Warning: I don’t usually use strong language in my blog. This post is an exception. Sometimes a spade has to be called a spade… or an asshole has to be called an asshole. If you are offended by strong language, please stop reading now.

I am writing this blog entry on account of the fact that a famed lion in Zimbabwe, a 13-year old male named Cecil, was killed by an asshole. An asshole whose pecker is too limp, I suppose, so he has to supplement his masculinity by killing rare, magnificent animals.

The asshole’s name is reportedly Dr. Walter Palmer, an American dentist from Minnesota. And yes, Dr. Palmer, you are a class one asshole. A disgusting, sad, pathetic, sick moron. (Palmer is on the left in the archival picture below, but his smiling buddy is a sad, pathetic, sick moron, too.)

A picture like this actually makes you feel proud? Happy? The carcass of a beautiful big cat gives you a sense of accomplishment? That you made the world better? Contributed something to humanity? Something for your children to remember you by? Or are you just one of those jackasses who doesn’t care one way or another, so long as you can prove that you have money to waste and creatures to kill?

The killing itself was reportedly quite gruesome. Shot not by a gun but by an arrow (possibly to avoid the noise that might have called attention to the fact that the lion was illegally lured from a nearby national park; the jackasses claim though that this is a way to “honor” the animal) the lion escaped and was tracked for a day or two before it was finally shot dead, skinned, its head removed as a trophy.

To be clear: I eat meat. I am perfectly comfortable with people hunting for food or survival. Yes, that includes hunting for seals, too. But hunting for glory? In the 21st century? When we have the power to destroy most living things on this planet in a matter of minutes? Yes, successful hunters had reasons to be proud back in centuries past when hunting skills were essential for survival. But today? The real heroes are those who help preserve fragile ecosystems, who save species from extinction. The real heroes are those African park rangers, for instance, who earn pennies a day trying to protect such glorious creatures from sickos like Palmer.

This animal was not killed for food or because it threatened someone. It was killed because a pathetic asshole wanted to collect its preserved head as a trophy.

I was hoping that Dr. Palmer is still in Zimbabwe; that he would be caught there and would spend a few years rotting in an unpleasant, dirty, hot, smelly African jail. Sadly, it appears that he is safely back in the US, and he is unlikely to be charged.

Fuck you, Dr. Palmer. Really, really, really fuck you. Fuck you for drawing pleasure from destroying some of the most magnificent things that exist on our shared planet. It is shitheads like you that make me want to get off the planet at the earliest opportunity. You might think that what you have done was legal… but it only shows the kind of human garbage that you really are. So from the bottom of my heart… fuck you.

This is an idea my wife and I have been thinking about for months: a Web site that lists Prime Minister Stephen Harper’s political sins, where visitors can vote by assigning the number of cats that, in their opinion, Mr. Harper must adopt to atone for said sins.

Finally I realized that rather than coding the site from scratch, I can implement it using existing blogging software and plugins.

So here it is: catsforharper.ca.

In the coming days/weeks, I will keep adding topics. Votes, which require registration (to cut down on comment spam and clickbot activity), are welcome.

And now we are down to three cats in the house.

Our long-haired kitty, Fluffy, came to the end of her life today. Having lost nearly all her mobility due to not one but two tumors (one near the heart, another one compressing her spine), and often lying in her own waste in the past week, we came to the conclusion that it was time to let her go.

So today, a very kind and compassionate Dr. Lianna Titcombe of Claire Place Mobile Veterinary Services came to our house and euthanized Fluffy, after we said our final goodbyes.

I knew what was happening, I have been through this before, I know there are people in the world going through suffering unimaginably worse than ours. Yet it still broke my heart.

Fluffy was a stray that we adopted her back in 2008. She looked like a miniature mammoth with her winter fur.

In contrast, yesterday she was more like a rag doll: wherever you put her down, that’s where she stayed, her once luscious fur matted with urine.

But her eyes were still hers. And her purring motor was still in excellent working order. And she still enjoyed the final treat that we gave to her before she was sedated.

Damn, my heart breaks still.

$$\renewcommand{\vec}[1]{\boldsymbol{\mathrm{#1}}}$$Continuing something I began about a month ago, I spent more of my free time than I care to admit re-deriving some of the most basic identities in quantum physics.

