Can two perfectly round, perfectly hard spheres ever actually touch?

Question

A geometric point is defined as having no dimensions. It seems to me that two spheres, if they are perfectly hard, so they cannot bend at all, and they are perfectly round, would only be able to touch on a "point." And a "point" has no dimesions.

Answer 1

In fact, John Kennedy, look at the spheres on the nanoscopic scale.
Here we see that the spheres will 'touch' until the forces of repulsion between the electrons on the spheres surface cannot permit any further approach.

You see, there will never be any contact and the point you mentionned is not present itself.

I however appreciate your approach (very pragmatic) to the problem - a point is itself infinitely small and it cannot exist.

Answer 2

You're running into the same problems Newton did when he tried to explain how you could find the instantaneous velocity of an object using calculus. Since velocity is distance over time, it was hard to explain how you could find out how far an object moves over an infinitesimally small amount of time. Obviously, the time can't be zero, but it has to be virtually zero. (In fact, calculus wasn't really accepted as a formal, rigorous branch of mathematics until Cauchy came up with the idea of limits. Newton had no limits.)

The idea of a point, or an instant, is more conceptual than physical. Both spheres would share the same point conceptually, even though, in practice, two spherical balls couldn't possibly share the same point.

Answer 3

What's your "point"? Haha, couldn't help myself.

If the question was "what is the size of the area where the two hard spheres touch, the answer would be zero. That does not mean they don't touch. The "extent" of the contact is simply zero, the size of the point where they DO indeed touch.

It's very mathematical, like two lines that cross at a point. They touch, too.

Answer 4

Since this is in the physics section, you have to realize that we can't be talking about mathematically perfect spheres, because any object is made out of atoms, and therefore can't be perfectly spherical. We could end the discussion by saying that when two spheres that are as nearly perfect as possible touch, they are touching on one atom... BUT...

What is the definition of touch at the level of the atom? In fact, when you are "touching" anything with your hand, you're actually not in contact with it. You're just close enough to it for the electrons surrounding the atoms in your skin to be repelled by the electrons surrounding the atoms in the object (via electromagnetic force).

Answer 5

The idea of a dimensionless point is strictly theoretical and does not exist in reality. In reality your spheres are made up of "stuff". Ultimately atoms which are in turn made up of smaller stuff. eventually you will reach a point where there is nothing smaller and at that point the dimensions of the elementary particle will be where the touching is occuring.

Answer 6

Obvious observation would tell you that yes, the spheres are touching. However the argument of the dimensionless 'point' is invalid because a point refers to a positioning in space. Since both spheres share one particular position in space, the 'point', they are touching.

Answer 7

Although touching at a point is infitinely small, they still touch.

Answer 8

i suppose that's why one pool ball almost hits the other one but the 2nd one speeds away because they can never touch.

Answer 9

Hmmmm. Good point.

Answer 10

A point is "One Dimensional"! So, it does have dimension.