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Are there cosmological models in which Planck's constant varies?

  1. Dec 21, 2007 #1
    If we take Planck's constant to be a measure of quantum fluctuations, which seems natural in the world-view of https://www.physicsforums.com/showthread.php?t=204567", then it also seems natural to ask whether Planck's constant might vary over cosmological scales, just as temperature is a measure of thermal fluctuations and varies over cosmological scales.

    I had better note here that the difference between quantum fluctuations and thermal fluctuations, in a random field world-view, is a fundamental one of symmetry properties: quantum fluctuations are invariant under the Poincaré group, while thermal fluctuations are invariant only under a little group (of the Poincaré group) that leaves a time-like vector invariant. A moderately detailed account is given in the above topic and in the various published papers it cites.

    I'm not competent to enter detailed discussions on cosmology, but hopefully my question will be answerable: "Are there cosmological models in which Planck's constant varies?"

    One justification for taking thermal fluctuations to be strongly related to quantum fluctuations in principle is the Unruh effect, under which the quantum vacuum appears thermal to an accelerating observer. Similarly, under the Hawking effect, variations of the metric have thermal properties, as one would expect from the principal of equivalence. General covariance would appear to require a unified description of thermal and quantum fluctuations. Since a variation of quantum fluctuations would presumably have effects comparable to those of variations of thermal fluctuations -- in an approximate description it would exert a force -- it seems possible that one reconceptualization of metric variation might be as variation of quantum fluctuations.

    There is a supplementary point that I would also like to make. If we ever talk about "quantum fluctuations", which Physicists often do without offering any details of what quantum fluctuations might be, then there arises the question of quantum entropy as the thermodynamic dual of Planck's constant, just as thermal entropy is the thermodynamic dual of temperature. Note that entropy is not a Lorentz invariant concept, its definition requires a phase space to be introduced. The existence of quantum fluctuations, if taken seriously, has serious consequences for arguments that fundamentally rely on entropy.
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  3. Dec 21, 2007 #2


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    A variable 'h' would have observable consequences - e.g., spectral lines of distant objects would be out of whack with local [laboratory] spectrums.
  4. Dec 22, 2007 #3


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    A variation of h is, in principle, physically equivalent to a variation of c. This is because the variation of any dimensional constant has no meaning at all because there is no way to tell whether the constant varies or our standards of measurement vary.

    The same applies for variable c theories. Here you may visualize more clearly that it is not possible to differentiate between a variation of c or a variation in the definition of the measurement units of meter or second. Note that the value of c = 299 792 458 m/s is defined according to those of m and s.

    Only the variation of dimensionless constants has a physical meaning, like for example the fine structure constant alpha. However, the variation of alpha can be formulated in different ways that are equivalent: as a variation of c or as a variation of h. The choice will depend on your preference for one formulation or another.

    I am not aware that there is any physically meaningful way to distinguish between both possibilities. A theory that claims about the variation of h should IMHO clarify this point first.
    Last edited: Dec 22, 2007
  5. Dec 22, 2007 #4
    A variation of the metric results in changes of spectral lines too, right? My point is not so much that [tex]\hbar[/tex] does vary, so much as that we can think of the metric changing or we can think of [tex]\hbar[/tex] changing. Not even that, of course, because the metric has more than the one degree of freedom that [tex]\hbar[/tex] would give. More that if quantum fluctuations varied from place to place, we wouldn't expect an effective physical model for that variation of quantum fluctuations to be given by just one degree of freedom.

    I'm curious whether coordinate independence with respect to metric vs. quantum fluctuations might be productive or not. Hence my question whether there are existing models that have introduced variations of [tex]\hbar[/tex] to satisfy some perceived requirement or another. I wouldn't expect my theoretical concerns to be the same as other people's, but I would be curious to see what their concerns might be, supposing that any serious cosmological models have introduced ideas that are even approximately along this line.
  6. Dec 22, 2007 #5
    I guess my response to this is very similar to my response to the previous post. Indeed it fairly accurately explicates how I had more loosely thought about the variation of Planck's constant.

    In the light of hellfire's post, for which many thanks, I'm not saying that Planck's constant does vary, only that it seems to me there is a coordinate dependence to taking quantum fluctuations to be constant while the metric varies.

