You actually need to make the calculation in the framework of special relativity. For such high speeds, you cannot consider time as absolute.
And Einstein is not wrong, in contrast to what said the other comment. There is no proof he is (otherwise please show it to me). Note that having an alternative explanation is a totally different story that saying the explanation commonly considered is wrong. I also do not know about this alternative explanation and cannot therefore judge its relevance.
RE: Traveling at the speed of light