Last April 17, twelve brave guinea pigs (non-specialists and mostly non-scientists) came to my home in Hamilton NJ to learn.
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This forum is the story of our journey.
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My fascination is that the quantum properties of electrons, whose causative factors emerged in seconds after big bang, result in chemical bonding. It’s neat and beautiful: can I get others to understand, and myself to understand it better, so we can discuss it? In other words, my theme is that the basic structure of the universe results, ultimately, in molecules.
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OUR FIRST MEETING
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One look at ‘TheOfficial Meeting Outline’ for April 17 and you would see: it was too ambitious. In one session: the big bang, three of the four forces, Heisenberg’s Uncertainty Principle, Schrodinger’s equation, orbitals, the periodic table! What was I thinking! My hands were shaking. I’d prepared this ambitious outline because I was afraid that if I didn’t MAKE PROGRESS, people wouldn’t see the magical story that I see. But unfortunately, it was too much. People were lost by the time I’d finished. My first meeting was not the success I’d hoped.
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So, let’s think of that meeting as an introduction the topics I want to cover, and I willwalk through what the group did. At least, most of my guests agreed to come back!
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7:00 PM:
We settled down to coffee and snacks while I spent a few minutes on the Scientific Method, with emphasis, I hope, on the human side: the triumph and the controversies. Also: people got to know each other: the artist and budding writer, the philosopher (my colleague at Rutgers, Jeff Buechner) the animal rescue enthusiast, the corporate executive, the environmental activist who efforts have preserved an important fossil reef, the author (Jennifer Morgan).
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7:12: Next: MATTER.
Protons, neutrons, electrons. I used a worksheet to describe how small these particle are: (see attached). A brief mention of the strong a weak nuclear force, and it is time to build nuclei!
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7:15: We used plastic Easter eggs for protons and wads of duct tape for neutrons. Neutrons, I say, are ‘nuclear glue’. My homily regarding strong and weak forces and quantum spin properties is completely lost amid the groans and yelps. The Easter eggs and duct tape wads don’t stick together well! The nuclei keep falling apart! but quick: an opportunity. The universe was well into its formation before the larger nuclei were formed, after all. It’s not easy to put nuclei together. The unwieldy bundles of too many Easter eggs (protons) and too few duct tape wads (neutrons) are ‘unstable nuclei’ read: radioactive nuclei.
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Now, some group members spontaneously collaborate to make larger bundles by combining small ones. On their own they have discovered FUSION (the combining of smaller nuclei)—which happens during stellar nucleosynthesis. Finally, we counted the Easter eggs in our largest bundle: 13. It was aluminum.
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I go the periodic table (taped to my dining room cabinet) to explain how we organize the elements. We find aluminum. We find atoms corresponding to the smaller wads, boron, nitrogen. We find carbon. We try to imagine the wad that would be gold, or uranium (the largest nuclei that is found in nature, I explain.) Progress. Some understanding. We drink coffee.
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7:20 I am half way through my time, and the main theme is yet to come: Electrons. I used grapes for electrons. Time to add the grapes to our aluminum to complete our atom!
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7:23 I explain charge and electromagnetic force. (We play with magnets, quickly quickly. At least, no one is yawning.) The grapes (electrons) will be attracted to the Easter Egg wads (protons). Where will they go?
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7:25: I explain that nature seeks the lowest energy level. Therefore, I ask, should we attach our grapes to the surface of the nucleus and let them lazily sit? No! Heisenberg’s uncertainty principle (I explain it quickly, including the formula and the mention of Plank’s constant) tells us that we cannot know position and speed of tiny particles like electrons. ‘Stopped’ doesn’t work. Electrons must always move.
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So, let’s have our grapes skim right on or above the surface. No! They have to have allowed an energy state. I try to explain allowed energy state. This goes poorly, partly because my own understanding is not complete.
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7:28: I have purchased a little trick flashlight and now I shine it through two slits. It’s partly an artifact, but I get an interference pattern. The guests seem to like this and make their own interference pattern. Electrons, too, are waves, I say, and would make an interference pattern if we sent them through two slits. I show De Broglie’s equation (Planks constant again!) Electrons are both waves and particles. I give everyone wavelengths cut from glitter paper. There is no time to make standing waves, as I’d planned, so I have my guests create circular ‘orbits’ around imaginary nuclei. How many ‘wavelengths’ do we use? This is a visualization, an analogy, for an allowed state—see, I ask, how some circles are possible, others aren’t? Let’s count the wavelengths. It’s an integer, correct? Well, that will be our ‘quantum number’. We can describe our ‘allowed circles’ with ‘quantum numbers’. Some seems to get it, some are baffled. That’s okay. Proceed.
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7:35: I explain: we have to use quantum theory to see where to put the electrons. I introduce Schrodinger’s equation. I rip through an explanation of equations: You put information in, you get a solution out. How many cakes do you have if you bake two a day and you bake three days? Total cakes equal (two a day) times (three days), y = 2x. Voila, an equation. Equations have variables and operations, I say. Schrodinger’s equation is like that, I say, only fantastically harder, and it has more variables. I show the equation, a quick explanation of the terms, and wish I have more time to explain its history and importance.
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7:38: I say things like this:
Schrodinger’s equation is a wave equation. It is a postulate. No one completely understand why it works.
It contains variables about the electrons and their states
It requires complex mathematical operations that take years of study to understand
It has three quantum numbers that constrain the allowed states
It contains an imaginary number i. This causes the ‘solutions’, ‘output’, to be divided into phases that can be opposite to one another and change in complicated ways.
