Galactic Interactions

The Greatest Mystery In All Of Physics

Because this is me, I must start with a lot of disclaimers. First, the title is catchy, but many would disagree with the mystery I’ve identified. Even I might. So, please try to avoid flaming me for my choice. Second, very shortly I will post “The Most Elegant Solution In All Of Physics,” a post that might allow one to argue that what I’m about to identify as the greatest mystery isn’t a mystery at all! Groundwork laid, here we go….

In physics, there is this quantity “mass” that we use to describe how much “stuff” there is in a particle. Technically speaking, “mass” is the energy content of an object measured by an observer when that object is at rest with respect to the observer, and when the observer is viewing that object as a closed system from the outside. (In other words, we don’t know anything about “internal energy,” because the object is just a thing.)

The thing is, there really are two different kinds of mass. First, there is inertial mass, which describes how much an object resists being pushed around by any kind of force. Second, there is gravitational mass, which describes how strongly an object couples to the gravitational field. And, yet, to the best precision we’ve been able to measure, these two kinds of mass are exactly the same. So much so that in introductory physics classes we just call it “mass”, and students may not even realize that there’s anything surprising about the fact that the two are the same!

If you’ve taken freshman Physics, you’ve seen a couple of equations. (Yes, I’m about to post equations; they’re very simple, and even people who are “not math people” can understand what I want you to understand about them; please bear with me!)

First, we have the second-most famous equation in all of Physics:

i-b566fd6c8cac9205167e9e790721668e-f_ma.png

In this equation, a is acceleration. If something is at rest, you must accelerate it to get it moving. F is the force it takes to move an object with acceleration a, and m is that object’s mass, or how much inertia the object has. It takes more force to get a heavier object moving; this is intuitive, and matches our everyday experience.

The second equation I write in a slightly non-standard form:

i-117456387af9795d8932efe2872f8a34-f_gmmr2.png

Here, F is the gravitational force between two objects, one of mass big-M, and one of mass little-m. G is the universal gravitational constant (basically, a parameter of our Universe that describes how strong gravity is in general), and r is the distance between the two objects.

For present purposes, think of this slightly differently. Assume that M is a really big mass– say, the Earth– and that m is a much smaller mass&ndash: say, you. Then, the quantity in parentheses, (GM/r^2), describes how strong the gravitational field of the Earth is. Put in the radius of the Earth for r. Multiply that by your mass, and you get how much the Earth is pulling on you due to its gravity.

In freshman physics, we get so used to using these two equations that we never stop to think… why should the little-m in those two equations be the same? Indeed, perhaps we should be writing the equations as follows:

i-59f89059eab1052378359ceb5f5729dc-f_minertiala.png

i-f40e5371703d11b25d5e7b0b39d34ed8-f_gmmgravr2.png

The two concepts are very different. Inertial mass says how much an object resists being pushed around by any force whatsoever. Gravitational mass says how much an object couples to the very specific force of gravity. Why are they the same? To try to put this in higher relief, consider another formula that many see in freshman physics:

i-868752006e59ade75efca28498b68a63-f_qqr2.png

This is the electric force between two objects, one of charge big-Q, the other of charge little-q. (It’s conventional to use the variable q for charge; don’t ask me why, I have no clue.) Or, to put it another way, the quantity in parentheses is the electric field strength created by a particle of charge big-Q a distance r away (where the 1/4πε_0 represents the strength of electric forces in general, and is just a constant). Then, little-q tells you how strongly the particle with charge little-q couples to that electric field. If you then wanted to figure out how much the particle moved around, you’d need its inertial mass. Notice, however, that the electrical charge is completely different from the inertial mass. One says how strong something couples to a field, the other says how much you need to push something around to get it moving.

Yet, with gravity, how much an object couples to the field is exactly the same as how much the object resists moving around. This isn’t true with any other force. There’s clearly something special about gravity.

So here’s my candidate for the greatest mystery in all of physics: why are inertial mass and gravitational mass the same?

Coming soon to this blog: the solution, in the form of Einstein’s General Relativity.

