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Equivalence of inertial and gravitational mass

  1. Jul 28, 2015 #1
    Is there any credible hard evidence that this equivalence extends to all moving bodies? We accept on good grounds that the apparent mass of moving objects is enhanced by motion, to a measurable degree that increases indefinitely as observed speeds of relative motion approach c. Likewise, a spinning object acquires extra mass/energy from its motion. Examples are the rotating planet Jupiter, and spinning neutron stars. Is such a body's universal gravitational attraction for, say, its orbiting satellites and other things ponderable enhanced by the mass-equivalence of the body's rotational kinetic energy, so affecting the orbital periods of satellites, for instance?

    Do we by now just take as a matter of faith that the equivalence of gravitational and inertial mass always prevails? That the mass-energy of moving stuff gravitates exactly as does what we deem to be 'familiar static' massive stuff, e.g. lumps of iron or even herds of lumbering elephants? Or is it a consequence of unassailable logic that I've missed? or just of using Occam's razor?
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  3. Jul 28, 2015 #2
    There is sufficient evidence to a high degree of accuracy that one should not think it is only a "matter of faith." With the volume of available supporting evidence and no contradictory evidence, the case is strong.

    One can always hypothesize that experimental contradictions might exist in realms for which accurate experimental evidence is not yet available.
  4. Jul 28, 2015 #3


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    Hi Paulibus, it's good to see you. I think it is an interesting question. Somehow the concept of gravitational mass would be made precise, I suppose, to exclude effects of motion (e.g. such as rotation) on the gravitational field.
    I'll let others answer that question for the classical theory---I just wanted to mention something. Here are some 16 peer-reviewed citations to a 2010 paper that strikes me as really bizarre. Some of the citations are from articles appearing 2013, 2014, 2015...
    This strange 2010 paper was published in Springer's Applied Physics B and is still being cited.
    Inertial and gravitational mass in quantum mechanics
    E. Kajari, N.L. Harshman, E.M. Rasel, S. Stenholm, G. Süßmann, W.P. Schleich
    (Submitted on 10 Jun 2010)
    We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the spatial modulation of the corresponding energy wave function is determined by the third root of the product of the two masses. Moreover, the discrete energy spectrum of a particle constrained in its motion by a linear gravitational potential and an infinitely steep wall depends on the inertial as well as the gravitational mass with different fractional powers. This feature might open a new avenue in quantum tests of the universality of free fall.
    17 pages, 7 figures, accepted in Applied Physics B

    A blogger at the MIT Technology Review got very excited about this paper and wrote a wide audience piece about it: http://www.technologyreview.com/vie...ry-separates-gravitational-and-inertial-mass/

    June 14, 2010
    New Quantum Theory Separates Gravitational and Inertial Mass
    The equivalence principle is one of the corner stones of general relativity. Now physicists have used quantum mechanics to show how it fails.

    This post got 176 comments so far---and some of the comments are as recent as 2013. So although frankly I don't know what to make of this, it seems to have excited a sustained response. The equivalence principle may have limits to its applicability.
    Last edited: Jul 28, 2015
  5. Jul 28, 2015 #4


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    The authors come from a condensed matter/instrumentation background and the paper seems notable mostly for discussing parameterizations of differences between the equivalence principle and alternative theories where inertia mass and gravitational mass are merely proportional that could be tested in various kinds of experiments using precision instrumentation. The fact that the paper is expressly non-relativistic makes fairly clear that this is about framing experimental tests of the equivalence principle rather than advancing a theory of how gravity really is that has such a difference. Some of the interest may flow from its relevance to the SAGAS space probe that is designed to contain multiple high precision instruments to test for minute anomalous gravitational effects in the solar system.

    Going back to the original post, there are some experimental tests of the impact of things like rotation and motion on gravity in the form of frame dragging experiments and gravito-magnetic effects, IIRC. The place to look for the equivalence principle to break down would be to look at the rest mass of fundamental particles arising from the Higgs field interaction of that particle and comparing that to the total mass-energy of that particle, for example due to kinetic energy, and seeing if the kinetic energy impacts inertia, so something like that.
    Last edited: Jul 28, 2015
  6. Aug 9, 2015 #5
    Still puzzling. Consider photons -- entities without rest mass that are nevertheless endowed with energy E = h.nu just because they wobble in time. And energy is mass, given by m = E/c^2. I guess this mass should be labelled 'gravitational' because photons gravitate and light is known to be deflected by massive astronomical bodies, just as the Big E deduced a hundred years ago.

    Question I now have: if photons gravitate and have gravitational mass, they must attract one another. Photons in a beam of electromagnetic radiation must then fall together as they propagate. Does this falling together or, as it were, self-focusing property of photons, have any previously undetected observable consequences that are now perceptible with twenty-first century facilities? For example for energetically massive gamma photons that beam towards us from remote and violent places in the sky?
  7. Aug 9, 2015 #6

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    They don't. This isn't even a meaningful statement.

    They don't.

    You seem to be following the strategy of posting a bunch of statements, hoping the incorrect ones will be corrected. This is not only inefficient, but it tends to make the people who are trying to help you cross.
  8. Aug 10, 2015 #7
    I seem to have worded my question in an irritating way. But I take issue with the statement in post #6 that photons don't have 'gravitational' mass. They don't have 'rest' mass, but they do gravitate: their geodesic trajectories through spacetime are indeed affected by matter concentrations like those in our solar system, and photons are indeed red-shifted when they climb up gravitational gradients. They must therefore be endowed with the property commonly called mass; but strictly should be called mass/energy. The fact that photons exert pressure on a reflecting surface shows that photons also have 'inertial' mass, another synonym for mass/energy. Or is this kind of discussion better framed in terms of momentum?
  9. Aug 10, 2015 #8
    Huh?? I'm fairly sure photons do have "mass" in the sense that they gravitationally attract other objects.