It can’t be solved. The equation could not be solved with any known mathematics.So can we know where the electron is?
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7:40: Yes, I say. We can square the wavefunction. Squaring imaginary numbers makes them usable. Scientists obtain solutions telling where the electrons are, but only probabilities, not certainties.
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Some guests have glazed eyes. Time for more activity with our Easter eggs and grapes!
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7:42: I show them a simple s orbital, a solution to Schrodinger’s equation. It is described by three quantum numbers. (Remember our analogy, I say.) Let’s put our grapes in this orbital, I say. (All 13 grapes—it’s aluminum, remember?) Putting all our grapes in the lowest energy orbital would be best, correct? No! Egads, we are not done yet, and I have to explain spin. I do my best. Electrons are Fermions and cannot have an identical particle with the same energy state. I explain about the Fermions needing to turn around twice to get back to the beginning. I do a little trick with a glass on my palm. The grapes can’t all go in the same orbital.
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7:46: So we need more orbitals, because we have 13 grapes. So we enter more variables and more allowed energies in our equation and make more solutions, all the time higher in energy and farther from the nucleus. The allowed energy states, the ‘orbitals’, I say, are like an upside down skyscraper, like an upside down Taipei 101. As we go out, each ‘story’ each ‘floor’, becomes farther from the nucleus and more complex. This means, I say, that atoms are mostly empty space. I show them p, d, f orbitals (taped to my walls.)
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I suggest we put in one grape per orbital. Correct? NO! We put two in each orbital. This is because electrons have two spins states. Now each electron has unique and different quantum numbers, as required because they are fermions.
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7:50: I need to wrap this up. I can see the bafflement. It is best just to quit. Carbon, I say, has four orbitals (‘four apartments’) in the ‘second story’. It is four electrons away from being filled, from having full occupancy. I point dramatically to the periodic table, count four to the end of the second shell. Calculations, I say, show that ‘filled occupancy’ is more stable. Voila! Carbon needs to make four bonds. I point to a picture showing the structure of diamond. I hold up a marshmallow with four toothpicks, and attach more marshmallows and more toothpicks. Carbon is unique and amazing. It makes four bonds. From it, DNA is made. I am done.
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The guests each got a chance to talk next. They are neat and special people and we had a fun discussion. We agreed that we need to meet again. We agree we need to discuss ‘quantum properties’ and for fun, quantum weirdness. I will try to explain spin state better, wave particle duality, and the thing with the glass in the palm of my hand. Jeff Buechner will give a brief talk on the logic of spin states. We will drop marbles into a tank of water, blow across the tops of beer bottles, make more allowed states with our glitter wavelengths. We will talk of ‘spooky action at a distance’ and multiverses.
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The next meeting is May 8. Stay tuned.
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Counting at a rate of one atom per second, for 48 hours per week, it would take the entire population of the world 10 million years in order to reach Avogadro’s number (5).
In order to obtain Avogadro’s number of grains of sand, it would be necessary to dig the entire surface of the Sahara desert (whose area of 8 X 106 km2 is slightly less than that of the United States) to a depth of 2 meters (6).
References:
(1) D. Todd, “Five Avogadro’s Number Problems”, Journal of Chemical Education, 62, 76, 1985.
(2) D. Kolb, “The Mole”, Journal of Chemical Education, 55, 728-732, 1978.
(3) P.S. Poskozim, J.W.Wazorick, P. Tiempetpaisal and J.A. Poskozim, “Analogies for Avogadro’s Number”, Journal of Chemical Education, 63, 125-126, 1986.
(4) F.A. Bettelheim and J. March, Introduction to General, Organic and Biochemistry, 2nd edition, New York, W.B. Saunders, 1988.
(5) W.L. Masterton, J. Slowinski and C.L. Stanitski, Chemical Principles, 6th edition, New York, W.B. Saunders, 1985
(6) Henk van Lubeck, “How to Visualize Avogadro’s Number”, Journal of Chemical Education, volume 66, page 762, September 1989. -
Lastly, I am reading quite a few books to help me.
Here are a few
The most helpful is:
Particle or Wave:
The Evolution of the Concept of Matter in Modern Physics
Charis Anastopoulos
Princeton University Press.
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This author explains exactly what I want to, and does so very well
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To help me understand the math:
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In Pursuit of the Unknown: 17 Equations That Changed the World
by Ian Stewart
Basic Books
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Ian Stewart is a really good math writer
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Magick, Mayhem, and Mavericks: The Spirited History of Physical Chemistry Hardcover
by Cathy Cobb
#Chemical Principles
Zumdahl and DeCoste
Brooks/Cole -
Salon Two was ‘quantum weirdness”.
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In a way, we went off topic from our theme ‘the carbon atom’, but people wanted to do it and I was interested to learn about the topic.
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First, we reviewed some concepts from our first salon. To emphasize that the protons and neutrons form the nucleus, we played a game to learn about the STRONG NUCLEAR FORCE.
A good discussion is found in the book “Atom” by Isaac Azimov; I’ll excerpt: “We can imagine protons and neutrons constantly exchanging (mesons). The positive charge transfers (carried by meson) from (proton to neutron) in exceedingly rapid alternation. No proton can feel repulsion, because before it has time to react it is a neutron.
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I imagined a game of ‘hot potato’ with my guests. (Azimov had the same analogy.) We all stood. Some of us had a green balloon—a meson—and that made us a proton. If we were next to another ‘Green Balloon Carrier’, we had to give our balloon away quickly so that we didn’t repel each other and explode the nucleus. In this way, supposedly, the actual nucleus stays together. (Azimov and other authors go on to add some further ideas to this picture.)
