Meanwhile...

Obituaries are a thing.

America is an odd culture. We avoid the topic of death like a plague yet the Internet is packed with discussions of people who read the newspapers (and Internet) obituaries everyday of their lives and why they do it. A cursory examination of Google Scholar did not turn up any studies, nor could I find any data, on people who read obituaries.

There are many citations on Google Scholar about obituaries, though...how to read them, how to write them, how and why to research them, what they tell us about the people they discuss, what they tell us about society in general.

It's interesting reading. You might take some days to study obituaries.

Why am I talking about them? 

Well, it's a lead in to my excuse for my absence from this blog for a couple of months.

First, a very close friend died. Learning can be…somber, but it's always potentially edifying. I learned that, as you get older and old friends die off, it gets easier to shrug it off. Bereavement is about loss, not pity for the deceased. After you loose enough, you get used to it and life teaches you that everything isn't necessarily about us. The world goes on.

When you know you are dying, you can either say, "I'm dying," or "I'm going to live until I die." Mike showed that it is entirely possible to do the latter with all the determination of a 20-something with nothing but life ahead of them. Another person I knew who "died well" was my father. You can learn a lot from folks like that.

A week later, I went to church and couldn't sing. The next day, my annual episode of bronchitis was in full swing. I have learned to expect it every year. Some truths are just nasty. So, for a month, I sat around hacking my brains out and wearing myself down.

A close friend and college math professor was scheduled to attend a mathematics conference in town and I had said that I would go with him. It was the week after my hacking cough had let up and I was flat worn out but I keep my word, and I really did want to go since I'm an amateur mathematician and it would give me something to blog about. I had the opportunity to go as his guest, which meant a 95% discount. On my pension, it was an offer I could not refuse.

Of course, it was mostly sitting through lectures and strolling around math art exhibits and vendors (I bought gifts for folks). There was a surprising lot about my own, not so deep interests - math education and statistics. So, at least I enjoyed further abrading my life force. And I got some close-ups of the big blue bear.

At least, between bear and horse, the more personable one is the more accessible.

Finally, I'm on the mend and I've even knocked out another terminal hike (that leaves three to go) and that will be the subject of my next blog.

I recommend not avoiding mental adventures like community lectures and conferences because you think they will be boring. It's all mindset. Things that you expect to be boring usually are.

Shake out the obituary section of a newspaper. Look at some obits online. Do they have a consistent structure? Do you know an obituary reader? If so, why do they enjoy reading obituaries? What do obituaries tell us about our attitudes toward death? What do obituaries tell us about our attitudes toward life?

Orbits

Before we look at what's up there, we need to understand how what's up there works. The same forces that operate down here drive what's up there. There's a problem though. An orbiting planet isn't the same thing as a mass whirling around on a string. For one thing, the string constrains the motion of a whirling object to a strict circle while gravity does not.

Frankly, it's hard to study orbital mechanics on Earth. Henry Cavendish finally nailed down the force of gravity, Newton's universal gravity constant, 71 years after Newton's death. He did it by suspending two very heavy objects at the opposite ends of a rod by a hanging, thin rod, and setting it oscillating. Then he did it again, setting a massive object near one of the hanging weights (the setup is called a torsion pendulum and its exquisitely sensitive.) The difference in the periods of oscillation gave him the information he needed to calculate the gravitation constant.

Other than that, have you ever tried to bring a planet into your bedroom?

Barring that, I have my gravity simulator (you saw it in the blog "Something about mass") and, although it isn't a perfect model of planetary orbits, it's surprisingly good.

First, let me point out that Newton learned more about mechanics by looking at the planets than by watching apples drop off a tree. As for the value of the acceleration of an object under the influence of gravity, Galileo had already done that work. Newton's first law of mechanics is actually Galileo's law of uniform motion. When Newton said, "If I have seen further, it is by standing on the shoulders of giants," he meant it quite literally. Newton was not a man given to bouts of humility.

Kepler's laws of orbital mechanics came before Newton. Newton's job was to tie it all together and figure out how the mechanics of planets was the same as the mechanics of an ox cart or that of a falling apple. So let's play with planets.

[Small ball around large ball]

The two balls are steel, so they're the same density. They don't orbit for long because they're close and exert more "gravity" and, more, because the model creates a lot more friction than the vacuum of space.

Newton deduced that the force of gravity between two masses increased with the product of the two masses and decreased with the square of the distances between them. He threw in a "universal gravitational constant" that makes the units and scaling work out. That's what Cavendish figured out years later.

The shape of the orbit is clearer when a smaller ball (BB) is used.

[Tiny ball orbiting around large ball]

Kepler worked out the shape of planetary orbits from the massive number of precise observations made by his mentor, Tycho Brahe. His first of three laws stated that planets move in elliptical orbits. Notice that, regardless how I start these balls rolling, they end up in elliptical orbits. That's not a result of the way the fabric is stretched. I tried to make sure that it was stretched evenly in the embroidery hoop.

