I know that currently HTML5 video compatible browsers use the Accept-Ranges header to seek inside streams, but it is far from an ideal solution. The browser needs the full index information of the file to do this effectively, and this is not possible for live-stream optimized formats, like fragmented mp4 and chunked mkv (or WebM).
Is there a feature of HTTP or an extension which operates with timestamps (instead of bytes).
I know it is unlikely that such a standard is supported in browsers yet, with these early implementations. I am just interested if even such standard or proposition exists.
No, the http protocol is not aware of the content in the body as such. You might be able to run a cgi that delivers the file and it would accept a timestamp as a parameter to continue the stream from that position.