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HOWEVER, my guests felt confused by the science and asked multiple questions. This made it hard to proceed to the next game I envisioned, beta decay. I had envisioned us tossing out a little spongy toy that lights up, while at the same time, changing a neutron to a proton (adding a green balloon), thus demonstrating WEAK NEUCLEAR FORCE. I meant to have us count our protons (balloons) and discover what new element we had made. I also meant to demonstrate positron emission. We DID do these games, but extremely rapidly; too fast to make sense, I’m afraid. Clearly, these games and activities with the nucleus would have to another salon—and a really good one, too, probably. Over fifteen (!!!) minutes had passed; I had to move on.
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To remind us of spin, a guest (Darcy) turned around twice while balancing a glass on her palm. I tried to demonstrate conservation of angular momentum with guest holding glitter arrows and me with a mirror; and THAT has to be its own salon.
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Now we had to go to our main event.
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A. Spooky Action at a Distance.
We placed right- and left-handed (paper) gloves in separate envelopes. I had two people turn away from each other; one guest opened her envelope. (Glove was left-handed.) I sad: “We know that the other envelope contains the right-handed glove even if we were a millions miles away, correct?” Yes, correct, but not so spooky. But wait.
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B. Next, I had to reemphasize wave particle duality. I did a terrible job, I think. But basically, people had to understand that small particles are waves and can create interference patterns if they go through two slits. If we try to examine them, the waves turn into particles, and go through one slit or the other, and the interference pattern disappears. Remembering Dewy, I played a lot of confusing games to help us discover this on our own; I think next time, I would just say it. Sometimes, it’s just better to tell people something.
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(From a book I am reading now, “Particle at the End of the Universe” by Sean Carrol: An on-line contest to describe quantum weirdness in five words produced this winner: ‘Don’t look: wave. Look: particle.’)
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C. Weird Effects: I used as my model a book: “Where Did All the Weirdness Go?” by David Lindsey. Here’s my outline, which I hope is basically correct, I am doing my best to interpret the book and this isn’t my field. I will recommend the book to readers here.
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I. Two Slit Experiments
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Send the particles one at a time (even years apart!). They hit so as to make an interference pattern. Interferes with ‘itself’. Each particle is a part of a wave function. It isn’t really a particle. It has information for all the other particles contained in the wave function
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We think that when they come together they ‘interact’ with each other to form the pattern. But they don’t. They behave as a wave function, a single quantum entity. No matter how we word it: each particle (or the particle’s wave function) is aware of the second slit while it ‘goes through the first’.
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BUT: If you cover one slit, and then another, and send them one at a time, they do not make a pattern.
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II. Now install behind one slit, a detector. The interference pattern vanishes. The particle has been ‘caught’ (i.e. we ‘looked’), the wave function collapses. _Before_ we collapsed the wave function–somehow particles are affected by both slits. After detection—the particle has gone through one and not the other.
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II. Delayed choice experiment: Beam splitter
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Does same thing as two slit experiment—creates interference by bouncing particles off mirrors and reconverging them.
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BUT NOW, we can put the detector a long way after the slit—the particle has to have decided what to do BEFOREHAND.
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The particle going through doesn’t know what kind of experiment it will be: a ‘look’ / ‘where is the particle’ experiment or a ‘don’t look’ / ‘create an interference pattern’ experiment.We can imagine the path is long enough that someone can toss a coin and decide randomly—YET somehow the particle still knows what kind of experiment it will be—before the coin is even tossed.
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III. “A vs. B” and “Light vs. Dark”
This is tough and complicated in any book I read; I will refer you to this excellent article by Timothy Ferris1, where he calls it “Sweet Sour Hard Soft”. Basically, it describes how the structure of the world changes itself to keep you from making a measurement that absolutely you have cleverly set up to BE ABLE TO MAKE! (But the universe is one step ahead.)
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IV. Spooky Action at a Distance, revisited.
A neutral pion (a type of particle) decomposes into two electrons; one must be spin up and the other spin down (because total spin of the universe is conserved) and now they travel far, far apart.
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We measure spin of these electrons with a magnetic field. If one is up the other is down. BUT, if we turn our field sideways, one is left, the other is right—they can be millions of miles apart and it would work.
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It is as if the quantum world had never heard of space–as if, in some strange way, it thinks of itself as still being in one place at one time. Such behavior is called nonlocal.
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Three explanations for “Quantum Weirdness”, called “interpretations,” have emerged. 1
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a. The first, the Copenhagen interpretation, (Neils Bohr) asserts that we should simply accept that we cannot know the state of a quantum system until it is measured, and so we should stop worrying about it. It is pointless to speculate about whether the missing information “exists.”
b. The second, or many worlds interpretation, says the entire universe splits, with each act of measurement, into two universes. (Hugh Everett) Before measurement, both outcomes coexist. After measurement, the other result carries on in a separate universe. An infinity of other universes are born.
c. hidden-variables interpretation. (David Bohm) He calls the weirdness quantum potential, a gently acting field. Quantum potential would seem to violate special relativity– sending signals that travel at faster-than-light speed.
‘We humans, having come along when the universe was already billions of years old and are big creatures, able to see stars in the sky but not atoms in an apple, but the universe was not always big and classical. Once it was small and quantum, and possibly it has not lost the memory of those times. It may well turn out that
effects are woven through the universe in something like the way that a chef folds a cream into a sauce.’1
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Here is a clue to how it might work: Photons do not “experience” time.
