# Is there any physical quantity that does not have uncertainty?

I saw this video and I got a thought: Is there any physical quantity that does not have uncertainty? Basic models are:

for lenght

for time end energy (so for mass too) and I realized that (based on the video) photons near to each other have uncertain amount of substance - so the result will be uncertain luminosity too. And what about electrical charge? Is there some uncertainity for it?

• I think you mean 'parameter,' not 'quantity' , as e.g. there's no uncertainty in how many legs I have. – Carl Witthoft Sep 14 '14 at 12:22
• @CarlWitthoft Yes - that is not a constant, but there is uncertainity for instance in number of photons in laser. – foggy Sep 14 '14 at 12:43
• The uncertainty principle does not apply to counting the number of items (even photons). It applies, as the albedic answer suggests, to physical variables. – Carl Witthoft Sep 14 '14 at 13:07
• But amount of substance is a full physical variable. It is really not a constant, as is the case with location X momentum, but we couldn't really say number of photons in laser, even if we would have perfect detector - and that is the same, as in the case of other quantities - I really recommend the video in the description. – foggy Sep 14 '14 at 13:19
• @CarlWitthoft: I suspect you have two, but I'm not certain about it. – Nikolaj-K Oct 19 '14 at 21:39

Any physical variables come in 'canonically conjugate pairs' cannot be simultaneously measured with arbitrarily high accuracy. Canonically conjugate pairs are those variables whose corresponding operators do not commute; means the order in which they occur when they form a product makes the difference. examples: position and momentum, energy and time, angular position of the momentum vector and the corresponding component of the angular momentum.

Uncertainty comes with pair of variables, not with a single variable. The pair of physical variable whose corresponding operates do commute (not conjugate pairs) can be measured without uncertainty. For example, time and position of a particle can be measured simultaneously and is not limited with uncertainty.

Of course, there are uncertainties associated with all the measurements. Whatever we measure may not be perfect, always there will be uncertainties. Those uncertainties are related to experimental or instrumental limitations. But the uncertainty what we see in the quantum world (Heisenberg's Uncertainty principle) is inherent in nature. Even with a perfect instrument/experimental setup, this uncertainty will be there for the conjugate pairs!

Furthermore, if you are a beginner, "Alice in Quantumland" By Robert Gilmore would be interesting. Alice when she meet the electron, it is moving to and fro very rapidly. When she ask to stand still for a moment, the electron reply "I am afraid there is not room enough. However I will try". Then the electron slows down. This time the electron looks so fuzzy and out of focus and the electron say "I am afraid that the more slowly I move, the more spread out I become. That is the way the things are here in Quantumland".... So, the uncertainty associated with the conjugate pairs are inherent and that is the way the things are in Quantumworld! :)

Refer this for your question regarding electric charge:

• you cannot define canonically conjugate pairs by 'do not commute'. There are many operators that do not commute, which are not canonical conjugates. – ulf Nov 25 '14 at 7:25

I'm convinced that nothing in this world can be measured without uncertainty. Take the measurement of a current. One have to use in this case an ammeter which has to be a low as possible resistor. But it has to have an ohmic resistor. Take the measurement of electric potential. One have to take a voltmeter which has to be a high as possible resistor. But it's not perfect too and the resistance is not infinitely high. In both cases the measurement has some uncertainty. So in the macroscopic world the uncertainty is a common thing. Then ever a physician measure something he will write the result in the form $x \pm y (unit)$.

To be a little more sophisticated One can say that to catch the moment of the full moon is an impossible thing. What ever you calculate I ask you to calculate it with a higher precision. At some point we end with an atomic clock. But this clock has an uncertainty too.

What Heisenberg told us is the predictable value of uncertainty on the atomic and subatomic level. His principle is true until it is not possible to manipulate (or measure) particles with smaller quants (which we dont know at the moment).

• The OP is asking about quantum uncertainty, which is qualitatively different from uncertainty in measurements in general. – Ben Crowell Oct 20 '14 at 1:21