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!