Particles that have mass must travel ‘distance’ slowly. Photons travel distance at the speed of light—they do not travel in time. So a photon “traveling” from point A to point B does so, from its point of view, in zero time, meaning that, in the photon’s sense, the two points aren’t separate! Bohm and others have likened the implicate (i.e., folded in) universe to a hologram. Shatter a hologram, put one of its fragments in the laser beam, and what you see is not a piece of the original image but all of it.#
I would like to say that next, Jeff Buechner gave an excellent talk about logic and quantum weirdness, apparently giving us his original, unpublished thoughts (so I won’t ‘publish’ them here xz.) This was the part of the salon got truly neat. We ended there, and agreed to meet again.
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To debrief this salon, and to encapsulate my guests comments: Once again, I tried to do too much. Clearer, simpler, please!! Less is more! Also—I forget that my guests might have forgotten something, thus I should hang posters showing what we learned last time, so they can look at them. Still, they had fun, got the ‘gist’ of it, and are willing to come back!
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My next salon will be back to the main theme: How the sequence of the big bang affected the carbon atom and matter and life as we know it. I am reading a lot to prepare. We will discuss the Higgs field, breaking symmetry, the particle zoo, inflation, the forces, and we will try ‘to not do too much’.
#1. http://www.stanford.edu/dept/HPS/writingscience/Ferris.htm from The Whole Shebang: A State-of-the-Universe(s) Report (1997). -
- The Salon’s theme is the atom, and the structure that allows complex molecules to form, and the properties of the electron and nucleus that bring that about. In this meeting, we explored how the particles and their properties emerged in the first stages of the Big Bang. The participants agreed that this salon went the best—that’s interesting because I didn’t quite understand the material. We were able to debate the meaning of what I presented. In this salon, we learned about the force particles and matter particles. If I understand correctly, our universe started without these, but they emerged in the first second as a result of symmetry breaking. This is also called the Higgs mechanism.
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- We learned that the universe is governed by quantum rules (see the last salon), even at the very beginning. Here are the topics we covered.
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- When the universe was 1 millionth of a trillionth of a trillionth of a trillionth of a second old.
- This is Plank time. The universe is smaller than an electron at this point.<sup>1 </sup>Scientists can’t know what is happening now. If we imagine an even smaller universe, it would be smaller than quantum mechanics allows–a contradiction. At any rate, whatever ‘it’ was, the universe emerged out if it, what it was before, we can’t know.
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- But a tiny slice of time later, the Universe was outside of Plank Time. All particles and fields had the same values and were identical. The particles do not have mass.
- By the way, what is a particle? It is a vibration in a field. What is a field? Well, the books I read said a field has a number at every point. No one in the salon could interpret this!<sup>10</sup>
- But—we could interpret mass!
- What is mass?
- It interacts with gravity
- It has inertia (DEMO: we imagined two flying spheres, one made of marshmallow, and one made of lead. Which one would take more force to halt with your hand?)
- It is a form of energy. E = mc<sup>2</sup>
- Relating to above, I had once calculated that the explosion at Nagasaki was the result of 0.7 grams of matter changing to mass. I held up a peanut—about that much mass that had changed to energy. There is a lot of energy in mass.
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- Next we talked about Spontaneous Symmetry Breaking. (Thisis the Higgs mechanism. We (salon members) were undecided: was the structure of the universe there from the beginning, or was it decided in the Symmetry Breaking? At any rate, the properties of the universe were not evident at the high temperatures following Plank time. At the very beginning there is superforce, superfield, after cooling and symmetry breaking, see all the different forces and particles emerge.
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- We tried to understand the Higgs Mechanism:
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- We envisioned a Mexican Hat Type Roulette wheel with marble. (I had found several pictures which I projected on my computer.) The Marble is a wavefunction that could give different solutions, like Schrodinger’s equation.The Mexican Hat represents energy level. If the marble is motionless, it is vacuum, no particles, no energy are present. If marble is super high energy, it sits on top of apeak (or is it peaks?) like the peak(s) of a Mexican hat. If universe should cool, the wave function slides off peaks to lower energies and we are stuck with result (unless it was all decided from the beginning and it couldn’t happen any other way!).
- (Question: Is it vacuum if it sits motionless at the top of the hat?)
- For example—one wavefunction split into 3 entities: the photon, the W and the Z particles.The photon acquires no mass, but acquisition of mass by W, Z breaks symmetry: three different forces, 3 different particles, with different masses.
- The Mexican Hat Type Roulette is the underlying shape of our universe. How many peaks does it have, what shape? We don’t know. At high energy, its shape doesn’t matter. The theorist ‘infers’ the shape to explain the particles we see. (However to account for ‘every thing’ we see, theorists must have bowls in more than 4 dimensions.)
- A Higgs Boson was made every time symmetry was broken. They are massive! (Compared to other particles, that is) Scientists found one!!!! (in a particle accelerator) July 4, 2012, scientists at CERN announced that they’d found a particle that behaved the way they expect the Higgs boson to behave.
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- Bottom line as I understand it: At super high energy, the universe was one pure force. At lower energies, the universe cooled into certain structure, which included particles and forces. Maybe the structure was pre-determined, maybe it was pure chance that we got the forces and particles we did, maybe something in between these two extremes.