    It has seemed to me that thinking about this might be productive: considering such coordinate dependencies has been productive in the past.
  7. Dec 22, 2007 #6


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    Peter, I didn't answer because
    (1) I don't know of any models in which [tex]\hbar[/tex] changes and
    (2) this doesnt mean very much because I don't have a sufficiently wide familiarity with the cosmology literature

    So I couldn't see how to respond in a helpful way. My inclination would be to write email to somebody with an encyclopedic knowledge.
    For some reason, Steve Carlip comes to mind. Angry Physicist, a UCDavis grad student, posts here and has a blog. He has a lot of nerve and energy. If you asked Angry, he might ask Carlip for you. My impression is Carlip has an incredible memory. He probably doesnt have as many people bugging him with emails as more visible people like Michael Turner (Chicago) or David Spergel (Princeton). I can see feeling shy about writing email to one of them, but not about Carlip. If he didnt know he would suggest someone to ask. It is not exactly a dumb question.

    There is the point hellfire made about the dimensionful constants. I personally do not have a clear idea of how we could tell, in other words I do not see the operational meaning of changing either c or hbar. But I believe that you do! You indicated something of this. I personally find this difficult to get a grip on but encourage you to look into it. The worst thing that could happen is you would find that it is impossible for hbar to change (because no operational meaning, no relevant observation) contrary to what you now suspect, and the upside is discovering something new.

    three years ago I might have said that G could not change, because c, hbar, G are fundamental dimensionful. but exposure to Reuter and Percacci work has undermined my confidence in that. they make G "run" with scale. it is an unstable time in physical theory. things one thought were dependably solid suddenly turn liquid and run. :smile:
    Last edited: Dec 22, 2007
  8. Dec 24, 2007 #7
    I posted [post=1550277]a somewhat wild post on a QM thread about Bell inequalities[/post] that derives from the question posed by this thread, which came to the realization halfway through that if a change of the metric can be considered to be a change of Planck's constant in a different coordinatization, then by moving an experiment to a region of space-time where there is a different gravitational field we can effectively reduce the quantum fluctuations of the apparatus.

    If we can reduce quantum fluctuations, then we can consider quantum fluctuations to be eliminable in principle, as we do thermal fluctuations (which we can only reduce a lot, not to zero, but we proceed as if they are eliminable). Consequently, we can again consider classical measurements to be an ideal that in principle can be approached more closely than we currently can engineer. There are many issues of detail to consider in such an approach, of course. In time we will see whether I can work them out.
  9. Dec 26, 2007 #8


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    there are some pretty heavyweight physicists (like Michael Duff, John Barrow, John Baez, and several others on the sci.physics.research newsgroup) that would not concede that any dimensionful constant varying would have measurable consequences. only varying dimensionless constants. http://arxiv.org/abs/hep-th/0208093 http://xxx.lanl.gov/abs/physics/0110060

    might you mean, perhaps, that a variable [itex]\alpha[/itex] would have observable consequences?
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  10. Dec 27, 2007 #9


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    I think that variable dimensionful constants might make sense. If you measure today c = 299 792 458 m/s and tomorrow c = 300 000 000 m/s you may conclude that either c is varying or that m or s are varying. Both descriptions are equivalent in their kinematics. Lacking of a theory that describes how such changes may take place providing a dynamics for the changes we cannot make a difference between both posibilities.

    However, both are very different phenomena. The first relates to a change in the causal structure of space-time. The second to a change in matter that makes it possible to us to define m and s according to some rules. A theory may regard a change in c and a change in m or s to be equivalent not only kinematically but also dynamically providing equivalente physical mechanisms for the change of both. However, it seems meaningful to me that there may be also theories that regard both phenomena to be dynamically inequivalent providing physical mechanisms or dynamics for only one of both.

    A similar scenario takes place in cosmology for example, with the expansion of space. If you would measure today a distance L in meters to a galaxy and tomorrow L', you may conclude either that space expanded or that m shirnked. Both descriptions are kinematically equivalent. However, our established theory of gravitation provides only a dynamics that explains the expansion of space. There is no possibility within general relativity to account for shrinking rulers without introducing additional postulates. Thus, both situations are not dynamically equivalent. At least not if one assumes certain metaphysical principle of simplicity and avoiding of introducing inobservable entities.

