tag:blogger.com,1999:blog-1055612246610286525.post6231773795449670687..comments2020-02-21T07:40:46.717+00:00Comments on The Fictional Aether: Why bother trying to explain gravitational waves? My answer (with explanation)Unknownnoreply@blogger.comBlogger9125tag:blogger.com,1999:blog-1055612246610286525.post-38845284643474529392016-03-17T15:20:44.658+00:002016-03-17T15:20:44.658+00:00I've already done the equivalent of the ants w...<a href="http://fictionalaether.blogspot.com/2015/03/the-eclipse-of-gravity.html" rel="nofollow">I've already done the equivalent</a> of the ants walking North to illustrate how curvature can lead to an apparent force. But I don't think that taking this picture and bumping it up into 4D is really what happens in GR. If I take a constant-time slice of the Schwarzschild metric, the stretching of space along a line, in comparison to the flat metric, is not naturally represented as a curved line in a 2D space -- it's just that the 1D direction has been stretched. Or am I missing something?Mark Hannamhttps://www.blogger.com/profile/06011146336221492349noreply@blogger.comtag:blogger.com,1999:blog-1055612246610286525.post-13487675276805007902016-03-16T18:58:46.022+00:002016-03-16T18:58:46.022+00:00Well, for the effects of curvature, you can always...Well, for the effects of curvature, you can always do the two ants walking north from the equator. Starts in parallel, brought together by the curvature of the Earth. The embedding here is important though. We see a 3D space that happens to be embedded in a 4D spacetime. The ant follows a path on a 2D space embedded into a 3D space. Further, a ball has both intrinsic and extrinsic curvature. No analogy is perfect because ultimately, we are fitting mathematics to data and a good scientist should be able to accept when the mathematics fits physical measurement (with the usual caveats of overfitting, yada,yada,yada), irregardless of whether everyday life leaves you with a "physical intuition" of the result. One of the first lessons I figured out on my own in graduate school was there is absolutely no law of nature which states that human intuition is of any value.<br /><br />-JasonAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1055612246610286525.post-22240765524144488042016-03-13T15:20:10.773+00:002016-03-13T15:20:10.773+00:00Tori are fun, but it's still a 2D surface embe...Tori are fun, but it's still a 2D surface embedded in a 3D space. Mark Hannamhttps://www.blogger.com/profile/06011146336221492349noreply@blogger.comtag:blogger.com,1999:blog-1055612246610286525.post-34713157721369852692016-03-11T06:49:42.869+00:002016-03-11T06:49:42.869+00:00I don't know about an intuitive curved 3D spac...I don't know about an intuitive curved 3D space, but perhaps you could use tori to illustrate it. Start with a flat torus and a "donut" torus and explain how a 2D person living on the surface of the torus would be able to tell what kind they were in. Then extend it to 3D flat and curved tori.Anonymoushttps://www.blogger.com/profile/07124499558818789776noreply@blogger.comtag:blogger.com,1999:blog-1055612246610286525.post-32896372033767160702016-03-11T06:40:23.630+00:002016-03-11T06:40:23.630+00:00Nice article. I particularly like the "GR doe...Nice article. I particularly like the "GR doesn't tell us why it happens, it just tells us that it does" and following bit. Might just steal that (I'll credit you of course :) )<br /><br />I've been known to draw triangles on my wine glass in lipstick to try and explain curvature at parties. It's good fun! Chennihttps://www.blogger.com/profile/18353590483308864196noreply@blogger.comtag:blogger.com,1999:blog-1055612246610286525.post-82734806975328037592016-03-10T06:03:08.925+00:002016-03-10T06:03:08.925+00:00These days I get confused about curvature, too. Is...These days I get confused about curvature, too. Is there an "everyday" example of a 3D curved space, *without* taking a 2D surface and bending (embedding) it in a 3D space? This is a real question -- I don't spend that much time these days thinking about these basic GR notions, so I really don't know. Mark Hannamhttps://www.blogger.com/profile/06011146336221492349noreply@blogger.comtag:blogger.com,1999:blog-1055612246610286525.post-68293665470209263802016-03-10T04:50:35.655+00:002016-03-10T04:50:35.655+00:00Nice post. I tend to first focus on the effects of...Nice post. I tend to first focus on the effects of curvature and then connect curvature to energy. I've found that if people already grog curvature determining motion, which is easier to demonstrate, then they'll be much more open to energy setting the shape of space-time.<br /><br />-JasonAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1055612246610286525.post-69788391363203994592016-03-08T20:49:06.919+00:002016-03-08T20:49:06.919+00:00The bending of light is not the same as diffractio...The bending of light is not the same as diffraction, because the light does not change speed -- it has not entered a "different medium", as happens when light goes from, say, glass to air. Instead, space and time are curved by the mass of the sun, and the light follows the shortest route in spacetime, which happens to be a curve. Bending of light is also predicted by Newton's theory, if you also consider light as a particle with mass, but the effect is half of that predicted by Einstein's theory. That's why the bending of light was such a triumph for Einstein's theory: his theory predicted the correct result (without knowing the answer beforehand). <br /><br />In Einstein's theory, if the Sun disappears, the change in the gravitational field will take eight minutes to reach the Earth (the light travel time). In Newton's theory, we will notice the loss of the Sun instantly. <br /><br />In Newton's theory, changes in the gravitational field do not radiate away -- they are felt instantly everywhere in the universe. That was what bothered Einstein so much that he spent 10 years coming up with an alternative.Mark Hannamhttps://www.blogger.com/profile/06011146336221492349noreply@blogger.comtag:blogger.com,1999:blog-1055612246610286525.post-2934481004745965822016-03-08T20:15:52.634+00:002016-03-08T20:15:52.634+00:00Talk at Bristol Astro Society, 4 March 2016.
I fou...Talk at Bristol Astro Society, 4 March 2016.<br />I found your talk very interesting, it being both informative and humorous - a good combination. But I have a couple of points I would like to follow up if I may:<br />1. A member of the audience asked if the gravitational deflection of light was like difraction, and your answer was emphatically NO, echoed by others in the audience. But if light slows down in a stronger gravitational field, then light from a distant star passing close to the sun will be bent, just as light from the sun is bent when it passes through the atmosphere at sunset - the sun appears higher in the sky than it actually is, just like the stars of Eddington's measurements.<br />2. You indicate that Newton's theory had gravity act instantaneously at a distance, but so does Einstein's theory. The gravitational field of Newton is "attached" to the body, so if the body is at rest, or moving uniformly, the gravitational field will also. If another body enters the field at some distance away, it will immediately feel the effect of the gravity from the first body. Similarly with Einstein: the distorted spacetime will be be at rest or move with the body, so that again if a distant body enters the field, it too will instantly feel the effect of the warped spacetime.<br />Although Newton didn't consider gravitational waves, we can assume that, on the basis of his theory, if the gravitating body were to suddenly accelerate, the disturbance of the gravitational field will radiate away - I don't think the speed of propagation can be determined. A similar thing happens with Einstein's theory, but here the speed can be determined.<br />Thank you for your time.Anonymousnoreply@blogger.com