# I Are physical constants subject to the uncertainty principle?

1. Feb 28, 2016

### 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.

2. Feb 28, 2016

### Staff: Mentor

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

3. Feb 28, 2016

### mathman

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

4. Feb 29, 2016

### vanhees71

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

5. Feb 29, 2016

### A. Neumaier

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

6. Mar 1, 2016

### .Scott

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 any one measurement attempt is constrained by HUP, any arbitrarily large (but finite) number of attempts averaged together would also be limited by HUP.

7. Mar 1, 2016

### mathman

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.

8. Mar 2, 2016

### .Scott

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"?

9. Mar 2, 2016

### Staff: Mentor

Assumption of the model and if its consistent with experiment.

Thanks
Bill

10. Mar 2, 2016

### mathman

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

11. Mar 2, 2016