Comments

  1. #1 NJ
    February 26, 2007

    OK, naive mineralogist question here: What would be the consequences if they weren’t the same?

  2. #2 Jonathan Vos Post
    February 26, 2007

    NJ: Eotvos experiments of sufficient accuracy would give non-null results. The Moon, whose iron-rich core in aluminum-rich crust is off center, would have measurably different orbital dynamics (perhaps at level detectable by bouncing laser beams off those corner reflectors left by Project Apoillo astronauts).

    Trivial or pointless to a layman, perhaps, but it would be a Nobel-prize winning experiment if such results were found.

  3. #3 Rob Knop
    February 26, 2007

    Indeed, I have a friend who is working on measuring the orbit of the Moon to centimeter or millimeter accuracy in an attempt to see any deviations from the predictions of General Relativity. See http://physics.ucsd.edu/~tmurphy/apollo/

    More broadly speaking, the “Galileo experiment” wouldn’t work to sufficiently high precision. The fact that objects of different masses fall at the same rate is a consequence of (or, indeed, a restatement of) the equivalence of inertial and gravitational mass. Differences between the orbits of things of different composition, indeed, are exactly that: things of different mass falling at different rates.

  4. #4 Benjamin Franz
    February 26, 2007

    I guess I am in the “naive Mach’s principle” camp. It just doesn’t seem especially mysterious on that level to me: They are are measured to be the same simply because they are two different ways of measuring the same thing. The questions then occur on a different level: What types of theories and universes are compatible with Mach’s principle?

  5. #5 Melissa G
    February 26, 2007

    Gravity is wacky!

  6. #6 Rob Knop
    February 26, 2007

    Benjamin– whether or not it’s surprising depends on the point of view you’re coming from.

    The way we usually talk about it in Freshman physics, where the force of gravity is “just another” force, it’s surprising.

    If you want to talk about Unification and gravity somehow mixing in with the other three forces, it’s surprising.

    If, on the other hand, you start a priori with the idea of gravity as geometry, then it’s not surprising.

  7. #7 Keith
    February 26, 2007

    What if m(inertial) and m(gravitational) wern’t exactly equal but just proportionate. The gravitational law would hold but the constant would have a different value.

  8. #8 Rob Knop
    February 26, 2007

    Keith — in that case, we’d just interpret it as a different value of G. That would be indistinguishable from them being the same.

    Contrast to electrodynamics: you can double the mass of an object without changing its electric charge.

    -Rob

  9. #9 amesolaire
    February 27, 2007

    Can someone please explain to me why modern ether theories are considered as fringe and are generally dismissed as junk science? I’m a layman but I find the idea that the Universe is filled with electron-positron dipoles (as a medium for EM-waves, among other things) very convincing. In one such theory (A.Rykov) the force of gravity is just the result of polarization of said dipoles (“ether”), hence the relationship between electric and gravitational forces – both are manifestations of the Coulomb’s law. Notice that the Michaelson-Morley experiment does not rule out this kind of ether. (I’m genuinely interested, so please don’t take it out on me if you find the above preposterous)

  10. #10 Rob Knop
    February 27, 2007

    Can someone please explain to me why modern ether theories are considered as fringe and are generally dismissed as junk science?

    I’ll try to write more on this at some point– although I’ll probably write more in general about “junk science detection” methods. I’m pretty sure that Mark Chu-Carroll here has written some on this, and others have as well.

    In general, any theory that requires some other well-established theory to be wrong should be approached with extreme suspicion. Sometimes, they may be OK; that was the case with MOND for a long time. (MOND is a theory that says that dynamics of galaxies can be explained by deviations of gravity from the Newtonian relationship in regimes of extremely low acceleration, rather than via the invocation of dark matter.) Most of us were immediately suspicious of MOND, because anything that starts with modifying such a well-established bit of Physics as the Newtonian limit of GR sets off our suspicion alarm; however, MOND survived for a while because if you thought enough about it, it was working in a regime where we hadn’t really tested Newton’s gravity as well as we might have liked. Nowadays, I think that MOND should be relegated to the regime of discarded theories alongside the steady-state Universe, but there are some who disagree with me.