    I guess that similar arguments apply to a variation of c or h. However, the theory that claims a variable c or h should IMO clarify such points first.
    Last edited: Dec 27, 2007
  11. Dec 27, 2007 #10
    Thanks rbj and Hellfire both. Very helpful. I guess that if, for instance, we were to make Planck's constant a variable in Physical models, that changes what is and is not a dimensionless constant.

    As far as a minimal change of existing Physics is concerned, it's obviously better to keep to taking the metric to vary. If we take quantum fluctuations to be a meaningful concept, however, and we introduce into our Physical models changes of quantum fluctuations (almost certainly not just a scalar, so we probably shouldn't talk about "changes of Planck's constant") from place to place in space-time, then we would have to introduce a new set of dimensionful constants.

    Presumably constant quantum fluctuations would have some effect on measurements, but variations of quantum fluctuations from place to place would result in more subtle consequences, which would mirror the mass-independent force interpretation of the metric connection. That's by analogy with standard thermodynamics, in which it's variations of temperature that are fairly directly measurable, because we observe heat flows as a result, but the absolute temperature of a material that is in thermal equilibrium with its surroundings determines gross mechanical properties due to the thermodynamic phase of the material. Equally, on the quasi-classical view I'm pursuing here, constant quantum fluctuations at different amplitudes would presumably have consequences for the mechanical properties of space-time, so that in very strong gravitational fields there could be phase changes, but varying quantum fluctuations would have more immediately observable consequences.

    Recall that part of my argument is that the Unruh effect, taken with the principle of general covariance, seems to require that we consider thermal and quantum fluctuations to be very closely related (although very often the literature on the Unruh effect expresses outright shock that the QFT vacuum appears to be a thermal state to a non-inertial observer, because of the infinite change of the number of particles that this represents).

    Also of note is the closeness of my argument about quantum fluctuations to Poincaré's argument about the conventionality of metric representation of forces.

    I've also thought for a long time that the "dumb hole" literature, and the work of http://ltl.tkk.fi/personnel/THEORY/volovik.html", for example, has something to offer to this point of view.

    As to detail, Hellfire, absolutely needed, but conceptual thinking is the starting point for detail.
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  12. Dec 27, 2007 #11


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    what precisely are you measuring if you were to detect a change in c from 299792458 m/s to 300000000 m/s?

    let's revert the definition of the meter back to what it was before 1960 (when the meter was defined as the distance between two scratch marks on a platinum-iridium bar that was living in Paris somewhere), otherwise there is no meaning to a concept of such a measured change.

    hellfire, i'm willing to run with this a little with you. i've had long email conversations with Michael Duff and John Baez (a few years back) about this. remember, just like when measuring a length with a ruler (in which one is counting tick marks on an existing standard) all physical measurements are fundamentally of dimensionless values.

    (later edit): actually, hellfire, i got mixed up about who was saying what. you and i are singing the same tune. but i am still curious, from the perspective you had in your earlier posts, what it would mean exactly if we "measure today c = 299 792 458 m/s and tomorrow c = 300 000 000 m/s".
    Last edited: Dec 27, 2007
  13. Dec 27, 2007 #12


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    no, i think that Planck's constant is dimensionful in any case where the system of units are defined in such a way that does not assign [itex]\hbar[/itex] to something.

    if you measure everything in Planck units, then i guess Planck's constant is the dimensionless 1, but there is no way have a variable Planck's constant in any model, since it will always be 1 and will literally disappear from equations of physical law (like Schrodinger's). if you measure everything in Planck units, there literally is no Planck's constant, or speed of light, or gravitational constant to vary. they just go away.
  14. Dec 27, 2007 #13
    OK, Planck's constant, in my approach a measure of Lorentz invariant quantum fluctuations as well as a unit of action, is a constant by definition. If quantum fluctuations vary from place to place, the scalar component, say, will vary from [tex]1.0\hbar[/tex] to [tex]0.99\hbar[/tex] to [tex]1.01\hbar[/tex], say.
  15. Dec 28, 2007 #14


