Different states of Nut & Bolt

[werunom]

On one side I have [state1] a nut and a bolt, side by side. On the other side, [state2] a nut fastened over a bolt. What is the difference between these two matter concentrations?

Of course, some energy has to be spent to fasten the nut. But it is not the process and the energy to bring about the process I am talking about; I am just comparing one volume in space where the nut is beside the bolt and another volume where nut is fastened over the bolt.

So, considering the nuts and the bolts on either side as matter concentrations formed out of fundamental particles,
> what could be the difference [as in energy, etc.] when I compare these two volumes of matter in space?
> That is, how and in what sense does the volume consisting of the nut fastened over the bolt differs from the other?

Thanks.

 

[Curl]

why would the volumes be different?

 

[werunom]

No No. I didnt mean to convey that. Excuse.

By stating "Two volumes of matter in space" I just meant to convey the "block" or "part" of space which contains the nut and the bolt.

"I am just comparing one volume in space where the nut is beside the bolt and another volume where nut is fastened over the bolt" - In this sentence, 'volume' does NOT mean as "volume of the cube", but is used in general sense of that part of the space which is cordoned, consists of, contains, etc.

 

[torquil]

An interesting mathematical difference is the topological difference of the occupied spaces in each case:

When the nut and bolt are not connected, your have one volume with the topology of a 3-ball (the bolt), and one equivalent to a 3-torus (the nut).

If you considered them mathematically connected when the nut is screwed on, you then only have one volume with the topology of a 3-ball.

But this is not really relevant for questions about physical properties such as energy.

For energy consideration, you have to have a detailed model for the interaction (e.g. electromagnetic and gravitational) between the two parts.

 

[werunom]

Thanks for your reply.
As you pointed out, yes... there would be topological difference. But I was not looking for that difference.

Any idea on how to model these two states? Of course, I am not asking for the entire step-by-step procedure, but something to start with. From there, I till try to carry on.