MadSci Network: Physics
Query:

Re: How can two objects touch by the following principles?

Date: Mon Oct 11 08:53:33 1999
Posted By: John Link, MadSci Admin
Area of science: Physics
ID: 935450031.Ph
Message:

We can convince ourselves that we can never touch anything, by the argument that you have put forth. So, what is wrong? Surely we actually can touch things!

Realistically, when the distance becomes so small that the electrons in one finger begin to affect the electrons in the other finger, then the fingers are touching! Any further decrease in the distance only increases the interaction between the two fingers' electrons. So I would say that there is a practical maximum number of times that you would have to cut the distance in half.

From the mathematical point of view you are describing the limit

lim (x/2^n) as n goes to infinity.

It can be shown that this is equivalent to

x/infinity,

which is mathematically equal to zero. Now, I admit that this does not happen until an infinite number of steps is taken to cut the distance in half, but it does eventually occur. So we can "prove" mathematically that the distance eventually becomes zero, but it takes forever for that to occur.

I have appealed above to the PRACTICAL limit, which is the distance at which the electrons of your two fingers interact. But even if you want to define the practical limit as being the smallest distance we can discuss in quantum theories, it is not many steps from my electron practical limit. The Planck length is about 4E-35 meters (see this previous answer) and the "practical distance" I talk about above is about 1E-10 meters (the size of the hydrogen atom).

How many steps of halving the distance would it take to get down to these sizes? Above I said that the distance is x/2^n, where x is the starting distance. Let's let x equal one meter. We can find n by doing some algebra on the formula: n = -ln(d) / ln(2) where d is the distance we want to get down to, and ln() is the natural logarithm. For our distance of 1E-10 meters it takes only 33 halving steps, and for the Planck distance it takes only 114 steps!! So it doesn't take very many steps to get down to the smallest distance our theories can work with, and even less steps to get down to my practical limit!!!

John Link, MadSci Physicist


Current Queue | Current Queue for Physics | Physics archives

Try the links in the MadSci Library for more information on Physics.



MadSci Home | Information | Search | Random Knowledge Generator | MadSci Archives | Mad Library | MAD Labs | MAD FAQs | Ask a ? | Join Us! | Help Support MadSci


MadSci Network, webadmin@www.madsci.org
© 1995-1999. All rights reserved.