Interested in Black Holes, Neutron Stars, and White Dwarf Stars

[PAllen]

So what you are trying to tell me is that none of you could write a book telling people like me what the heck you are talking about. My attempt at using this forum is not helping me so I will be deleting my account if I can. If I can't then you won't be hearing from me again.

An interesting bit of history here is that Newton's time it was common to use natural language in a formal way to describe precise calculations and logic. This is not at all the same as popular descriptions of physics, without the formality. This old practice was replaced because it was much harder to use than symbolic math.

 

[Nugatory]

Actually, while there is no natural definition of simultaneity in a general curved spacetime, in a static spacetime, like the one we're discussing in this thread (Schwarzschild spacetime), Einstein clock synchronization actually does work as a simultaneity convention

This is true - it’s why we can get away with minimally caveated statements about clocks deeper in gravity wells running slow - but the question was about “a second at the event horizon” with an infalling clock and that simultaneity question is less tractable.

 

[PeterDonis]

the question was about “a second at the event horizon” with an infalling clock

For an infalling clock at any altitude (even way above the horizon), or for any clock that is at or below the horizon, the convention I described does not work at all. The convention I described only works for static clocks--clocks hovering at a fixed altitude above the horizon. I should have made that clearer in my previous post.

 

[vanhees71]

So what you are trying to tell me is that none of you could write a book telling people like me what the heck you are talking about. My attempt at using this forum is not helping me so I will be deleting my account if I can. If I can't then you won't be hearing from me again.

The problem is that if you really want to explain "modern physics", i.e., special and general relativity and, even more so, quantum theory, you cannot do this really well without using the only adequate language we know to express it, which is mathematics. In the case of general relativity (GR) it's the language of differential geometry, which is a pretty advanced topic.

My university (Goethe University Frankfurt, Germany) has a tradition to start the theoretical physics course already in the 1st semester, which is a challenge, because you need math to do theoretical physics. There the intro lecture on General relativity is for BSc students in the 5th semester (or higher), because you need some math (multivariable calculus) and also a good deal of physics.

 

[Ibix]

You were the one who easily went through the event horizon as if nothing special happens there. I said to use a second at the event horizon as you said " AT the horizon, time just goes on ticking at one second per second." I wanted you to tell me how much time expires far from the black hole during that second assuming you understood that meant far outside the gravity of the black hole.

This has been addressed a couple of times in different ways, but I wanted to clarify a point here. You can cross the event horizon and you will notice nothing unusual about your clock - so "time stops at the horizon" is clearly not accurate. But you asked about the ratio between the tick rates of a clock at the horizon and one at infinity - and the problem here is that you assume a clock can be at the horizon for finite time. It can't. It can pass through the horizon but it cannot stop there. It can stop anywhere above the horizon and hover (given an arbitrarily powerful rocket) and then you can compare its tick rate with any other hovering clock, but the horizon is the threshold at which it becomes impossible to hover even in principle so you cannot compare it to a distant clock.

So it's true that a clock can pass unscathed through the event horizon of a sufficiently large black hole, but you cannot compare its rate there to the rate of a clock outside the hole because it cannot stay there to be compared. Attempting to describe a clock hovering at the horizon is contradictory, which is fundamentally why there's a coordinate singularity in Schwarzschild coordinates there since they rely on hovering clocks.