For planets, as well as balls in the gravity simulator, the large ball is at one of the focuses of the small Ball's elliptical orbit.

Also, watch the way the ball speeds up in those tight turns. Kepler's second law states that the planets sweep out equal areas in equal times. That means that, when the planet is farther from the sun, it moves slower. 

His third law is harder to see on the simulator, but it says that, of two planets, the one orbiting further from the sun will have been a longer period (year) than the other.

[Balls of equal size]

When two balls of equal size are on the simulator, they orbit each other. Actually, that's true of all the orbits. It's just that, when the difference is large, it's hard to see the larger ball move. Even in space, planets and stars orbit around common centers. For instance, binary stars sling each other around a common center.

[Three balls of different density]

Here, I roll a small steel ball, an aluminum ball, and a wooden ball around the large steel ball. You probably could have guessed that the less dense wooden ball would orbit the longest. Also, notice that it's orbit is less elliptical.

[Tiny ball with different forces]

Here, I tried to roll the ball at different speeds (including, off the simulator). Notice the shapes of the paths. Even the ball's path at "escape velocity" is curved.

In fact, not all orbiting bodies take an elliptical orbit, but they do all follow conic curves. The Earth's orbit is almost, but not quite, circular. On the other hand, comets and other "space junk" may just graze the gravitational field of the sun on a hyperbolic curve, or loop around once on a parabolic path, and never return.

[Swarms]

A collection of BBs make a nice little solar system. The really fascinating thing is when they are going in opposite directions.

[Two swarms]

Notice how they end up all going in the same direction! Ever wonder why all the planets orbit the sun in the same direction? Remember that, not only the sun is pulling them, but they are also pulling each other. It turns out that star systems are self-organizing.

The early history of Earth was violent. Collisions were common in the early solar system. In fact, our moon was probably the result of such a collision, a chunk knocked out of our planet by a traveling piece of space debris. Over time, such collisions became rarer. You've just seen one of the reasons why.

The gravity simulator is fun and offers a lot of possibilities for studying gravity and orbital mechanics. For instance, you could easily build a large version using a hula-hoop...or a trampoline! You might also check out different materials for the membrane. Plastic food wrap causes less friction.

Something about mass

I've had the delight of playing with a variety of balances from analytical balances that have to be protected from drafts and are precise to fractions of a milligram (that's a thousandth of a gram), to standard laboratory balances that will give you, oh, a few hundredths of a gram. And I've had several balances that came with various science kits. You won't find a statement if precision for those.

In one of my pharmacy labs, we had to synthesize aspirin and then purify it...because then we had to take it and, although the byproducts of aspirin are not horribly toxic (they didn't tell us that beforehand), they're not ideal snacks for happy-happy time. After taking our own aspirin, we measured the rate that it went through us. We were the people walking around campus with brown paper bags full of amber medicine bottles full of urine. Precision was important, but the laboratory scales gave us plenty for what we needed.

One of the most precise scales I've seen from a kit is the one from Penny Norman's Science Wiz Physics kit. Here, I use it to measure a gram of table salt.

[A gram of salt]

All this begs the question, "What is mass?"

I remember the stock answer from school, "mass is the amount of matter in a body," but I also remember the definition of matter, "Matter is that which has mass." That sounds a little too convenient...too circular. And what did they mean by "amount"?. Look at the picture at the top of this article. There's a gram of brass in the reference mass and a gram of table salt. It sure looks like there's more table salt (by volume) than there is brass.

I'm going to claim that the gram of table salt contains about 1x 10^22 molecules of sodium chloride and, to explain that, let me start close to the bottom.

Atoms are made of electrons, protons, and neutrons. Protons and neutrons are made of various other debris, notably quarks, but we don't need to go that far. A proton has a mass of 1.6726219 x 10^-24 grams. A neutron has a mass of 1.674927471 x 10^-24 grams. An electron has a mass of 9.10938 x 10^-28 grams. Electrons don't have enough mass to even consider, so let's forget them for the time being. The mass of the other two particles are so similar that we can just define an atomic mass unit as the mass of one proton or neutron. 

Table salt is impure sodium chloride and, to simplify things, let's ignore the impurities. What's the mass of a sodium atom? It has 11 protons and 12 neutrons so the mass of a sodium atom is 22.98976928 atomic mass units. Wait a second….but that's what my periodic table says. The fact is, the most common sodium atom has 11 protons and 12 neutrons, but there are other kinds of sodium atoms in nature that have more or less than 12 neutrons. It's the number of protons in an atom that makes it the element that it is. The number of neutrons can vary and you call the different kinds of sodium "isotopes" of sodium. If you take an average of the atomic masses of all the different isotopes of sodium according to their relative prominence in nature, you come up with 23.98976928 atomic mass units.