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- We (the salon members) went on: At approximately 10<sup>-34</sup> secondsthe Universe is filled with a quark-gluon plasma. INFLATION begins (as a result of Higgs). Here is an explanation (not accepted by all scientists!) The Mexican hat has a depression in its top. Our universe’s wavefunction (the marble) gets stuck in it as universe cools. It is stuck so it has artificially high energy. The universe is cooling but its wavefunction is stuck at high energy! Things go rapidly awry. Normally, expansion would dilute the universe’s energy smoothly. This ‘artificial, ‘’vacuum” energy does not diminish. It is like a car with accelerator stuck. The universe doubles its size in a trillion trillionth trillionth of a second, and again, and again, and again. The energy density also doubles. The extra, artificial ‘vacuum’ energy becomes, eventually, particles (and galaxies, etc.) This explains why universe is flat and looks the same all over and has so much density of particles and objects. In addition, the mechanism of inflation is needed to provide symmetry breaking that gives ‘Spin’ . Remember, spin is essential to explain the structure of the atom.<sup>6 **</sup>
- How did inflation stop?? In some theories, tunneling is responsible. Tunneling is a quantum mechanical phenomenon. A tiny portion of an object’s wavefunction exists at an unlikely position. But the wavefuction breaks there. So, the wavefunction of the universe tunnels through the barrier that kept the universe at artificial high energy.
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- Now we talked about the Higgs field, which we gathered was different from the Higgs mechanism. The Higgs field gives particles mass. It affects different particles in different ways. Photons can slide through unaffected, while W and Z bosons get bogged down with mass. Particles got mass by interacting with the Higgs field, which occupies the entire universe. (Like the other fields covered by the standard model, the Higgs one would need a carrier particle to affect other particles, and that particle is known as the Higgs boson, the one that was found. ) Particles that interact with Higgs field have mass, more strongly they interact, more mass. Sean Carrol has a ‘Celebrity Crossing Room’ analogy. Tom Cruise (a celebrity) would interact with the people in the room strongly and be slowed. I would not react with them, and could travel freely. (I would have less mass.) Why do some particles interact more strongly—we don’t know. We talked about the Higgs search. It was an attempt to make waves in the Higgs field to prove it’s really there. I was surprised to learn that protons and neutrons and other composite particles (made up of quarks, for e.g.) get most of their mass from other mechanisms. But electrons and other elementary particles do get their mass from the Higgs field. If the electrons had no mass, they would not keep their places in atoms, and matter would explode. (see salon 1) Life as we know it seems to be dependent on our Higgs field.
- This is not mentioned much in literature, but it was mentioned in a book by Sean Carrol. From P. 146 Sean Carrol’s book: The absence of Higgs field would mean that the quarks and hadrons would have slightly different mass (they get some mass from strong nuclear force) and that would affect atoms slightly. Any change to the mass of the electron would be hugely significant. Change the mass of the electron just a little, and all life would instantly end.
- Bottom line: change the Higgs field and carbon would not be the element of life.
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- Now we moved to Universe is less than one/ten thousandth second old:
- Hadrons (neutrons, protons) form. They are made from quarks. One billion and one baryon forms for every anti baryon. Obviously this is important for both the atom and the universe.
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- To end the salon, we talked about some larger particles that are found in particle accelerators, the particle zoo standard model. The mass we see on earth is made of atoms, which are made of protons, electrons and neutrons. However, scientists have found larger analogs of these in particle accelerators (i.e., they don’t exist except at high energies.) There are 3 families (3 flavors.
- proton, neutron electron
- Bigger proton, neutron electron
- Even bigger proton, neutron electron 3 families!
- The important thing is all this emerged very early, and apparently via symmetry breaking. Before that, all these things were equal.
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- As an appendix, we got a chart with some details about the standard model, which we went through briefly. The chart was from the internet, anyone can find one, just google ‘standard model’. With the chart in front of us, we covered these details:
- Fermion vs. Boson
- Fermions have spin 1/2(or 3/2, 5/2) and cannot occupy the same state at the same time.<sup>1</sup>They take up room. (Electrons are fermions. So are quarks, which make up protons and neutrons.) THEY ARE THE STUFF WE RECOGNIZE
- Bosons have spin 0 (like Higgs), or spin 1 like photon, or spin 2, (graviton) and don’t have to take up space. They can pile on top of eachother.<sup>2,3</sup>
- THEY CARRY THE FORCES WE RECOGNIZE
- FERMIONS CAN BE: Baryon (like protons) vs. Lepton (like electron). a. Baryoncan feel strong nuclear force. You find them in NUCLEUS. They are ALL made of QUARKS. They tend to be massive.
- Leptons do not feel strong nuclear force. THEY DO NOT HAVE TO BE IN NUCLEUS. If they are charged (like electron) they hover around nucleus. If they are not charged, like neutrino, they fly off into space and they do not seem to affect our world. Elections and neutrinos are almost massless. ELECTRONS MAKE A BIG DIFFERENCE to our world.
- Bosons carry forces:
- Gravity field, gravitonsare ripples in field (not needed in or description of carbon 12)
- Electromagnetic field: photons are ripples(particles when you look! See salon 2)
- weak, or ‘electro weak’ W+, W-, Z (this are actually the same as photons, only massive. The acquisition of mass by W and Z happened during symmetry breaking. (Govern certain decays; carbon-12 doesn’t depend on them much)
- strong: ripples are gluons (these are mesons)
- Higgs boson isn’t one of our ‘forces’. It’s field in non-zero in empty space; it broke symmetry and gave us mass.
- Every field is there whether or not there are particles interacting with it. We don’t understand them more fundamentally—maybe we will some day
- All forces are interactions with a field.Matter is interaction with Higgs field
- 3 families (3 flavors) Only the least massive are seen. The others are made in particle accelerators.
- With no Higgs field, the three flavor of electron would be identical. Higgs breaks symmetry.
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- Bottom line: without the properties that arose during symmetry breaking, the atom would not form as it did.Things that are important for carbon that came about via symmetry breaking.
