# Do antimatter apples fall up?

by Dr. Robert E. Buxbaum,

The normal view of antimatter is that it’s just regular matter moving backwards in time. This view helps explain why antimatter has the same mass as regular matter, but has the opposite charge, spin, etc. An antiproton has the same mass as a proton because it is a proton. In our (forward) time-frame the anti-proton appears to be attracted by a positive plate and repelled by a negative one because, when you are going backward in time, attraction looks like repulsion.

In this view, the reason that antimatter particles annihilate when they come into contact with matter –sometimes– is that the annihilation is nothing more than the matter particle (or antimatter) switching direction in time. In our (forward) time-frame it looks like two particles met and both disappeared leaving nothing but photons (light). But in the time reversal view, shown in the figure below, there is only one normal matter particle. In the figure, this particle (solid line) comes from the left, and meets a photon, a wiggly line who’s arrow shows it traveling backwards in time. The normal proton then reverses in time, giving off a photon, another wiggly line. I’d alluded to this in my recent joke about an antimatter person at a bar, but there is also a famous poem.

This time reverse approach is best tested using entropy, the classical “arrow of time.” The best way to tell you can tell you are going forward in time is to drop an ice-cube into a hot cup of coffee and produce a warm cup of diluted coffee. This really only shows that you and the cup are moving in the same direction — both forward or both backward, something we’ll call forward. If you were moving in the opposite direction in time, e.g. you had a cup of anti-coffee that was moving backward in time relative to you, you could pull an anti -ice cube out of it, and produce a steaming cup of stronger anti-coffee.

We can not do the entropy test of time direction yet because it requires too much anti matter, but we can use another approach to test the time-reverse idea: gravity. You can make a very small drop of antimatter using only a few hundred atoms. If the antimatter drop is really going backwards in time, it should not fall on the floor and splatter, but should fly upward off the floor and coalesce. The Laboratory at CERN has just recently started producing enough atoms of anti-hydrogen to allow this test. So far the atoms are too hot but sometime in 2014 they expect to cool the atoms, some 300 atoms of anti hydrogen, into a drop or two. They will then see if the drop falls down or up in gravity. The temperature necessary for this study is about 1/100,000 of a degree K.

The anti-time view of antimatter is still somewhat controversial. For it to work, light must reside outside of time, or must move forward and backward in time with some ease. This makes some sense since light travels “at the speed of light,” and is thus outside of time. In the figure, the backwards moving photon would look like a forward on moving in the other direction (left). In a future post I hope to give instructions for building a simple, quantum time machine that uses the fact that light can move backwards in time to produce an event eraser — a device that erases light events in the present. It’s a somewhat useful device, if only for a science fair demonstration. Making one to work on matter would be much harder, and may be impossible if the CERN experiments don’t work out.

It becomes a little confusing how to deal with entropy in a completely anti-time world, and it’s somewhat hard to see why, in this view of time, there should be so little antimatter in the universe and so much matter: you’d expect equal amounts of both. As I have strong feelings for entropy, I’d posted a thought explanation for this some months ago imagining anti matter as normal forward-time matter, and posits the existence of an undiscovered particle that interacts with its magnetism to make matter more stable than antimatter. To see how it works, recall the brainteaser about a tribe that always speaks lies and another that always speaks truth. (I’m not the first to think of this explanation).

If the anti hydrogen drop at CERN is seen to fall upwards, but entropy still works in the positive direction as in my post (i.e. drops still splatter, and anti coffee cools like normal coffee), it will support a simple explanation for dark energy — the force that prevents the universe from collapsing. Dark energy could be seen to result from the antigravity of antimatter. There would have to be large collections of antimatter somewhere, perhaps anti-galaxies isolated from normal galaxies, that would push away the positive matter galaxies while moving forward in time and entropy. If the antigalaxies were close to normal galaxies they would annihilate at the edges, and we’d see lots of photons, like in the poem. Whatever they find at CERN, the future will be interesting. And if time travel turns out to be the norm, the past will be more interesting than it was.

# Musical Color and the Well Tempered Scale

by R. E. Buxbaum, (the author of all these posts)

I first heard J. S. Bach’s Well Tempered Clavier some 35 years ago and was struck by the different colors of the different scales. Some were dark and scary, others were light and enjoyable. All of them worked, but each was distinct, though I could not figure out why. That Bach was able to write in all the keys without retuning was a key innovation of his. In his day, people tuned in fifths, a process that created gaps (called wolf) that prevented useful composition in affected keys.

