tag:blogger.com,1999:blog-22973357.post2987478462207075064..comments2021-07-30T15:23:00.163-04:00Comments on Sabine Hossenfelder: Backreaction: Impressions from the Loops '07Sabine Hossenfelderhttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comBlogger69125tag:blogger.com,1999:blog-22973357.post-85795920663895268332007-07-24T04:37:00.000-04:002007-07-24T04:37:00.000-04:00Hi Anonymous:Neglecting the question of who father...Hi Anonymous:<BR/><BR/>Neglecting the question of who fathered whom, I don't know what you disagree on, since you say exactly what I say too. Best,<BR/><BR/>B.Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-265142467760972232007-07-23T17:16:00.000-04:002007-07-23T17:16:00.000-04:00Bee:"General covariance is invariance under arbitr...Bee:<BR/>"General covariance is invariance under arbitrary coordinate transformations. You can have that on a fixed background. What I said is that the background itself should be subject to a general covariant evolution law, as e.g. it is in GR."<BR/><BR/>I disagree!<BR/><BR/>There should be "no prior geometry" for a "geometric, coordinate independent formulation of physics". <BR/><BR/>By "priorAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-24332911864553737542007-07-16T09:56:00.000-04:002007-07-16T09:56:00.000-04:00Hi Robert,yes, I agree, the argument still has to ...Hi Robert,<BR/><BR/>yes, I agree, the argument still has to be transformed. Best,<BR/><BR/>B.Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-60750454143882122902007-07-16T05:15:00.000-04:002007-07-16T05:15:00.000-04:00a scalar quantity is defined to be one that is inv...<I>a scalar quantity is defined to be one that is invariant under general coordinate transformations.</I><BR/><BR/>Strictly speaking it's not. An invariant under coordinate transformations is a constant scalar. You still have to transform the argument.<BR/><BR/>I think a lot of the invariant/covariant confusion comes from people mixing active and passive transformations but if you are careful Roberthttps://www.blogger.com/profile/06634377111195468947noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-13441194767358898422007-07-13T16:13:00.000-04:002007-07-13T16:13:00.000-04:00See e.g.Geometry, Topology and Physics, by M. Naka...See e.g.<BR/><BR/><A HREF="http://www.amazon.com/Geometry-Topology-Physics-Graduate-Student/dp/0852740956" REL="nofollow">Geometry, Topology and Physics, by M. Nakahara</A> Chapter 7.10.3Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-7176783902951604892007-07-13T16:09:00.000-04:002007-07-13T16:09:00.000-04:00Bee:"The Dirac eq. \slash D \Psi = 0 is a Lorentz ...Bee:<BR/>"The Dirac eq. \slash D \Psi = 0 is a Lorentz scalar, and generally covariant (\slash D = gamma^nu D_nu with D_nu = \nabla_nu + Gauge fields_nu, and \nabla the Levi Civita Connection). Again, provided that you transform the quantities appropriately (e.g. the anti-comm. of the Clifford algebra is in general g_munu not \eta_munu)."<BR/><BR/>And how will \psi (a Lorenztz bi-spinor) Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-80249956658403570172007-07-13T13:37:00.000-04:002007-07-13T13:37:00.000-04:00Hi Bee,I thought that in Minkowski space the Dirac...Hi Bee,<BR/>I thought that in Minkowski space the Dirac equation was (disregarding the gauge field connection and the mass):<BR/>\slash\partial\psi=0<BR/>which is only Lorentz covariant but not generally covariant. Where am I wrong?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-44740089681179921902007-07-13T13:07:00.000-04:002007-07-13T13:07:00.000-04:00Sorry, but you are not making any sense. There is ...Sorry, but you are not making any sense. There is nothing 'unphysical' about the coordinate system of an accelerated observer. It's just a coordinate system. What you are trying to say is (I think) there is a difference between a local orthonormal base and a coordinate system. I agree on that. The Dirac eq. \slash D \Psi = 0 is a Lorentz scalar, and generally covariant (\slash D = gamma^nu D_nu Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-53736074502688818072007-07-13T12:44:00.000-04:002007-07-13T12:44:00.000-04:00Hi Bee,Maybe one should distinguish "coordinate sy...Hi Bee,<BR/>Maybe one should distinguish "coordinate systems" and "physical frames of reference".<BR/>In flat space only inertial frames are "physical", i.e. physical laws stay the same under Lorentz transformations.