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- ** spin and the early universe: Fermions and bosons are 2 aspects of a single entity. But—this meant extra dimensions had to be added to our ‘Mexican hat’. The quantum arrow can switch direction in extra dimension to change boson into fermion. Fermions have quantum arrow in an extra space dimension. Need to turn around twice to face forward. <sup>2</sup> Without exclusion principle, (fermions can’t pile up) electrons would glob onto nucleus. Quarks would instead of making protons; they would make vast globs of quark stuff.<sup>5</sup>
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- OUR QUIZ and some FUN FACTS (we had fun with a quiz, we answered these critical thinking questions):
- We used some household objects to show that even though the electron is tiny compared to the nucleus, its wavefunction is huge, but the massive electron in the bigger families would have a smaller wavefunction. I held up balloons, cotton calls, tic tacs and large sponges, and had salon members guess which wavefunction went with which family.
- Fun Facts
- Scientists made anti helium!!!!!<sup>8</sup> In 1965 : two antiprotons and antineutron combined to form anti helium
- Different carbon:
- Muon is the ‘electron’ of family 2. Muons have mass 207 times the mass of electron.
- They have made muon atoms—the muon replaced the electron!!!!! <sup>9</sup>
- (It only lasted 1/500000 of a second.) HOW WOULD IT BE DIFFERENT?
- Tau lepton is 3500 times as massive as electron . Bigger than proton!
- They have not made Tau lepton atoms.
- How would atom be different if electron were Tau lepton?
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- That was our salon 3! To me, the most important point is that the Higgs mechanism and Higgs field are responsible for the properties of the electron, which is in turn responsible for the carbon atom and life.
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Last semester, some of my students wanted to read my salon three post, but I decided it was too hard to read. So I re-wrote it. I see I can’t edit the above post, but, what the heck, I’ll just post the edited post. THIS IS SALON THREE JUST LIKE ABOVE, made more understandable, hopefully, for my students (and you!!)
SALON THREE
The Salon’s entire theme (salon 1-3) is the atom, and the bonding that allows complex molecules to form, and the properties of the electron and nucleus that bring that about.
In this meeting, we explored how the particles and their properties emerged in the first stages of the Big Bang. It seems to me that the most important thing is how the properties of the electron merged, because I have come to see that chemical binding depends on the electron. It’s also interesting that no one book or article addresses this—you have to read multiple sources. This important question does not seem to have captured popular imagination.
The participants agreed that this salon went the best—that’s interesting because I didn’t quite understand the material. We were able to debate the meaning of what I presented.
Here are the topics we covered.
- The force particles
- The matter particles
- When they emerged.
- Symmetry breaking, also called the Higgs mechanism. (If I understand correctly, our universe started without a differentiation among the forces and particles, but the particles and forces as we know them emerged in the first second of the big bang as a result of symmetry breaking.
- We learned that the universe is governed by quantum rules (see the salon 2), and was even at the very beginning.
Here is the timeline we discussed, and what emerged.
When the universe was 1 millionth of a trillionth of a trillionth of a trillionth of a second old.
This is Plank time. The universe is smaller than an electron at this point.1 Scientists can’t know what is happening at this point. If we imagine an even smaller universe, it would be smaller than quantum mechanics allows–a contradiction. At any rate, whatever ‘it’ was, the universe emerged out if it, what it was before, we can’t know.
But a tiny slice of time later, the Universe was outside of Plank Time. All particles and fields had the same values and were identical. The particles do not have mass.
(By the way, what is a particle? It is a vibration in a field. What is a field? Well, the books I read said a field has a number at every point. No one in the salon could interpret this!10)
But—we (the salon members) could interpret mass!
- What is mass?
- It interacts with gravity
- It has inertia (DEMO: we imagined two flying spheres, one made of marshmallow, and one made of lead. Which one would take more force to halt with your hand?)
- It is a form of energy. E = mc Mass and energy are two manifestations of the same thing.
- Relating to above, I had once calculated that the explosion at Nagasaki was the result of 0.7 grams of matter changing to mass. I held up a peanut—about that much mass that had changed to energy. There is a lot of energy in mass.
Next we talked about Spontaneous Symmetry Breaking. (Thisis the Higgs mechanism. )
We tried to understand the Higgs Mechanism:
We envisioned a Mexican Hat Type Roulette wheel with marble. (I had found several pictures which I projected on my computer.) The Marble balanced on the very top of the Mexican Hat is a wavefunction that could give different solutions, like Schrodinger’s equation. The Mexican Hat represents energy level. The marble somehow comes to sit on top of apeak (or is it peaks?) like the peak(s) of a Mexican hat. At this energy, all particles and energies merge, because their energies are so high. The universe is stuck there, because the barrier on the top of the ‘hat’ holds it. If the wave function slides off peaks to lower energies the properties of the particles and forces emerge. We are stuck with result (unless it was all decided from the beginning and it couldn’t happen any other way!).
This is important, because it seems it is here our familiar properties emerge, the ones so important to chemistry and bonding. We (salon members) were undecided: was the structure of the universe there from the beginning ready for the ‘marble’ to find its level, or was the structure decided in the Symmetry Breaking? (We envisioned the universe’s wavefunction stuck in the artificial high level, and rolling to a lower level. Was the surface (floor?) of that lower level there all along? One member seems to think she’d been told in an earlier seminar, that the structure of the universe was there; I had envisioned it being formed now. At any rate, the properties of the universe were not evident at the high temperatures following Plank time. At the very beginning there is superforce, superfield; after cooling and symmetry breaking, all the different forces and particles emerge.
