The textbooks have physics applications. Farsight has...?
Ego? Delusions of Grandeur??
The textbooks have physics applications. Farsight has...?
Farsight: You're standing on a gedanken planet holding a laser pointer straight up. The light doesn't curve round, or slow down as it ascends, or fall down. It goes straight up. Now I wave my magic wand and make the planet denser and more massive. The light still doesn't curve round, or slow down as it ascends, or fall down. I make the planet even denser and more massive. The light still doesn't curve round, or slow down as it ascends, or fall down. I make the planet even denser and more massive, and take it to the limit such that it's a black hole. At no point did the light ever curve round, or slow down as it ascends, or fall down. So why doesn't the light get out?
Prof. Shapiro:
Once you are inside the event horizon (surface) of a Schwarzschild black
hole, you cannot remain stationary but must fall inward. The
force of gravity, if you like, is sufficiently strong that nothing can
remain or orbit on a sphere of constant area, but must fall inward
and, in a finite time as measure on your watch, plunge into the
singularity at the origin. While you are falling inwards, all light
rays you emit must plunge inward as well.
S. Shapiro
Prof. Baez:
It actually does slow down as it ascends... if you time it using a clock on a distant star. Light always has the same speed as measured by someone right next to it. But you've probably heard how "a gravitational field slows down time":
http://en.wikipedia.org/wiki/Gravitational_time_dilation
This means that someone on a distant star will see things near the surface of your super-massive planet moving slower than normally. This applies to light coming out of the planet, too. At some point, the light no longer escapes at all!
None of this stuff makes real sense until you go ahead and do the math. Purely verbal explanations are much too vague. So, I really recommend some books on general relativity to help you get to the bottom of this stuff:
http://math.ucr.edu/home/baez/einstein/node15.html
My rough "explanation" is aimed merely at pointing you toward the weak link in your chain of reasoning.
Best,
jb
The time dilation goes infinite because the light clock stops. And like Moore said, the light can't get out because the light has stopped. And it hasn't just stopped for some distant observer. Put an observer in front of that clock at the event horizon, and he's stopped too. He doesn't see it ticking normally. You can't make a stopped clock tick by putting a stopped observer in front of it.
Duh! That's because we see it red shifted to infinity from any remote FoR, and of course from a local frame, everything passes through the EH as per normal.....From the local frame of anyone falling into a BH, there is no length contraction, no time dilation, no nuthin! One will then cross the EH, and then all paths lead to the Singularity region.
Much as I disapprove of this "Farsight bashing" by members who seem to have no other interest than this (and certainly no demonstrated physics or maths knowledge), let me pick him up on a rather serious mis-reading.....
Ah yes but, but, but.....When people post in science threads, claiming things not recognised by mainstream science, misquoting and mis-reading as you yourself have acknowledged, they are "open season" as far as I am concerned
Differential geometry is not an easy subject, especially for a "layman" - you clearly know none.As a layman,
Differential geometry is not an easy subject, especially for a "layman" - you clearly know none.
I rest my case
As Professor Moore said, ...
Prof Moore said:Much of what l saw on the parts of the thread I read was nonsense. General relativity is subtle and (in my experience) arguments based on intuitive models are likely to be misleading at best and are "not even wrong" at worst. Definitively answering the questions of the type raised requires more careful framing of the question itself within the context of the tools that general relativity provides, and then very careful and (usually very complicated) calculation. In many cases, the answers to even deceptively simple questions requires a numerical solution, and numerical solutions are tricky to set up and often difficult to interpret. So I would distrust any argument based on intuitive reasoning (including my own) without firm support by a detailed calculation.
I'm not avoiding it. It just hasn't come up, and it doesn't really explain anything. I thought tex worked here? It doesn't work on a preview, so let me try to show your expressions using John Forkosh's rendering service:
The problem comes when r2 equals rc . Then you're dividing by 1 minus 1 and the result is undefined.
Agreed. All a proper time interval is, is a measure of how much regular cyclical motion has been going on inside a clock. And at a place where the speed of light is zero, there isn't any.
I think the Schwarzschild expression says it adequately, and there's an obvious problem when r equals r0:
The time dilation goes infinite because the light clock stops. And like Moore said, the light can't get out because the light has stopped. And it hasn't just stopped for some distant observer. Put an observer in front of that clock at the event horizon, and he's stopped too. He doesn't see it ticking normally. You can't make a stopped clock tick by putting a stopped observer in front of it.
Last para of Prof Moore...
Prof Shapiro says..(Post # 527 above)
Paddoboy,I cannot really comment, as the mathematics is out of my league, but Rajesh, here's a chance for you to make a name for yourself in two ways...[1] Contact both professors and inform them of their mistake, and [2] Submit a paper of your version of events for peer review.
Thanks tashja. I'm a little surprised by the reply from S Shapiro, in that he hasn't answered the question. Here it is for reference:Farsight, hi. A couple of replies:
That's incorrect. Einstein said space is neither homogeneous nor isotropic. And note this Baez article which says this:Much as I disapprove of this "Farsight bashing" by members who seem to have no other interest than this (and certainly no demonstrated physics or maths knowledge), let me pick him up on a rather serious mis-reading... Farsight is fond of quoting Einstein's Leyden address, which I confess I haven't read. I paraphrase - "space-time is neither homogeneous nor isotropic." This, Farsight claimed, IS spacetime curvature (due to gravity).
No he doesn't mean that. He meant what he said. When Einstein said space-time he meant spacetime, when he said space he meant space. The distinction is crucial!So if E. had been addressing a roomful of differential geometers, they would have been asleep by then - he wasn't it was a public address. Look - by "inhomogeneity" E. means that spacetime (the spacetime 4-manifold) cannot be covered by a single coordinate chart - in this circumstance of course this manifold is not literally (globally) flat, which is well known
No he doesn't. He means space is non-isotropic. That it isn't the same in all directions. Point down to the floor, then up to the ceiling. The space down there isn't the same as the space up here. If it was, your pencil wouldn't fall down.By "non-isotropic" he appears to mean that the metric is semi-Riemann - that is that not all coordinate functions carry the same sign. Again this is well-known to differential geometers.
I'm not coy. Methinks you need to read that Leyden Address properly. Read this too: Inhomogeneous vacuum: an alternative interpretation of curved spacetime.So, yes, Farsight is correct in this restricted sense, but seems not quite to understand why. Or maybe he does, and is coy about sharing?
Simple division by zero leading to an undefined result. If one clock is ticking at some rate and the other one isn't ticking at all, you cannot define a ratio between their tick rates. And if you put a stopped observer in front of a stopped clock, you still have an undefined result. Zero divided by zero is not one. It is undefined. The stopped observer does not see the stopped clock ticking normally "in his frame". Light has stopped. So he sees nothing.farsight, Please refer your response above wherein you state that problem comes when r2 = rc. The dt1/dt2 is a comparative ratio between two proper time interval in two different frames....
Based on above it is clear that if one of your frame (you have chooses r2) is placed at EH (at rc), then dt2 = 0. Once dt2 is = 0, what is the mathematics you are suggesting by insisting on problem with dt1/dt2 ?
That was the answer given by Shapiro. And it is mathematically and physically equivalent to all the other answers.I'm encouraged that nobody has come out with the "infalling space" crackpot nonsense.
Farsight, you just took the most favorable interpretation of your nonsense and rejected it.Space isn't curved where a gravitational field is. It's inhomogeneous.