tag:blogger.com,1999:blog-22973357.post5977409303303011535..comments2023-09-27T07:44:19.769-04:00Comments on Sabine Hossenfelder: Backreaction: Dear Dr B: What does the universe expand into?Sabine Hossenfelderhttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comBlogger44125tag:blogger.com,1999:blog-22973357.post-9062991738656344552019-12-06T20:17:37.618-05:002019-12-06T20:17:37.618-05:00There was a time when our world seemed flat, a tim...There was a time when our world seemed flat, a time when you could dream of the waters of the sea, falling precipitously into a bottomless abyss ... where? What? There was a time when the entire Universe looked like an aggregate of objects revolving around the Earth, but it was we and everything else that revolved around the Sun. There was a time when everything seemed limited to one hundred Jesús Merinohttps://www.blogger.com/profile/09085774921848258626noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-49692646086851759352018-09-14T21:11:26.694-04:002018-09-14T21:11:26.694-04:00FWIW, Hawking's idea that "there's no...FWIW, Hawking's idea that <i>"there's nothing north of the North Pole"</i> never worked for me.<br /><br />It fails for me as a metaphor, because of course you can go north of the North Pole -- you just need a rocket ship. Our sense of "north" does not end on Earth, but continues into space. The <i>context</i> changes quite a lot, but the direction of north still Wyrd Smythehttps://www.blogger.com/profile/06694506351266400927noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-33360642423291173872018-09-14T09:15:33.660-04:002018-09-14T09:15:33.660-04:00Hello Sabine and thank you for taking time to answ...Hello Sabine and thank you for taking time to answer laymen questions!<br /><br />However, as a philosophical layman i feel like i need more clarity.<br /><br />What I think I got from your answer is that we can know (assuming that the best explanation of observed phenomena is space expansion of course) that there is sapce expansion, and we can describe it and measure it without assuming that theAnonymoushttps://www.blogger.com/profile/10068008143564489491noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-80588076915564597682018-09-08T02:06:11.986-04:002018-09-08T02:06:11.986-04:00Traruh: No. Traruh: No. Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-87981869883817043682018-09-07T14:26:42.033-04:002018-09-07T14:26:42.033-04:00Is the 4-->10 embedding related to why string t...Is the 4-->10 embedding related to why string theory 'likes' 10 dimensions?<br /><br />Traruh Synredhttps://www.blogger.com/profile/09350151173614156180noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-16249804998014024682018-09-07T14:22:53.270-04:002018-09-07T14:22:53.270-04:00The expansion without expanding into anything does...The expansion without expanding into anything doesn't seem that weird to me. Imagine an infinite 'rubber' sheet that is being stretched by internal forces (e.g., it was initially compressed ['dark energy']).<br /><br />Like any analogy this one has its pitfalls, but it seems to deal with the 'expanding into' issue.There always plenty of room at infinity. Traruh Synredhttps://www.blogger.com/profile/09350151173614156180noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-56150571800629961152018-09-05T02:05:59.280-04:002018-09-05T02:05:59.280-04:00The main reason I think curved spacetime needs to ...The main reason I think curved spacetime needs to be embedded in a higher dimensional flat spacetime in a quantum gravity theory, is because you ultimately want to calculate the path integral of the curved spacetime. You cannot trace the path of an n-dimensional object in an n-dimensional universe. You need higher dimensions to draw it into. You cannot trace the path of a point particle inside a Patat Jehttps://www.blogger.com/profile/01677169592055512438noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-18706448493342260092018-09-04T15:43:34.157-04:002018-09-04T15:43:34.157-04:00" Now you ask what does the universe expand i..." Now you ask what does the universe expand into? It doesn’t expand into anything, it just expands "<br /><br />This is a very profound statement. It implies that all reality is contained within our particular universe. And that there are no other universes or anything else for that matter.Anonymoushttps://www.blogger.com/profile/10664294321325943333noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-15896885668008578812018-09-03T11:49:22.891-04:002018-09-03T11:49:22.891-04:00I viewed the "Zogg of Betelgeuse" explai...I viewed the "Zogg of Betelgeuse" explainer on "Shape of Universe" suggested by Lawrence Crowell ... nicely done video series, BTW!