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**Scaling - Inverse relationship between uncertainty and mass**

I’m trying to express Heisenberg's Uncertainty Principle in a simplified formula that is not boundary unlimited and still capture what I believe is an inverse relationship between uncertainty and mass - the "scaling hypothesis".

I started with this mathematical definition of uncertainty: h: m Delta x Delta v >h which I got from a lecture by Prof. Wolfson. As usual, m = mass; delta x = the uncertainty in position, delta v = the uncertainty in velocity not momentum but I don't think that matters here; and h = Planck’s constant). I don't know what the equation form of this definition is but later in his lecture, Prof. Wolfson says: "If we look at the mass and divide both sides of the equation by m [mass], we get: [Uncertainty =] Delta x Delta v greater than h over the mass. He goes on to say: "That means for massive objects like a tennis ball or me or a car, the product of the uncertainty in position and uncertain velocity is miniscule."

I took this to be mathematical support for what I'm calling the "scaling hypothesis". A friend, while not disagreeing with the claim that uncertainty decreases as mass increases, says the math does not support it. Why? He says the equation contains a boundary variable which I'm guessing is the >h factor. If in fact he is right, I would like to restate the equation to remove the boundary and retain the uncertainty/mass relationship.

Prof. Wolfson does not express any concern about the inclusion of >h in the equation leaving me to believe he thinks the math supports his conclusion. He goes on to say that Planck’s constant is a tiny tiny number so the uncertainty principle has a negligible effect on macroscopic objects. Even so, I think my friend is on solid ground in pointing out that >h does not set an upper boundary only a lower one; hence, the math does not support the claim.

Moreover, since I'm trying to relate increases in mass to decreases in uncertainty in a simple formula, I'm not sure what role Planck’s constant has. I know it must be a non-zero value, if it weren't, uncertainty would not be an issue. But I don't know how Planck’s constant bears on mass and uncertainty; except, perhaps, that h provides a minimal value for mass. In any case, by trimming the formula to: (Delta x Delta v over m), I get rid of the >h boundary issue without undermining the physics since >h has a miniscule effect on uncertainty.

BTW, What is the equation form of the definition h: m Delta x Delta v >h?

Dave1939