Monthly Archives: July 2023

Relativity’s twin paradox explained, and why time is at right angles to space.

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One of the most famous paradoxes of physics is explained wrong — always. It makes people feel good to think they understand it, but the explanation is wrong and confusing, and it drives young physicists in a wrong direction. The basic paradox is an outgrowth of the special relativity prediction that time moves slower if you move faster.

Thus, if you entered a spaceship and were to travel to a distant star at 99% the speed of light, turn around and get here 30 years, you would have aged far less than 30 years. You and everyone else on the space ship would have aged three years, 1/10 as much as someone on earth.

The paradox part, not that the above isn’t weird enough by itself, is that the person in the spaceship will imagine that he (or she) is standing still, and that everyone on earth is moving away at 99% the speed of light. Thus, the person on the spaceship should expect to find that the people on earth will age slower. That is, the person on the space ship should return from his (or her) three year journey, expecting to find that the people on earth have only aged 0.3 years. Obviously, only one of these expectations can be right, but it’s not clear which (It’s the first one), nor is it clear why.

The wrong explanation appears in an early popular book, “Mr Tompkins in Wonderland”, by Physicist, George Gamow. The book was written shortly after Relativity was proposed, and involves a Mr Tompkins who falls asleep in a physics lecture. Mr. Tompkins dreams he’s riding on a train going near the speed of light, finds things are shorter and time is going slower. He then asks the paradox question to the conductor, who admits he doesn’t quite know how it works (perhaps Gamow didn’t), but that “it has something do do with the brakeman.” That sounds like Gamow is saying the explanation has to do with deceleration at the turn around, or general relativity in general, implying gravity could have a similarly large effect. It doesn’t work that way, and the effect of 1G gravity is small, but everyone seems content to explain the paradox this way. This is particularly unfortunate because these include physicists clouding an already cloudy issue.

In the early days of physics, physicists tried to explain things with a little legitimate math to the lay audience. Gamow did this, as did Einstein, Planck, Feynman, and most others. I try to do this too. Nowadays, physicists have removed the math, and added gobbledygook. The one exception here are the cinematographers of Star Wars. They alone show the explanation correctly.

The explanation does not have to do general relativity or the acceleration at the end of the journey (the brakeman). Instead of working through some acceleration, general relativity effect, the twin paradox works with simple, special relativity: all space contracts for the duration of the trip, and everything in it gets shorter. The person in this spaceship will see the distance to the star shrink by 90%. Traveling there thus takes 1/10th the time because the distance is 1/10th. There and back at 99% the speed of light, takes exactly 3 years.

The equation for time contraction is: t’ = v/x° √(1-(v/c)2) = t° √(1-(v/c)2) where t’ is the time in the spaceship, v is the speed, x° is the distance traveled (as measured from earth), and c is the speed of light. For v/c = .99, we find that √1-(v/c)2 is 0.1. We thus find that t’ = 0.1 t°. When dealing with the twin paradox, it’s better to say that x’ = 0.1x° where x’ is the distance to the star as seen from the spaceship. In either case, when the people on the space ship accelerate, they see the distance in front of them shrink, as shown in Star Wars, below.

Star Wars. The millennium falcon jumps to light speed, and beyond.

That time was at right angles to space was a comment in one of Einstein’s popular articles and books; he wrote several, all with some minimal mathematics Current science has no math, and a lot of politics, IMHO, and thus is not science.

He showed that time and space are at right angles by analogy from Pythagoras. Pythagoras showed that distance on a diagonal, d between two points at right angles, x and y is d = √(x2 + y2). Another way of saying this is d2 =x2 + y2. The relationship is similar for relativistic distances. To explain the twin paradox, we find that the square of the effective distance, x’2 = x°2 (1 – (v/c)2) = x°2 – (x°v)2/c2 = x°2 – (x°v/c)2 = x°2 – (t°2/c2). Here, x°2 is the square of the original distance, and it comes out that the term, – (t°2/c2) behaves like the square of an imaginary distance that is at right angles to it. It comes out that co-frame time, t° behaves as if it were a distance with a scale factor of i/c.

For some reason people today read books on science by non-scientist ‘explainers.’ I These books have no math, and I guess they sell. Publishers think they are helping democratize science, perhaps. You are better off reading the original thinkers, IMHO.

Robert Buxbaum, July 16, 2023. In his autobiography, Einstein claimed to be a fan of scientist -philosopher, Ernst Mach. Mach derived the speed of sound from a mathematical analysis of thermodynamics. Einstein followed, considering that it must be equally true to consider an empty box traveling in space to be one that carries its emptiness with it, as to assume that fresh emptiness comes in at one end and leaves by the other. If you set the two to be equal mathematically, you conclude that both time and space vary with velocity. Similar analysis will show that atoms are real, and that energy must travel in packets, quanta. Einstein also did fun work on the curvature of rivers, and was a fan of this sail ship design. Here is some more on the scientific method.

