zeno's paradox and the black hole
in [Relativity]
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From: Mathal on 13 Jun 2010 00:15 This is from wikipedia In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Now, with the beginning of a black hole a very similar paradox arises. The very conditions that result in a black hole coming into being cause time in this region of space-time to slow down. The closer to the moment that this region of space-time is to the 'black hole start' moment the slower time progresses. The infinite progression of zeno's paradox is the black hole- You can't get there from here. Mathal
From: dlzc on 13 Jun 2010 01:00 Dear Mathal: On Jun 12, 9:15 pm, Mathal <mathmusi...(a)gmail.com> wrote: > This is from wikipedia > > In the paradox of Achilles and the Tortoise, > Achilles is in a footrace with the tortoise. > Achilles allows the tortoise a head start of > 100 metres. If we suppose that each racer > starts running at some constant speed (one > very fast and one very slow), then after some > finite time, Achilles will have run 100 metres, > bringing him to the tortoise's starting point. No, the tortoise's starting point was next to Achilles. You mean "where the tortoise was when Achilles started". > During this time, the tortoise has run a much > shorter distance, say, 10 metres. More likely 1 meter. > It will then take Achilles some further time > to run that distance, by which time the tortoise > will have advanced farther; and then more time > still to reach this third point, while the > tortoise moves ahead. Thus, whenever Achilles > reaches somewhere the tortoise has been, he still > has farther to go. Therefore, because there are > an infinite number of points Achilles must reach > where the tortoise has already been, he can never > overtake the tortoise. Incorrect. Achilles passes the tortoise in finite time. What is more Achilles went through an infinity of infinities in getting through the first 100 meters. Zero's paradox was a joke, and you didn't get the punchline. > Now, with the beginning of a black hole a very > similar paradox arises. The very conditions > that result in a black hole coming into being > cause time in this region of space-time to slow > down. No. Infallers don't experience that. > The closer to the moment that this region of > space-time is to the 'black hole start' > moment the slower time progresses. For static stuff, sure. > The infinite progression of zeno's paradox is > the black hole- You can't get there from here. Can and do. But thanks for playing. http://arxiv.org/abs/astro-ph/0611552 http://arxiv.org/abs/1005.2877 http://arxiv.org/abs/1004.4532 http://arxiv.org/abs/1003.4404 http://arxiv.org/abs/1001.5451 You know we are surrounded by them, so you can play these games, or you can try and understand how they form. David A. Smith
From: BURT on 13 Jun 2010 01:27 On Jun 12, 10:00 pm, dlzc <dl...(a)cox.net> wrote: > Dear Mathal: > > On Jun 12, 9:15 pm, Mathal <mathmusi...(a)gmail.com> wrote: > > > This is from wikipedia > > > In the paradox of Achilles and the Tortoise, > > Achilles is in a footrace with the tortoise. > > Achilles allows the tortoise a head start of > > 100 metres. If we suppose that each racer > > starts running at some constant speed (one > > very fast and one very slow), then after some > > finite time, Achilles will have run 100 metres, > > bringing him to the tortoise's starting point. > > No, the tortoise's starting point was next to Achilles. You mean > "where the tortoise was when Achilles started". > > > During this time, the tortoise has run a much > > shorter distance, say, 10 metres. > > More likely 1 meter. > > > It will then take Achilles some further time > > to run that distance, by which time the tortoise > > will have advanced farther; and then more time > > still to reach this third point, while the > > tortoise moves ahead. Thus, whenever Achilles > > reaches somewhere the tortoise has been, he still > > has farther to go. Therefore, because there are > > an infinite number of points Achilles must reach > > where the tortoise has already been, he can never > > overtake the tortoise. > > Incorrect. Achilles passes the tortoise in finite time. What is more > Achilles went through an infinity of infinities in getting through the > first 100 meters. Zero's paradox was a joke, and you didn't get the > punchline. > > > Now, with the beginning of a black hole a very > > similar paradox arises. The very conditions > > that result in a black hole coming into being > > cause time in this region of space-time to slow > > down. > > No. Infallers don't experience that. > > > The closer to the moment that this region of > > space-time is to the 'black hole start' > > moment the slower time progresses. > > For static stuff, sure. > > > The infinite progression of zeno's paradox is > > the black hole- You can't get there from here. > > Can and do. But thanks for playing. > > http://arxiv.org/abs/astro-ph/0611552http://arxiv.org/abs/1005.2877http://arxiv.org/abs/1004.4532http://arxiv.org/abs/1003.4404http://arxiv.org/abs/1001.5451 > > You know we are surrounded by them, so you can play these games, or > you can try and understand how they form. > > David A. Smith Light has no escape speed like matter. Matter looses speed but light does not. How is outward going light going do be dragged backward by gravity? Where would its constant speed go? Mitch Raemsch
