What is the name for the Heisenberg uncertainty principle?

[kent davidge]

TL;DR Summary

besides the one in the title

In quantum mechanics the name is Uncertainty principle. But outside of QM, what is the name for those inequalities?

 

[lekh2003]

Well, the uncertainty principle has a meaning in physics, and there isn't really a special name for characteristic equations that look exactly like the uncertainty principle. This question doesn't really mean anything.

 

[Klystron]

Summary:: besides the one in the title

In quantum mechanics the name is Uncertainty principle. But outside of QM, what is the name for those inequalities?

Niels Bohr wrote often about complementary or conjugate variables. While within QM perhaps you are thinking of his theory of complementarity? From the linked article:

In physics, complementarity is both a theoretical and an experimental result of quantum mechanics, also referred to as principle of complementarity. Formulated by Niels Bohr, a leading founder of quantum mechanics, the complementarity principle holds that objects have certain pairs of complementary properties which cannot all be observed or measured simultaneously.

A reaction to Bohr by Werner Heisenberg (in the same artcle):

Bohr has brought to my attention [that] the uncertainty in our observation does not arise exclusively from the occurrence of discontinuities, but is tied directly to the demand that we ascribe equal validity to the quite different experiments which show up in the [particulate] theory on one hand, and in the wave theory on the other hand.

 

[martinbn]

It is also known by the same names in harmonic analysis.

 

[Vanadium 50]

Do you perhaps mean the Cauchy-Schwartz inequality?

 

[martinbn]

Do you perhaps mean the Cauchy-Schwartz inequality?

I don't think that's what he means!

 

[vanhees71]

It's the Heisenberg-Robertson uncertainty principle. The correct interpretation is that quantum theory predicts that you cannot prepare a particle where both position and momentum are well determined, i.e., if you prepare the particle to be at a well-defined position (i.e., with a narrow position-probability distribution peaked sharply at a point in position space), then necessarily its momentum distribution is broad.

Quantitatively it says that in any (pure or mixed) quantum state the standard deviations of the components of the position vector of a particle and its momentum components is
$$\Delta x_i \Delta p_i \geq \hbar/2.$$
It follow directly from the very fundamental properties of the quantum theoretical notion of states and the description of observables in terms of self-adjoint operators on a Hilbert space. It's a direct consequence of the positive definiteness of the scalar product and the associated Cauchy-Schwarz in equality as @Vanadium 50 mentioned above.

 

[Vanadium 50]

I don't think that's what he means!

I'm not sure even he knows what he means. But I think my guess is at least a potential answer to the question he posed.

 

[A. Neumaier]

Perhaps you were looking for the Nyquist theorem?

 

[martinbn]

Perhaps you were looking for the Nyquist theorem?

Why is this your guess?

 

[DaveE]

Perhaps you were looking for the Nyquist theorem?

This is as classical as classical physics can be. I'm not aware of any uncertainty in the sampling processes, although information is lost (by definition) and that can create uncertainty when trying to go backwards (reconstruction).

 

[A. Neumaier]

Why is this your guess?

It's essentially the same inequality.

 

[martinbn]

It's essentially the same inequality.

How!

 

[EPR]

Summary:: besides the one in the title

In quantum mechanics the name is Uncertainty principle. But outside of QM, what is the name for those inequalities?

It has no meaning outside QM. What were you trying to ask?

 

[vanhees71]

Well, there's some meaning in classical waves too. E.g., if you want a nicely monochromatic electromagnetic wave (light) you have to live with that it is wide-spread in position and vice versa.

The relation to the Nyquist theorem thus simply is that it tells you about the relation of the width of distributions related by a Fourier transformation.

 

[Riemann Mirari]

Summary:: besides the one in the title

In quantum mechanics the name is Uncertainty principle. But outside of QM, what is the name for those inequalities?

principle of complementarity