Thought experimenting and conjecures about space's limits.
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newolder wrote:A singularity is when some term(s) in a description stop being finite. For example, a term containing the reciprocal of radial distance from a given origin, 1/r, tends to infinity as r approaches 0.
newolder wrote:Such terms appear in solutions to General Relativity theory when matter densities get large. However, GR may not provide a complete description where a more correct quantum gravity theory is required.
newolder wrote:For example, the Heisenberg uncertainty principle (HUP) may preclude an object with momentum from ever being located at a singularity since its position, x, and momentum, p, operators do no commute. Instead, the HUP yields dp dx >= h/2π and as dx -> 0, dp -> inf and it is no longer possible to locate the object there.
newolder wrote:The Wheeler-de Witt equation is another route to removing the universe’s initial singularity by a process of “rounding off” space and time dimensions such that t=0 does not occur.
newolder wrote:A further method to avoid singularities is to allow the spacetime to become “logarithmic” on approach to a limit. Again, 1/Log(0) is undefined and unattainable in such scenarios.
newolder wrote:Also, the addition of 1 (or more) extra dimension(s) to space provides paths around any singularity as described above.
newolder wrote:IOW, there are many ways for theoreticians to get around singularity problems and the above methods do not make an exhaustive list.
...
But is there a rationale to this IF the point at which we are discussing is a singularity? That is, if the Universe has an sincere 'age', then it has some point at which time and space becomes zero.
Some feel that the ekpyrotic universe model has a lot going for it — it solves the flatness and horizon problems like inflationary theory does, while also providing an explanation for why the universe started in the first place — but the creators are still far from proving it. Stephen Hawking has bet Neil Turok that findings from the European Space Agency’s Planck satellite will verify the inflationary model and rule out the ekpyrotic model, but Hawking has been known to have to pay out on these sorts of bets in the past.
Scott Mayers wrote:In order to understand physics regarding grand or general theories, I'd like to discuss the limits in physics, such as singularities,
shapes of space (like whether we could or could not find an 'edge' on the large scale, or any points in space and/or time.
What I think is useful is to reintroduce the paradoxes of Zeno, given these have significant influence on the thoughts by past scientists that evolved into modern theories, such as the Big Bang or Steady State models.
So here's the first challenge. Zeno's challenged us to think of standing a finite distance from a wall and asked whether we could reach it or not. (?) His explanation is that we couldn't because to reach any distance closer to the wall, like say half way from where you start, it takes some given amount of time. If you then reach half of half of the original distance, it still takes some time to get there. We can repeat this process without end. To Zeno, this proves we cannot ever reach the wall, let alone any given point.
Of course, for most familiar with this, it is absurd but is what contributed to the evolution of Calculus' limits.
But is there a rationale to this IF the point at which we are discussing is a singularity? That is, if the Universe has an sincere 'age', then it has some point at which time and space becomes zero. But can you ever reach that point going backwards in time and 'touch' it or do you only reach it infinitesimally (meaning never actually reach it?
Scott Mayers wrote:In order to understand physics regarding grand or general theories...
Cito di Pense wrote:Scott, if you want to bring limits into your discussion in a rigorous way, rather than in just a wibbly metaphorical way, you'd better start by showing you understand how to use the limit concept as presented in mathematics, rather than just name-dropping it. Starting a new thread invites us to begin at that beginning, rather than by pressing directly on to cosmological beginnings, as if we should assume there are and then construct a philosophical argument on that assumption. That would be fine, but you can't get any more out of that than you put into your assumption, and any further argument you provide is going to depend critically on the assumption with which you began.
I think what you really are nervous about is that we don't have a set of observations sufficient to settle the issue, and so it seems that you just want to try substituting assumptions for the data we do not have. This is not likely to be productive at all, pending your attempts to show us all how it's done, but that will involve more show than tell.
The limitations of the data are that we don't see photons deeper in history than the surface of first scattering. It's been pointed out to you that additional investigations may provide other kinds of data than optical, but that they are currently not definitive in resolving your question. Science lives with the condition that results are definitive within a particular scope of observations, and scientists are not out to satisfy inquiries that are purely philosophical in direction by means of data. Calculus by itself is completely insufficient to contribute adequately to a discussion of cosmology. General relativity, for one, takes us a bit beyond calculus, although the mathematical objects used therein do present derivative quantities.