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    but, again, if you measure everything in terms of Planck units (length, time, mass), there ain't no [itex]\hbar[/itex]. it's not even there in any equations of physical law. (you would replace it with 1.) so there would be nothing to vary, even hypothetically. [itex]\hbar[/itex], c, G are only parameters of physical reality because of the anthropocentric units we cooked up as a historical accident (or the Zogopocentric units that the aliens on the planet Zog cooked up). Nature doesn't care about what units we use. but Nature has seemed to indicate a preference of scaling, an indication of where her tick marks are on her ruler, clock, and weighing scale. if we choose to follow her lead, there ain't no [itex]\hbar[/itex], c, G. they don't exist and there would be nothing to vary.

    now, conceptually, the (dimensionless) number of Planck Lengths in the Bohr radius (about 1025) could vary and physical reality would be different it that happened and we could meaningfully measure it. same with the number of Planck Times in the period of whatever Cesium radiation (about 1034) they presently use define a second. likewise with the masses of particles relative to the Planck Mass (about 10-22, depending on which particle). but (and i know there are real physicists out there with VSL theories and such) i think the only meaningful way to measure (or perceive) anything is relative to something else and if we choose to measure stuff against the corresponding Planck unit, there just ain't no [itex]\hbar[/itex], c, or G. and if you extend the convention to charge, in a similar way as electrostatic cgs units have, there ain't no Coulomb's constant [itex]1/(4 \pi \epsilon_0) [/itex] either. but if the electronic charge varied relative to that "Planck charge", that also is meaningful and we would know a difference (it is equivalent to a change in the fine-structure constant, which i suspect would be what would be the net varying parameter that might lead you to think that Planck's constant is varying. if [itex]\alpha[/itex] changes, you might claim that it's because of a varying Planck's constant, i might prefer to think of it as a varying e, someone else - a VSL proponent - might blame it on a varying c. all are equivalent and end up meaning the same thing. we would just be using different systems of natural units to describe reality. but Nature doesn't give a fig what units we use.)
    Last edited: Dec 28, 2007
  16. Dec 28, 2007 #15


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    The usual two-way measurement for the speed of light with the standards of lenght and time previously defined. Doesn't this make sense? IMHO it does and different results could be expected in principle. Then you could regard this as a change of c or as a change of m or s. However, there may be a difference between both then looking for the physical mechanism responsible for the change and a theory that postulates only one of both may be simpler or more according to usual physical principles.
    Last edited: Dec 28, 2007
  17. Dec 28, 2007 #16
    I think that units are not something that are wiped away just by us writing some constants as 1. Firstly, variables in Physics have semantic meaning, a small part of which is conveyed by units.

    Secondly, the conversion factors between different standards are important. What seem to be natural units today may not seem to be natural units in the future, under a different theory, then the values of h, G, and c relative to those new standards will be important. Nature doesn't give a fig which units we use, but the smooth operation of science depends on us telling other scientists which system of units we use. Papers say, "taking natural units, ..." or "using MKS units, ...", unless a journal requires a particular standard or unless the theoretical context makes natural units obviously what was used. Sometimes it's helpful to put h, G, and c back into an equation.

    I would say that the speed of light does vary, insofar as the metric changes from one place to another (this also in response to hellfire). The measured speed of light using a particular experimental apparatus will change from one place to another as the gravitational field changes. The measured speed of light in a particular national standards laboratory could be taken to be a constant. If the gravitational field at that laboratory changes, however, because of an earthquake, say, we would decide to compensate for that change instead of changing the standard, so maintainance of the standard depends on our theory. Insofar as standards are defined to be relative to standard conditions, at sea level, 20C, etc., the national laboratory makes whatever theoretical compensations it thinks are necessary when converting its experimental results in its conditions to the standard conditions. Detailed metrology does matter to experimentalists.