From: Inertial on 13 Jun 2010 01:35 "Mathal" <mathmusical(a)gmail.com> wrote in message news:81030343-37ff-44b5-ae45-af5e8765cd9c(a)g1g2000pro.googlegroups.com... > This is from wikipedia OK .. so we can't blame you then :) > In the paradox of Achilles and the Tortoise, Achilles is in a footrace > with the tortoise. Achilles allows the tortoise a head start of 100 > metres. If we suppose that each racer starts running at some constant > speed (one very fast and one very slow), then after some finite time, > Achilles will have run 100 metres, bringing him to the tortoise's > starting point. During this time, the tortoise has run a much shorter > distance, say, 10 metres. It will then take Achilles some further time > to run that distance, by which time the tortoise will have advanced > farther; and then more time still to reach this third point, while the > tortoise moves ahead. Thus, whenever Achilles reaches somewhere the > tortoise has been, he still has farther to go. Therefore, because > there are an infinite number of points Achilles must reach where the > tortoise has already been, he can never overtake the tortoise. That's one versions .. yeup. Of course, we know that such an infinite sum of finite times and distances has a finite limit. > Now, with the beginning of a black hole a very similar paradox arises. > The very conditions that result in a black hole coming into being > cause time in this region of space-time to slow down. The closer to > the moment that this region of space-time is to the 'black hole start' > moment the slower time progresses. The infinite progression of zeno's > paradox is the black hole- You can't get there from here. Not the same argument .. because there the time intervals are getting longer, not shorter.
From: Mathal on 13 Jun 2010 09:35
On Jun 12, 10:00 pm, dlzc <dl...(a)cox.net> wrote: > Dear Mathal: > > On Jun 12, 9:15 pm, Mathal <mathmusi...(a)gmail.com> wrote: > > > This is from wikipedia > > > In the paradox of Achilles and the Tortoise, > > Achilles is in a footrace with the tortoise. > > Achilles allows the tortoise a head start of > > 100 metres. If we suppose that each racer > > starts running at some constant speed (one > > very fast and one very slow), then after some > > finite time, Achilles will have run 100 metres, > > bringing him to the tortoise's starting point. > > No, the tortoise's starting point was next to Achilles. You mean > "where the tortoise was when Achilles started". > > > During this time, the tortoise has run a much > > shorter distance, say, 10 metres. > > More likely 1 meter. > > > It will then take Achilles some further time > > to run that distance, by which time the tortoise > > will have advanced farther; and then more time > > still to reach this third point, while the > > tortoise moves ahead. Thus, whenever Achilles > > reaches somewhere the tortoise has been, he still > > has farther to go. Therefore, because there are > > an infinite number of points Achilles must reach > > where the tortoise has already been, he can never > > overtake the tortoise. > > Incorrect. Achilles passes the tortoise in finite time. What is more > Achilles went through an infinity of infinities in getting through the > first 100 meters. Zero's paradox was a joke, and you didn't get the > punchline. > > > Now, with the beginning of a black hole a very > > similar paradox arises. The very conditions > > that result in a black hole coming into being > > cause time in this region of space-time to slow > > down. > > No. Infallers don't experience that. > > > The closer to the moment that this region of > > space-time is to the 'black hole start' > > moment the slower time progresses. > > For static stuff, sure. > > > The infinite progression of zeno's paradox is > > the black hole- You can't get there from here. > > Can and do. But thanks for playing. > > http://arxiv.org/abs/astro-ph/0611552http://arxiv.org/abs/1005.2877http://arxiv.org/abs/1004.4532http://arxiv.org/abs/1003.4404http://arxiv.org/abs/1001.5451 arXiv.org > astro-ph > arXiv:astro-ph/0611552 Didn't bother reading it. In the abstract one of the authors speaks of early black holes being the quasars we see. Then he mentions neutrino dark matter and neutrino balls. Did you read this? I doubt it. You seem more intelligent than that. All the abstracts refer to the objects as black holes and then go on to speculate on the mechanisms causing matter to form such massive objects. That may be interesting but it's a side track. > > You know we are surrounded by them, so you can play these games, or > you can try and understand how they form. > > David A. Smith I know super massive objects lie at the heart of galaxies. By tracking the paths of stars near our own object we can compute it's mass. Time does not operate the same everywhere in the universe. Massive objects slow time around themselves. The infaller doesn't experience time slowing down but outside in the rest of the universe time carries on at or near our pace. Given 100 trillion years the infaller will still not reach the fabled event horizon but he or she or it will still be blissfully falling, unaware of what is going on elsewhere or elsewhen. Mathal |