Avogadro's number is 6.0221409 x 10^23. That's the number of particles (atoms, molecules, etc.) in a mole of a substance and a mole is the number of grams that is the same as the number of atomic mass units of one particle. Since the atomic mass unit of sodium is about 24 and the atomic mass unit of chlorine is about 35.5, the atomic mass of sodium chloride (one sodium atom and one chlorine atom) is about 59.5. A mole of sodium chloride is 59.5 grams and a gram of sodium chloride is 1/59.5 mole. That means that you can divide Avogadro's number by 59.5 to find the (approximate) number of molecules of sodium chloride in a gram - 1x 10^22 molecules.

All of which gets us no closer to understanding what mass is. It has something to do with gravity. You find the mass of an object by comparing how hard gravity pulls on it to how hard gravity pulls on something else.

That "pull" is a problem, too. How does anything pull on anything? You might think you pull a wagon, but think again. Where do you apply pressure to the wagon...on the inside of the handle. You push against the inside of the wagon's handle. Can you really pull anything?

This bothered Isaac Newton all his life. He worked out all of how gravity works. He knew that mass is connected with gravity...somehow. By figuring out how planets have to interact to stay in their observable orbits, he knew that the force of attraction between bodies had to be the product of their masses divided by the square of the distance between them. A constant had to be thrown in to make the numbers work out but Newton never knew the value. Henry Cavendish came up with the value in 1798, 71 years after Newton's death.

What is gravity? The best Newton could do was "action at a distance". He was not amused.

Over the following years, there were all kinds of weird theories. One was that, as an object moved through some strange "ether" that filled the universe, it flowed around and would catch other objects up like things are pulled along in the wake of a fast moving boat. Imagine the dismay at the end of the 19th century and the beginning of the 20th when scientists had to accept that the universal ether does not exist.

At about the same time, Albert Einstein came along and figured out (part of) how it works. Here is mass and gravity according to Einstein.

[Gravity according to Einstein]

General and special relativity are weird...granted, but they are the most experimentally verified parts of physics, so there's little chance that that weirdness isn't a real part of our universe.

The gravity simulator above is a collection of Legos constructed to support an 11 inch embroidery hoop with a square of Lycra stretchy fabric clamped securely in it. The gooseneck assembly hanging over it holds my cell phone video camera.

Einstein's idea was that, instead of gravity being an attractive force between massive objects, any object with any mass distorts space around it and, then, other objects fall into the distortion just like the small ball bearing fell toward the large ball bearing.

The simulation isn't perfect. It suggests that mass distorts space into another spatial dimension. That isn't necessarily so.  It may just distort space into itself. The distortion is called a field, and there are other kinds of fields. If you set a magnet near one of these steel ball bearings, the magnet and the ball bearing will come together. 

This "action at a distance" of Newton can now be explained as a "falling together".

We're certainly going to be looking a lot in the future at these "falling togethers" and you'll see more of my gravity simulator very soon.

But the weirdness deepens. I've heard physicists express the conviction that, matter and energy are not the realities of our universe - the only things that are real are fields  So why do matter and energy seem so real to us and fields are so hard to wrap our brains around 

That has a lot to do with how our brains code the world around us. Brains are primarily interested in survival and the important things in our world related to survival are things like not being crushed in rock slides or falling off cliffs, building houses, finding food and water. To survive, we most need to be able to handle matter and energy. If fields are at the bottom of it all, that's interesting, but it's not what we need to pay attention to, so as humanity grew up, our brains learned to pay attention to survival things. 

We can measure fields, but we can't perceive them directly.

So, what is mass?

In 2012, physicists at the giant international particle accelerator at CERN confirmed the existence of a subatomic particle called the Higg's boson which is responsible for the attribute of matter called "mass". It creates a field in what we perceive as matter called the Higg's field, and that is what we recognize as mass.

This exercise in weirdness is as far as we are going to go in this blog. I try to crack open the world to show you how it works, but I'm a social psychologist that just happens to have a lot of other interests and I have my limits. Do physicists actually understand the weirdness they're dredging up? Maybe, maybe not, but all they do know makes the weirdness a necessary corollary. I've also heard physicists say that, if the universe was the way it seems to be, it wouldn't exist, so we have a ways to go.

It's only fair that I don't leave you thinking that there's no mystery in the universe...that everything is straight forward and that I can just open anything up and let you see inside.

But now, I'm going to back up to the part I can poke around in and start at the beginning...pretty much the world of Newton. Things will get quite weird enough.

As Jason Nesmith says, "Never give-up, never surrender!" (movie reference, there). Physics can be weird, but don't let that stop you. Amateur scientists make important discoveries and any swimmer will tell you - going out into the deep end is fun. The Teaching Company, MIT Opensourceware, local colleges and universities, many other resources are out there waiting for you...waiting to show you how deep you can go…..oooh, scary!