    When we say that we should only be interested in measuring dimensionless constants, that is firstly only relative to a particular theory, and secondly ignores all our technological use of the theory, which requires us to characterize experimental apparatus relative to standards, etc. That requires transport of standards from place to place, with proper attention to what we understand, according to our current theoretical understanding, to be the relevant differences of conditions at those different places.
  18. Dec 28, 2007 #17


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    not if the meter is defined to be "the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second." but if it defined to be "one ten-millionth of the length of the meridian through Paris from pole to the equator" or "the distance, at 0°, between the axes of the two central lines marked on the bar of platinum-iridium kept at the BIPM, and declared Prototype of the meter", then it does make sense. i guess you said as much.

    but if the definition of the meter was reverted so that it was both conceivable and meaningful that the experiment used to measure c resulted in a change of value (perhaps even a trend) that exceeded experimental error, the salient difference really is that the number of Planck Lengths per meter (as it is defined, which, if the meter stick is a "good" meter stick and doesn't lose or pick up atoms, amounts to a change in the dimensionless number of Planck Lengths per atom size, somewhere around the Bohr radius) and/or the number of Planck Times per second (as it is defined which, if your Cesium clock is a "good" clock and doesn't drop clock pulses from the Cesium radiation amounts to a change in the dimensionless number of Planck Times per period of radiation of Cesium) has changed. in my opinion (as an engineer, not a physicist) the salient difference is the change of either of those dimensionless values. check out the John Barrow quote at the Wikipedia Planck units article. i've copied and quoted it here to many times.
  19. Dec 31, 2007 #18


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    true. but nature doesn't care about our semantics.

    sure. that's why there are different sets of natural units. like Stoney Units, or Atomic Units. and if you measure the same quantity to be changing (say, the fine-structure constant), the cause of that change will ostensibly be different, depending on which set of natural units are used. some people might blame it on a changing c. other's a changing [itex]\hbar[/itex]. still other (like me) prefer to blame a changint [itex]\alpha[/itex] on a changing e. all are equally valid, since nature doesn't care if we use Planck units, Stoney units, Atomic units, etc.

    it's helpful to us. humans. but Nature doesn't care.

    i thought that the physics is that, even in a gravitational field, the speed of light is the same locally. over larger distances, there are other issues. i could be in free fall traveling a parabolic trajectory where the apogee happens to be right by where you are standing on a cliff. at the point of the apogee, you and i would literally be in the same frame of reference and would measure the speed of the same beam of light to be the same. but i am in free fall, an inertial frame and you are not.

    yup. you're right. but Nature doesn't necessarily care about what experiementalists care about. but good experimentalists should care about what nature does, so fundamentally, these measurements really are about dimensionless values. the measurement of some quantity in relation to another quantity of the same dimension of "stuff".

    but how, other than an accident of history, do we define those standards? unless you use some form of "natural units" (Planck units are the natural units i like best) you cannot avoid some arbitrary, anthropomentric definition of those standards. Nature doesn't care about that.

    yup. that is what metrology is about. that is specifically what a "transfer standard" is.

    although we human beings need to make use of them, Nature doesn't care about transfer standards.
  20. Jan 1, 2008 #19
    Er, you guys r a bit over my head but..

    The length of a meter is defined in terms of light and time...the distance that light travels, in a vacuum, in the fraction 1/299,792,458 of a second. It is a definition. How would it be possible to measure it as anything else without assuming that the extra(or lesser) time were the result of distance variation? Ok similar scenarios for the other examples imagined.

    Essentially c is a conversion factor between time and space. I have the feeling you know this !! Of course!! So what is the element I miss in trying to follow your discourse?
  21. Jan 1, 2008 #20
    Actually, there is a way in which G, a dimensionful quantity, might be said to vary in a way that could be detected experimentally, and without the ambiguities of interpretation which would accompany a variation in those other dimensionful quantities. The reason for this is the operational
    distinction present in the testing of the Einstein Equivalence Principle (EEP), where it is necessary to
    separate between "tangent space physics" (testing non-gravitational physics by doing local experiments
    where gravity can be neglected) and "local gravitational experiments" (doing local experiments where
    gravitation cannot be neglected, e.g. a Cavendish experiment).

    One may in principle have a situation where every possible tangent space physics experiment showed
    no variation in any (dimensionless) quantity, but where local gravitational experiments showed
    variations over time or from place to place. Of course such hypothetical variations would also show up as measured dimensionless quantities - but their interpretation would be more straightforward since
    one in effect measures gravitational quantities using units operationally defined from atomic physics.

