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

[Peter Cole]

Unfortunately, this strategy will have limited usefulness at best for learning physics.

The problem is that, if you're reading books about physics with very little math, those books cannot give you a model you can reason from correctly. That's because there is no such model without math. Physicists don't use math because they want to make it harder for lay people to learn physics. Physicists use math because it's the only tool that works for building models of physical systems that you can reason from correctly.

So when you read a bunch of stuff in a book about physics that doesn't have math in it, even if it's a book written by a physicist, the stuff the physicist is telling you in the book is not anything you can actually reason from. If physics could be done that way, physicists would be doing it that way instead of using math, since using math is hard and requires a lot more training. What the physicist is actually doing when he writes a book like that is taking the underlying mathematical model that he already knows, extracting some interesting conclusions from it, and then describing those conclusions to you in ordinary language. But there's not enough information in what he's telling you to allow you to reconstruct the underlying model he's using to get those conclusions, and without that underlying model, you have no valid basis for further reasoning.

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.

 

[phinds]

I said to use a second at the event horizon as you said ... 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.

Reasonable assumptions. Answer is ... the simple answer is "an infinite amount of time". The more technically correct answer is, sort of, "the lifetime of the BH", so something like 10E60 to 10E80 years depending on the size of the BH. You can't really get to an understanding of the answer without math.

 

[Nugatory]

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.

The problem here is that that question is not as well posed as you're thinking.

One second elapses on the wristwatch of the guy deep in the gravity well. For the sake of definiteness, let's say that it is the second between when their wristwatch reads 04:15:23 and 04:15:24. You ask how much time "expires far from the black hole during that second". To answer this we need a clock far from the black hole; we look at what that clock reads at the same time that the wristwatch reads 04:15:23; we look at it again at the same time that the wristwatch reads 04:15:24; we subtract the first reading from the second; and that difference is the time expired that you've asked for. This is pretty much how we determine how much time passes between any two remote events: we have a clock, we look what it says at the same time that the remote events happen, we compare the two readings.

But (and this is the part that trips up most people at first) this procedure crucially depends on how we define "at the same time". Your question does not have any meaningful answer until you provide a definiition of "at the same time". In the flat spacetime of special relativity where there are no gravitational effects there is a definition (at least in inertial frames) that is so natural that it would be perverse not to use it: Einstein clock synchronization. In curved spacetime there is no comparably natural definition and no answer to your question unless and until you tell us what you mean by "at the same time".

 

[Nugatory]

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.

You might also try getting hold of the (now available online) book "Spacetime Physics" by Taylor and Wheeler. It's mathematically solid but well within the grasp of a high school senior, and a few tens of hours with it will be more rewarding than all the time you've wasted so far searching through the dumbed-down pop-sci treatments.

 

[PeterDonis]

In the flat spacetime of special relativity where there are no gravitational effects there is a definition (at least in inertial frames) that is so natural that it would be perverse not to use it: Einstein clock synchronization. In curved spacetime there is no comparably natural definition

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. The difference from flat spacetime is that the elapsed time for two observers at different altitudes between two sets of "corresponding" events (events on each of their worldlines that happen at the same time) will be different--the one at the higher altitude will have more elapsed time. So in this case, unlike flat spacetime, Einstein clock synchronization doesn't actually "synchronize" clocks--clocks synchronized this way won't continue to run at the same rate, so the same readings on two separate clocks will not continue to occur "at the same time" according to the simultaneity convention that was established. All it does is provide a "natural" simultaneity convention ("natural" because it matches up with a symmetry of the spacetime). So "Einstein simultaneity" would be a better name for this process in a stationary curved spacetime.

(Note, btw, that similar remarks to the above apply to Rindler coordinates in flat spacetime--you can also define "Einstein clock synchronization" for a family of observers at rest in Rindler coordinates, but it will have the same limitations as above.)

(There is also a more technical definition of the "natural" simultaneity convention I'm describing for a static spacetime, in terms of the hypersurfaces that are orthogonal to the appropriate timelike Killing vector field. But that, of course, takes us far beyond "B" level. I mention it only to show that the "naturalness" of this convention does have some basis in an invariant geometric property of the spacetime; it isn't purely a matter of preference for a coordinate choice.)

 

[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.