geordief

That is the first time I have learned of the term "hypercube" but it doesn't seem to be specific to 4D hyperbolic space (despite the prefix "hyper" in it) * Maybe I am asking about a class of hypercube and specifically one in 4 dimensions and where one of them is time (or perhaps more accurately where one of the dimensions is a spacial length like "ct") and has the minus sign giving us the hyperbolic space. * a "hypercube " seems to have n dimensions if I am reading it right.

In Spacetime there are 4 dimensions which form a hyperbolic space. In everyday 3D geometry the gridlines form "cells" which take the form of common or garden cubes with 6 faces. What does the corresponding arrangement look like in 4D hyperbolic space? Are there any descriptions I can find -or even drawings? Can I refer to these objects as "cells" ? How many "faces" are they to correspond to the 6 in 3D space? Is that number 8?

Thanks(a little learning is a dangerous thing ) I have edited my post and hopefully that error has been ironed out- and the post is a little clearer as a result. To address the rest of your post ,I don't think you have addressed my question directly (perhaps because it was badly formed ) I am prepared to accept that I am in error but I was hoping that the error could perhaps be shown up more closely. As for the points you raised about the two men walking towards the N.Pole from the equator are they supposed to be idealised 2 dimensional creatures ?-because it seems to me that they must know that they exist in 3 (if not 4 dimensions) if they want to tie their shoelaces and brush their hair

I am posting in this subforum * because I do not know if this is actually the accepted theory (or one of them) and if I am just a slow learner..... This is my question.: Does mass and energy curve spacetime because spacetime , firstly is just a mathematical model with lines along parallel to the 4 axes that meet at all the points {x,y,z,t} that are the set of all possible events? In the real world (not the model) there are areas of mass/energy where "events" cannot take place because the "spot is taken" . As a result ,for the model to be accurate we have to make a "detour" ** around these particular areas when we draw the lines parallel to 4 axes and this is the "curvature of spacetime" (in the model) * let's hope I was right to post here. ** A bit like the way the running water a stream goes around a rock which is poking out above the surface.

@Lyudmilascience You might be right and I may have just failed to articulate my thought. Perhaps there will come a time when I will understand better what it is I was trying to say -or maybe come to a different appreciation of the idea. I prefer not to try and reanalyse my post though as I can easily tie myself up in knots when I go down that road.....

I have asked this question before ** so it feels like I am trolling and was not happy with the answer I got. Anyway, it is the size of the universe. To me it feels like it is so big that "size" really doesn't describe it. It does me no good to say to myself "of course it may be infinite so what do you expect" Again , if it was finite I might say to myself "well it is small then if you can somehow sum it up". What I see is something in nowhere land and the question I have is "does this "size" have an import? Not in any implications but in its own right. Is it just an invitation to say "so what?" and think of something else that actually means something or is there anything to it more than just a gut feeling? This is what got me thinking about it (again) http://www.dailymail.co.uk/sciencetech/article-3522529/Journey-heart-galaxy-Incredible-Hubble-images-capture-clusters-centre-Milky-Way-stunning-detail.html Edit: I promise not to post this topic again ** just the once....

Are there any representations using 3D as in films like Avatar that make a better job of displaying the way space time is curved in the presence of mass? Also is it correct to say that ,when we open our eyes every morning we are in fact looking at the world in 4D (or 3d+1) dimensions -just that speeds are very low ?

I only introduced the extra black hole for purposes of demonstration. I concede that it doesn't add anything essential to the situation since spacetime seems to be always curved to one degree or another . Perhaps there is too much about black holes in the daily news these days and it has got to me. The test masses you bring up do not oscillate in the direction of the earth but the presence of the Earth does affect their motion does it not?

to a layman it seems like they are closely related though. Is the connection that mass (et al) curves spacetime and that gravitational waves (as an analogy) "pass a current" through that curvature?

Well I never expected anything to add linearly. My question was not rhetorical (as phrased it can be taken either way I see now but I actually intended it to be taken in a "neutral" way) . It was straight bat -a request for further clarification. But to address your question as to what I expected to be added it was (a) those "vectors" in Strange's animation in post #48 and (b) (if they exist) corresponding vectors associated with the pre-existing gravity field through which that gravitational wave is passing (I added a "convenient" black hole to the right hand side of the animation -off the page - to highlight /emphasize this existing gravitational field. I have no doubt my question holds many confusing misconceptions but I have tried to be as clear as I can Perhaps I could have more simply asked " What is the mechanism whereby a gravitational wave interacts/combines with the gravity field through which it passes?" thanks I think I have had enough lessons for the time being

Is " the sum of two gravitational waves" correct terminology in this case ? The black hole to the right of the animation (the one that I put there in my mind's eye) is not actually producing gravitational waves is it? Would it be correct to refer to that gravitational field (at the point where it meets the gravitational wave ) as a "standing wave" ? or just a field with "curved fronts" that look like a wavefront. So ,if my terminology is correct (or comprehensible) then I was asking how this "standing wave" (= the local gravitational field) interacts with the disturbance caused by the binary black hole . I appreciate that it is non linear. but I am interested to learn (if I have) that both are basically the same beast -one is static and the other dynamic . I hope I am seeing that right.