    This is also the reason why, IMO, the use of Planck units is unfortunate since it mixes atomic and
    gravitational quantities and thus obfuscates their natural distinction as obtained from the EEP.
  22. Jan 1, 2008 #21


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    as in free fall, right?

    or is this where your laboratory is in free fall? i thought the difference (in the outcome of an experiment in local space) between inertial and free fall around a mass is supposed to be zero.

    but how would you take those dimensionless numbers that are the raw result of the experiment and turn them into a dimensionful quantity for G? it's still G referenced against a like-dimensioned quantity. what it that reference quantity?

    again, it's not just me:

    i like Planck units because what they normalize are these scaling parameters of free space. there are no prototypes, particles, or "thing" that some property is normalized by definition of unit. but it doesn't matter because, as far as i know, Nature doesn't give a rat's ass what set of units (including some choice of natural units) we use. if you come up with an experiment that indicates to you that G has changed, i think i (or a more competent physicist than i, a neanderthal electrical engineer) could take the same experimental results (which are dimensionless numbers, usually ratios of like-dimensioned quantity) and express the very same behavior in the experiment as a change of the ratio of particle masses to the Planck mass (where Duff uses the letter [itex]\mu[/itex]). just like, say if the fine-structure constant (which can be directly measured in different manners) shows a change in time (or position "hey, [itex]\alpha[/itex] is different over there at Zog than it is here."), it is equivalently valid to blame that change on a changing c, [itex]\hbar[/itex] or e (or [itex]\epsilon_0[/itex] if you aren't cgs) or some combination of these. but you can't tell which one (pick whatever set of natural units allow the dimensionful quantity of your choice to vary, you can't free up all of them) and it wouldn't really matter since our perception of reality would be operationally the same.

  23. Jan 1, 2008 #22
    Whether or not the laboratory is in free fall or not is not important. What is important is that doing a
    "tangent space physics" experiment, space-time curvature should be negligible to any perferred level,
    so that one is in effect only testing non-gravitational physics. On the other hand, when doing a "local gravitational experiment", the only space-time curvature should be due to the test bodies, and any space-time curvature due to the surroundings should be negligible to any preferred level.
    The reference quantity is of course atomic units, operationally defined from atomic physics. The point
    here is that there are two in principle fundamentally different types of experiment; one type involving gravitational quantities and the other not. This means that it is in principle possible to have two fundamental types of units; one which is operationally defined from atomic systems where gravity is negligible, the other which is operationally defined from gravitational physics. One simple example would be to use some fraction of the Earth's orbit around the Sun to define a "gravitational second" and the usual definition based on cesium to define an "atomic second". Measured in "atomic seconds", it is in principle possible that the "gravitational second" (as well as any other gravitational quantity) would vary, but such that any experiment not involving gravitational physics would not.
    Yes, I know it's not just you. However, I find the papers of Duff rather superficial since he is obviously
    not aware of the matters I have discussed above.
    It seems that you have missed my point entirely. The fine structure constant is a number which may be
    found experimentally by doing "tangent space physics", i.e. atomic physics without involving gravity.
    In this case all your arguments apply. However, they do not if you are measuring G since this
    quantity is not operationally measurable without involving gravity.

    And no, you could not take any indication of a variable G and turn it into a statement of variable
    masses exactly because this would be inconsistent with the class of non-gravitational experiments
    telling you that the masses have not changed. The best you could do would be to say that the
    (active) gravitational mass have changed, which is pretty much synonymous with a variable G.

    The clean distinction that should be made between gravitational and atomic units and the fact that
    Planck units do not respect this distinction, is the reason why I dislike Planck units. Any experimental
    result for which this distinction is important would be more difficult to interpret using Planck units.
    Last edited: Jan 1, 2008
  24. Jan 2, 2008 #23


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    well then, "of course". if you use atomic units (what Duff was calling "Bohr units", i dunno why he used a different label for it), then, in terms of those units, a variation of G is conceivable. but why would Nature choose the same system of units that you chose? you can use atomic units and say that the masses of particles remained constant, someone else could use Stoney units or Planck units to describe exactly the same phemomena and say that G remained constant and it's the masses of these subatomic particles that have changed. it describes the same thing.