I started with the single-particle case of a harmonic oscillator. Such an oscillator is characterized by the classical Lagrangian

$$L=\frac{1}{2}m\dot{\vec{q}}^2-\frac{1}{2}k\vec{q}^2-V(\vec{q}),$$

and the corresponding Hamiltonian

$$H=\frac{\vec{p}^2}{2m}+\frac{1}{2}k\vec{q}^2+V(\vec{q}).$$

By multiplying this Hamiltonian with $$\psi=e^{i(\vec{p}\cdot\vec{q}-Ht)/\hbar}$$, we basically obtain Schrödinger’s equation:

$$\left[i\hbar\partial_t+\frac{\hbar^2}{2m}\vec{\nabla}^2-\frac{1}{2}k\vec{q}^2-V(\vec{q})\right]e^{i(\vec{p}\cdot\vec{q}-Ht)/\hbar}=0.$$

The transition to the quantum theory begins when we accept that linear combinations of solutions of this equation (i.e., $$\psi$$-s corresponding to different values of $$\vec{p}$$ and $$H$$) also represent physical states of the system, despite the fact that these “mixed” solutions are not eigenfunctions and there are no corresponding classical eigenvalues $$\vec{p}$$ and $$H$$.

Pure algebra can lead to an expression of $$\hat{H}$$ in the form of “creation” and “annihilation” operators:

$$\hat{H}=\hbar\omega\left(\hat{a}^\dagger\hat{a}+\frac{1}{2}\right)+V(\vec{q}).$$

These operators have the properties

\begin{align*}
\hat{H}\hat{a}\psi_n&=\left([\hat{H},\hat{a}]+\hat{a}\hat{H}\right)\psi_n=(E_n-\hbar\omega)\hat{a}\psi_n,\\
\hat{H}\hat{a}^\dagger\psi_n&=\left([\hat{H},\hat{a}^\dagger]+\hat{a}^\dagger\hat{H}\right)\psi_n=(E_n+\hbar\omega)\hat{a}^\dagger\psi_n.
\end{align*}
where

$$E_n=\left(n+\frac{1}{2}\right)\hbar\omega.$$

This same derivation can be done in the relativistic single particle case as well.

Moreover, it is possible to define a classical scalar field in the form

$${\cal L}=\frac{1}{2}\rho(\partial_t\phi)^2-\frac{1}{2}\rho c^2(\vec{\nabla}\phi)^2-\frac{1}{2}\kappa\phi^2-V(\phi),$$

which leads to the Hamiltonian density

$${\cal H}=\pi\partial_t\phi-{\cal L}=\frac{\pi^2}{2\rho}+\frac{1}{2}\rho c^2(\vec{\nabla}\phi)^2+\frac{1}{2}\kappa\phi^2+V(\phi).$$

The transitioning to the quantum theory occurs by first expressing $$\phi$$ as a Fourier integral and then promoting the Fourier coefficients to operators that satisfy a commutation relation in the form

$$[\hat{a}(\omega,\vec{k}),\hat{a}^\dagger(\omega,\vec{k}’)]=(2\pi)^3\delta^3(\vec{k}-\vec{k}’).$$

This leads to a commutation relation for the field and its canonical momentum in the form

$$[\hat{\phi}(t,\vec{x}),\hat{\pi}(t,\vec{x}’)]=i\hbar\delta^3(\vec{x}-\vec{x}’),$$

and for the Hamiltonian,

$$\hat{H}=\hbar\omega\left\{\frac{1}{2}+\int\frac{d^3\vec{k}}{(2\pi)^3}\hat{a}^\dagger(\omega,\vec{k})\hat{a}(\omega,\vec{k})\right\}+\int d^3xV(\hat{\phi}).$$

More details are provided on my Web site, at https://www.vttoth.com/CMS/physics-notes/297.

So why did I find it necessary to capture here something that can be found in first chapter of every semi-decent quantum field theory textbook? Several reasons.

• First, I wanted to present a consistent treatment of all four cases: the nonrelativistic and relativistic case for both the particle and the field theory.
• Second, I wanted to write down all relevant equations without omitting dimensions. I wanted to write down a Lagrangian density that has the dimensions of energy density, consistent with a scalar field that has the dimensions of length (i.e., a displacement).
• Third, I wanted to spell out some of the details of the derivation that are omitted from nearly all textbooks yet, I am obliged to admit, almost stumped me. That is, once you see the derivation the steps are reasonably trivial, but it is still hard to stumble upon exactly the right way to apply the relevant identities related to Fourier transforms and Dirac deltas.
• Lastly, I find it revealing how this approach can highlight exactly where a quantum theory is introduced. In the particle theory case, it is when we assume that “mixed states”, that is, linear combinations of eigenstates also represent physical states of a system, despite the fact that they do not correspond to classical eigenvalues. In the case of a field theory, the transition occurs when we replace Fourier coefficients with operators: implicit in the transition is that once again, mixed states are included as representing actual physical states of the system.

