If only dimensionless constants are physically meaningful, and both Planck's constant, $h$, and the speed of light, $c$, are in the denominator of the expression for the fine structure constant, $\alpha$, then is there any way of distinguishing, by measurements or experiments, between an increase of $h$ and an increase of $c$ (assuming a definition of $c$ in terms of a meter rod, rather than itself)?
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2What do you mean by "operationally distinguishable"? What operations? – sammy gerbil Feb 28 '17 at 04:10
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Distinguishable by measurements, as, for example, when MJ Duff writes "the time variation of dimensional constants, such as ℏ, c, G, e, k,... which are merely human constructs whose number and values differ from one choice of units to the next, has no operational meaning." See "operationalism" – austinlorenz Feb 28 '17 at 04:17
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1What book or article are you quoting from? Where are you directing me to find "operationalism"? That sounds like the philosophy of science. Are you asking about a cosmological context? ... Your quote says changes in $h$ or $c$ have no operational meaning but does not say that they are indistinguishable by any measurement. – sammy gerbil Feb 28 '17 at 04:28
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MJ Duff's comment on Davies: https://arxiv.org/abs/hep-th/0208093 – austinlorenz Feb 28 '17 at 04:29
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Operationalism: https://plato.stanford.edu/entries/operationalism/ – austinlorenz Feb 28 '17 at 04:30
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If $h$ and $c$ (along with $G$, I suppose) are fundamental constants, then it makes no sense to speak of their change because there is no other more fundamental standard w.r.t. which they may be compared. – Deep Feb 28 '17 at 04:33
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Do we have/want a time-varying-constants tag? – innisfree Feb 28 '17 at 04:37
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2Operationalism means that the meaning of a concept is synonymous with its method of measurement, so I take Duff's quote to mean that there is no way of distinguishing between a change in dimensional constants by means of measurements. According to Duff, if a dimensionless constant were to vary with time, then the choice of units would determine which dimensional constants we could regard as having changed, and no measurement would. – austinlorenz Feb 28 '17 at 04:39
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1Possible duplicate of Is it possible to speak about changes in a physical constant which is not dimensionless? Possibly related to units and nature – sammy gerbil Feb 28 '17 at 04:46
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1The stanford link says that Bridgman came up with Operationalism in 1927. But it seems that Einstein was ahead of him. This was published in 1916. https://www.marxists.org/reference/archive/einstein/works/1910s/relative/ch08.htm – mmesser314 Feb 28 '17 at 05:23
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2The references to Duff's two papers (one a trialogue with two others) are really the best answers to this. The first one is Duff's paper referenced in sammy gerbil's first reference in his comment above, the second is referenced in the accepted answer to sammy's second reference in the comment above. In those PSE answers the best , and truly excellent, answer is by Pisanty (on the first one). Beadles answers the second one and summarizes the second paper. Worthwhile reading those and reading those two Duff (one with others) papers. – Bob Bee Feb 28 '17 at 05:58
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What Duff says makes sense. Only a change in a dimensionless combination of units can be detected.
The argument seems to be that every physical constant (unit) must be defined and measured in terms of others. So we cannot tell if a change is in the unit being tested or one of the units which we assume to be constant. Which set of units could have changed depends on how the unit in question is defined.
sammy gerbil
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This is an experimentalist's answer:
What is the fine structure constant?
A dimensionless constant which characterizes the electromagnetic force
The coupling constant is also called the "fine structure constant" since it shows up in the description of the fine structure of atomic spectra. It appears naturally in the equations for many electromagnetic phenomena.
Alternatively, there are other equivalent forms:
e is the elementary charge;
π is the irrational number Pi;
ħ = h/2π is the reduced Planck constant;
c is the speed of light in vacuum;
ε0 is the electric constant or permittivity of free space;
µ0 is the magnetic constant or permeability of free space;
ke is the Coulomb constant;
RK is the von Klitzing constant;
Z0 is the vacuum impedance or impedance of free space.
It is known that the coupling constant changes with the energy of the interactions:
Figure 5: Evolution of the inverse of the three coupling cons tants in the Standard Model (left) and in the supersymmetric extension of the SM (MSSM) (right). Only in the latter case unification is obtained. The SUSY particles are assumed to contribute only above the effective SUSY scale MSUSY of about 1 TeV, which causes a change in the slope in the evolution of couplings. The thickness of the lines represents the error in the coupling constants
The a_1 is the electromagnetic constant in this plot, and has been measured to change, i.e. an experimental fact.
The question then is, for the measured change in the dimensionless by construction number, can we also find which of the dimensionfull constants is contributing to the change? The answer is :an independent experiment is needed , devised to measure any changes in the dimensionfull numbers individually. Something must be changing, the individual constants have been found by independent measurements at low energies.
There is no algebraic way that from one measurement, two values can be deduced, i.e. from a change in alpha, a unique change in one of the various dimensionfull constants. One needs two equations for two unknowns and here there is only one.
I would be in favor of the change being in the permittivity or the permeability of free space, as quantum field theory populates it with various fields, but in any case, an independent measurement is necessary.
