A couple of days ago I was thinking, as one does, about the equivalence of gravitational mass and inertial mass. For those of you who don't know what I'm talking about, all mass has two properties:
- It is attracted to other mass (gravity).
- It resists having its motion changed (inertia). This is true even out in the deepest expanses of empty space where it's free of both gravity and friction.
- Quite remarkably, these two properties are exactly equal.
This is why a 10-pound bowling ball and a five-ounce baseball fall at the same speed if you drop them from the leaning tower of Pisa. The bowling ball has 32x more mass, so gravity attracts it 32x more strongly. However, it also has 32x more inertia, so it resists gravity 32x more than the baseball. Result: both balls fall to the earth at the same speed.
But then I got to thinking more. The source of gravitational attraction is the curvature of spacetime. But what's the source of inertial resistance? I fiddled with that a bit, trying to either remember or figure out the answer. Some quantum mechanical property? Just an uninteresting alternate way of saying objects travel on geodesics? Something to do with conservation of momentum and therefore the translational symmetry of space? Finally I gave up and googled it. And the answer is: no one knows.
Isn't that something? Inertia is everywhere and it's a concept so simple everyone understands it. But where does it come from? The precise equivalence of gravitational and inertial mass is one of those well-known mysteries because it's part of the familiar story of Albert Einstein's derivation of General Relativity. It even has a name. Until today, however, I had never realized that the very existence of inertia remained a deep and unsolved mystery of physics.
It's OK that we don't understand inertia. As I understand it, we don't understand gravity either. Apparently we have the Einstein theory of gravity and a quantum theory of gravity and have failed to reconcile them. One of life's oddities is no one doubts gravity, many people doubt evolution, but we understand evolution better than we understand gravity.
The contradiction between general relativity and quantum mechanics is that there is at present no successful quantum theory of gravity. Yet the existence of certain types of black holes seems to require both general relativity and quantum mechanics to explain, suggesting both theories are correct. It seems strange to our ape brains that gravity requires its own theory entirely separate and different from quantum mechanics.
Stephan Hawking used quantum theory to predict Hawking Radiation (what a coincidence that the phenomenon and the discoverer have the same name!) coming from Black Holes. It is not yet supported by empirical evidence.
I don't understand the math well enough, but there are areas where quantum mechanics and general relativity/gravity give contradicting predictions, so one or both need to change, but no one has come up with ways to reconcile the two. If you want a quick PhD, and to add your name to the sequence "Newton, Einstein, ?", just solve that problem. Good luck.
There is no quantum theory of gravity. There are several ideas but at most one of them can be true and perhaps none of them.
The reason it is hard is because quantum mechanics allows superposition. Consider the two slit experiment. To explain the resulting interference pattern, you have to assume that each photon went through both slits. It is in a superposition of states.
Photons possess energy and energy creates a gravitational field that depends on the distance from the source. But since the photon cannot be localized to a single slit, that means there are two possible distances so the gravitational field must be in a superposition of two states. But the Einstein field equation doesn't allow superpositions.
There is a fundamental incompatibility between their most basic assumptions, and no one really has a handle on that, after 100 years of working on it.
Higgs boson, right?
Yes, the Higgs field, moderated by the Higgs boson, gives rise to inertial mass. But there is presently no connection to gravitational mass. The Higgs boson itself has an inertial rest mass, measured at CERN to be 125 GeV (actually shorthand for energy as GeV, billions of electron-volts, divided by the speed of light squared). This is around 133 times the inertial rest mass of the proton or neutron, which make up most of the mass of atoms that we are familiar with.
The problem of reconciliation of all forces is in part due to the relative weakness of gravity as compared to the strong nuclear force that holds together nuclear matter. The ratio is around 10^(-39). Yeah, ten to the minus thirty-ninth power. So, gravitons (hypothetical quanta of gravity) have wavelengths measured in light-years, whereas a proton has a wavelength of femtometers (10^-15 m).
So, particles display quantum mechanical behavior quite naturally, while gravity always looks like a type of field.
The way I read Kevin's post, he's saying that inertia itself has no explanation, not just that the equivalence of gravitational mass and inertial mass. That equivalence is still unexplained, but I thought inertia is in some sense explained by the Higgs field. The answer isn't, as Kevin would have it, "no one knows."