- For example—one wavefunction split into 3 entities: the photon, the W and the Z particles.The photon acquires no mass, but acquisition of mass by W, Z breaks symmetry: before symmetry breaking one kind of particles with no mass, after, three different forces, 3 different particles, with different masses.
- The Mexican Hat Type Roulette is the underlying shape of our universe. How many peaks does it have, what shape (and was the shape there all long?)? We don’t know. At high energy, its shape doesn’t matter. The theorist ‘infers’ the shape to explain the particles we see. (However to account for ‘every thing’ we see, theorists must have surface in more than 4 dimensions.)
A Higgs Boson was made every time symmetry was broken. They are massive!(Compared to other particles, that is) Scientists found one!!!! (in a particle accelerator) July 4, 2012, scientists at CERN announced that they’d found a particle that behaved the way they expect the Higgs boson to behave.
Bottom line as I understand it: At super high energy, the universe was one pure force. At lower energies, the universe cooled into a certain structure, which included particles and forces. Maybe the structure was pre-determined, maybe it was pure chance that we got the forces and particles we did, maybe something in between these two extremes.
We (the salon members) went on: At approximately 10-34 seconds: the Universe is filled with a quark-gluon plasma. INFLATION begins (as a result of Higgs). Here is an explanation (not accepted by all scientists!) The Mexican hat has a depression in its top. Our universe’s wavefunction (the marble) gets stuck in it as universe cools. It is stuck so it has artificially high energy. The universe is cooling but its wavefunction is stuck at high energy! Things go rapidly awry. Normally, expansion would dilute the universe’s energy smoothly. This ‘artificial, “vacuum” ‘ energy does not diminish. It is like a car with accelerator stuck. The universe doubles its size in a trillion trillionth trillionth of a second, and again, and again, and again. The energy density also doubles. The extra, artificial ‘vacuum’ energy becomes, eventually, particles (and galaxies, etc.) This explains why universe is flat and looks the same all over and has so much density of particles and objects. In addition, the mechanism of inflation is needed to provide symmetry breaking that gives ‘Spin’ . Remember, spin is essential to explain the structure of the atom.6 **
How did inflation stop?? In some theories, tunneling is responsible. Tunneling is a quantum mechanical phenomenon. A tiny portion of an object’s wavefunction exists at an unlikely position. The wavefuction symmetry breaks there, in the unlikely position. So, the wavefunction of the universe tunnels through the barrier that kept the universe at artificial high energy.
Now we talked about the Higgs field, which we gathered was different from the Higgs mechanism. The Higgs field gives particles mass. It affects different particles in different ways. Photons can slide through unaffected, while W and Z bosons get bogged down with mass. Particles got mass by interacting with the Higgs field, which occupies the entire universe. (Like the other fields covered by the standard model, the Higgs one would need a carrier particle to affect other particles, and that particle is known as the Higgs boson, the one that was found. ) Particles that interact with Higgs field have mass, more strongly they interact, more mass. Sean Carrol has a‘Celebrity Crossing Room’ analogy. Tom Cruise (a celebrity) would interact with the people in the room strongly and be slowed. I would not react with them, and could travel freely. (I would have less mass.) Why do some particles interact more strongly—we don’t know.
We talked about the Higgs search. It was an attempt to make waves in the Higgs field to prove it’s really there. I was surprised to learn that protons and neutrons and other composite particles (made up of quarks, for e.g.) get most of their mass from other mechanisms. But electrons and other elementary particles do get their mass from the Higgs field. If the electrons had no mass, they would not keep their places in atoms, and matter would explode. (see salon 1) Life as we know it seems to be dependent on our Higgs field.
This is not mentioned much in literature, but it was mentioned in a book by Sean Carrol. From P. 146Sean Carrol’s book: The absence of Higgs field would mean that the quarks and hadrons would have slightly different mass (they get some mass from strong nuclear force) and that would affect atoms slightly. Any change to the mass of the electron would be hugely significant. Change the mass of the electron just a little, and all life would instantly end.
Bottom line: change the Higgs field and carbon would not be the element of life.
Now we moved to ‘Universe is less than one/ten thousandth second old’:
Hadrons (neutrons, protons) form. They are made from quarks. One billion and one baryon forms for every anti baryon. Obviously this is important for both the atom and the universe. (If there weren’t an excess of baryons, the anti and regular would have annihilated each other, and we would have no baryons)
To end the salon, we talked about some larger particles that are found in particle accelerators, the particle zoo ‘standard model’. The mass we see on earth is made of atoms, which are made of protons, electrons and neutrons. However, scientists have found larger analogs of these in particle accelerators (i.e., they don’t exist except at high energies.) There are 3 families (3 flavors. )
- proton, neutron electron
- Bigger proton, neutron electron
- Even bigger proton, neutron electron 3 families!
The important thing is all this emerged very early, and apparently via symmetry breaking. Before that, all these things were equal.
My important take home message: The Higgs mechanism seems to have determined the properties of the electron. The electron is important for chemical bonding. Why and how did the properties emerge in just the way they did? Was the structure ‘pre-determined’? Spin, apparently emerged during inflation. Because of the properties that emerged, the position of the electron in the atom is hugely far away from the nucleus. This is essential for chemical bonding (and life).What happened? Was it random? What do scientists know about it that I haven’t discovered?
If you scroll to the fun quiz we took at the end of the salon, you see we imagined an atom made with one of the larger ‘electrons’ from the second family (the muon electron) and the third family, the Tau electron. We learned that with these massive electrons, the atom would be tiny! The electrons would all sit close to the nucleus and there would be no bonding. The exact properties of the electron is so important.