    Most junk science out there, however, doesn’t just modify a well-established theory in a regime where it’s not terribly well tested. They throw out well-established theories and the results of all the experiments that confirm them in wide regimes. When you see that sort of thing, 999,999 times out of 1,000,000 (at least), you’re dealing with crackpot science rather than an intuitive genius.

    I read the beginning of the article you pointed two and saw this:

    “This is despite the paradox that an isolated rotated object should not experience centrifugal forces.”

    That sentence alone is enough to convince me that this guy is a clueless crackpot who should be ignored.

    First, centrifugal forces are scary things. First, in one sense, they aren’t real forces; they are artifacts of being in a rotating reference frame. Second, an isolated object does feel them. Put a cylinder of gas deep, deep into intergalactic space in a static Universe that’s not expanding (so there’s no traditional gravity anywhere), set it spinning, and the gas will differentiate just as if it were in a centrifuge here on Earth.

    That sets off my crackpot alarm enough for me to know that there’s no need to read the rest of this guy’s paper. I don’t trust him to have a tenth of a clue to know what he’s talking about.

    -Rob

  11. #11 Rob Knop
    February 27, 2007

    Doh… “pointed to,” not “pointed two.” Thinking sentence n+1 while typing sentence n can be hazardous.

    -Rob

  12. #12 amesolaire
    February 27, 2007

    Rob,

    Thank you for your very kind and considerate response. I agree with the point that hypotheses and theories requiring us to discard experimental results are not worth considering.

    I am afraid that with my initial sentence I conditioned you to a certain attitude towards the hypothesis I’m referring to, which I should have been more careful about.

    The author of said hypothesis is the chief of a seismometry lab, which does not exactly qualify him as an easy physics crackpot candidate, but does not preclude him from being one either. Still, the meaning of the sentence you are talking about, it appears, has been lost in translation (he is russian). I think what he meant by that was to illustrate that if you assume the Mach’s view of inertia, then you might agree that “an isolated rotating object should not experience centrifugal forces”, which is obviously not true, i.e. constitutes a paradox. I might be wrong on that, and I’m not really prepared to address every point of contention, but I’d be happy to have such points identified.

    I’m weary of wasting your time and that of your readers, but on the other hand I find the inability to neither generate on my own nor gather expert opinion in either direction on something that seemingly makes sense, frustrating. So if anyone can give me arguments either for or against his line of reasoning – I’d be eternally grateful.

    Thank you again.

  13. #13 Keith
    February 27, 2007

    Adding to my comment yesterday.

    You state that m(inertial) and m(gravitational) are exactly the same.

    I suspect that the value of the gravitational constant was determined by assuming that they are the same so I smell a circular argument here.

    Suppose a constant does exist that relates the gravitiational mass of an object to the inertial mass; for fun let’s call it Keith’s Constant.

    For your statement to be true it is necessary to prove that Keith’s constant equals exactly 1.

    Can it be done?

    Keith

  14. #14 Rob Knop
    February 28, 2007

    I suspect that the value of the gravitational constant was determined by assuming that they are the same so I smell a circular argument here.

    Sure. So say that m(inertial) and m(gravitational) are perfectly proportional, instead. The rest of the argument is still there; for no other force do you have that perfect proportionality. Yes, we choose G so that they have the same numerical value, but that doesn’t really make the argument circular.

    -Rob

  15. #15 Rob Knop
    February 28, 2007

    Re: proving that “Keith’s Constant” is 1, the fact that GR work so well tells us that just as the speed of light gives a natural, universal scaling between space and time, the gravitational constant (together with the speed of light) gives a natural, universal scaling between mass, space, and time.

    If GR didn’t work, then we wouldn’t have that, so I offer the empirical validation of GR as the proof that Keith’s Constant is 1.

    Just as it’s completely arbitrary to measure distance in meters and speed in seconds, it’s arbitrary to choose G to be whatever you want it to be; by choosing it, you’re effectively choosing the mass units you’re using. But everything still falls at exactly the same rate, so the equivalence between inertial and gravitational mass remains.

