How can we be sure of Planck’s constant when we have never measured anything to that accuracy?

Question

Any constant in physics or chemistry comes from experimental design and consistency in measurements. For example, if you divide multiple of pressure and volume with the multiple of moles and temperature, you will get the constant R for any ideal gas.

However, given how small planck’s constant is, how can we assume its accuracy?

In: Physics

Answer 1

Because it’s been defined as a fixed value. The Planck Constant is EXACTLY 6.62607015×10^−34 J⋅Hz^−1 because thats HOW units like Joule and Hertz are defined. If we can eventually measure something that small, the machines will calibrate themselves by assuming the Plank Constant is correct and adjust the energy/frequency readings until that’s true.

And keep in mind all of these units are made up. They’re a way of understanding and expressing the natural world. There is no reason we couldn’t have made the Planck Constant equal to one, but that would force us to redefine how big a Joule is, how long a second is, change the definition of a Kilogram, and force us to redo and redefine most of physics. Instead, we defined certain naturally occurring phenomenon as set values and based eveything off of that

Probably the easiest example is the speed of light. Instead of basing it off of the meter and worrying about how our measurement techniques will change in the future, we flipped it around. The speed of light is EXACTLY 299792458 m/s, and a meter is defined as EXACTLY 1/299792458 of that. This ratio is the same no matter the situation, no matter the conditions, no matter how you measure it. Same as the Planck Constant.

Not sure how familier you are with the prototype kilogram, but that’s probably the best example of why we WANT to fix certain values instead of relying strictly on measurements. The kilogram was originally defined as the mass of a particular object. There were several identical copies made and shipped all over the world, but the one in Paris was considered THE kilogram. But over time the mass of these objects diverged. Oxidation, dust, small bits flaking off, weird quantum stuff…. According to the most accurate measurements in the world, the Prototype Kilogram “changed” it’s mass. But since the Kilogram was defined as EXACTLY that object it still weighted 1kg, even though it’s mass was different than the last time. So every time the prototype kilogram was weighed, the “value” of the kilogram had to be updated.