement, whether or not consciousness is involved, and the rest of this debate that continues unabated for more than a century already.

Whether it is my arrogance or ignorance, however, when I read such stuff, I beg to differ. I feel like the alien Narim in the television series Stargate SG-1 in a conversation with Captain (and astrophysicist) Samantha Carter about the name of a cat:

CARTER: Uh, see, there was an Earth physicist by the name of Erwin Schrödinger. He had this theoretical experiment. Put a cat in a box, add a can of poison gas, activated by the decay of a radioactive atom, and close the box.
NARIM: Sounds like a cruel man.
CARTER: It was just a theory. He never really did it. He said that if he did do it at any one instant, the cat would be both dead and alive at the same time.
NARIM: Ah! Kulivrian physics. An atom state is indeterminate until measured by an outside observer.
CARTER: We call it quantum physics. You know the theory?
NARIM: Yeah, I’ve studied it… in among other misconceptions of elementary science.
CARTER: Misconception? You telling me that you guys have licked quantum physics?

What I mean is… Yes, in 2021, we “licked” quantum physics. Things that were mysterious in the middle of the 20th century aren’t (or at least, shouldn’t be) quite as mysterious in the third decade of the 21st century.

OK, let me explain by comparing two thought experiments: Schrödinger’s cat vs. the famous two-slit experiment.

The two-slit experiment first. An electron is fired by a cathode. It encounters a screen with two slits. Past that screen, it hits a fluorescent screen where the location of its arrival is recorded. Even if we fire one electron at a time, the arrival locations, seemingly random, will form a wave-like interference pattern. The explanation offered by quantum physics is that en route, the electron had no classically determined position (no position eigenstate, as physicists would say). Its position was a combination, a so-called superposition of many possible position states, so it really did go through both slits at the same time. En route, its position operator interfered with itself, resulting in the pattern of probabilities that was then mapped by the recorded arrival locations on the fluorescent screen.

Now on to the cat: We place that poor feline into a box together with a radioactive atom and an apparatus that breaks a vial of poison gas if the atom undergoes fission. We wait until the half-life of that atom, making it a 50-50 chance that fission has occurred. At this point, the atom is in a superposition of intact vs. split, and therefore, the story goes, the cat will also be in a superposition of being dead and alive. Only by opening the box and looking inside do we “collapse the wavefunction”, determining the actual state of the cat.

Can you spot a crucial difference between these two experiments, though? Let me explain.

In the first experiment involving electrons, knowledge of the final position (where the electron arrives on the screen) does not allow us to reconstruct the classical path that the electron took. It had no classical path. It really was in a superposition of many possible locations while en route.

In the second experiment involving the cat, knowledge of its final state does permit us to reconstruct its prior state. If the cat is alive, we have no doubt that it was alive all along. If it is dead, an experienced veterinarian could determine the moment of death. (Or just leave a video camera and a clock in the box along with the cat.) The cat did have a classical state all throughout the experiment, we just didn’t know what it was until we opened the box and observed its state.

The crucial difference, then, is summed up thus: Ignorance of a classical state is not the same as the absence of a classical state. Whereas in the second experiment, we are simply ignorant of the cat’s state, in the first experiment, the electron has no classical state of position at all.

These two thought experiments, I think, tell us everything we need to know about this so-called “measurement problem”. No, it does not involve consciousness. No, it does not require any “act of observation”. And most importantly, it does not involve any collapse of the wavefunction when you really think it through. More about that later.

What we call measurement is simply interaction by the quantum system with a classical object. Of course we know that nothing really is classical. Fluorescent screens, video cameras, cats, humans are all made of a very large but finite number of quantum particles. But for all practical (measurable, observable) intents and purposes all these things are classical. That is to say, these things are (my expression) almost in an eigenstate almost all the time. Emphasis on “almost”: it is as near to certainty as you can possibly imagine, deviating from certainty only after the hundredth, the thousandth, the trillionth or whichever decimal digit.

Interacting with a classical object confines the quantum system to an eigenstate. Now this is where things really get tricky and old school at the same time. To explain, I must invoke a principle from classical, Lagrangian physics: the principle of least action. Almost all of physics (including classical mechanics, electrodynamics, even general relativity) can be derived from a so-called action principle, the idea that the system evolves from a known initial state to a known final state in a manner such that a number that characterizes the system (its “action”) is minimal.

The action principle sounds counterintuitive to many students of physics when they first encounter it, as it presupposes knowledge of the final state. But this really is simple math if you are familiar with second-order differential equations. A unique solution to such an equation can be specified in two ways. Either we specify the value of the unknown function at two different points, or we specify the value of the unknown function and its first derivative at one point. The former corresponds to Lagrangian physics; the latter, to Hamiltonian physics.

This works well in the context of classical physics. Even though we develop the equations of motion using Lagrangian physics, we do so only in principle. Then we switch over to Hamiltonian physics. Using observed values of the unknown function and its first derivative (think of these as positions and velocities) we solve the equations of motion, predicting the future state of the system.