As an appendix, we got a chart with some details about the standard model, which we went through briefly. The chart was from the internet, anyone can find one, just google ‘standard model’. With the chart in front of us, we covered these details:
- Fermion vs. Boson
- Fermions have spin 1/2 (or 3/2, 5/2) and cannot occupy the same state at the same time.1 They take up room. (Electrons are fermions. So are quarks, which make up protons and neutrons.) THEY ARE THE STUFF WE RECOGNIZE
- Bosons have spin 0 (like Higgs), or spin 1 like photon, or spin 2, (graviton) and don’t have to take up space. They can pile on top of eachother.2,3
THEY CARRY THE FORCES WE RECOGNIZE
- FERMIONS CAN BE: Baryon (like protons) vs. Lepton (like electron).
- Baryons can feel strong nuclear force. You find them in NUCLEUS. They are ALL made of QUARKS. They tend to be massive.
- Leptons do not feel strong nuclear force. THEY DO NOT HAVE TO BE IN NUCLEUS. If they are charged (like electron) they hover around nucleus. If they are not charged, like neutrino, they fly off into space and they do not seem to affect our world. Elections and neutrinos are almost massless. ELECTRONS MAKE A BIG DIFFERENCE to our world.
- Bosons carry forces:
- Gravity field, gravitons are ripples in field (not needed in or description of carbon 12)
- Electromagnetic field: photons are ripples (particles when you look! See salon 2)
- weak, or ‘electro weak’ W+, W-, Z (this are actually the same as photons, only massive. The acquisition of mass by W and Z happened during symmetry breaking. (Govern certain decays; carbon-12 doesn’t depend on them much)
- strong: ripples are gluons (these are mesons)
- Higgs boson isn’t one of our ‘forces’. It’s field in non-zero in empty space; it broke symmetry and gave us mass.
- Every field is there whether or not there are particles interacting with it. We don’t understand them more fundamentally—maybe we will some day
- All forces are interactions with a field. Matter is interaction with Higgs field
- 3 families (3 flavors) Only the least massive are seen. The others are made in particle accelerators.
- With no Higgs field, the three flavor of electron would be identical. Higgs breaks symmetry.
Bottom line: without the properties that arose during symmetry breaking, the atom would not form as it did.Things that are important for carbon that came about via symmetry breaking.
** spin and the early universe: Fermions and bosons are 2 aspects of a single entity. But—this meant extra dimensions had to be added to our ‘Mexican hat’. The quantum arrow can switch direction in extra dimension to change boson into fermion. Fermions have quantum arrow in an extra space dimension. Need to turn around twice to face forward. 2 Without exclusion principle, (fermions can’t pile up) electrons would glob onto nucleus. Quarks would instead of making protons, would make vast globs of quark stuff.5
OUR QUIZ and some FUN FACTS (we had fun with a quiz, we answered these critical thinking questions):
We used some household objects to show that even though the electron is tiny compared to the nucleus, its wavefunction is huge, but the massive electron in the bigger families would have a smaller wavefunction. I held up balloons, cotton balls, tic tacs and large sponges, and had salon members guess which wavefunction went with which family.
Fun Facts
- Scientists made anti helium!!!!!8 In 1965 : two antiprotons and antineutron combined to form anti helium
- Different carbon:
Muon is the ‘electron’ of family 2. Muons have mass 207 times the mass of electron.
They have made muon atoms—the muon replaced the electron!!!!! 9
(It only lasted 1/500000 of a second.) HOW WOULD IT BE DIFFERENT?
Tau lepton is 3500 times as massive as electron . Bigger than proton!
They have not made Tau lepton atoms.
How would atom be different if electron were Tau lepton?
That was our salon 3! To me, the most important point is that the Higgs mechanism and Higgs field are responsible for the properties of the electron, which is in turn responsible for the carbon atom and life.
Notes: I used three books plus some web sites.
IssacAzimov: The Atom
David Lindley: The End Of Physics: The Myth Of A Unified Theory
Sean Carrol: The Particle at the End of the Universe: How the Hunt for the Higgs Boson Leads Us to the Edge of a New World
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- Heisenberg uncertainty: We can’t have a single point at start of universe singularity. There is a point at which theories no longer work—when size of universe is as small as it can be—further implies that universe is smaller that quantum mechanics allows-a contradiction—called plank time—we can’t understand the universe when it is younger than plank time
- Interchanging fermions would leave configuration same but wavefunction must be multiplied by negative 1 and only 0 can be multiplied by negative one and be the same. It has to spin around twice to bring spin to the front, so interchanging it would leave it backwards. (fermions would be able to ‘pile on’ if our world was 2 dimensions)
- P 286 Sean Carrol
- spin 0: 1 spin state spin ½: 2 spins states. Proton has spin ½and 2 spin states. (this happens to be important for MRI)Spin 2: 4 spin states. Etc
- Lindley p 178
- Lindley p 189
The extra dimensions that give fermions spin ½ means that there must be a partner to the electron that is spin 1, a boson, that doesn’t obey exclusion principal. They are called super partners , Lindly, page 192. It is very massive because of a un-symmetry in Higgs mechanism, and we don’t see it. The search for super partners in the most important search now!
- Lindley p 190
- Azimov p 223
- P 241 Asimov
- This is more about fields from Sean Carrol : Symmetries give rise to the forces in nature. How? Guage symmetries—I can change my system at my local point and compare to yours. It comes with a connection field that lets us compare. The connection fields are the boson field (the force carrying fields). They push particles in different directions depending on how they interact. For local forces, must be (almost) massless bosons, so can stretch over long distances
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