<br /><br />Zogg explains you can have a torus-shaped surface and still be euclidean & flat. <br /><br />But that doesn't seem right. Imagine a 2D torus surface and a flat-world physicist living inside the surface. <br /><br />Suppose Unknownhttps://www.blogger.com/profile/14136922143569965933noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-81152849151616880962018-09-02T09:46:02.367-04:002018-09-02T09:46:02.367-04:00Observe an ongoing irresolvable debate of which ma...Observe an ongoing irresolvable debate of which math models are appropriate to the task. Nobody wonders whether postulates are appropriate. Newton postulated (outright or tacit) wrong values for lightspeed (infinite), Planck's and Boltzmann's constants (zero). Newton opened <i>Principia</i> postulating the Equivalence Principle. All but the last are empirically wrong. The EP has only Uncle Alhttps://www.blogger.com/profile/05056804084187606211noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-16671052410531050092018-09-01T17:18:59.091-04:002018-09-01T17:18:59.091-04:00For the embedding one needs an isometric emmbeddin...For the embedding one needs an isometric emmbedding, so Nash theorem is the one to look at. And better the one, if there is one, about the lorentzian case.Anonymoushttps://www.blogger.com/profile/06098439870046873701noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-76473789329270346262018-09-01T17:02:14.998-04:002018-09-01T17:02:14.998-04:00A 4-dimensional curved spacetime needs a 90-dimens...A 4-dimensional curved spacetime needs a 90-dimensional flat spacetime with 87 space dimensions and 3 time dimensions to be embedded in. Source: <br /><br />Clarke, C. J. S., "On the global isometric embedding of pseudo-Riemannian manifolds," Proc. Roy. Soc. A314 (1970) 417-428<br /><br />Reference https://www.physicsforums.com/threads/Patat Jehttps://www.blogger.com/profile/01677169592055512438noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-26679109694929840182018-08-31T18:57:36.951-04:002018-08-31T18:57:36.951-04:00I just remembered these animations by "Zogg o...I just remembered these animations by "Zogg of Betelgeuse" on how the universe has no edge. These are pretty good and funny in places.<br /><br /> https://www.youtube.com/watch?v=_k3_B9Eq7eMLawrence Crowellhttps://www.blogger.com/profile/12090839464038445335noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-79854917537469642242018-08-31T06:54:03.368-04:002018-08-31T06:54:03.368-04:00I made an error in my last post here. I wrote &quo...I made an error in my last post here. I wrote " curvature factor Λ ~ 10^{52}m^{-2}," when in fact the curvature factor or cosmological constant is very small Λ ~ 10^{-52}m^{-2}.<br /><br />I have to further write that Bee has written a reasonable account of how the observable universe expands. The one problem I have noted with physics is how it shocks our intuitive idea of the world, Lawrence Crowellhttps://www.blogger.com/profile/12090839464038445335noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-5772343591177729032018-08-31T05:29:20.314-04:002018-08-31T05:29:20.314-04:00JQ,
In the balloon analogy, the universe is only ...JQ,<br /><br />In the balloon analogy, the universe is only the surface of the balloon. As any analogy, it has its shortcomings. The ants should actually not crawl on the surface, but they should be two-dimensional ("flat world") ants crawling in the surface. The side of the surface, hence, isn't relevant in this analogy. Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-36741152134828679892018-08-31T05:27:25.882-04:002018-08-31T05:27:25.882-04:00Babak,
Everything inside our universe is embedded...Babak,<br /><br />Everything inside our universe is embedded in that universe. Hence, there can't be a real-life example. Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-30170492564965931092018-08-31T05:25:52.256-04:002018-08-31T05:25:52.256-04:00Hallelujah! It took Google three months but finall...Hallelujah! It took Google three months but finally comment notification is working again!Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-43839108831048553182018-08-30T09:54:29.285-04:002018-08-30T09:54:29.285-04:00Babak, no, clearly not! Everything that we see exp...Babak, no, clearly not! Everything that we see expanding, like balloons or bellies after brunch, can be seen as expanding into space. We like to see it that way, because we live here. But now we're trying to answer the question, "What is the expansion of space like?" This is not so mundane. <br /><br />The best analogy is maybe to the math of two dimensional surfaces, like balloons DougOnBloggerhttps://www.blogger.com/profile/16411970226629138387noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-73233280466280831662018-08-30T09:17:11.633-04:002018-08-30T09:17:11.633-04:00Sabine,