    If you have an indestructible opaque box with two kilograms of matter (say, hydrogen) and antimatter (say, anti-hydrogen) inside it, it will gravitationally attract other objects. Both when it had unreacted hydrogen and anti-hydrogen inside, and when they reacted and filled the box with photon gas.
  10. Aug 10, 2015 #9


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    "Mass" is in that case called energy. Not mass :P
  11. Aug 10, 2015 #10
    I was vaguely involved with an experiment where we dropped heavy water in a free-fall absolute gravimeter. Apparently heavy water has some serious motion going internally, on the atomic scale, and the thought was that perhaps that would result in a slower acceleration in freefall. Equivalence prevailed, at least down to a microgal (1 Gal = 1cm/s^2).
  12. Aug 12, 2015 #11
    There is no consensus (yet?) on the definition of word "mass". Some people use it only for rest mass, not all people.

    However, the poster who asked whether photons have "mass" clearly meant the definition of word "mass" which means gravitational attraction, by use of the "gravitational" qualifier:

    > > Question I now have: if photons...have gravitational mass
    > They don't.
  13. Aug 12, 2015 #12
    Thanks, Haushofer. It's time that we got away from semantics. I would still like to know whether the photons that comprise a beam of radiation attract one another, or not, and to have the reasons for the reply, whatever it is, spelled out.
  14. Aug 12, 2015 #13
    I've always been confused by this position, but just chalked it up to my lack of understanding.

    But, clearly, the path of light is effected by gravitational fields. And... as Paulibus points out... given the mass/energy relationship, the differentiation seems to be primarily semantic.

    Can someone clarify this for me?
  15. Aug 12, 2015 #14


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    Gravity couples to mass-energy. Photons have mass-energy. Photons don't have mass of any kind. In my experience, nobody calls mass-energy to which gravity couples, "mass" when they really mean "mass-energy". Particles like photons and gluons that don't have rest mass are qualitatively different from particles that have rest mass even if it is tiny like neutrinos.

    Where there is confusion in the use of the term "mass" it is usually between "rest mass" and relativistic mass as a result of special relativity in objects moving at a meaningful percentage of the speed of light, with relativistic mass inferred from relativistic momentum.
  16. Aug 12, 2015 #15


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    Photons are gravitationally attracted to each other, because they have mass-energy and all things with mass-energy are attracted to all other things with mass-energy via gravity.

    The effect, however, is generally tiny to the point of being almost impossible to measure experimentally because (1) Newton's constant, G, is so small, (2) the conversion factor E=mc^2 means that it takes a huge amount of photon energy to be equivalent to a small amount of mass for gravitational purposes, and (3) a stream of photons (I don't really like the terminology "beam of radiation" for a variety of reasons related to how photons propagate from point A to point B in quantum mechanics, which is by every possible route and not just in a straight line) are not concentrated in one place which dilutes their gravitational pull over the area they are spread across. To illustrate how small those effects are, my understanding is that they are sufficiently small that the LHC does not need to correct for them in its uber-precision calculations.

    It is much easier to experimentally observe gravity act on photons than to experimentally observe photons exerting a gravitational pull, even though both are happening simultaneously (e.g. electromagnetic flux is an input in the stress-energy tensor of general relativity).

    The combined mass-energy of all the photons in the universe at any one time is about 0.01% of the mass of all of the ordinary matter in the universe (disregarding dark matter and dark energy), and is spread far more evenly, so a typical test particle in outer space would be ordinarily pulled in multiple directions by gravitational pulls from various photons in its vicinity whose combined effect would cancel out to a great extent. https://van.physics.illinois.edu/qa/listing.php?id=14672

    The difference between mass and mass-energy, however, is not just semantics. It is a fundamental concept that you need to understand the question you are asking in the first place in a way that has a meaningful answer.
    Last edited: Aug 12, 2015
  17. Aug 13, 2015 #16


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    Per GR, there are interesting cancellation effects for gravitation of light. Two light beams propagating in the same direction will not attract each other (nor will 'pieces' of the beam attract each other). However, two anti-parallel light beams will attract each other. Unfortunately, the effect is dozens of orders of magnitude too small to detect, even for powerful lasers.

    This paper provides a good discussion:


    [edit: An amusing calculation at the end of this paper is to compare the interaction of two anti-parallel laser beams 10 cm apart. The mutual deflection caused is 80 orders of magnitude less than the affect on the beams estimated for gravitational radiation originating in the Virgo cluster!]
    Last edited: Aug 13, 2015
  18. Aug 13, 2015 #17


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    It has been established that the kinetic energy of electrons contributes to the mass of ordinary matter to a detectable degree. In passing, the following well known paper discusses this:

  19. Aug 14, 2015 #18
    Thanks for your reply #15, ohwilleke. You wrote : "The difference between mass and mass-energy, however, is not just semantics. It is a fundamental concept that you need to understand the question you are asking in the first place in a way that has a meaningful answer." Yes, mass is an ordinary word whose place in physics has been usurped by the physically more specific relativistic concept of mass-energy. Perhaps we need a succinct physics word to replace both terms?
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