Relatively Confusing

In special relativity, every inertial observer is responsible for setting up his own system of synchronized clocks. One of the counterintuitive surprises is that these clocks disagree on how long ago any specific event is if the two inertial observers are in relative motion - according to the rule that t' = gamma*(t-v x/c^2), where t' is the time measured by the observer we shall call moving, v is the relative velocity, x is the distance of the event (from the standpoint of the "stationary" observer, c is the speed of light and gamma = 1/Sqrt(1-(v/c)^2).

For quite modest speeds v, gamma is nearly exactly one but the time differences can still be large for distant events - that is, those for which x is large.

Steve Lundburg continues to confuse and bebother his hapless readers with relativity stuff. Here is a bit of his latest effort. After noting that there are some indications that Betelgeuse might be about to supernova, he notes that an observer standing on the ground would disagree with one in a moving car about when the supernova "happened." He managed to confuse a lot of his commenters by failing to clarify what he meant by that, and by not showing anything like the equation for t' above. He reports:

How much do we have to disagree? By about a half an hour, if I’ve done my arithmetic right.

Well gamma is very close to one, as I said, a car moves at about 10^-7 of light speed, and x is about 10^10 seconds (in units where c=1), so the difference between t and t' is roughly 1000 seconds, so I guess he did the arithmetic right. The comments show how baffled he left his commenters, though.

This example tends to show why such special relativity based computation can be pretty confusing, of course, which I suppose is one reason that cosmologists need to go to some trouble to avoid some ambiguities. Betelgeuse is relatively close to us and cars don't go very fast, but distant galaxies are ten million times as far away and moving millions of times as fast as that car.