We don’t know exactly how Bach tuned his instruments as he had no scientific way to describe it; we can guess that it was more uniform than the temper produced by tuning in fifths, but it probably was not quite equally spaced. Nowadays electronic keyboards are tuned to 12 equally spaced frequencies per octave through the use of frequency counters.  Starting with the A below “middle C”, A4, tuned at 440 cycles/second (the note symphonies tune to), each note is programmed to vibrate at a wavelength that is lower or higher than one next to it by a factor of the twelfth root of two, 12√2= 1.05946. After 12 multiples of this size, the wavelength has doubled or halved and there is an octave. This is called equal tempering.

Currently, many non-electric instruments are also tuned this way.  Equally tempering avoids all wolf, but makes each note equally ill-tempered. Any key can be transposed to another, but there are no pure harmonies because 12√2 is an irrational number (see joke). There is also no color or feel to any given key except that which has carried over historically in the listeners’ memory. It’s sad.

I’m going to speculate that J.S. Bach found/ favored a way to tune instruments where all of the keys were usable, and OK sounding, but where some harmonies are more perfect than others. Necessarily this means that some harmonies will be less-perfect. There should be no wolf gaps that would sound so bad that Bach could not compose and transpose in every key, but since there is a difference, each key will retain a distinct color that JS Bach explored in his work — or so I’ll assume.

Pythagoras found that notes sound best together when the vibrating lengths are kept in a ratio of small numbers. Consider the tuning note, A4, the A below middle C; this note vibrates a column of air .784 meters long, about 2.5 feet or half the length of an oboe. The octave notes for Aare called A3 and A5. They vibrate columns of air 2x as long and 1/2 as long as the original. They’re called octaves because they’re eight white keys away from A4. Keyboards add 4 black notes per octave so octaves are always 12 notes away. Keyboards are generally tuned so octaves are always 12 keys away. Based on Pythagoras, a reasonable presumption is that J.S Bach tuned every non-octave note so that it vibrates an air column similar to the equal tuning ratio, 12√2 = 1.05946, but whose wavelength was adjusted, in some cases to make ratios of small, whole numbers with the wavelength for A4.

Aside from octaves, the most pleasant harmonies are with notes whose wavelength is 3/2 as long as the original, or 2/3 as long. The best harmonies with A4 (0.784 m) will be with notes with wavelengths (3/2)*0.784 m long, or (2/3)*0.784m long. The first of these is called D3 and the other is E4. A4 combines with D3 to make a chord called D-major, the so-called “the key of glory.” The Hallelujah chorus, Beethoven’s 9th (Ode to Joy), and Mahler’s Titan are in this key. Scriabin believed that D-major had a unique color, gold, suggesting that the pure ratios were retained.

A combines with E (plus a black note C#) to make a chord called A major. Songs in this key sound (to my ear) robust, cheerful and somewhat pompous; Here, in A-major is: Dancing Queen by ABBA, Lady Madonna by the BeatlesPrelude and Fugue in A major by JS Bach. Scriabin believed that A-major was green.

A4 also combines with E and a new white note, C3, to make a chord called A minor. Since E4 and E3 vibrate at 2/3 and 4/3 the wavelength of A4 respectively, I’ll speculate that Bach tuned C3 to 5/3 the length of A4; 5/3*.0784m =1.307m long. Tuned his way, the ratio of wavelengths in the A minor chord are 3:4:5. Songs in A minor tend to be edgy and sort-of sad: Stairway to heaven, Für Elise“Songs in A Minor sung by Alicia Keys, and PDQ Bach’s Fugue in A minor. I’m going to speculate the Bach tuned this to 1.312 m (or thereabouts), roughly half-way between the wavelength for a pure ratio and that of equal temper.

The notes D3 and Ewill not sound particularly good together. In both pure ratios and equal tempers their wavelengths are in a ratio of 3/2 to 4/3, that is a ratio of 9 to 8. This can be a tensional transition, but it does not provide a satisfying resolution to my, western ears.

Now for the other white notes. The next white key over from A4 is G3, two half-tones longer that for A4. For equal tuning, we’d expect this note to vibrate a column of air 1.05946= 1.1225 times longer than A4. The most similar ratio of small whole numbers is 9/8 = 1.1250, and we’d already generated one before between D and E. As a result, we may expect that Bach tuned G3 to a wavelength 9/8*0.784m = .88 meters.

