I Are physical constants subject to the uncertainty principle?

[Happiness]

Are physical constants, such as the elementary charge or the gravitational constant, subject to Heisenberg uncertainty principle, theoretically and empirically?

Theoretically in the sense that infinite precision of these constants will directly violate HUP. Empirically in the sense that, for instance, the mass of an object cannot be determined to infinite precision so the gravitational constant, which is calculated from masses, cannot too.

Some constants such as magnetic permeability are defined exactly. So I presume it only makes sense to ask the question for constants that are not defined exactly.

 

[bhobba]

Of course not. The dead give-away is - constant. In QM constants are just that - a constant that multiplies the state hence have one eigenvalue - that constant. This there is no variance or uncertainty. when observed - you always get that constant

Thanks
Bill

 

[mathman]

HUP applies to any measurement you may make to check the value of a constant, not the constant itself.

 

[vanhees71]

Most constants are just conventions defining units. In Planck units all observables are measured with dimensionless numbers :-).

 

[A. Neumaier]

But the original question makes sense for the fine structure constant, which is independent of the choice of units.

 

[.Scott]

Are physical constants, such as the elementary charge or the gravitational constant, subject to Heisenberg uncertainty principle, theoretically and empirically?

Theoretically in the sense that infinite precision of these constants will directly violate HUP.

Since you have invoked the phrase "infinite precision", I take it you are willing to consider the most extreme argument. Any single attempt to measure the speed of light would result in a finite precision constrained by the HUP and the mechanics of the measurement - though, most likely limited by other more mundane mechanical constraints. Since anyone measurement attempt is constrained by HUP, any arbitrarily large (but finite) number of attempts averaged together would also be limited by HUP.

 

[mathman]

Since you have invoked the phrase "infinite precision", I take it you are willing to consider the most extreme argument. Any single attempt to measure the speed of light would result in a finite precision constrained by the HUP and the mechanics of the measurement - though, most likely limited by other more mundane mechanical constraints. Since anyone measurement attempt is constrained by HUP, any arbitrarily large (but finite) number of attempts averaged together would also be limited by HUP.

The average of a large number of independent measurements will tend toward the true value. The point I made above is that there is a difference between the measured value of a constant (HUP limited) and the true value, which is exact, even though known approximately.

 

[.Scott]

The average of a large number of independent measurements will tend toward the true value. The point I made above is that there is a difference between the measured value of a constant (HUP limited) and the true value, which is exact, even though known approximately.

If all the resources of the universe could not, in theory, resolve a physical constant to more than 100 or 200 places, then by what reasoning is that constant "exact"?

 

[bhobba]

If all the resources of the universe could not, in theory, resolve a physical constant to more than 100 or 200 places, then by what reasoning is that constant "exact"?

Assumption of the model and if its consistent with experiment.

Thanks
Bill

 

[mathman]

There is a difference between the value of a constant (exact) and a measurement (approximate).

 

[Vanadium 50]

First, even classically there is no such thing as a perfect measurement. So we should sweep that off the table.

Second, since this is an I, I can assume you know what the uncertainty principle is - it isn't making the statement "everything is uncertain", it is making a statement about pairs of conjugate variables. For a constant, what is its pair?

Finally, even if a constant were part of a conjugate pair, QM doesn't prohibit measuring it to arbitrary accuracy - only simultaneous measurement of both members of the pair.