geordief

thanks. I am going out now ,so I will have to look at this later as all I will have is a smartphone phone until this evening and that is a bit limiting. I will keep at that Wikipedia article....

I feel comfortable with your posts (having gone through them a few times). The Wikipedia article is much harder and I have doubts that I can digest too much of it even though it felt familiar and comfortable at first I have been trying trying to understand the affine space section (in that article). Is the (or a) point there that ,if we choose an origin in the "parent" space then no point in the affine space has fixed connection with that point? Your quote"I hope you liked the method of studying the simpler lower dimensions and extending both the results and differences to higher ones." Yes ,indeed I like the approach of starting with the dimensions we are used to and then (hopefully) generalizing. Baby steps hopefully will lead to a wider perspective.

thanks. That was a lot of work for you I have followed your post well enough so far I think Just a small question (it might not be the right time to answer) :Does that topological definition of a surface applying to 3D space not seem to preclude its applicability in 4D spacetime ? I was under the possibly naive impression that topology did have relevance to GR..

What ,like this ? or maybe https://i.pinimg.com/originals/c0/92/b8/c092b8fa1a046287a0a733ebf9438619.jpg ?

Would you know (or assume) that another dimension existed if an object appeared at a different place in the existing dimensions without leaving a trace of its passage? I understand that posited extra dimensions exist at very small scales so we would never see them on our commute to work.

Just quoting you simply in case you didn't notice that I answered you just above and to bring your attention to it ;-)

But the relation of the 2 constants to to c would be the same,I suppose,. It seems interesting to me that ,if the permeability was equal to the permittivity (obviously ridiculous a la "apples and oranges") the form of the relation between the three components would reduce to c is inversely related to permittivity (or permeability). simply by the form of the equation. I am not sure if that has any significance.

No, not at all. I was waiting for you to show me the diagrams but ,yes I would have a follow up question or two in the mean time if that's OK. When you say "connected set of locally flat points" does "connected"** have a special ,technical meaning- or just joined by some relation? And "flat" , is that defined by a derivative(s) being constant at the point? And are all the hypersurfaces 2-dimensional then? (I was imagining somehow they would be "one dimension down" from the space they were*in -that is a mistaken idea ,I suppose?) *ie I was imagining that a "surface" in spacetime might be a 3-dimensional set of all points that shared the same time according to an arbitrary point of reference -and that that might be generalized. **You used the concept of "connection" earlier in another thread http://www.scienceforums.net/topic/101620-intrinsic-curvature/ "The relationship between two charts is called a connection. This is usually established by the 'parallel transport rule'". Are you using the word in the same way in both contexts?

I understand that both these constants are experimentally observed . Can I deduce from that that there is no particular reason why the numbers noted should be what they are? Is there a close relation between those two constants and the speed of a massless object in a vacuum?

What is (unless there is more than one definition,perhaps?) the mathematical definition of a surface in a general sense? I am interested to know in the context of intrinsic curvature but feel I need to get this concept well understood first. For example must a mathematical "surface" in a 4-D space be 2-dimensional (like a skin) or is it 3-dimensional (like a volume)? If it is 3-dimensional,what defines it as a surface?

that's an unnatural diet.

Yes,I noticed that too.

Yes ,I miss that too. I use lots of minuses ,pluses and exact quotes when I search.And try to second guess google sometimes. It also annoys me when geographically related searches come up first (I think Duckgogo works for that) This sort of thing https://www.google.ie/search?q="gravity+waves"+-"gravitational+waves"&oq="gravity+waves"+-"gravitational+waves"&aqs=chrome..69i57.22656j0j7&sourceid=chrome&ie=UTF-8

Does "gravity wave" actually mean anything in physics? (is there scope for confusion so that the use of that term might refer to a different phenomenon;or could it simply be an indication that the user of the term simply misunderstands what it does refer to?)

I am wondering what aspects can be said to be correct with the analogy.If the whole thing is put into a detailed computer simulation could it actually be used to make any accurate predictions? What would happen if one attempted to model the Solar System for example.? How soon the playout deviate noticeably from the reality ?(assuming the simulation was entirely faithful to the required proportions and velocities of all the bodies involved) Aside from that it is clearly a fantastic pedagogic device (might also make a good virtual reality game along the lines of fairground dodgems ) If the trampoline was made of spandex would the ratios of the adjacent sides of the stretched parallelograms correspond to any actual space/time ratios that would actually occur? (in the basic analogy) Yes I have seen that . It seems closer to how I have understood curvature but I have not learned the inner mechanisms involved as the maths is beyond me. Perhaps eventually I will understand them (a very long term project)

I have read a good few people complain that the rubber sheet or trampoline analogy is a bad one. Or rather perhaps what they say is that it is taken too literally and that it is not well enough described as simply an analogy and so, like all analogies breaks down at certain points. I want to ask at what points this analogy is actually accurate. For example ,if we actually drew grid lines on the rubber sheet and placed a metal object in the centre how accurately would the distorted parallelograms depict the spacetime graph lines that are actually used to model spacetime in the vicinity of massive or energetic object? Is there anything in fact about the analogy that is really accurate rather than broadly representational? I may have asked this before(or someone else may have) :Who came up with this analogy? Not Minkowski was it? Or perhaps Einstein in need of a little populist outreach?

Does the scenario change at all (and become more feasible) if we are talking about the smallest possible BHs?(or just smaller ones)

So even a direct hit at relativistic speeds would only be expected to produce Hawking radiation? Would their EHs still merge completely in that presumably entirely ("exponentially entirely" ) improbable scenario?

Is there anything unexpected that could arise from 2 BHs colliding at speed? Would this just be another form of a Black Hole merger or would this be a (obviously just a thought experiment) way of breaking up the Black Holes and liberating what has accumulated inside ? I realize the concept seems ridiculous (I actually hit the submit button too soon and by mistake and so had to continue with the post) but what is the answer (can it be said?)

Not one of the "Carry on" films ,was it?

On another forum someone (Janus I think) explained that the movements of stars within our galaxies could be interpreted as extremely long wavelength ,extremely low frequency "sound waves" Perhaps he referred to "density waves" Unless I misinterpreted...

The Ligo Gravity Waves are not sound waves . What did you mean to ask? How do Gravity waves travel through the vacuum of space?

I have read that the temperature of BHs is about absolute zero Why is this?Nothing has any freedom to move? Is there any concept of one location in a BH being any way different from any other?

Hope I am not getting off the subject but is there anything at all known or theorized about the internal structure of a black hole? (discounting theories about the singularity said to lie at the centre) For instance does the concept of "further in" mean anything and if it does what might happen as things go "further in"?