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Inertia: The Mass, The Mystery

Matter, it’s what’s for dinner. It’s what’s not for dinner. It’s what makes up all the things that are thingy. It’s all those elements you learned about on the periodic table. It’s why you can’t trust an atom (they make everything up). How much matter exists inside your pumpkin gives your pumpkin its mass. And, how much mass it has is directly related to its inertia.

Years of teaching freshmen high school science has left me with some indelible memories. One of these concerns the definition of Inertia. I ask them each year, “What is Inertia?” Invariably, at least one of them says, “Oh, oh, I know, I know.”

“Yes,” I say, “Go ahead.”

“Ok, Inertia is a property of matter,” they say, smiling, knowing they are correct.

“Ok,” I say, “but what is it?” At this point, their smile turns into a smirk, because they think I am joking.

“I just told you, It’s a property of matter. Bill Nye told me!”

‘Thanks Bill,’ I say inside my head, ‘Thanks for that gem.’ Out loud I say, “Ok, so thanks to The Science Guy you know it has something to do with matter, but what property are we referring to?” And then, the confusion begins. It takes them a while to get over the fact that Bill didn’t really teach them all that much in this case. Eventually, we establish that the property refers to a certain resistance that a massive object has when you try to change its motion.

I pass around a tennis ball and a civil war cannon ball, both roughly the same volume and I ask them to (one at a time) shake them back and forth in their hands. The shake test, I tell them, can be used on Earth and/or in space to detect the amount of matter present in an object. The more matter (mass) in an object, the more it will resist you when you try to change its motion. It doesn’t matter where you are, the cannonball is harder to shake back and forth. It has more mass and therefore more inertia. It is both harder to set into motion and harder to stop once it is already moving. A speeding train is just as dangerous in space as it is on Earth. Its inertia is so great that you will not simply stop it by putting your hand out in front of you. You need to get out of the way. Likewise, moving an elephant is almost as hard in space as it is on Earth. The difference is only due to the friction forces the elephant has with the ground when you are on Earth. In space, without ground friction, there is still so much mass there, it will resist your push and may move a bit, while you will move drastically the other way (you both have spacesuits on by the way. We wouldn’t want to harm anyone in our mental exercises).

Great, now that you’ve been reminded about the basics of inertia, let’s take a deeper dive into physics. What makes mass do this? How can it possibly resist changes in its motion? To answer this question, we must first ask, what is matter made of?

Atom, Atomic Structure, protons, neutrons, electrons
FREEP!K @brgfx

Matter is made of atoms, you say. Ok, what are they made of? Protons, neutrons, and electrons, you answer. Great, but (and you guessed it) what are they made of? You do some research. Most of us are not aware of this, but protons and neutrons are composite waves/particles made out of many quarks and gluons which vibrate, exchange energies, and pop into and out of existence while maintaining an overall net number of three quarks. For protons this is two ups and one down quark and for neutrons it is the opposite, two downs and one up. Gluons are exchanged back and forth between the quarks and help hold the proton or neutron together (I mean, there’s a reason they call them Glu-ons, right?). While protons and neutrons maintain about the same mass of 1amu, electrons are much less massive, having 1/1836 of an amu. What is an amu, you say? Well, since you asked, it’s based on a typical carbon atom, Carbon-12, which has a total of 12 protons and neutrons in its nucleus. Take that mass, divide it by 12 and you get 1amu, which equals about 1.67x10^-24g. Yes, we are talking about really tiny things here. It would take about 600 sextillion (a number with 21 zeros after it) to make 1 gram of protons! Makes you wonder how many protons you had for breakfast, doesn’t it? Ok, maybe not. But seriously, in all things you can touch are uncountable numbers of protons, neutrons, and electrons.

Ok, you say, so now you are going to tell me the quarks are made up of even smaller particles, right? Sorry, wrong. In all of our experiments and even in our theories, quarks are currently believed to be what we call elementary particles, as are electrons. Fundamental particles, these are what Democritus imagined when he originally named atoms, “atomos” (meaning indivisible in Greek). Einstein tells us, with his famous equation, E = mc^2, that these elementary particles (with mass), just like all particles, are convertible to pure energy (without mass). At the quantum level, the smallest levels of existence, energy sometimes creates particles (with mass), and particles are sometimes converted into energy (without mass). Particles are sometimes condensed and sometimes spread out (and we call them waves). You and I and every thing that we see are made of these strangely-acting particles/waves, this energy in another form. It has mass.

When energy becomes a particle, how does it suddenly gain mass? Good question. We believe this has to do with something called the Higgs Boson. When particles interact with the Higgs Field, they gain mass. The more they interact, the more mass they have, as explained here. Yes, this is all still theoretical, but all the evidence we have points in this direction.

Now that we have a better idea about what mass is, we can attempt to tackle the inertia question: what makes matter capable of resisting changes in its motion? To be clear, a change in motion is more accurately described as an acceleration. We are slowing an object down, speeding it up, or changing its direction. Try out this thought experiment: put some gas in a massless container (I know, cheating, right?), and at any given temperature the pressure on the inside of the container will reach an equilibrium where it will not be pushing the container in any one direction. Now, shove the container to the right. Suddenly, the pressure increases on the left side of the container and decreases on the right. This happens because at any moment, if before the shove, particles were hitting the sides at about the same rate, when the left wall approaches the particles and the right wall recedes from them, a pressure difference is established. A net force on the container pushes to the left, acting just like inertia. What’s fascinating is that you can do this same experiment with any type of matter (with the same mass) and you’ll get the same result, and, wait for it, you can do it with light too! Even though light has no mass, it still can act like

Solar Sail, Light Sail, Light Pressure
Light Sail, Credit: MacKenzi Martin

particles (photons) and exerts pressure on objects. Have you ever heard of a light sail? Light has momentum, and therefore, even energy can experience inertia! Not convinced? Check out this great PBS video. The fascinating thing to realize here is that none of these objects (or even the energy) had inertia to begin with; inertia, it turns out, is an emergent property. Accelerate the object, or the light, and it responds with inertia.