The Higgs mechanism doesn't work for neutrinos. Nevertheless, they have mass.
"This is why a 10-pound bowling ball and a five-ounce baseball fall at the same speed if you drop them from the leaning tower of Pisa. ..."
I think the interesting property is that an iron ball, or a copper ball or a gold ball (and so on) all fall at the same speed. That a two pound iron ball falls at the same speed as a one pound iron ball doesn't seem surprising. Since you would expect two one pound iron balls to fall at the same speed and this not to change as you bring them closer together until they are mashed into one two pound ball.
"The source of gravitational attraction is the curvature of spacetime."
This isn't really correct. It is just a way of thinking about (visualizing) gravity's effects with our measly human brains.
To the extent any physics is correct, that statement is correct.
It is just a convention that inertial mass and gravitational weight are the same on earth.
On other planets the gravitational weight is different. In other words, inertia never changes but the weight of an object changes according to the gravitational environment.
A small object weighs differently on different planets, however, the same object always responds to the push of a rocket in the same way anywhere in the universe.
Gravitational mass is NOT the same thing as gravitational weight.
^^^^^^^^^^^^^^^^^^^^^ this
Anyone who doesn't understand the difference between mass and weight should not be posting on this thread.
Don't forget, your 32x more massive ball also has 32x momentum at the same speed of the 5 ounce ball.
Just a re-phrasing of that inertia thing--at rest, stay at rest; in motion, stay in motion, as per Sir Isaac Newton. (fig newtons named after town in Mass.)
If the Newton cookies were named for Sir Isac, they'd be Apple Newtons?
😉
via Wikipedia--Newton was incorporated as Cambridge Village (1681), renamed Newtown (1691) then Newton (1766).
Technically there's no such thing as gravitational attraction. Imagine a rubber cloth with a grid drawn on it. A mass in the middle will pull the cloth toward it so that the grid lines are distorted. A particle moving along the lines of the grid thinks it's moving in a straight line but in fact it's constantly deviating a bit towards the mass. At each step, the small deviation speeds up the particle so it accelerates as though there was a force pulling it even though the particle itself doesn't feel anything and is in free-fall. The distortion of each square is due to its connection to its neighbor. When you move a mass, the change in geometry spreads out at the speed of light which is how gravitational waves form.
Perhaps people have been too lazy to figure this out?
Gravity is not a force, Because we live in curved space, we are always falling and the only thing that stops us, for example, is the floor. We move along a geodisc- all objects with mass do the same.
"Gravity, said Einstein, actually moved matter along the curving pathways embodied in spacetime — paths imprinted by mass and energy themselves. As expressed decades later by the physicist John Archibald Wheeler, mass grips spacetime, telling it how to curve, and spacetime grips mass, telling it how to move."SCIENCE NEWS
"Gravity is indeed a real force, but not in the traditional sense. In other words, gravity is not a direct, classical, action-at-a-distance force between two objects. However, in the broader sense, gravity is indeed a force because it describes the resulting interaction between two masses."Texas A&M
Did Einstein say gravity is not a force?
Einstein showed mathematically that gravity is not really a force of attraction between all objects with mass, as Newton thought. Instead, gravity is a result of the warping of space-time. Einstein's ideas have been supported by evidence and are widely accepted today.CK.ORG
Are you sure about that Kevin? I don't understand quantum field theory or the standard model, but there are certainly claims that the Higgs field, mediated by the Higgs boson, in some sense explains inertia.
I've known about the equivalence of gravitational and inertial mass for a long time (I'm a physics major), but I have always assumed that the reason that there is no explanation for that equivalence is because we fundamentally do not understand how the universe works.
Quantum mechanics is the equivalent of "Cross the street when the light is green", not "This is how you build a street."
I'm a poet, not a physicist, but I have been thinking about this for a long time, and developed a kooky theory that time works the opposite of how we all think it works.
I grew up thinking the past causes the future. Now I think the future causes the past.
First look at quantum mechanics. In any QM interaction, what will happen is not determined by what has happened in the past. What will happen is determined by resolving all the possible things that might happen in the future. At the fundamental level, it's not the past but the future that determines what happens.