    -Rob

  16. #16 raj
    February 28, 2007

    You state that m(inertial) and m(gravitational) are exactly the same.

    I suspect that the value of the gravitational constant was determined by assuming that they are the same so I smell a circular argument here.

    Actually, that last is incorrect, and can be shown to be incorrect by a couple of simple experiments. First, measure the inertial mass of two test particles–that’s fairly easy to do. And thereafter measure the force of the gravitational attraction between the two–that’s fairly easy to do, too. And from the latter experiment and Newton’s equation solve for “G,” Newton’s constant.

    Next, run another experiment. Substitute for one of the test particles in the first experiment, a test particle of another inertial mass. As I suggested above, we know how to measure inertial masses, so we know how to measure the inertial mass of the new test particle, too. And then measure the force of the gravitational attraction between the new test test particle, and the remaining test particle from the earlier experient. Use Newton’s equation, solve for “G,” and voila! you’ll get the same value to within a margin of experimental error. It isn’t that complicated.

    It really is an interesting fact that inertial mass and gravitational mass are precisely the same.

  17. #17 raj
    February 28, 2007

    Question for Prof. Knop. Isn’t it the case that the similarities in the force equations for gravity and electrodynamics have more to do with the fact that they are central (point source) force equations, than other things? In those cases, inverse-square relationships actually do make a lot of sense. But, IIR my electrodynamics course correctly, electrodynamics equations involving, for example, planar surfaces such as those in typical capacitors are much more complicated than mere inverse-square relationships.

  18. #18 Wayne McCoy
    February 28, 2007

    I have another mystery. Why is the velocity of light in vacuo finite? What is it about spacetime that constrains c to be about 3 x 10^8 m/s? Is there some field (e.g., Higgs), or possibly the structure of spacetime itself, with which the electromagnetic field of photons interacts, thereby impeding the motion of the photon through it? Or is it that spacetime is an illusion (some current theories suggest this) and thus “motion of photons” is also an illusion? Of the first suggestion, there are the current theories of the aether (similar to but not the same concept that provoked the Michelson-Morley experiment). On the second, some interpretations of string theory suggest that space and spacetime are illusory. What’s your take on this?

  19. #19 philw
    March 1, 2007

    Speakng of String Theory, I think it would be an excellent topic for an essay or 3. As a non-scientist but science fascinated ex-engineer, I have real problems with a system of thought that has produced no significant falsifyable predictions, unlike GR and the other well tested theories you cite previously. Why is there such group think by the vast majority of theorists? Tenure track?

  20. #20 Wayne McCoy
    March 1, 2007

    @philw

    Actually, there are some significant falsifiable predictions of string theory. Lisa Randall of Harvard and others will be testing whether there are multiple hidden dimensions that string theory requires to be a coherent and consistent theory, in series of experiments that will begin later this year or early next, when the Large Hadron Collider in Europe cranks up. Stay tuned. In the mean time, take a look at Lisa Randall’s excellent book, “Warped Passages: Unraveling the Mysteries of the Universe’s Hidden Dimensions,” and don’t be too swayed by Lee Lee Smolin just yet.

  21. #21 philw
    March 1, 2007

    Good luck with the LHC experiments. I’ll await the results. Meanwhile have someone there contact physicist John Cramer who needs to warn them about The Hive.

  22. #22 Rob Knop
    March 1, 2007

    Why is the velocity of light in vacuo finite?

    I’m not sure there’s a good answer to this.

    I can answer “why do we believe the speed of light in vacuo is finite,” and that is that the theory that results from starting with that postulate is extremely well tested by experiment.

    But why should it be that way? Dunno. It just is.

    -Rob

  23. #23 Trevor Hearnden
    March 2, 2007

    I’m new here os this may have come up before? It may also be a bit off topic but it concerns gravity. I understand there are two very different ways of looking at gravity: the warping of space-time as described in General relativity and the exchange of Gravitons as postulated in many particle theories including string theory. Gravitons and indeed gravity are said to be limited to the speed of light like everything else. So how do the gravitons cross the event horizon of a black hole? Clearly something must if the proposed giant black holes in Galactic centers exist.

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