The Heisenberg Uncertainty of Bowling Balls

[Jagella]

I was recently thinking about the Heisenberg Uncertainty Principle which states that we can not know a subatomic particle's position and momentum at any instant. We can know one or the other measure but not both at the same time. The more we know about one, the less we know about the other.

Can this same principle apply to macro objects like bowling balls? If we wish to know a bowling balls' average velocity, we measure the time it takes to roll down the alley to the pins and divide that number into the length of the alley. Obviously, we know little about the ball's position, though, because it moved down the entire length of the alley. We can consider the first half of the alley and measure the average velocity of the ball down that distance. Doing so reduces the uncertainty of the ball's position by one-half, but now we know only one-half about the ball's average velocity because we are not measuring the ball's velocity down the entire alley, only one-half of the alley.

It seems to me that the measurement of average velocity and position are what Bohr would call "complimentary" measurements. When one measurement increases in accuracy, the other decreases in accuracy.

An obvious objection might be raised at this point. We can apply Newton's laws of motion and basic differential calculus to determine the ball's instantaneous velocity at any position along its path down the alley. We then would know its exact position and velocity.

Does this argument demonstrate that Heisenberg's Uncertainty Principle does not work on the macro level? I believe that what measurements we may make on the macro level are only approximations, and therefore we really don't know the bowling ball's exact position and velocity. The ball has substantial volume and is made up of trillions of atoms. What point in the volume of the ball can we refer to when we consider its position? Classical physics is fine for making approximate measurements on the macro level, and it makes some sense to speak of simultaneous position and velocity for practical purposes. If we zoom down to the level of atoms, though, experiments demonstrate that the greater precision begins to show that measuring a particle's position precludes measuring its momentum, and vice versa.

What I'm wondering is just how do experiments demonstrate Heisenberg's Uncertainty Principle. Can anybody help me with this issue?

Jagella

 

[Clever-Name]

It's important to note that NO measurements can be exact. ALL measurements are approximations.

With that being said it really doesn't make any sense to apply HUP to macro-scale objects. Your bowling ball example doesn't really make any sense either because we can SEE where the bowling ball is as it's rolling down the lane. We might not be able to exactly pinpoint it's position but let's just say we can be accurate to half a meter at any given time. Even with the massive uncertainty [itex] {\Delta}x = 0.5m [/itex] the mass of the bowling ball makes any uncertainty in momentum negligible.

For example, with the above uncertainty in position and a mass of let's say 6kg (found a bunch of different values with google).

[tex] {\Delta}x{\Delta}p \ge \frac{\hbar}{2{\pi}} [/tex]
[tex] {\Delta}xm{\Delta}v \ge \frac{\hbar}{2{\pi}} [/tex]
Assuming it's equal to...
[tex] {\Delta}v = \frac{\hbar}{{\Delta}xm2{\pi}} [/tex]

Plugging in numbers we end up with an uncertainty in the velocity of:

[tex] {\Delta}v = 5.57 \times 10^{-36} [/tex]

Which as I'm sure you can tell is ridiculously small.




While this example is not exactly what you described in your post I just used it to point out the idiocy in using HUP at a macroscale. It only really makes sense to use it when dealing with point particles or small enough molecules that you can approximate them as points.

 

[Jagella]

It's important to note that NO measurements can be exact. ALL measurements are approximations.

That's true, but I think it's fair to say that “approximation” in the context of trying to apply the uncertainty principle to macro-scale objects might mean “comparatively imprecise.” Physicists' measurements of subatomic particles and their motion are vastly more precise than measurements applied to bowling balls. I'm sure that's what Bohr meant by “approximation.”

Your bowling ball example doesn't really make any sense either because we can SEE where the bowling ball is as it's rolling down the lane.

That's an interesting point. Are you saying that we need not measure the ball's position? In the case of subatomic particles, we cannot see them but need to rely on some kind of measurement to know their location. Is that correct?

Δv=ℏ/Δxm2π


Plugging in numbers we end up with an uncertainty in the velocity of:

Δv=5.57×10−36

Which as I'm sure you can tell is ridiculously small.

Well, it's small all right. If I use your calculations, the smaller the mass of the object, the greater the uncertainty in its velocity. At some point the uncertainty in the velocity isn't so “ridiculously small” anymore.

While this example is not exactly what you described in your post I just used it to point out the idiocy in using HUP at a macroscale.

I'm sure that one need not be an idiot to try to see what happens to Heisenberg's Uncertainty Principle on the macro level. I think it's only natural to try to answer such questions. You may wish to check the June 2011 issue of Scientific American. It includes an article Living in a Quantum World that discusses quantum mechanics on the macro level.

Have a good day.

Jagella