- #71
DrStupid
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- 502
russ_watters said:I'm asking what relevant difference there is that makes one description useful and the other not.
The difference is no singularity in one description and a singularity in the other.
russ_watters said:I'm asking what relevant difference there is that makes one description useful and the other not.
Dale said:That is infinite. Infinite means that if you pick any finite number, it gets bigger.
There is no infinite number. Infinite is inherently a limit.DrStupid said:That just means that the limit is infinite but not the numbers and we are talking about the numbers.
Dale said:There is no infinite number. Infinite is inherently a limit.
I agree, so I would not pick that point. I would stay away from the center because that is where the singularity is and we expect our models to break down there. So pick another point where we expect the model to work, and all I said above applies.zonde said:It is not obvious that by analogy adopting proper time of particle at the center of collapsing body would be a good strategy in case of OS solution.
Yes, this is understood. Hence the OP’s “absurdum” and then the rebuttal follows validly pointing out that the observer’s coordinate chart doesn’t change the local physics at all.zonde said:But in that chart infinite time dilation for collapsing body would be reached at infinite future of this coordinate chart or in plain English - never.
That is only because you are choosing a bad point to examine. Outside the singularity at the center the analogy is good. I was considering a point away from the singularity.zonde said:So the point is that analogy between Schwarzschild and OS regarding infinite time dilation is far from obvious.
That isn’t my wording, it is the OP’s. The OP’s wording is poor, but he is clearly (sloppily) referring to the infinite time dilation in the limit as you approach the event horizon. If you want to make an issue of his wording then take it up with him, not me. I won’t defend his wording, but I also don’t think it is worth correcting.DrStupid said:If you know that, why do you claim, that an "ever increasing finite time dilation" "is ifinite"? It always remains finite and defined.
The physical situation does not depend on the coordinate chart at all. That is the whole point of writing physics in terms of tensors.zonde said:I would like to add that from my previous post it seems that conclusion about physical situation might depend on the size of adopted coordinate chart.
This isn’t a philosophy forum. However, this statement does shed light on why you have been posting as you have. Zeno’s Paradox is considered resolved in the scientific literature, don’t waste our time here please.zonde said:However philosophers have not reached consensus how the paradox should be solved.
Dale said:That isn’t my wording, it is the OP’s.
Dale said:The OP’s wording is poor, but he is clearly (sloppily) referring to the infinite time dilation in the limit as you approach the event horizon.
Oops, Yes you are right. The OP actually said infinite time dilation in post 27, so in context @zonde was discussing infinite time dilation which I understood. So if you want to take issue with the wording then do so with him, not me or the OP.DrStupid said:which is the wording of zonde and not the OP (again see #67).
Read his post 27. He is clearly objecting to the infinite time dilation. He considers infinite time dilation to be absurd so he is making an argumentum ad absurdum argument against the formation of the horizon. I am not missing his point at all, I understand both his point and also the argument he is using to support his point. I am defending the correct rebuttal of his argument.DrStupid said:No he doesn't. He clearly assumes that this singularity will never be reached. That is equivalent to an always finite time dilation. If you do not see that, than you are actually missing the basic point of his idea.
zonde said:So the obvious choice for distant observer is to keep his own time for coordinate chart.
Dale said:Read his post 27. He is clearly objecting to the infinite time dilation.
Yes. Argumentum ad absurdum.DrStupid said:"don't see how time dilation could ever reach infinity at any point"
I am not. That is how argumentum ad absurdum works.DrStupid said:Please stop turning his argumentation into the opposite.
Dale said:I agree, so I would not pick that point. I would stay away from the center because that is where the singularity is and we expect our models to break down there. So pick another point where we expect the model to work, and all I said above applies.
We also do not pick the center of the Schwarzschild solution, so I was not even considering picking the center of the OS solution.
Do you mean that predictions of our models do not depend on chosen coordinate chart? Because obviously physical situation (reality) does not depend even from our models of physical situation, whether they are more or less correct or rather totally flawed.Dale said:The physical situation does not depend on the coordinate chart at all. That is the whole point of writing physics in terms of tensors.
Yes, that is a better way to say it.zonde said:Do you mean that predictions of our models do not depend on chosen coordinate chart?
I don’t think the predictions of black holes or frozen stars are the same. I think a black hole described with one set of coordinates is the same as a black hole described with another set of coordinates.zonde said:If predictions are totally the same whether we describe collapsed stars as black holes or frozen stars, who cares what actually they are.
Ok, so this is a good picture to use. The event horizon has two sections. One section is the cylinder with straight edges going up off the top of the page, and the other section is a kind of round cap on the end of the cylinder.zonde said:But singularity is not there from the start. Say look at this picture (taken from https://arxiv.org/abs/1201.3660):
View attachment 229237
At first there is event horizon and only later singularity appears. In any case there is no singularity at the center of ordinary gravitating body. And it makes sense to pick the center as matter at rest at the center is not falling anywhere.
Dale said:We already discussed that above, it has already been resolved for some time now. As far as I know there is no current problem which would be resolved.
Posts 1, 33, 35, 37.Zedertie Dessen said:Could you point our where?
Dale said:Posts 1, 33, 35, 37.