@TanMath : no, I'm talking about Planck's constant here. The dimensionality of action can be expressed as energy x time or momentum x distance. That distance isn't the Planck length.
@JohnDuffield Can you explain what is the coordinate speed of light in Simple English? Unfortunately, your Wiki link is from the standard Wikipedia, which uses complicated English.
@JohnDuffield (I'm ignoring the fact that you sent another link to me that uses complicated English). So when I send a light beam from my location towards a black hole, the light beam approaches the event horizon, and suddenly it stops moving?
@Bass : no. The descending light beam goes slower and slower and slower until it grinds to a halt. I kid ye not. Rather counterintuively, a descending light beam slows down, whilst an ascending light beam speeds up. You can check that with Don Koks the PhysicsFAQ editor, who wrote this article.
@JohnDuffield If a black hole of one solar mass is a light year away, how much time passes until my light beam stops completely? If it gets slower and slower, maybe it never reaches the event horizon? (your link again uses complicated English).
@Bass : one year by your local clock. The light stops at the event horizon. That's why it's the event horizon. Flip it around and imagine you're holding a laser beam pointing straight up. If you're above the event horizon the light gets out. If you're at the event horizon, it doesn't.
@Bass : you measure the relative speeds using optical clocks. If an optical clock at one elevation is running at twice the rate of an optical clock at a lower elevation, then the coordinate speed of light at the higher location is twice the coordinate speed of light at the lower location.
@Bass : re "far away, for example one light year. Wanna know from Duffield how long it takes for the light to slow down and stop at the EH". One year by your reckoning.
@JohnDuffield But if the black hole wasn't there, it would take a year too. So the light has no time to slow down, it must suddenly stop. This contradicts your previous statement.
@Bass : you said the black hole is a light year away. A light year is the distance travelled by light in one year. It takes a year because that's the definition of a light year.
@JohnDuffield Exactly. But compare case 1 with black hole to case 2 without black hole. The distance is the same in both cases, one light year. The time too, one year in both cases, as you say. So the speed must be the same in both cases too. This means the light cannot slow down. But previously you said it does slow down.
@Bass : it does slow down. Let's say we have a stretch of space that's two light years in extent. We send light from one side to the other, and reflect it off a mirror. After four years we see the reflection. Now we put a black hole in the middle, and arrange for the light to skim past it. When we send light from one side to the other it takes longer than 4 years. What we have is a Shapiro delay:
@JohnDuffield Let's stay at our original experiment. So speed is not the same in the two cases, you say, because it slows down. Distance is the same per definition. So the time to reach the EH must be different. But before, you said that the time is the same. Smells like contradictory spirit.
@Slereah : there is no need for any Hawking chronological protection conjecture because you don't travel along a worldline or around a CTC. There is no motion in spacetime.
@Bass : no, because your original scenario has a definition problem. When you say "a light year away" what you're saying is "at such a distance that light takes a year to get there". To avoid this you have to switch to the Shapiro-delay scenario.