Ok, so we have particle/waves that have mass because of the Higgs Boson and display inertia when accelerated; now I suppose you’re going to tell me that Einstein is responsible for figuring this all out. Yes and no. Einstein died before Higgs even proposed there might be a boson that gave particles mass. However, he did have several important connections to the inertia part of the story. First, his discovery of how the Photoelectric Effect required light to behave as particles (photons), which led to the currently accepted particle/wave duality mentioned earlier. Second, his Equivalence Principle, which we’ll get to in a minute, solved an inertial mystery that had been around since the time of Newton.

Newton’s First Law of Motion concerned inertia: a stationary object will remain still, a moving object will keep moving. Exert a force on it and it will change its motion according to his Second Law of Motion: a = F/m, an object accelerates in direct proportion to how much force is applied to it and inversely proportional to its mass. If a similar force is applied to objects with different masses, the object with less mass will accelerate that much more (because it has less inertia).

Great. Now, Newton also put mass into his gravity equation: F(g) = Gm1m2/d^2, or the force of gravity on an object is equal to the gravitational constant multiplied by the masses of the two objects involved, divided by how far apart they are, squared. Now, ignore the math if you want to, but here’s the mystery: when Newton calculated an object’s mass due to inertia (when a force was applied to it), it always came out to be the same amount as its mass when he used his gravitational force equation. In Newton’s world of fixed space and fixed time, where gravity is a force, there was no reason that these numbers should be the same. Thus, the mystery.

Cue Einstein (about 230 years later). The mystery puzzled him, and may have helped him figure out a founding pillar in his General Theory of Relativity: the Equivalence Principle. In it, Einstein imagined a spaceship in deep space, and a person inside the ship with no windows. Have the ship be stationary, or move at any constant speed, and the person inside

Einstein's Equivalence Principle, acceleration, gravity
Einstein's Equivalence Principle

would feel weightless. However, accelerate the ship at 1g (the same as acceleration due to gravity on Earth’s surface) and the person inside would have no way of telling the difference between the room on the ship and a room on the surface of Earth. Thus, Einstein made the leap showing how gravity can be thought of as acceleration (it is equivalent in a limited, local environment). Given this equivalence, Einstein reasoned, inertial and gravitational mass must also be the same.

I invite you now to close your eyes, relax and notice that there is currently a force on your body. Go ahead, do it now. I’ll wait. What direction is this force on you? If you said “up,” then you are among the few who did. Most of us have been raised on Newtonian mechanics and his Law of Gravity in which the force is downward. However, even Newton would agree there is an upward support force being exerted on your body by the ground (or your chair, as the case may be). Einstein noticed this too, but disagreed about the downward force. He would say, look, you feel heavy because you have inertia and there is an upward force being exerted on your body. Any time a force pushes you, your mass says “hold on now, there’s some inertia here you’re going to have to deal with!” The same is true in an accelerating car, or a spaceship. You feel pushed back in an accelerating car. You are currently feeling this in a vertical direction because spacetime is curved by the Earth and the Earth’s surface is pushing you up. When you are falling, you no longer have the sensation of being pushed on, because you are not! There are no forces on your body when you are falling. Freefall is just that, free of force (we’re ignoring air resistance here).

Ok, you say, reasonable enough. But, you say, if Earth’s surface is pushing me up, and there’s no downward gravitational force to balance it out, how come we aren’t moving upward, accelerating upward? Doesn’t Newton’s Second Law still exist? Indeed it does. Absolutely. Einstein would invite you to think about what you are accelerating in relation to. He believed that there are no frames of reference that are better or more correct than others. For example, drop a ball off a cliff and it appears to fall, to accelerate downward, if we are standing on the cliff looking down at it. Put a camera on the ball (assume it’s not rotating) and you will see that the Earth is what accelerates upward when the ball “falls”. The ball is simply following the spacetime curvature, a geodesic. The Earth is being pushed up by electromagnetic forces of repulsion all the down to its center. These forces keep the Earth from collapsing in on itself, as it would normally do based on its self-created spacetime curvature. In order to keep from following this curvature, to not succumb to freefall, the Earth’s surface accelerates upward at a rate of 9.8m/s/s, as explained by Derek Muller in this excellent Veritasium video, Why Gravity is NOT a Force.

Since gravity is not a force, the strict definition of weight (how much gravity pulls down on you) falls apart. When you step on a scale, the scale has a reading due to the ground pushing you up, and your responding inertia. That’s it. Your upward acceleration can be seen as an acceleration away from the geodesic, away from the path you would take if no forces were acting on you. Spacetime curvature can be interpreted as space moving, contracting. It accelerates down through the ground, towards the center of mass. With respect to the curved spacetime, you are accelerating when you stand on Earth’s surface!

So, the next time you get tired just sitting there, you can blame it on the ground. It was pushing on you. Invoke inertia. It's ok, everyone does it, even if they don't know it!


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