Can anyone show me the calculation to prove this?

[hyde]

Please show me the calculation to prove this statement:

"...if an atom were magnified to the size of the solar system, a (super) string would be the size of a tree" http://www.pbs.org/wgbh/nova/elegant/scale.html

I can't prove this, and I don't know what I'm doing wrong. Here's my work:

assume:
length of string = 10^-35 m
length of atom = 10^-10 m
length of tree = 10^0 m
length of solar system = 10^13 m

magnification from atom to solar system: 10^23 times

magnification from string to tree: 10^35 times

They don't match! Am I doing something wrong or is it the statement that's wrong?

 

[paultrr]

The Size of a String

You might consider that PBS as good as it is tends to do what we term Popular Science shows. Popular Science at times makes generalized statements that may or may not be fully accurate when it comes to trying to work things out by math. I would suggest that the comment was strickly giving an approximation, as often shows up in popular science books also. The math, worked out would then give you a far more accurate scale or size discription.

 

[selfAdjoint]

Planck length & string length

Originally posted by hyde
Please show me the calculation to prove this statement:

"...if an atom were magnified to the size of the solar system, a (super) string would be the size of a tree" http://www.pbs.org/wgbh/nova/elegant/scale.html

I can't prove this, and I don't know what I'm doing wrong. Here's my work:

assume:
length of string = 10^-35 m
length of atom = 10^-10 m
length of tree = 10^0 m
length of solar system = 10^13 m

magnification from atom to solar system: 10^23 times

magnification from string to tree: 10^35 times


They don't match! Am I doing something wrong or is it the statement that's wrong?

You have assumed the size of a string is the Planck length ~ 10^-35 m. But that is not necessarly the case, indeed string physics does not treat the Planck length particularly but assumes continuity, and indeed analyticity in the string environment.


So maybe 10^-23 m for the string is correct.