For equal tuning, the next white note, F3, will vibrate an air column 1.059464 = 1.259 times as long as the A4 column. Tuned this way, the wavelength for F3 is 1.259*.784 = .988m. Alternately, since 1.259 is similar to 5/4 = 1.25, it is reasonable to tune F3 as (5/4)*.784 = .980m. I’ll speculate that he split the difference: .984m. F, A, and C combine to make a good harmony called the F major chord. The most popular pieces in F major sound woozy and not-quite settled in my opinion, perhaps because of the oddness of the F tuning. See, e.g. the Jeopardy theme song, “My Sweet Lord,Come together (Beetles)Beethoven’s Pastoral symphony (Movement 1, “Awakening of cheerful feelings upon arrival in the country”). Scriabin saw F-major as bright blue.

We’ve only one more white note to go in this octave: B4, the other tension note to A4. Since the wavelengths for G3 was 9/8 as long as for A4, we can expect the wavelength for B4 will be 8/9 as long. This will be dissonant to A4, but it will go well with E3 and E4 as these were 2/3 and 4/3 of A4 respectively. Tuned this way, B4 vibrates a column 1.40 m. When B, in any octave, is combined with E it’s called an E chord (E major or E minor); it’s typically combined with a black key, G-sharp (G#). The notes B, E vibrate at a ratio of 4 to 3. J.S. Bach called the G#, “H” allowing him to spell out his name in his music. When he played the sequence BACH, he found B to A created tension; moving to C created harmony with A, but not B, while the final note, G# (H) provided harmony for C and the original B. Here’s how it works on cello; it’s not bad, but there is no grand resolution. The Promenade from “Pictures at an Exhibition” is in E.

The black notes go somewhere between the larger gaps of the white notes, and there is a traditional confusion in how to tune them. One can tune the black notes by equal temper  (multiples of 21/12), or set them exactly in the spaces between the white notes, or tune them to any alternate set of ratios. A popular set of ratios is found in “Just temper.” The black note 6 from A4 (D#) will have wavelength of 0.784*26/12= √2 *0.784 m =1.109m. Since √2 =1.414, and that this is about 1.4= 7/5, the “Just temper” method is to tune D# to 1.4*.784m =1.098m. If one takes this route, other black notes (F#3 and C#3) will be tuned to ratios of 6/5, and 8/5 times 0.784m respectively. It’s possible that J.S. Bach tuned his notes by Just temper, but I suspect not. I suspect that Bach tuned these notes to fall in-between Just Temper and Equal temper, as I’ve shown below. I suspect that his D#3 might vibrated at about 1.104 m, half way between Just and Equal temper. I would not be surprised if Jazz musicians tuned their black notes more closely to the fifths of Just temper: 5/5 6/5, 7/5, 8/5 (and 9/5?) because jazz uses the black notes more, and you generally want your main chords to sound in tune. Then again, maybe not. Jimmy Hendrix picked the harmony D#3 with A (“Diabolus”, the devil harmony) for his Purple Haze; it’s also used for European police sirens.

To my ear, the modified equal temper is more beautiful and interesting than the equal temperament of todays electronic keyboards. In either temper music plays in all keys, but with an un-equal temper each key is distinct and beautiful in its own way. Tuning is engineering, I think, rather than math or art. In math things have to be perfect; in art they have to be interesting, and in engineering they have to work. Engineering tends to be beautiful its way. Generally, though, engineering is not perfect.

Summary of air column wave-lengths, measured in meters, and as a ratio to that for A4. Just Tempering, Equal Tempering, and my best guess of J.S. Bach’s Well Tempered scale.

R.E. Buxbaum, May 20 2013 (edited Sept 23, 2013) — I’m not very musical, but my children are.

# Chaos, Stocks, and Global Warming

Two weeks ago, I discussed black-body radiation and showed how you calculate the rate of radiative heat transfer from any object. Based on this, I claimed that basal metabolism (the rate of calorie burning for people at rest) was really proportional to surface area, not weight as in most charts. I also claimed that it should be near-impossible to lose weight through exercise, and went on to explain why we cover the hot parts of our hydrogen purifiers and hydrogen generators in aluminum foil.

I’d previously discussed chaos and posted a chart of the earth’s temperature over the last 600,000 years. I’d now like to combine these discussions to give some personal (R. E. Buxbaum) thoughts on global warming.

Black-body radiation differs from normal heat transfer in that the rate is proportional to emissivity and is very sensitive to temperature. We can expect the rate of heat transfer from the sun to earth will follow these rules, and that the rate from the earth will behave similarly.

