Planck's Constant/Uncertainty Principle

[noobphysicist]

I just got to the chapter of Quantum Physics in this book for amateurs. A couple of questions:

If Planck's constant was smaller than it actually is, then how the uncertainty principle be affected? What if Planck's constant was zero?

ALSO:

When you flip a coin, the outcome is uncertain. Does this uncertainty come from quantum uncertainty? If so, please explain to me their relation.

I did some googling but I'd like to know what you guys know about this

 

[Simon Bridge]

1. if planks constant was zero then the one could get arbitrarily fine statistics.
There are two forms of Heisenberg's uncertainty - what does your book say it is?

2. Coins are far too big for quantum uncertainties to show up.
The glib statement for beginners is: classical statistics is a description of the experimenters state of knowledge of the system - quantum statistics is the description of the Universes state of knowledge of the system. When you toss a coin, but before you look, the Universe still knows if it is heads or tails. If an atom could be spin-up or spin down ... the Universe doesn't know which way up it is until someone measures it.

Bear in mind - there is no classical description of quantum mechanics to help you understand it.
You just have to get used to the math.

 

[noobphysicist]

I see, and what if Planck's constant was not exactly zero, but just smaller? Would one still get "arbitrarily fine statistics"?

 

[Dale]

If Plancks constant were smaller we would just be using different units. Often we set Plancks constant to 1 for convenience. The numerical value of Plancks constant tells nothing about physics, only about our units.

 

[Simon Bridge]

I think the question was poorly phrased - ask instead "what would it mean if the uncertainty constant were a different value?"

The constant in the uncertainty principle is already smaller than Plank's constant by a factor of four-pi.
If it were, say $\hbar /10$ instead of $\hbar /2$, that would allow for finer statistics but not arbitrarily fine.

Fundamental constants are (it appears) all related to each other.
The non-trivial way that you can imagine a fundamental constant, like Plank's, having a different value (as opposed to just changing the units) would put us, effectively, in a different Universe - one where the constants have different relationships. That would naturally impact all areas of physics, not just the uncertainty principle. It's a much bigger topic (an active field of study in cosmology for eg) and can easily become much more speculative than the forum will allow.

The uncertainty principle is usually taught as follows:
http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html
... should help you see how it turns out that the uncertainty constant is not $\hbar /10$.

 

[noobphysicist]

If Plancks constant were smaller we would just be using different units. Often we set Plancks constant to 1 for convenience. The numerical value of Plancks constant tells nothing about physics, only about our units.

I see, interesting.

 

[noobphysicist]

I think the question was poorly phrased - ask instead "what would it mean if the uncertainty constant were a different value?"

The constant in the uncertainty principle is already smaller than Plank's constant by a factor of four-pi.
If it were, say $\hbar /10$ instead of $\hbar /2$, that would allow for finer statistics but not arbitrarily fine.

Fundamental constants are (it appears) all related to each other.
The non-trivial way that you can imagine a fundamental constant, like Plank's, having a different value (as opposed to just changing the units) would put us, effectively, in a different Universe - one where the constants have different relationships. That would naturally impact all areas of physics, not just the uncertainty principle. It's a much bigger topic (an active field of study in cosmology for eg) and can easily become much more speculative than the forum will allow.

The uncertainty principle is usually taught as follows:
http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html
... should help you see how it turns out that the uncertainty constant is not $\hbar /10$.

Thank you.