geordief

Have analogies got any benefits at all? Or are they just like a straw a drowning man might grasp at when ,if he but knew it the water beneath had a rock to stand on. ? Do they allow a student to glimpse a hazy outline of a theory or a model before he or she has got up close?

"on page 6 they give an analogy whereby spacetime is denser around massive bodies." was actually from my post#1 (the OP) ,studiot. You seem to have formatted the quotes incorrectly and attributed it to Tim88. Not sure if that changes the sense of your post or not....

Thanks as always I appreciate your (and others' ) forbearance -I sometimes wonder about the concatenation involved in my own mentation No I do like that analogy (if analogy it is) where the surveyor works out the curvature without benefit of elements outside the set of points in the line .(I may have seen other examples of this -figure 3 in http://www.cco.caltech.edu/~kip/scripts/PubScans/BlackHoles-Thorne-Starmus.pdf ,for example **) Can I extrapolate from your kerbline analogy to suppose that in a 3d+1 space-time environment we can calculate curvature (or perhaps something closely related to it) by first considering the line joining 2 extremely neighbouring points in the space-time manifold and then another line connecting one of these two points with a third point ? Would the "angle" (perhaps a group of angles?) between these 2 lines show the curvature of space in the local area?? Or would it at least have a close mathematical relation ship to the local curvature ? ** the ant walking up and out of the black hole

Can try and dig a bit deeper into your analogy? What ,in spacetime would the points A and P (well the set of points along the rubber band ) correspond to? My first thought would be events or potential events in spacetime. Would that be correct? A concatenation of (potential) events ? Or am I badly misunderstanding the GR/SR model ? Can my (mis?)understanding be shown up by your surveyor's analogy? Or is this an area your analogy doesn't "reach" ? Are points A and P simply 2 points in space along the line taken by a body (or a beam of light) connecting 2 other points in space (or space-time depending on terminology)?

Yes ,sorry I didn't mean "misrepresentations" in a judgemental way -I was trying to be objective but used the language ambiguously.

Don't all analogies rely on misrepresenting the actual situation? Will the best analogy just have the best (=most overlookable) flaw ? When it comes to 4D representations is it possible to design a computer graphic that will show how it would look like from a 5th dimension? Or would that be pointless since ,as I have read Spacetime has intrinsic curvature and so (if I understand right) can not be embedded in an external dimension anyway ? By the way , those posited extra dimensions (in String Theory?) do they only apply at the quantum level?

We are talking about a 4D volume inside a 4D "parallelogram". I think one of its apexes is at an event in Space-Time (hope I have not put my foot in my mouth yet) Can this 4D volume have anything "inside" it or is it simply a mathematical construct that allows us the calculate the space/time ratio at that point? If I am still "on board" , is this ratio closely connected (mathematically) to the curvature of space-time at that point?

And (at least as a mathematical concept) space-time is not compressed so much as squashed. Time,say is compressed and the spatial dimensions are correspondingly stretched? So the overall "volume" of space time is unchanged? Does that also answer my "volume" question (or at least define the question ) in posts #5 and #7 ? All I need is to relate that "volume" to a measurement for mass-energy (with units that cover both ) Can that be done?

I have been searching for the "author" of the rubber sheet analogy for the curvature of Space Time and the question has arisen as to whether there exist better analogies. I can well imagine that all analogies are likely to be flawed and misleading to one degree or another but perhaps they can be educational provided (as is not the case with me personally) the mathematical model is well embedded in the mind of the student. Be that as it may ,I have come across this alternative analogy. Are there other ,better ones? http://www.academia.edu/815814/Reflections_on_a_Variational_Principle_in_Space_Gravity_and_Light on page 6 they give an analogy whereby spacetime is denser around massive bodies. quote: "The explanation of displacement of light-source location, whether star or quasar,as a gravitational lens in a gravitational potential field certainly improves on the rubbersheet analogy. Spacetime localized, that is, compressed by a massive body, such asthe sun, can be visualized as becoming denser around the body. In gravitational redshift, to pass through the increased denseness, a light ray contracts in height thus lengthening its frequency until it passes out of the lens"

OK .Will do.

By the way ,is that quote Einstein pictured space as a three-dimensional version of a thin rubber sheet. wrong (as an analogy) ? Should/could it really read (not necessarily accepting that Einstein did picture anything along any rubber sheet line ) Einstein pictured space-time as a four -dimensional version of a thin rubber sheet. ? Would that take it from an analogy to a closer description,perhaps a correct one?