Then look at simple motion. When I set a thing in motion, I give it a future. That future is what is different about the thing compared to what the thing was before I set it in motion.
Inertia is the future's commitment to some object in motion.
The future determines what will happen, not the past. The past doesn't cause the future, the past only limits what the future can do.
This is metaphysics, not physics; and I can't find any physicist to agree with me, though recent work on "retrocausality" appears to lean in my direction; but physics only cares about how things happen, not why things happen, and we poets want why.
I know folks who've spent a career trying to measure if there is a difference between the two, and it's really, really hard needless to say. E.g., you take a "torsion balance" consisting of a very heavy, balanced mass on a very thin wire, with sides made of different materials, and try to determine if the earth tugs one side more strongly than the other.
That's a rough and dirty description, but more or less what they're doing, under the proviso that almost any other source of noise or forces can overwhelm gravity. The example that was always used in classes was picking up any magnetic metal with a refrigerator magnet. It's that tiny magnet vs. the whole earth, and the magnet wins.
And although gravity is really, really weak, it's also impossible to "shield" against, unlike electromagnetism (although that, too, can be difficult to shield against when you start trying to eliminate fields to extremely high degrees).
And there are folks over in Germany doing the Galileo experiment with quantum systems. Make "Bose-Einstein Condensates" (ultra-cold atoms all in the same quantum state) and drop them in vacuum towers and see if different materials drop at the same rate. Crazy difficult experiments.
So far, as far as anyone has measured, inertial mass and gravitational mass are the same.
I really don't understand your hypothesis. Mass is defined as a specific amount of material. Gravitational and Inertial mass are just two different ways to measure mass.
Inertia is also frame of reference dependent. All the objects in a car are inert with respect to each other and are all being pulled downward by gravity and being pushed up by the car.
I can help you with this. Think of electrostatics. Electric charge is that property of matter that determines the force between two charged bodies (via Coulomb's law), which is very similar in form to Newton's law of gravity. Inertial mass is the constant of proportionality between force applied and acceleration achieved (Newton's 2nd law). When you want to calculate the acceleration caused by an electrical force, you use the charge to calculate the force and the (inertial) mass to calculate the acceleration resulting from that force. Think of gravitational mass as the "charge" in the force law for gravity (no need to drag general relativity into this for present purposes). Comparing Coulomb's law and Newton's law of gravity drives this point home. The mystery is that "gravitational charge" is always exactly equal to inertial mass, and no one knows why that should be the case.
Uh, actually it's because gravitons are spin-2 bosons and couple to everything. No mystery there at all.
Uh, I don't think that answer is very helpful to someone who doesn't get the doesn't understand the distinction between inertial and gravitational mass...
Because not everything is charged, i.e., photons don't couple to everything? I found your analogy misleading. You would have done better to say that not everything has the same (electric) charge-to-mass ratio.
Also, it's good for people to Look Stuff Up.
I'm sorry you had trouble following my explanation, but with only two classical forces to work with, pickens is slim. Note that my answer to Ken was in form exactly the answer pjcamp1905 gave to Yikes. Probably because it's the most straightforward way to explain the difference to someone who doesn't already know. Now your approach is fascinating:
Ken: I really don't understand your hypothesis. Mass is defined as a specific amount of material. Gravitational and Inertial mass are just two different ways to measure mass.
You: It's because gravitons are spin-2 bosons and couple to everything. No mystery there at all.
Uh huh, yep, a clearer explanation can scarcely be imagined.
You in between with nonsenseical explanation: gobble pork chop big mac. Nope, can't imagine why you'd leave that out. Not at all.
You could have said take an empty can of paint and a full one and pull on them both with a magnet. The empty one will accelerate faster because paint isn't magnetic. But whatevs. You do it your way, I'll do it mine and I'm guessing you didn't bother to follow through on my suggestion with the google thing.
I did not imagine that explaining the difference between gravitational and inertial mass would devolve into a flame war, but here we are. You should take you paint can explanation on the road and see how it does. The analogy to electrostatics is literally the only coherent explanation for that on this thread (and, once again, I am not the only one to offer it). I can hardly imagine how you could post your comments to me without experiencing excruciating embarrassment, but each to their own.
