pop up flash can only support sync speed up until 1/200..
if u're using external flash then 1/4000 will be okay if the flash is powerful enough..

u guy know that light travels very fast right?
but after 1/250 the light wont be sufficient to reach the subject, esp when ur subject is far (when using pop up flash)
by getting an external flash, u can get power.. the flash will add more power to the flash/light that will make sure the light reaches the subject to catch up with the 1/4000 shutter..

but not all external flash can do it...
in nikon, its know as FP, its automatically enabled in sb600, sb700 and sb900.. other model ie sb30, sb400 i havent check yet..

thatis the logical part of the answer..
for the more 'technologycal' part u have to wait for someone else expert to explain..

Here is a good write up on flash sync speed to give some light on the subject matter.

http://www.kenrockwell.com/tech/syncspeed.htm

http://www.kenrockwell.com/tech/syncspeed.htm#fp

It's kinda funny to read about light having insufficient speed to reach the subject etc.. you need to know how the shutter works in the first place.. and the equivalent electronic shutters in DSLR.

BTW, I am a Nikon F2A user (yes a classic 'pro' film camera) and Coolpix 5700.