Uncertainty principle at the macroscopic level

[preitiey]

what will be the scenario if Heisenberg's uncertainty principle is applied at macroscopic level?

 

[.Scott]

That's kind of hard to do without really messing things up. Let's increase the Planck constant so that the Planck length increases from 1.6 10^-35 meters to about a centimeter. The first problem I'm running into is trying to hit the correct key on my keyboard. They're only slightly further apart than the Planck length, so it's not clear that they're in different places. Also, it seems I can tell either where they are or how fast they're moving, but not both very accurately.

 

[preitiey]

Can we practically think of this dimension for Planck's constant? If yes, that means we are assuming the energy of quanta and its frequency of approximately same value and that too quite large. possible so?

 

[Chandra Prayaga]

In view of the earlier posts, I am not sure what the original question meant. Are we talking about applying the same uncertainty principle (with the standard value for Planck's constant) to macroscopic phenomena around us, or are we talking about a mythical universe in which Planck's constant is huge?

 

[preitiey]

Yes, I am talking about applying this principle to macroscopic level, that means to a level where we can watch it significantly. Will this principle hold for macroscopic dimension?

 

[phinds]

Yes, I am talking about applying this principle to macroscopic level, that means to a level where we can watch it significantly. Will this principle hold for macroscopic dimension?

The HUP is not limited to any particular size, BUT ... for all practical purposes it is irrelevant at the macroscopic level. You could watch a macroscopic object for MUCH longer than the universe has already existed and you would never see any change.

 

[preitiey]

Here one thing I am confused with:
we know p = mv, v is the velocity of the particle.
if velocity is known, momentum can be calculated. But velocity is determined by the displacement of the particle within some time range. so for that time range, we know where the particle is. This means we know both momentum and position simultaneously. What's wrong here?

 

[phinds]

Here one thing I am confused with:
we know p = mv, v is the velocity of the particle.
if velocity is known, momentum can be calculated. But velocity is determined by the displacement of the particle within some time range. so for that time range, we know where the particle is. This means we know both momentum and position simultaneously. What's wrong here?

There has been some lively discussion here about whether the HUP applies to a single measurement or not. That is, some people argue that you can in fact know the velocity and momentum of a single particle at a single time. What is not in any dispute at all, however, is that you won't get the same answer twice in a row.

That is, if you could set up the EXACT same starting conditions on a quantum particle multiple times and each time measure the velocity and momentum of the particle you would get a different answer each time and the distribution of the answers would follow the HUP.

So "knowing" both the velocity and momentum of a quantum object really doesn't really tell you what you think it tells you.

 

[PeroK]

what will be the scenario if Heisenberg's uncertainty principle is applied at macroscopic level?

The uncertainty is there, but it's too small to notice.

Here one thing I am confused with:
we know p = mv, v is the velocity of the particle.
if velocity is known, momentum can be calculated. But velocity is determined by the displacement of the particle within some time range. so for that time range, we know where the particle is. This means we know both momentum and position simultaneously. What's wrong here?

In QM you have:

$<p> = m\frac{d<x>}{dt}$

This is a relation between expectation values of position and momentum. It's not a relation between specific measurements of position and momentum.