It's already clear from our understanding that because of expansion, some photons will never reach us, so looking for an 'edge' as you call it by naive concepts of 'looking' is not in the cards. Discussions of multiverses are currently very rudimentary at the level you will apprehend, and very abstruse at the level of physics and mathematics that you will not.
Spearthrower wrote:Philosophy, not science.
newolder wrote:A singularity is when some term(s) in a description stop being finite. For example, a term containing the reciprocal of radial distance from a given origin, 1/r, tends to infinity as r approaches 0.
hackenslash wrote:Scott Mayers wrote:In order to understand physics regarding grand or general theories, I'd like to discuss the limits in physics, such as singularities,
The problem with this is that 'singularity' is undefined, which would seem to be a necessary first step. I note that you wibbled a fair bit about singularities in the prior thread, with similar issues.
Here I am raising a topic of RATIONALISM first,
Scott Mayers wrote:...
A 'singularity' is, in geometric terms, AT MINIMAL, is either an assymptote, a virtual point, or a real point.. The question is to determine the possibilities of it being real with respect to the real geometry of space.
If it can't pass the mathematical logic, it can't pass the science on principle.
You are getting ahead of yourself on the other issues. I'm getting simple here to try to prove something.
Leave out GR or QM from this unless we can develop it from here.
Scott Mayers wrote:Cito di Pense wrote:Scott, if you want to bring limits into your discussion in a rigorous way, rather than in just a wibbly metaphorical way, you'd better start by showing you understand how to use the limit concept as presented in mathematics, rather than just name-dropping it. Starting a new thread invites us to begin at that beginning, rather than by pressing directly on to cosmological beginnings, as if we should assume there are and then construct a philosophical argument on that assumption. That would be fine, but you can't get any more out of that than you put into your assumption, and any further argument you provide is going to depend critically on the assumption with which you began.
I think what you really are nervous about is that we don't have a set of observations sufficient to settle the issue, and so it seems that you just want to try substituting assumptions for the data we do not have. This is not likely to be productive at all, pending your attempts to show us all how it's done, but that will involve more show than tell.
The limitations of the data are that we don't see photons deeper in history than the surface of first scattering. It's been pointed out to you that additional investigations may provide other kinds of data than optical, but that they are currently not definitive in resolving your question. Science lives with the condition that results are definitive within a particular scope of observations, and scientists are not out to satisfy inquiries that are purely philosophical in direction by means of data. Calculus by itself is completely insufficient to contribute adequately to a discussion of cosmology. General relativity, for one, takes us a bit beyond calculus, although the mathematical objects used therein do present derivative quantities.
It's already clear from our understanding that because of expansion, some photons will never reach us, so looking for an 'edge' as you call it by naive concepts of 'looking' is not in the cards. Discussions of multiverses are currently very rudimentary at the level you will apprehend, and very abstruse at the level of physics and mathematics that you will not.
This is my thread. If you don't like my approach leave. But don't tell me what I do and do not know. I would run circles around your head. And your insult is just acting as troll. Instead of ASSUMING something of me, PRETEND that I might have something of value (that is, assume charity rather than predefine me negatively.)
Thank you.
Scott Mayers wrote:Then ask first.
This is comparing geometrical/mathematical concepts in a thought experiment to try to make sense of space. If you have any math background, as above, it is either an assymptote or a real point included in the system.
So the question is: can real space have a singularity that is real or virtual. Is it an assymptote or a real point?
I am introducing Zeno's paradoxes because they are relevant here (and have been to all theoretical scientists of the modern [the 'rationalist' era from approximately Galileo to Einstein.]
Spearthrower wrote:
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Science is from Latin scire, to know.
But that's obviously irrelevant because the term 'science' as we're using it is a formal methodology concerned with empirical observations.Here I am raising a topic of RATIONALISM first,
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Spearthrower wrote:Scott Mayers wrote:Cito di Pense wrote:Scott, if you want to bring limits into your discussion in a rigorous way, rather than in just a wibbly metaphorical way, you'd better start by showing you understand how to use the limit concept as presented in mathematics, rather than just name-dropping it....
This is my thread. If you don't like my approach leave. But don't tell me what I do and do not know. I would run circles around your head. And your insult is just acting as troll. Instead of ASSUMING something of me, PRETEND that I might have something of value (that is, assume charity rather than predefine me negatively.)
Thank you.
While requesting Cito or anyone else employ the principle of charity is perfectly reasonable, nothing else here is.
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