That the earth is getting warmer is seen as proof that the carbon dioxide we produce is considered proof that we are changing the earth’s emissivity so that we absorb more of the sun’s radiation while emitting less (relatively), but things are not so simple. Carbon dioxide should, indeed promote terrestrial heating, but a hotter earth should have more clouds and these clouds should reflect solar radiation, while allowing the earth’s heat to radiate into space. Also, this model would suggest slow, gradual heating beginning, perhaps in 1850, but the earth’s climate is chaotic with a fractal temperature rise that has been going on for the last 15,000 years (see figure).

Recent temperature variation as measured from the Greenland Ice. Like the stock market, it shows aspects of chaos.

Over a larger time scale, the earth’s temperature looks, chaotic and cyclical (see the graph of global temperature in this post) with ice ages every 120,000 years, and chaotic, fractal variation at times spans of 100 -1000 years. The earth’s temperature is self-similar too; that is, its variation looks the same if one scales time and temperature. This is something that is seen whenever a system possess feedback and complexity. It’s seen also in the economy (below), a system with complexity and feedback.

Manufacturing Profit is typically chaotic — and seems to have cold spells very similar to the ice ages seen above.

The economy of any city is complex, and the world economy even more so. No one part changes independent of the others, and as a result we can expect to see chaotic, self-similar stock and commodity prices for the foreseeable future. As with global temperature, the economic data over a 10 year scale looks like economic data over a 100 year scale. Surprisingly,  the economic data looks similar to the earth temperature data over a 100 year or 1000 year scale. It takes a strange person to guess either consistently as both are chaotic and fractal.

It takes a rather chaotic person to really enjoy stock trading (Seen here, Gomez Addams of the Addams Family TV show).

Clouds and ice play roles in the earth’s feedback mechanisms. Clouds tend to increase when more of the sun’s light heats the oceans, but the more clouds, the less heat gets through to the oceans. Thus clouds tend to stabilize our temperature. The effect of ice is to destabilize: the more heat that gets to the ice, the more melts and the less of the suns heat is reflected to space. There is time-delay too, caused by the melting flow of ice and ocean currents as driven by temperature differences among the ocean layers, and (it seems) by salinity. The net result, instability and chaos.

The sun has chaotic weather too. The rate of the solar reactions that heat the earth increases with temperature and density in the sun’s interior: when a volume of the sun gets hotter, the reaction rates pick up making the volume yet-hotter. The temperature keeps rising, and the heat radiated to the earth keeps increasing, until a density current develops in the sun. The hot area is then cooled by moving to the surface and the rate of solar output decreases. It is quite likely that some part of our global temperature rise derives from this chaotic variation in solar output. The ice caps of Mars are receding.

The change in martian ice could be from the sun, or it might be from Martian dust in the air. If so, it suggests yet another feedback system for the earth. When economic times age good we have more money to spend on agriculture and air pollution control. For all we know, the main feedback loops involve dust and smog in the air. Perhaps, the earth is getting warmer because we’ve got no reflective cloud of dust as in the dust-bowl days, and our cities are no longer covered by a layer of thick, black (reflective) smog. If so, we should be happy to have the extra warmth.

# Religion – Philosophy joke

“A philosopher is a blind man in a dark room looking for a black cat that isn’t there. A theologian is the man who finds it.” ~ H. L. Mencken

This joke is more sad than funny, I would say, as it speaks to the inability to grapple with the big questions of life in any really rational way. We’d like to communicate with God, so he speaks back, but we can’t quite. We’d like to be able to stop evil with religion, by holding up a cross or squirting holy water, but we can’t. We’d like to know how and why did the universe come to be, and what happens after death, but our best rational efforts are helpless, It’s as they should be, says the philosopher, but it’s sad that it is, and then the theologian (rabbi, priest, imam) says he’s got the answers and the powers too. It’s too sad for words.

The philosopher in this joke is (I imagine) a PhD scientist, like me. While rational thought is great, and a PhD scientist can actually predict quite a lot that will happen, We have no real clue of why things happen — except in terms of other things that we can’t explain. It seems clear that the answer to none of those big-issue questions can not be found in science or rational philosophy. Nor can science deal well with one-time events like the creation of the universe, or unmeasurable items like where the apparent zero-point energy of quantum mechanics comes from. Untestable, one time events are the basis of religion and not science: science is the opposite of religion.

