Joe's answer is spot on, but here's some background information on the
why you can't do it
The way the R-pi works is the SoC (System on a Chip) once it gets power immediately looks to the SD card for instructions on how to boot (basically, it's a little more complicated than that, but I'm guessing you don't want a 10 page dissertation

). This is hard written into the SoC and 100% cannot be changed. Not by us, and not even by the RPF. So without the SD card the system just sits there. It would be as if you motherboard lacked a bios, the computer just wouldn't be able boot! Several in the community have been looking at either using a USB device (be it hard drive or flash drive) as the main partition or setting up the SD card such that it loads a boot loader rather than boot directly into Linux. I think the second option is still a ways off from having a working implementation, but I think a couple people have successfully made use of an attached USB device