The Ukraine war could go for years. Don’t make a famine.

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Russia is a collapsing, corrupt state with no meaningful elections. It is also the biggest exporter of food, fertilizer, gas, and oil. Nearly 2 years ago, it invaded Ukraine, another collapsing, corrupt, food-exporting state with suspended elections.

Both countries are in the midst of demographic collapse, with Ukraine worse off. Ukraine was invaded though, and thus has the better claim to our support. Then again Russia has atomic bombs. It’s also the largest exporter of wheat (or was), while Ukraine is only the 5th largest (or was before the war). The other three big exporters are the US, Canada, and France. They have benefitted financially, but don’t have near enough output to make up for lost Russian and Ukrainian production.

Ukraine’s grain terminals in flames, Odessa..

Food and energy prices have gone up, world wide, and will probably continue to rise as the war stretches on. This could lead to a global famine and mass starvation, particularly in the poorest areas of Africa, the Mid East, and India. Unfortunately, the war is popular and patriotic, in Europe, Russia, Ukraine, and the US. It’s good business for our armaments industry, and for our recent mega-farmers (like Bill Gates). Also, for our political and spy class. They spend with little government oversight, and just recently misplaced $16 billion. Surely some of that lost money snuck back to the CIA and our politicians’ pockets. We’d have oversight, but “there’s a war on.”

As wars go, the death toll is low, a total of 354,000 dead and injured on both sides, as revealed by recently leaked documents. This is a small fraction of the countries population. Russia has lost 223,000 soldiers killed or wounded, 0.2% of the population, while the Ukrainians had lost 131,000. That’s 0.3%, many of them civilians. The death rate in the two countries during this time was 3.1 million people, 1.8% of the total, mostly from heart disease, accidents, and alcoholism.

The Ukrainian population. Lots of retirees, few kids, very few of military age. This is a disaster, not a country.

Even more destructive to Russia and Ukraine is the demographic collapse. The fertility rate in Russia is 1.5 child per woman, up fro 1.2 in 2000. For a stable population at low infant death, you need about 2.1 children per woman. Russia has had this low rate for a generation, at least 30 years. The net result is that we can expect that Russia’s population will drop by a third or so over the next generation, about 50 million. In Ukraine the fertility rate is even lower, 1.21 per woman, up from 1.1. It’s been this way for 30 years, the equivalent of killing off 1/2 of the population. Aside from leaving the countries full of old people, with no one to do the work, the demographic collapse is producing a cultural shift that virtually guarantees the breakup of Ukraine and the Russian federation. Europe also has this problem, but they have immigration, and that helps a little. Russia has no immigration, and recently resorted to kidnapping Ukrainian children.

The loss of Russian and Ukrainian exports means famine for the poor importers and food inflation for all.

The coming food and energy shortage is likely to lead to mass migration, I expect. Europe has stopped taking delivery of Russian food and energy, in solidarity with Ukraine. Meanwhile Russia has been destroying Ukrainian fields and food infrastructure. Russia ruined a dam last month, flooding Ukraine’s fields, and yesterday destroyed the grain terminals at the port of Odessa,. This was tit-for-tat since Ukraine destroyed a key bridge, and Crimea’s irrigation canal. What’s more, evidence suggests that Ukraine blew up the Nord Stream pipeline — a key source of finance for Russia and Germany. This sort of tit-for-tat escalated to WWI, fueled by a belief, on both sides, that they would win “decisively and quickly.”

The result of WWI is that Germany was the biggest loser, losing men and land, and suffering a killing famine in 1916. It militarized to prevent it happening again, leading to WWII. Germany is the biggest loser of this war, I’d say, aside from Ukraine. I fear it will militarize. Russia invaded Ukraine but claims a need to militarize. Biden’s promise that Ukraine’s will join NATO is a threat to Russia, as is our delivery of F16s, missiles and cluster bombs. We are killing Russians, and Putin doesn’t like it. Add to this, that Ukraine’s claim for independence rests mostly on its Nazi collaboration. For the good of everyone, maybe we can stop adding gasoline to this fire.

Ukraine deserves our support, I think, but that support need not go beyond small-ish arms, energy deliveries, and tariffs on Russian goods. I think we should Ukraine and Russia export food and energy. Even without WWIII, a world famine and a military Germany does no one any good.

Robert Buxbaum, July 20, 2023. When I was a teen, it was a given that war was bad. Now, for some reason, the kids are in for war, especially the more liberal classes. I find this absolutely bizarre.

Chemistry, chemical engineering joke

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A catalyst walks into a bar. The bartender says, “We can’t serve you.”

The catalyst asks, “Why not?”

The bartender says, “The last time you were here, you started something.”

Robert Buxbaum, July 14, 2023 (Bastille day). If you like this, maybe you’d like another, chemistry joke or this physics joke.