Could you throw me a tidbit and explain it a general introductory way why(or how) these vectors -the arrows you have shown in the animation in in your post#48- don't add linearly? Is it because they are not actually vectors but their equivalent in spacetime ? They wouldn't be tensors ,would they? Or are they just a schematic representation and not to be taken at all literally? PS :Sorry I can't work out how to put multiple posts into replies.....

If there is a black hole at 3 o clock (off the page) are all the vectors in that graphic lengthened towards the "east" ? (And of course the vectors pointing "west" would be shortened proportionally) Does the gravitational wave cause passing perturbations in the local gravitational field and do the vectors due to the gravitational waves add linearly to the vectors in the local gravity field?

Well ,if I was clear in what I thought might be being represented , is it possible to represent that in an accurate way ( a "bird's eye" view of the 2D plane as it bobs up and down) ? (It wouldn't be a pure 2D plane more like a "physical" thin slice of the 3D region)

Hope this is on topic. Does this animation (provided by Strange in his recent post) actually correspond to what that observer might see if somehow " markers" were inserted into the space surrounding the binary black hole system? https://upload.wikimedia.org/wikipedia/commons/b/b8/Wavy.gif I mean if the space was somehow visible by means of some kind of a huge population of visible particles like bubbles in a bubble chamber is that an accurate representation of what we would see? I know that is a ridiculous hypothesis . Does it work though in principle?

thanks, I will.

Strange,are the waves that are associated with particles in quantum theory moving waves or is this a "static field"? If we are talking of moving (dynamic?) fields are there wavefronts associated with the fields? If so,can these wavefronts intersect with one another?

I have had the same (I think it may be the same) idea as MSC previously. I felt it would be a big deal if feasible but I also have no idea how it could be shown. The way I pictured it as that what we call "particles" might be areas where the field became concentrated as a result of two separate wave fronts meeting(in the way waves meet each other at an angle) on the shoreline . The intersection of the wave front would be the location of the "particle". I wonder how fast these intersection points could move. If it was FTL then that alone would disprove my "idea".

Ok (it was a very wild stab) . Is one difference between what I was aiming at(trying to conjure up) and "cutting edge science" the fact that the only "teacher" available to them is reality itself (experimentation and interpretation ) ? Edit : I seem to be going off topic now .I will give it a rest.

Arguing from personal ignorance (as is appropriate here ) to take the trampoline analogy-which is widely described as flawed . If we physically jump up and down on one we land in a different spot to where we jumped off - depending on the curvature of the trampoline and our speed or momentum. Is there anything in general relativity that corresponds -or could correspond -to that displacement? If there was it might show that I (with help from someone else) could learn something by using an analogy .(even though the theory was already formed)

If it can be shown (by "proving" or just demonstrating a negative) that these examples do not exist -a set of zero- that would be an interesting* result. It would show that analogies only occur after and "never" before the formulation of models or theories You cannot actually prove this but can demonstrate it statistically (if no examples are forthcoming) . * only "interesting" perhaps.

You are not just talking about the way we learn from our life experiences in an undefined and seemingly amorphous way.? You seem perhaps to be trying to shoehorn a method onto this ad hoc way of learning about things.

Pretty off topic but Ada Lovelace took to backing the horses to finance Babbage's machine. With all her skills she still managed to lose her bets and her project. Something must have trumped her method and it turned out badly http://www.irishtimes.com/opinion/the-famous-mathematician-ada-lovelace-and-the-horse-named-after-her-1.2460532 and http://www.math.wichita.edu/history/women/ada.html "The correspondence of Lady Lovelace and Charles Babbage continued for eighteen years, the last of which were full of scandal, tragedy and failure. The two devised a fool-proof system of betting on the horses while working on mathematical theories of probability. Lady Lovelace, who had always had a passion for horse racing, became badly in debt, forcing her to sell the family"

possibly the point

Fun and excitement is all around but you will not find it in method. The method is the prelude (literal meaning of prelude is a clue -"before games" ) to the fun and excitement. "Work and play " is another meta analogy here.