CraigS

25-02-2011, 10:59 AM

Been doing some reading this week, and have encountered some interesting facts. As a result, I thought it may be interesting to start a thread to capture some factual, counter-intuitive snippets. (The counter-intuitiveness, of course, depends on the viewer) ;).

Here’s a couple I’ve encountered this week (credits to others):

Gravity:

1. The force on a point mass decreases as (1/r^2), when the mass is located outside the sphere. If the sphere is hollow, the force on a point mass inside the sphere is zero, and is independent of r. If the sphere is solid, and of uniform density, the force on a point mass inside the sphere, decreases with decreasing radial distance between the point mass and the centre of the sphere (decreases linearly with r).

2. Imagine an infinitely long line of mass (ie: a cylinder). The acceleration, ‘g’, due to the gravity of the line mass, at a perpendicular distance r from the mass, decreases as (1/r). (The ends contribute zero gravity).

3. Imagine an infinite plane of mass. The acceleration, ‘g’, due to the gravity of the plane at a perpendicular distance r from the plane, is a constant ! Ie: the acceleration due to gravity for an infinite plane of mass, is completely independent of the distance, r, from the plane!

Time and Quantum Mechanics:

4. Time is not an observable quantity in quantum mechanics.

5. In quantum mechanics, the observer and the observed, can be one in the same.

6. If something isn't observed, then it can be said to be in all states simultaneously.

Interesting ... please feel free to contribute any other counterintuitive facts you may have encountered !

(I suggest contributers stick with ‘facts’ which can be demonstrated and are reproducible. ;) )

:)

Cheers

Here’s a couple I’ve encountered this week (credits to others):

Gravity:

1. The force on a point mass decreases as (1/r^2), when the mass is located outside the sphere. If the sphere is hollow, the force on a point mass inside the sphere is zero, and is independent of r. If the sphere is solid, and of uniform density, the force on a point mass inside the sphere, decreases with decreasing radial distance between the point mass and the centre of the sphere (decreases linearly with r).

2. Imagine an infinitely long line of mass (ie: a cylinder). The acceleration, ‘g’, due to the gravity of the line mass, at a perpendicular distance r from the mass, decreases as (1/r). (The ends contribute zero gravity).

3. Imagine an infinite plane of mass. The acceleration, ‘g’, due to the gravity of the plane at a perpendicular distance r from the plane, is a constant ! Ie: the acceleration due to gravity for an infinite plane of mass, is completely independent of the distance, r, from the plane!

Time and Quantum Mechanics:

4. Time is not an observable quantity in quantum mechanics.

5. In quantum mechanics, the observer and the observed, can be one in the same.

6. If something isn't observed, then it can be said to be in all states simultaneously.

Interesting ... please feel free to contribute any other counterintuitive facts you may have encountered !

(I suggest contributers stick with ‘facts’ which can be demonstrated and are reproducible. ;) )

:)

Cheers