<BR/>On the other hand, if you pick some arbitrary coordinate system corresponding to some rotating frame the physical law will not be the same in such a frame. Take one physical law Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1196337246996753082007-07-13T09:53:00.000-04:002007-07-13T09:53:00.000-04:00You say: In flat space, general covariance is repl...<I>You say: In flat space, general covariance is replaced by Poincare/Lorentz covariance. The equation of motion of the graviton in flat space is "Box"h_\mu\nu=0 which tells you that the graviton is massless.<BR/>That equation is not generally covariant but only Lorentz covariant.</I><BR/><BR/>Look, you are again mixing up isometries with coordinate transformations. You can perfectly well Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-52142086714066561382007-07-13T09:37:00.000-04:002007-07-13T09:37:00.000-04:00K - a scalar quantity is defined to be one that is...K - a scalar quantity is defined to be one that is invariant under general coordinate transformations. For example the line element is. And the particle mass. You can look that up in any textbook on differential geometry. <BR/><BR/><I>We have been discussing quantum theories right?</I><BR/><BR/>I have mostly talked about GR, which I think so far is not a quantum theory.Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-41659572835597810302007-07-12T23:51:00.000-04:002007-07-12T23:51:00.000-04:00The last comment is of course for the well known c...The last comment is of course for the well known case (Minkowski background) but generically the quantities labeling the quantum states are invariants of the isometry group of the background metric. We have been discussing quantum theories right?<BR/><BR/>In flat space, general covariance is replaced by Poincare/Lorentz covariance. The equation of motion of the graviton in flat space is "Box"h_\Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-45105668377128331972007-07-12T23:38:00.000-04:002007-07-12T23:38:00.000-04:00Bee:"They need to know how to relate the measureme...Bee:<BR/>"They need to know how to relate the measurements from one observer to the other. A scalar is the simplest case, it remains invariant."<BR/>Under Poincare transformations, not under some general diffeos!<BR/><BR/>KAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-5077796692971802882007-07-12T13:01:00.000-04:002007-07-12T13:01:00.000-04:00Hi K,you wrote above "Sorry but once you fix the b...Hi K,<BR/><BR/>you wrote above <I>"Sorry but once you fix the background you break the general covariance."</I> I tried to explain why you can have general covariance on a fixed background. You instead referred to isometries that a fixed background might not have.<BR/><BR/>You can have observable quantities that are not invariant under coordinate transformation, i.e. not scalars. For example, theSabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-59154381366139724892007-07-12T12:50:00.000-04:002007-07-12T12:50:00.000-04:00Bee:" can't make sense out of what you say. Observ...Bee:<BR/>" can't make sense out of what you say. Observables are things one observes, and depend on the observer."<BR/><BR/>OK, but if two different observers are to agree on something the observable has be some sort of invariant, right?<BR/>I mean, in my specific example, in a fixed background, the states are labeled by the eigenvalues of quadratic Casimirs of the corresponding isometry group. Ianonymoushttps://www.blogger.com/profile/14926985211687774974noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-58954479734691175492007-07-12T10:49:00.000-04:002007-07-12T10:49:00.000-04:00I can't make sense out of what you say. Observable...I can't make sense out of what you say. Observables are things one observes, and depend on the observer. You say <I>"the physical observables are those that are invariant under the Poincare group, not the full diffeo group"</I>. Minkowski is a special case because you can define your std. coordinates (x,y,z,t) (up to Lorentz trafos), it's a flat background. Exactly this is the problem in a Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-69495929512392643502007-07-11T22:25:00.000-04:002007-07-11T22:25:00.000-04:00"I think we have a disagreement on the word 'invar..."I think we have a disagreement on the word 'invariant'. You are referring to isometries. Under a coordinate trafo x -> x'=Gx the metric remains unchanged g'= g. I.e. the Minkowski line element remains the same under the Poincare group. I am talking about general covariance, under a coordinate trafo the metric transforms as a tensor g' = GgG^T, or equations of