Certainty Gain by Uncertainty Power?

[Janitor]

We agree that the number is smaller but can it means also that the uncertainty is lesser? - Antonio

Actually, my point is that the number is only smaller if you choose units in which h<1. But there is nothing profound about choice of units, is there? Units in which h>1 are just as acceptable.

 

[Antonio Lao]

If your choice of unit is the same as a scale factor then there is big different. Given an area A and a scale factor s, the new area is given by $s^2A$. If s is smaller (s < 1) the new area is smaller. Bigger s (s > 1), bigger area.

The unit of h is actually angular momentum. So by squaring h we are actually gettting something square of angular momentum. What I want to know is what's the physical meaning of square of angular momentum? Somebody, maybe it was Russell, said that product is the same as addition (integration) if some logarithmic (exponential) function is involved like $e^x$.

 

[Janitor]

Antonio,

I don't have any useful thoughts at the moment on the issue of "how would you make a dimensionless number such as the fine structure constant bigger or smaller?" or "what's the physical meaning of square of angular momentum?"

To keep hammering away at my point, how would you critique this discussion between Peter and Paul?

Peter: "The mass of the Earth is really huge. It is 6 x 10^24 kg. When you square that, you get an even bigger number."

Paul: "On the contrary, the mass of the Earth is small. It is only 7 x 10^-7 in units of solar mass. When you square that, you get an even tinier number."

It seems to me that Peter and Paul are both misguided in thinking that the mass of the Earth can be fundamentally classified as either "big" or as "small."

 

[Antonio Lao]

Janitor,

You got a good point. Yours looks like reasoning behind the relativity of number among fractions and whole numbers.

A physical law with this kind of relativeness is the Law of Universal Gravitation.

$$F = G \frac{m_1 m_2}{R^2}$$

and Coulomb law

$$F = K \frac{q_1 q_2}{R^2}$$

This gravity force is effective, I think, whenever there is disparity in the mass (m1 >>> m2 , vice versa) or charge.

When m1=m2 such as the structure of a positronium, I cannot understand how the forces of gravity and electricity keep the electron and postiron apart (without crushing into each other)? What is it that keeps them apart? What force?
__________

The other is relativeness of viewing distances. The moon appears the size of my fist when I extend toward it because the fist is much nearer to me than the moon.

 

[matt grime]

re mod 2

Thanks. Could you explain further the above?

you wish fo A to be equivalent to -A, presuming you mean in some arithmetical sense, that implies 2A=0, thus you are in a field of characeristic 2, or similar

 

[Antonio Lao]

matt grime,

Thank you very much.