Are there infinite points between two objects?

[David1345628]

I'm not sure if anyone has an answer but is there an infinite amount of points an object could be in between two objects? Or is there at some very small level a finite amount of points an object could be at between two points? I am thinking about in existance, not just in a theoretical two points like in math. What I'm thinking is that between points A and B, as an object moves between them, couldn't you keep breaking up the amount of space it traveled per unit of time? Also, is there finite unit of time, or could that be broken up two into infinitely smaller pieces of time.

 

One way I have tried to think of it is with gravity:

 

F_g = G(M₁)(M₂)/(r²)

 

If the distance ® between two objects was zero (touching) then wouldn't there be no gravitational force between them? Yet wouldn't two touching objects still be attracted to one another meaning that there was a distance between them?

 

Does this mean that two objects never touch? They just get infinitely close to one another? I can't think of a way that two objects could touch (it just seems illogical).

 

If you have a any insight or any way that my thinking needs to be changed ...

[rktpro]

I think when you touch two objects together, they will become a single object having mass equal to the combined masses of the two objects. If, a third object is placed, you can calculate the gravitational force between the two.

[lemur]

Does this mean that two objects never touch? They just get infinitely close to one another? I can't think of a way that two objects could touch (it just seems illogical).

I don't know the answer, but consider this: If you had two magnets that were entirely one pole so that both magnets only repelled each other; and if the two magnets' fields were such that they could never collide with enough force to penetrate each other's fields so that the two pieces of iron would touch, would you say that the two fields "touched" or would you say that they just absorbed the force of collision until they reached a point of returning the energy, like an object that keeps going up until it turns around and starts falling? Does a ball launched into the sky "touch the sky" before falling? Does Earth "touch" the sun and the moon by the fact that their gravity fields intersect? What exactly do you mean by "touch" anyway?

[David1345628]

So also then is there a smallest unit of mass. Or is everything made of infinitely smaller things?

 

Can two objects be considered part of the same mass if they have a force holding them together only? Meaning if one moves the other moves?

 

I don't know the answer, but consider this: If you had two magnets that were entirely one pole so that both magnets only repelled each other; and if the two magnets' fields were such that they could never collide with enough force to penetrate each other's fields so that the two pieces of iron would touch, would you say that the two fields "touched" or would you say that they just absorbed the force of collision until they reached a point of returning the energy, like an object that keeps going up until it turns around and starts falling? Does a ball launched into the sky "touch the sky" before falling? Does Earth "touch" the sun and the moon by the fact that their gravity fields intersect? What exactly do you mean by "touch" anyway?

 

By touch I mean that the distance between two objects is zero

[lemur]

By touch I mean that the distance between two objects is zero

How do you define the boundaries of the objects with precision?

 

 

 

[swansont]

I'm not sure if anyone has an answer but is there an infinite amount of points an object could be in between two objects? Or is there at some very small level a finite amount of points an object could be at between two points? I am thinking about in existance, not just in a theoretical two points like in math. What I'm thinking is that between points A and B, as an object moves between them, couldn't you keep breaking up the amount of space it traveled per unit of time? Also, is there finite unit of time, or could that be broken up two into infinitely smaller pieces of time.

 

One way I have tried to think of it is with gravity:

 

F_g = G(M₁)(M₂)/(r²)

 

If the distance ® between two objects was zero (touching) then wouldn't there be no gravitational force between them? Yet wouldn't two touching objects still be attracted to one another meaning that there was a distance between them?

 

Does this mean that two objects never touch? They just get infinitely close to one another? I can't think of a way that two objects could touch (it just seems illogical).

 

If you have a any insight or any way that my thinking needs to be changed ...

 

In the physics model, yes — there are an infinite number of points. In reality, no.

 

The equations assume that the mass is a point, and that's a reasonable approximation for many applications. If you have a spherically symmetric object, it behaves as if all the mass were at a point, and you can treat imperfections a a series of point-like objects, because forces obey superposition (i.e. they add). What this tells you is you have to be aware of the limitations of your model. When the assumption about having a point particle breaks down, you adjust the model or the application of the model. The nucleus isn't a point particle, and that has implications in quantum mechanical treatment of the atom. You find that in reality, macroscopic objects don't actually "touch" because of electrostatic repulsion

[michel123456]

(...)

One way I have tried to think of it is with gravity:

 

F_g = G(M₁)(M₂)/(r²)

 

If the distance ® between two objects was zero (touching) then wouldn't there be no gravitational force between them? (...)

 

When you substitute r in the equation with zero, you are dividing by zero, which gives...[insert answer here]

 

@ Forum admin

Can you fix this?

the distance ® between

Edited April 2, 2011 by michel123456

[swansont]

@ Forum admin

Can you fix this?

 

Apparently not

http://www.scienceforums.net/topic/52768-autorendering/

[jajrussel]

When you use gravity: F_g=G(M₁)(M₂)/r²

When you say point A and point B a certain distance apart then move them closer together, regardless the distance change you still only have point A and point B. There are an infinite number of positions that A or B can hold, even with limited direction, unless you define what constitutes one change of position. When the two touch you have A&B, but neither can occupy the same position they can only in a sense touch.

So you have two points and so long as you have two points r will never be zero. You still have two points thus gravity.

Edited April 3, 2011 by jajrussel

[granpa]

space and time may indeed be discrete however

this results in a length scale which is definitely not observer independent

which makes it difficult to reconcile with relativity (unless c is made infinite)

 

This is the motivation behind double special relativity.

[jajrussel]

space and time may indeed be discrete however

this results in a length scale which is definitely not observer independent

which makes it difficult to reconcile with relativity (unless c is made infinite)

 

This is the motivation behind double special relativity.

 

I am not a scientist and am somewhat slow learning, so I am having difficulty understanding what you mean.

It seems to me that what makes space and time discrete is that space is measured in units of distance and time is measured in units of duration. I can use the inverse square law to understand why a distant very long line appears to be a very short line; then understand why something moving along that line appears to be moving very slowly when in fact it is moving very fast. Since the observation can change with my position the observation seems to be observer dependent.

Assuming that when you say c you mean the speed of light in vacuum; I don’t understand the need to declare c as infinite when the only obvious observation I can make is a more distant one where something moving at near c would appear to be moving more slowly and not faster.

But, since I am not sure what you mean this could be completely out of context.