motions transform accordingly. The Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-11565671949221296392007-07-11T22:01:00.000-04:002007-07-11T22:01:00.000-04:00I think we have a disagreement on the word 'invari...I think we have a disagreement on the word 'invariant'. You are referring to isometries. Under a coordinate trafo x -> x'=Gx the metric remains unchanged g'= g. I.e. the Minkowski line element remains the same under the Poincare group. I am talking about general covariance, under a coordinate trafo the metric transforms as a tensor g' = GgG^T, or equations of motions transform accordingly. The Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-22835795335078076122007-07-11T21:35:00.000-04:002007-07-11T21:35:00.000-04:00Bee:"yes, once you fix the background, your global...Bee:<BR/>"yes, once you fix the background, your global solution only allows certain symmetries (turn around, world stays the same) under which the metric stays identical."<BR/><BR/>That's exactly what I meant by saying that the fixed background is not diffeo invariant.<BR/><BR/>"you're still allowed to pick an arbitrary coordinate system, and the physical laws (and so the metric) will transform Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-52703479262583098052007-07-11T20:50:00.000-04:002007-07-11T20:50:00.000-04:00Yes, without a background manifold (metric) it's c...Yes, without a background manifold (metric) it's certainly background independent in a higher degree. I wonder though if we really need that. I.e. I would be fine with the type of background independence that we have in GR.Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-40377273472582781802007-07-11T20:47:00.000-04:002007-07-11T20:47:00.000-04:00Hi Bee,Bee:"I understood the point of the talk as:...Hi Bee,<BR/>Bee:<BR/>"I understood the point of the talk as: if you talk about BGI, make clear what you mean with it."<BR/><BR/>Well, I think what Moshe meant by BI is that the full guantum theory of gravity has no space-time background manifold, metric, etc. Those only emerge in a particular classical limit.<BR/><BR/>Contrast this with the LQG approach where they start with what they refer to asAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-56043727937561140532007-07-11T20:43:00.000-04:002007-07-11T20:43:00.000-04:00yes, once you fix the background, your global solu...yes, once you fix the background, your global solution only allows certain symmetries (turn around, world stays the same) under which the metric stays identical. you're still allowed to pick an arbitrary coordinate system, and the physical laws (and so the metric) will transform from one system to the other according to the transformation laws of general diff. invariance. e.g. you can transform aSabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1476283855140593452007-07-11T20:26:00.000-04:002007-07-11T20:26:00.000-04:00Bee:"I don't understand your remark above. General...Bee:<BR/>"I don't understand your remark above. General covariance is invariance under arbitrary coordinate transformations. You can have that on a fixed background."<BR/><BR/>Sorry but once you fix the background you break the general covariance. GR has general covariance as a theory but the solutions of GR (i.e the metric) only preserve certain isometries. It's just like in the Standard model, Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-37014664445093486642007-07-11T20:17:00.000-04:002007-07-11T20:17:00.000-04:00Hi K,I understood the point of the talk as: if you...Hi K,<BR/><BR/>I understood the point of the talk as: if you talk about BGI, make clear what you mean with it. I don't understand your remark above. General covariance is invariance under arbitrary coordinate transformations. You can have that on a fixed background. What I said is that the background itself should be subject to a general covariant evolution law, as e.g. it is in GR. Best,<BR/><BRSabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-2911553643366662882007-07-11T20:09:00.000-04:002007-07-11T20:09:00.000-04:00Bee:"I would say it means that the physical laws w...Bee:<BR/>"I would say it means that the physical laws we observe allow for a completely dynamical background geometry."<BR/><BR/>Dear Bee,<BR/>I think that what you said above descrives general covariance, not background independence.<BR/><BR/>After I heard Moshe's talk I understood that by background independence he meant that there is no spacetime manifold in a BI theory. Even though his talk Anonymousnoreply@blogger.com