We thus turn to the theologian. In a sense, he has the answer: it’s God, Jesus, Jihad, prayer… Perhaps these words mean the same thing, or perhaps something different. A theologian can talk about this for hours and leave them as incomprehensible as before. Likely he is as confused as you are, but doesn’t know it. While something like God does seem to underly the concept of time, or creation (the big bang), a one-word answer, like “God” isn’t really an answer. Even though there appears to be a God, God doesn’t seem contained within the word — he’s not there. And calling “God” doesn’t give us the power we’d want to save the drowning, or cure disease.

Though the theologian will likely tell you miracle stories, and show you a pretty picture: long-haired Jesus, seated Zeus, or a dancing woman with the head of an elephant, that’s God and it isn’t. The reason people believe the theologian, is optimism: we hope he knows. Besides, the theologian has a costume and he keeps on talking till he wears the audience down. Eventually they believe he sees the black cat in the dark room called God. And eventually we don’t care that he can’t do anything on the physical plane. A key trick he has in wearing us down, by the way, is that theologians work in pairs: one tells you the other is much smarter and holier than you; the other one tells you the same about the first. Eventually, you believe them both — or at least you believe you are stupid and evil.

The wise and good philosopher or theologian is very hard to find. He doesn’t talk too much, and instead lets his actions and example do the teaching and some good. He does charity and justice (Gen. 18:18) and makes good lemonade from the lemons life gives him. He will admit that he doesn’t really know which set of words and bows actually open up God’s warehouse (or if any are particularly effective) “God speaks within a cloud” (Ex. 40:34, etc.); “[His] thoughts are not our thoughts,” (Is. 55:8, etc.). “No man can see my face and live” (Ex. 33:20).

What is the percentage of leaders are like this? “In a thousand, I have found one leader of men”, says Solomon (Eccles 7:28). “The other 999 follow after the women” (Groucho Marx).

I can’t claim to understand God particularly well, but my hope is that you will not finish reading my post thinking you are stupid or evil for not understanding the theologian’s many words, and I can hope that you will seek justice, help the downtrodden, and make yourself something of value, like a good glass of lemonade. Then again, you might be tempted to run off to a bad theologian — to someone who will encourage you to pray long and hard, and who will get you to pay him for a picture of God that only he can provide — that is, for his special picture of the black cat, in the dark room, that can never be photographed.

Robert E. Buxbaum: Amateur philosopher, and maker of fine lemonade.

# My steam-operated, high pressure pump

Here’s a miniature version of a duplex pump that we made 2-3 years ago at REB Research as a way to pump fuel into hydrogen generators for use with fuel cells. The design is from the 1800s. It was used on tank locomotives and steamboats to pump water into the boiler using only the pressure in the boiler itself. This seems like magic, but isn’t. There is no rotation, but linear motion in a steam piston of larger diameter pushes a liquid pump piston with a smaller diameter. Each piston travels the same distance, but there is more volume in the steam cylinder. The work from the steam piston is greater: W = ∫PdV; energy is conserved, and the liquid is pumped to higher pressure than the driving steam (neat!).

The following is a still photo. Click on the YouTube link to see the steam pump in action. It has over 4000 views!

Mini duplex pump. Provides high pressure water from steam power. A mini version of a classic of the 1800s Coffee cup and pen shown for scale.

You can get the bronze casting and the plans for this pump from Stanley co (England). Any talented machinist should be able to do the rest. I hired an Amish craftsman in Ohio. Maurice Perlman did the final fit work in our shop.

Our standard line of hydrogen generators still use electricity to pump the methanol-water. Even our latest generators are meant for nom-mobile applications where electricity is awfully convenient and cheap. This pump was intended for a future customer who would need to generate hydrogen to make electricity for remote and mobile applications. Even our non-mobile hydrogen is a better way to power cars than batteries, but making it mobile has advantages. Another advance would be to heat the reactors by burning the waste gas (I’ve been working on that too, and have filed a patent). Sometimes you have to build things ahead of finding a customer — and this pump was awfully cool.

# Tiger Sculpture at REB Research

Here’s the latest REB Research sculpture: a saber-toothed tiger:

Saber-toothed Tiger sculpture at REB Research; the face follows you. A bit of our 3 foot geodesic dome is shown in the foreground.

It’s face follows you (somewhat); It was inspired by my recent visit to Princeton Univ — they had lots of tiger statues, but none that looked eerie enough as you walked by. Click here for: YouTube movie.

Normally, by the way, REB Research makes hydrogen generators and other hydrogen stuff. May 1, 2013