    that speed of orbit is not believed to be as stable as the cesium radiation. i think they can measure how much that orbit is slowing down.

    well sure. but it's just a choice of which standards you measure things against. Nature doesn't care. pretending, for the moment, that the orbit of the Earth around the Sun is rock-solid steady, then there would be no variation of the atomic second to the gravitational second.

    i think that it's a lot more likely that he has. for some reason, i (and the guys at sci.physics.research such as John Baez and others) have more confidence in a pretty well renown string theorist than an anonymous poster to PF.

    i'm still not sure who is not getting the point. it's a difference between using a nice (and currently relatively inexpensive) cesium clock versus some contraption that has a Cavendish-like experiment in it to measure time.

    not changed relative to what? Duff has dealt with this (the [itex] \frac{\Delta c}{c} [/itex] or [itex] \frac{\Delta G}{G} [/itex] thing).

    no, if one uses that semantic, one is saying that the masses of the object (and thus the stuff that makes up the objects) have changed. it's not synonymous. in Planck units, G does not change any more than the number 1 changes.

    i have not saying that Planck units are nice for doing atomic or sub-atomic experiments, but the topic is not about what is nice for doing atomic or sub-atomic experiments. it's about cosmological models and whether or not it would be meaningful in such a model if Planck's constant (or any other dimensionful constant) was different. whether it's the Standard Model or the Cosmological Constant (which is a dimensionless number when expressed in natural units) or a new model with parameters that might represent the amount of dark matter and dark energy, all of these at the fundamental level are fully described with only dimensionless parameters. what Baez talks about at http://math.ucr.edu/home/baez/constants.html and http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/constants.html . i can actually understand the point that these guys are making (and i hadn't at first as a search of sci.physics.research reveals), but i can't find any reference to this "tangent space physics" except for this thread at PF.

    certainly there are arbitrary choices of what the units or standards that physical quantity are referenced against, some choices will fix G or [itex]\hbar[/itex] or c or e or me or whatever. you can choose natural units that will allow for some subset of these to vary (with some hypothetical measurement) but not the others. or chose another system of units that fix them to defined values. they are not operationally different. they interpret the same measurement differently. Nature doesn't care how we interpret anything.
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  25. Jan 2, 2008 #24
    Recall that my starting point was the assumption that the EEP is valid. The EEP says that the local
    non-gravitational physics does not vary. And whereas you are certainly entitled to use any units you want, using units in terms of which the EEP is seemingly violated would be a rather silly thing to do
    if this result can be explained as coming from the gravitational sector via the use of inappropriate units.
    As far as I can see from his papers, Duff treats potiential variations of all fundamental "constants"
    on the same footing. But the EEP tells us that this is not necessarily a wise thing to do, since it says that there is a natural distinction between local non-gravitational physics and local gravitational physics.
    This means that there is a natural distinction between atomic units and gravitational units, and that
    to look for violations of the EEP, the smart thing to do is to use atomic units.
    Look, all I am saying is that using atomic units, it is a possibility that all conceivable local non-gravitational experiments will show no variations in the physics whatsoever all over space-time. From this one may conclude that the EEP holds. On the other hand, it is also possible that using
    Planck units, some of these experiments will show changes in the physics. A natural interpretation
    of such a situation would be that these changes are coming from the gravitational sector, or that G
    changes. It cannot be blamed on the variation of other constants or inertial masses of elementary
    It seems that you have assumed that the Strong Principle of Equivalence (SEP) is valid. But the EEP
    is weaker than the SEP, so it is in principle possible to separate between inertial mass, passive
    gravitational mass and active gravitational mass. The first two of these masses should be identical and
    not variable. However, it is possible that the active gravitational mass is variable and that the EEP still
    holds. In this case it is a matter of taste if the variation is attributed to G or to the active mass
    M. Using Planck units, any seemingly variation in the local non-gravitational physics coming
    from the use of these units may of course be attributed to M as well as to G.
    Or whether any dimensionful constant were variable in such a model, right? But this is what I tried to point out, i.e., that when answering this question, one should separate between a variable G
    on the one hand and other variable "constants" on the other. And as I have tried to explain, the reason
    for this distinction is the natural separation between local non-gravitational experiments and local
    gravitational experiments provided by the EEP. In particular this means that by doing both local
    gravitational and non-gravitational local experiments, it is possible to separate any variation of G
    from any variation in the other "constants". By contrast, any variation in, e.g., the fine structure constant would be apparent only via local non-gravitatonal experiments, so any such variation may equally well
    be blamed on a variable c, [itex]{\hbar}[/itex] or e.
    I explained what I meant by the phrase "tangent space physics". It's all standard textbook stuff. May
    I suggest that it is inappropriate of you to complain about this particular phrase without taking into account how it has been explained?
    But people care about interpretations of experiments, since interpretations are crucial in assessing how well natural phenomena are understood in terms of some theoretical framework. Therefore it is
    crucial to choose units which do not obfusciate such interpretations.
    Last edited by a moderator: Apr 23, 2017
  26. Jan 3, 2008 #25