I will just give you the reply I was drafting. jthorusen (post# 32) on this site http://physicsworld.com/cws/article/news/2011/sep/28/galaxy-clusters-back-general-relativity thinks it may have been Einstein but no one follows up on this.. I also found this :https://worldhistoryproject.org/1915/albert-einsteins-general-theory-of-relativity-is-published "General Relativity describes gravity as a warping of space itself, not as a force. Einstein pictured space as a three-dimensional version of a thin rubber sheet. If you put a heavy object on the sheet, it makes a dent, and therefore an object's path would be affected by that dent. So, planets orbit the sun because the space around the sun is curved in the 2-D equivalent of a funnel or basin." I have no idea if the author (http://burro.astr.cwru.edu/)was sure of this or just talking vaguely No , I meant the extent of apace time (mathematically) per se. Similar to the distance between events but something to measure the spacetime enclosure of a subset of events. Like a "volume of spacetime "

From a look around the internet ,I get the feeling that it may have been Einstein -or at least a few people attribute it to him. It doesn't come up in his quotations ,not surprisingly but I have found an academic who says that is how Einstein pictured it so perhaps it could have been his idea, As an aside is there a way of measuring the extent of spacetime and the amount of mass-energy in the same units (similarly to how time and space do when c is introduced as a conversion factor)? I used to listen to those broadcasts too (great music-it was the same wasn't it?)-a long time ago now.(viva the BBC)

Seems innocent enough to me. Just holding back a sneeze , surely? (impeccable manners)

That should have been one of the questions in the debate Maybe he will write a sexual seduction self help book for billionaires.

So ,if you know the spatial dimensions of an object at rest you can determine its motion wrt yourself (along all 3 spatial axes) by measuring its length contraction or expansion in the corresponding direction? So motion (wrt an observer) is a function of how "distorted" the object appears to an observer? Out of interest If the object is approaching directly at .9c would the contraction (or elongation -I am confused) be the inverse of the contraction of the same object receding at .9c?

Has Farage some primacy amongst his advisers for this debate? If so can we anticipate his line of advice? "Why don't you retire?" hopefully ....

So a bit similar to the way there is no maximum frequency?

I don't understand. You mean indirectly?

Are there such things as units of acceleration (not connected to gravity) ? Is there a maximum theoretical acceleration rate similar to the way there is a maximum speed ( c ) ?

Is the motion caused by rocket propulsion different to the other two motions (which you are perhaps saying are the same in GR)? Is that motion "un-relative" in that an observer in the FoR does know it is in absolute motion(if I am right) ?

Has anyone any advice to Hilary Clinton as to how to approach the second debate.? Should she be reactive or pro active? Are there any obvious mistakes she should beware of? Can she fall into a "too smart" trap ?(I don't think so) Does she just need to play it straight? Has she been given a home run provided she doesn't overmilk it.? Is there anything she can say to connect to Trump's base support and show that he does not deserve their support or does she have to direct her comments towards those who are supporting him because they do not like her or the Democrats.? If she offered to stand aside if he also agreed to ,would that work or could it backfire disastrously ? (I do think it is more important that Trump should not become the president than that she (or even any Democrat should)

Yes ,"what is motion?". Is relative motion so different from non-inertial motion that the description "motion" (as applied to either ) is misleading as the two phenomena are perhaps unrelated?

Does the principle of least action also apply at relativistic speeds? Or does it perhaps apply but not in an obvious way? (apologies in advance for display of ignorance or simplicity ) Has anyone attempted to explain the principle of least action or is it just one of those things that is "obvious" once it is noticed and accepted as presenting no possible anomalies?

Airbrush, on 08 Oct 2016 - 1:50 PM, said: This is as bad as it can get. He is boasting about sexual assault on women. That implies actions, not just talk as he claims. He is no better than Bill Cosby. As for the Evangelicals, he is bragging about grievous sin, adultery, and then "apologizes" by saying Bill Clinton has said worse, which makes this ok and merely a distraction. There are also LOTS of possible examples of this in the multitude of recordings at The Apprentice, but the custodian company is not responding. Probably they received a call from the GOP saying "Shut the hell up!" Funny is Trump starts his apology by saying he never said he was perfect!!! He just applauds for himself nonstop, calls himself brilliant, terrific, spectacular, genius, the only one that can fix things, but not perfect. Give me a break! He clearly has some kind of personality disorder, because his actions are pathological. It is called NPD. Not just simple amorality? What are his latest quotes "If you are a star you can do whatever you want" (or words to that effect ) ? Combined with salesmanship =manipulation . Does he actually need to be a psychopath? Does he have the streak of pushing boundaries as well? "I got away with that ,let's try this now" Are his base ever going to suspect that they have been manipulated? They think his motives are pure? He is not a politician?