Sigh. One of us knows what we're talking about. One of us doesn't. So no, this isn't a flame war; this is me explaining to someone who knows barely enough to be dangerous why their explanation is confusing (In fact, you don't know enough to cog that my response to your misleading explanation was snark.) There's no point in going any further unless you apologize, btw; I'm not wasting my time on yet another DK victim.
You are quite the paragon of cliquish antisocial behavior. When are you going to give pjcamp1905 the bad news about his terrible explanation? Just yell "spin-2 boson! photons! electricity isn't gravity!" at him and I'm sure he'll apologize profusely.
Why would there be two different measures of "mass?"
The reason the two balls fall at the same rate is only because the only action upon them in your example is gravity. If you exerted force on one of them by throwing it at the ground they would not head towards the ground at the same rate.
I don't know if its remarkable that they are the same, wouldn't it be more remarkable if they were somehow different? Would the universe even function if they were different?
This does not come close to explaining inertia v. gravity, of course which was your question I think.
Gravitational mass plays the same logical role for gravity as electric charge plays for electromagnetism. Would you find it odd if the charge of a particle were always equal to its inertial mass? I would. The only reason it doesn't seem that way is that, in contrast to charge, we used the same word for two logically distinct concepts.
Frame-dragging is kind of like inertia.
Not really. That's like saying electricity is kind of like gravity. They're both inverse square laws but that's where the resemblance ends. Mass does not scale with frame dragging.
I could go on about gravity coupling to energy, not mass (there goes that 'mystery'), or that the Higgs field isn't the sole mechanism for providing mass (only 10% of the mass of a proton derives from its quark constituents), but the salient observation is this: nobody asks 'what is gravity?' or 'what is inertia?', and haven't really since beginning with Newton himself. Instead, Newton gave a mathematical description of how gravity behaves (there are singularities in the Newtonian formulation of gravity as well, arguably worse than the ones found in GR.) 'What is intertia?' sounds like getting at the fundamentals at first. Then you realize that's on the same level as asking 'what is a (spatial) dimension?' Every theory will fall back on primitives beyond which there is no regress if you dig deep enough. What is a point? What is a line? Well, they're primitives, as Euclid himself recgonized and Hilbert formalized a couple of thousand years later.
I always thought that inertia was just the resistance of space-time to having its shape changed. If a mass moves, then it causes a change as space-time flattens out behind it but surges in front of it.
Just a little bit like a boat with water representing space-time.
Spacetime is not a thing in that sense. That's why that fabric analogy is so misleading. Spacetime is geometry and geometry doesn't resist anything.
Consider a counterexample: photons. They have zero mass, but they do not have zero energy. That energy content causes spacetime to curve around them. If inertial mass were due to spacetime resisting being curved, that would mean photons DO have mass.
Fun fact: Under the Newtonian model, light is also deflected by gravity. But the predicted amount turns out to be off by a factor of two.
BTW, everybody who hasn't studied this please look up Einstein's priniciple of equivalence. Saying that gravitiational and inertial mass are different is exactly the same thing as saying the principle of equivalence and hence General Relativity is wrong.
Gravitational mass plays the same logical role for gravity that electric charge plays for electromagnetism. Inertial mass tells you how much acceleration you get for an applied force of any sort, not just gravity.
Why is there inertia? That's not the right question because it is not operationally defined. You can't go down to the store room and check out an inertia meter. Inertial mass, on the other hand, is operationally defined and we know where it comes from -- the Higgs mechanism.
Except for neutrinos. The Higgs mechanism only works for particles that respect chiral symmetry (if they have spin, all the possible spin states exist). Neutrinos do not. All neutrinos from, say, beta decay are left handed. None are right handed. (handedness being defined as the projection of the spin vector on the momentum vector).
But neutrinos DO have mass. That's why they oscillate. LHC is looking for cracks in the Standard Model and not finding them but neutrinos already ARE a crack in the Standard Model. There is no explanation for their mass.
BTW, your Leaning Tower experiment would not turn out the way you expect, and neither did Galileo's, assuming he actually did it. Aerodynamic drag is enough to put a couple of feet between them when they hit the ground -- not easy to miss. This is a semistandard problem in every junior level classical mechanics textbook. Galileo was a big liar, but he had the skill of lying to reach a deeper truth.