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    Nature cares about the validity of the EEP (or the SEP or the WEP). the validity of the EEP affects how we measure and perceive things. if the EEP were not valid, things would be different and we would notice. Nature doesn't care what units you or i may choose to use. my choice of a system of units is not going to change the net outcome of any experiment. also the validity of the EEP is not precluded by the validity of the SEP which does include gravitational experiments (like a Cavendish-like experiment) and the SEP is supported by GR which remains the accepted physics of the day.

    no, he gives dimensionless universal constants a qualitatively different status than dimensionful constants. he says that a variation of a dimensionless parameter is meaningful (which is really all that we measure) and that the variation of a dimensionful parameter in and of itself (i.e. the dimensionful parameter changes and none of the dimensionless parameters change) is not meaningful because we could not measure it to know.

    no, the EEP conceptually differentiates or dichotomizes between classes of experiments. those that are about gravitation vs. those that are not. the EEP does not preclude the SEP. the EEP can be true and allow for the SEP to be true also.

    not really. it's just not making claims about experiments regarding gravitational effects. it's not insisting on a difference.

    i think i agree with that, but i don't see the salience of it. if the EEP is violated, so is the SEP. big deal, so then we toss GR out the window and Einstein was wrong all the time (and maybe there's a aether somewhere and we just haven't noticed it yet).

    right, and it doesn't preclude the SEP. and the SEP is really the essential "Equivalence Principle" and GR is just fine with it.

    i fail to see that as the "natural interpretation". it is your interpretation because of the system of units you chose to use and that Nature doesn't give a rat's ass about.

    yes. so does GR.

    yup, and then those masses aren't equivalent any more, are they?

    i fully agree with that. when you say that some experiment appears to indicate that G has changed (let's say we noticed that somehow the Earth and the other planets and moons just slid into different orbits), then (if nothing else has changed) the Planck Mass [itex] \sqrt{\hbar c/G} [/itex] has changed (by your reckoning) and the mass ratio of particles to the Planck Mass has changed. like

    [tex] \frac{m_p}{m_P} = \frac{m_p}{\sqrt{\frac{\hbar c}{G}}} [/tex]


    [tex] \frac{m_n}{m_P} = \frac{m_n}{\sqrt{\frac{\hbar c}{G}}} [/tex]


    [tex] \frac{m_e}{m_P} = \frac{m_e}{\sqrt{\frac{\hbar c}{G}}} [/tex]

    and whatever other particles in the sun that collectively pull on us (or warp space-time) and the planets we ride on. so how would the output of that experiment be different if it was G that remained constant and the particle masses changed? if the mass ratio of the Sun to the Planck Mass changed in the same way because the mass of the Sun was the reality that changed (because the masses of the particles that make up the atoms that make up the Sun have changed), how would the experiment turn out differently? it would be the same thing.

    no, if referencing all quantities against their corresponding Planck unit, it could only be M. there would be no G to vary. whether it's a graviational experiment or not.


    so reality will adjust itself to suit our interpretation(s) of it? so what if different groups of people (using different systems of natural units each that normalize different dimensionful "constant" parameters) interpret the reality differently. whose interpretation is reality expected to conform itself to?
    Last edited: Jan 3, 2008
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