I someone had 6 superconducting balls arr...Sabine,<br /><br />I someone had 6 superconducting balls arranged in a hexagon, with current traveling through these balls, would the current of each ball look like it is accelerating from every viewpoint within each ball? If so would that be an analogy of why our universe looks like it is accelerating?Michael John Sarnowskihttps://www.blogger.com/profile/00528454593064091302noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-15256521151841536502018-08-30T06:50:21.131-04:002018-08-30T06:50:21.131-04:00@ Phillip Helbig: Look up Whitney embedding theore...@ Phillip Helbig: Look up Whitney embedding theorem. The strong form where for an n dimensional space it can be smoothly embedded in 2n dimensions such as R^{2n}.<br /><br />There are ways of defining curvature. Riemannian curvature is defined entirely by the parallel translation of vectors within a manifold. It does not have any definition with respect to an embedding space of larger dimension. Lawrence Crowellhttps://www.blogger.com/profile/12090839464038445335noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-62085786611622809002018-08-27T12:35:44.487-04:002018-08-27T12:35:44.487-04:00Dr. Hossenfelder,
Does finite vs infinite space af...Dr. Hossenfelder,<br />Does finite vs infinite space affect whether it is embedded?<br />In a 2D analog, a sphere can be finite, when it expands, it doesn’t seem to need embedding. An infinite sheet can expand without embedding as well. A finite sheet can expand, but it seems to be expanding into something. <br />ThanksStuart Thomashttps://www.blogger.com/profile/02088622755203795464noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-25260764148991774582018-08-27T12:30:05.951-04:002018-08-27T12:30:05.951-04:00Since as a non-physicist I only have to worry abou...Since as a non-physicist I only have to worry about seeing empirical evidence in a way that’s visually sensible and consistent with observations, I dismiss the two dimensional curvature diagrams as being physically viewable. Instead I merely look at space-time curvature as being the scale for which space-time is relative to another observer. It may be wrong, but for an amateur just wanting Louis Tagliaferrohttps://www.blogger.com/profile/16698865662162457632noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-31801895348196357922018-08-27T08:47:17.537-04:002018-08-27T08:47:17.537-04:00Sabine,
thanks for your post, and also for the bl...Sabine, <br />thanks for your post, and also for the blog as a whole. I enjoy having occasional reads on your blog. <br /><br />May I ask a question about this post? <br /><br />Your daily-life analogy of ants on the ball was illuminating. Analogy, is used correctly, can impart the right insight and help avoid the incorrect one---like you did in this case. My question is, can you please also Baabackhttps://www.blogger.com/profile/00211828975971287662noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-31784387346868882452018-08-27T05:46:23.043-04:002018-08-27T05:46:23.043-04:00"Can you explain why a four-dimensional curve...<i>"Can you explain why a four-dimensional curved spacetime needs ten dimensions to be embedded in a flat spacetime? Why aren't, say, five dimensions of flat spacetime enough?"</i><br /><br />An m-dimensional space needs, in general, at least n dimensions to be embedded in, where n = m + (m-1) + (m-2) + ... + 1. So, for m = 2, n = 2 + 1 = 3 and for m=4, n = 4 + 3 + 2 + 1 = 10. <br Phillip Helbighttps://www.blogger.com/profile/12067585245603436809noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-5902281121177425302018-08-27T03:52:57.970-04:002018-08-27T03:52:57.970-04:00Would the balloon+ants analogy be more useful if t...Would the balloon+ants analogy be more useful if the ants were crawling in the inside of the balloon, and for whom the universe ends at the rubber surface?JQhttps://www.blogger.com/profile/14594234963607383324noreply@blogger.com