object size

[bodhi]

why does the object shrink in size when they travel close to the speed of light?

[ghwellsjr]

We say that this must happen in order to understand why it is that everyone measures the speed of light to be the same before and after they accelerate from one state of steady motion to a different state of steady motion.

[bcrowell]

When you ask a "why" question like this, the answer is always going to depend on what you start with as assumptions. If you ask Euclid why the Pythagorean theorem is true, he'll show you a proof based on his five postulates. But it's also possible to form a logically equivalent system by replacing his parallel postulate with one that asserts the Pythagorean theorem to be true; in this case, we would say that the reason the "parallel theorem" is true is that we can prove it based on the "Pythagorean postulate."

Ghwellsjr has given an answer based on the postulates that Einstein used when he first published relativity in 1905. That's perfectly valid, but in my view that approach is very old-fashioned. Here's the way I prefer to present the subject: http://www.lightandmatter.com/html_books/0sn/ch07/ch07.html This is basically a streamlined visual and geometrical presentation of an approach that dates back to 1911. Some published papers that use this method:

W.v.Ignatowsky, Phys. Zeits. 11 (1911) 972
Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51
Palash B. Pal, "Nothing but Relativity," Eur.J.Phys.24:315-319,2003, http://arxiv.org/abs/physics/0302045v1

[ctxyz]

why does the object shrink in size when they travel close to the speed of light?

The object does not "shrink" in itself, the length measurements effected by an observer in motion wrt the object are affected by the relative speed between the observer and the object.
bcrowell gave you the mathematical formalism of the above sentence.

[ghwellsjr]

Ghwellsjr has given an answer based on the postulates that Einstein used when he first published relativity in 1905. That's perfectly valid, but in my view that approach is very old-fashioned.
Actually, Ben, my answer is even more old-fashioned than Einstein's theory of relativity published in 1905. It goes back to the explanations offered by Lorentz, Fitzgerald, and Poincare several years earlier and has nothing to do with Einstein's two postulates, especially not his second one.