Note also how none of this has anything to do with interpretations. There is no “collapse of the wave function” or any such nonsense. That stuff happens when we introduce into our consideration a “measurement event”, effectively an interaction between the quantum system and a classical instrument, which forces the quantum system into an eigenstate. This eigenstate cannot be predicted from the initial conditions alone, precisely because the classical idealization of the measurement apparatus effectively amounts to an admission of ignorance about its true quantum state.

Microsoft is not the only company that can produce pointless operating system messages. My Samsung phone greeted me with a fine example this morning, as I tried to use its S Voice app to create a new alarm using a voice command:

I feel so much better, now that I know.

I have in my collection of photographs a picture, taken I suspect in the late 1960s or the 1970s by my father-in-law, from the top of the TV tower in Alexanderplatz, in downtown Berlin. The Berlin Wall in this picture is quite visible.

The other day, I was able to identify the exact perspective from which this picture was taken, using Google Maps. The city has changed a lot in the intervening decades (almost half a century!) but some prominent buildings remain quite recognizable. The Wall, of course, is long gone.

Also, there are a heck of a lot more trees. Budapest was like this, too: When I was growing up, there were barely any trees. That is because most trees were cut down for firewood during WW2 so in the 1960s, there were still very few mature trees in the city. Today, the street where I grew up is completely covered by a canopy of green.

For the past ten years, I have been thinking about NASA’s New Horizons probe as the space probe that will eventually fly by Pluto if all goes well and its systems perform as expected.

Well, that historic flyby happened today, and New Horizons sent back pictures to prove it. Best of all, it successfully re-established contact after performing its flyby observations. Now we will have to wait many months (more than a year, as a matter of fact) before all the collected data is radioed back to the Earth.

But we already have amazing photos. A sight never seen by a human being up until just over a day ago.

A few months ago, after a miserable half decade during which Greece lost one quarter of its economy, fed-up Greeks elected a far-left government that promised no more austerity, no more giving in to heartless European demands.

To bolster its legitimacy, the government held a nationwide referendum, in which Greeks voted in large numbers against accepting a (by then defunct) austerity package that was a precondition for more European bailouts and assistance.

And now… the Greek government agreed to an even worse austerity package than the one Greek voters just rejected?

What exactly happened here while I blinked?

In the past couple of days, I heard several commentators on CNN lament on the fact that China’s debt-to-GDP ratio is much higher (“three times” higher) than that of the US, and that this may be behind the current volatility of the Chinese stock market.

This, of course, is blatant nonsense. China’s government debt-to-GDP ratio is much lower than that of the US. It is in the low twenties, compared with over 100% in the United States. Here is a crude plot (crude because I graphically edited together two plots, but I had to change the vertical scale of one) that shows the two in comparison.

No, China doesn’t have a problem with government debt. China does have a problem with private debt. Look at this monstrous chart:

What this chart shows is alarming. No, still not three times the US private debt-to-GDP ratio (that factor of 3 only happens if you compare China’s total debt to US government debt, which is of course comparing apples to oranges), but it is significantly higher than that of the US. What’s worse is that China is still an emerging economy: in addition to the prosperous middle class of places like Shanghai, there are still close to (or more than?) a billion people in that country who live in third world poverty. (China’s per-capita GDP is $6,800; in the US, the figure is$53,000, nearly eight times higher.)

The wisdom I’ve been reading online is that an emerging economy just cannot afford to have the same level of private indebtedness as an advanced economy.

To be honest, I don’t know if it is true. For all I know, much of China’s debt is held by those who can actually afford it, the prosperous middle class with their SUVs and air conditioned homes in Shanghai or Guangzhou. Indeed, if we split China into two countries, one prosperous and one poor, the prosperous one may well qualify as an advanced economy, and it may be holding most of the debt.

Or not. But whatever the debt situation is in China or its impact on the stock market, it is still no excuse for CNN to keep babbling nonsense.

I like New Scientist. This weekly British popular science publication was able to maintain reasonably high standards. More or less.

But not last week. Typos or the occasional excess hype on the cover page are one thing, but what is the excuse for this?

For the record, the solar system is not traveling at two-thirds the speed of light in its voyage around the center of the Milky Way.

To their credit, it has since been corrected on the Web site, but still. Very disappointing.