This approach hits a snag when it comes to quantum physics: the nature of the unknown function is such that its value and its first derivative cannot both be determined as ordinary numbers at the same time. So while Lagrangian physics still works well in the quantum realm, Hamiltonian physics does not. But Lagrangian physics implies knowledge of the future, final state. This is what we mean when we pronounce that quantum physics is fundamentally nonlocal.

Oh, did I just say that Hamiltonian physics doesn’t work in the quantum realm? But then why is it that every quantum physics textbook begins, pretty much, with the Hamiltonian? Schrödinger’s famous equation, for starters, is just the quantum version of that Hamiltonian!

Aha! This is where the culprit is. With the Hamiltonian approach, we begin with presumed knowledge of initial positions and velocities (values and first derivatives of the unknown functions). Knowledge we do not have. So we evolve the system using incomplete knowledge. Then, when it comes to the measurement, we invoke our deus ex machina. Like a bad birthday party surprise, we open the magic box, pull out our “measurement apparatus” (which we pretended to not even know about up until this moment), confine the quantum system to a specific measurement value, retroactively rewrite the description of our system with the apparatus now present all along, and call this discontinuous change in the system’s description “wavefunction collapse”.

And then spend a century about its various interpretations instead of recognizing that the presumed collapse was never a physical process: rather, it amounts to us changing how we describe the system.

This is the nonsense for which I have no use, even if it makes me sound both arrogant and ignorant at the same time.


To offer a bit of a technical background to support the above (see my Web site for additional technical details): A quantum theory can be constructed starting with classical physics in a surprisingly straightforward manner. We start with the Hamiltonian (I know!), written in the following generic form:

$$H = \frac{p^2}{2m} + V({\bf q}),$$

where \({\bf p}\) are generalized momenta, \({\bf q}\) are generalized positions and \(m\) is mass.

We multiply this equation by the unit complex number \(\psi=e^{i({\bf p}\cdot{\bf q}-Ht)/\hbar}.\) We are allowed to do this trivial bit of algebra with impunity, as this factor is never zero.

Next, we notice the identities, \({\bf p}\psi=-i\hbar\nabla\psi,\) \(H\psi=i\hbar\partial_t\psi.\) Using these identities, we rewrite the equation as

$$i\hbar\partial_t\psi=\left[-\frac{\hbar^2}{2m}\nabla^2+V({\bf q})\right]\psi.$$

There you have it, the time-dependent Schrödinger equation in its full glory. Or… not quite, not yet. It is formally Schrödinger’s equation but the function \(\psi\) is not some unknown function; we constructed it from the positions and momenta. But here is the thing: If two functions, \(\psi_1\) and \(\psi_2,\) are solutions of this equation, then because the equation is linear and homogeneous in \(\psi,\) their linear combinations are also solutions. But these linear combinations make no sense in classical physics: they represent states of the system that are superpositions of classical states (i.e., the electron is now in two or more places at the same time.)

Quantum physics begins when we accept these superpositions as valid descriptions of a physical system (as indeed we must, because this is what experiment and observation dictates.)

The presence of a classical apparatus with which the system interacts at some future moment in time is not well captured by the Hamiltonian formalism. But the Lagrangian formalism makes it clear: it selects only those states of the system that are consistent with that interaction. This means indeed that a full quantum mechanical description of the system requires knowledge of the future. The apparent paradox is that this knowledge of the future does not causally influence the past, because the actual evolution of the system remains causal at all times: only the initial description of the system needs to be nonlocal in the same sense in which 19th century Lagrangian physics is nonlocal.

 Posted by at 12:48 pm
Feb 272021
 

Today’s “what on Earth were they thinking” moment arrived in the form of a statue:

Yes, a golden statue of Donald Trump.

Apparently, it’s not a joke. It is a bona fide prop for this weekend’s CPAC (Conservative Political Action Conference).

Apart from the blatantly obvious (even to heathen nonbelievers like me) reference to the Bible and its admonition concerning the Golden Calf, there are also the more modern-day comparisons to personality cults, such as those of Joseph Stalin or Trump’s BFF Kim Jong Un.

How could the party of Abraham Lincoln and Ronald Reagan sink this far, this quickly?

Just how badly broken is the American body politic for us to witness this… this abomination?

The mind boggles. I’ll leave it at that as I really have no answer and no coherent thoughts as I continue to stare at this deeply disturbing image.

 Posted by at 12:24 am
Feb 182021
 

I really cannot tell which impresses me more: The incredibly complex landing or the fact that there is now a de facto infrastructure in orbit around Mars, in the form of earlier spacecraft that provide communications relay capabilities for real-time tracking of the landing.

Or perhaps the fact that Perseverance also carries the Ingenuity helicopter. If successful, it will be the first drone to fly in the atmosphere of another planet.

The children of future settlers on Mars will be learning about these moments in school.

 Posted by at 4:06 pm