The metric tensor has 10 independent components that reduce to 6 if one imposes local conservation of energy and momentum. The graviton, on the other hand, only has two degrees of freedom. Given this, how does it then that a theory of the graviton can be equivalent to general relativity at least...
If the indeterminacy in the transverse position of null geodesics goes as \sqrt{L \, l_P}, shouldn't this have been already detected in applications of optics? Why do gravitational waves have any special significance here?
I had argued above with a somewhat obscure argument that anisotropic inertia might be a matter of convetion, but your argument is great, very clear and convincing.
Thanks for your answer to my question, it clarified more to me what you have in mind. I actually was thinking of that lagrangian with the constraint - \dot q^{\mu} \dot q_{\mu}=1 and I still do not see how the problem arises (that condition removes the 4 particle interpretation as you said). I...
May be it is meaningful to ask first about the relativistic theory. Shouldn't be a constraint between the components of the linear momentum in case that you are talking about one single particle?
If inertia is anisotropic, so is the propagation of light. It is not difficult to show that there exists a relation between the convention of a simultaneity definition and the isotropic and anisotropic propagation of light. Only the Einstein simultaneity definition leads to an isotropic...
I agree with marcus that the claim of a zero energy universe is not rigorous. Specially because we do not have a definition of gravitational energy in a FRW universe.
As far as I know, this idea is suggested by an argument similar to this one:
Assume that the zero energy balance between energy...
There is no inmediate - or intuitive - link between leaking of gravity and accelerated expansion. Leaking of gravity will arise in models of a 3D-brane embedded in 5D spacetime, with afaik some general assumptions about the quantum behavior of gravity. However, for cosmological models derived...
I am aware of that paper, but it does not answer my quetion. They do not relate this to any other postulated inconsistency in the large scale WMAP data, do they?
There should be a relation between the power spectrum on large angular scales and the peculiar velocities of bulk flows. They should be in conflict with the existing WMAP data for large scale density fluctuations. Is there any known attempt to relate this large scale flow to other recent...
Some results in functional analysis such as the Hahn-Banach theorem need not be part of the book. I am not very familiar with it and its consequences, but it is not completely new for me. I have however access to other functional analysis references to work on that if necessary.
The book I am...
I am looking for a book to study operator algebras: linear spaces, banach-, C*- and von Neumann-algebras, etc. on an introductory level for physics. After searching a bit it seems that "Operator Algebras: Theory of C*-Algebras and von Neumann Algebras" B. Blackadar should be a good choice. This...
This is a suggestive idea. There are models in which our universe is a part of a higher dimensional space-time. If this space-time in turn has some special properties, then the evolution of its intrinsic curvature may act as a kind of dark energy in our four dimensional space-time, accelerating...
I don't think this agrees with standard cosmology. There may be thermodynamical analogies between gases expanding in boxes and matter and radiation expanding with space in the universe, however the mechanisms that apply are very different. The standard cosmological models that are based on...
As I said, to talk about the entropy of the universe can be quite complex. However, if we restrict ourselves to the entropy of the CMB then things become simple.
Here you can apply the very basic definitions of entropy for gases. Entropy is not defined as a temperature, but a change of entropy...
The recombination is the epoch after which the cosmic radiation background mainly ceases to interact with electrons and allows them to get bounded to protons to form neutral hydrogen. Due to expansion of space most of the photons in the cosmic radiation background will lose energy and will never...
What makes you think that it should be decreasing? The entropy of a gas in adiabatic expansion, such as the CMB, is constant. But as mentioned before, the universe is not only the CMB.
I don't think this is correct. Carroll & Ostlie in "An Introduction to Modern Astrophysics" mention that the Hydra-Centaurus supercluster is also being pulled by the Great Attactor. Same you can read in this page here: http://www.solstation.com/x-objects/greatatt.htm. In wikipedia you can read...
I find your view very reasonable marcus. But I thnik that one can also interpret it in another way: space or spacetime is a metric, which in turn represents distances, and this turns "space expands" into "distances expand" that should be more inline with your view.
I started a thread a time ago with a similar question. You may want to use the search function to find it. It seems it is actually a postulate: it can be derived for specific representations such as the Fock representation that, however, restricts itself to positive mass solutions. There is no...
Charles Lineweaver does so in "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe". I think he is authoritative enough and this is a very important paper on this topic. Personally I would prefer "expansion of the universe" (that...
Yes, this is the microcausality condition.
If they are spacelike separated you can define a spacelike vector V that connects them. Then, you can easily show that there exists a Lorentz transformation that transforms V into -V. This will be a rotation of 180 degrees. If you try the same...
Because there is a greater flow than this virgocentric flow. It takes the Virgo supercluster and the Hydra-Centaurus supercluster towards the "Great Attractor". This is probably a concentration of more superclusters having the Norma cluster at its center. The virgocentric flow takes place within...
If you neglect gravitation, you can consider the entropy of the matter in the universe in the same way than a for gas. Due to the cosmological principle every comoving volume (stationary wrt the expansion) will have no heat transfer on its boundaries. This means that the expansion will be...
These are the result of using the Friedmann equations taking as "initial" conditions the Omega and H values for today.
Yes, this is the \Lambda-CDM, that assumes \Omega_m = 0.27, \Omega_{\Lambda} = 0.73 and H = 71 for today.
Increasing rate of expansion means a positive second derivative of...
A flat model remains always flat. With parameters \Omega_m = 0.27, \Omega_{\Lambda} = 0.73 and H = 71, the values at an age of about 27,500 billion years (twice the current age) are: \Omega_m = 0.02, \Omega_{\Lambda} = 0.98 and H = 61. In that epoch we would not have a coincidence anymore...
By the way, it is remarkable that the standard model of cosmology is the only flat model that fulfills this condition, and that the coincidence is better than 1%.
Usually \Omega_0 refers to the fraction of the total density and the critical density today \Omega_0 = \rho_0 / \rho_{c,0}. The term "universtal density" in that paper seems to me to be equivalent to the density at a given redshift, but I might be wrong.
Regarding the age coincidence of t = 1/H, I have made numerical calculations that show what parameters lead to such a coincidence, being the standard model of cosmology one among others. Some details here.
Yes, I had superclusters in mind, considering them on the same hierarchy than voids somehow. I think we should expect some galaxy clusters at z > 2, but no superclusters. However, after some reflection I do not think that this argument about superclusters is correct, because we can actually have...
I guess one of the conclusions about structure formation that can be inferred from the peculiar speeds is that there was no, or not substantial, structure formation in voids. Otherwise those structures should have moved away from the voids towards filaments or superclusters, and there is not...
I think this question was addressed many times in the literature but I was not able to make a clear picture for an answer. It is known that peculiar velocities of galaxies are too small to explain the formation of voids. Voids must have existed already before galaxies were in place with their...
That the orientation of spacetime changes is I think a very basic fact that is not questioned by any new paper. However, most of the recent papers explicitely require the physical state to be invariant under a change of orientation because fermions are not considered in the model.
I think...
This does not necessarily hold. Take for example the most simple bounce scenarios in loop quantum cosmology: in the previous contracting phase the orientation of space-time is the opposite than in the subsequent expanding phase. This could have consequences on a different behavior of matter at...
I came across this topic again and I have calculated the integral
\mathcal{I}(\Omega_{m,0}, \Omega_{\Lambda,0}) = \int_0^1 \frac{da}{\sqrt{ \Omega_{k, 0} + \displaystyle \frac{\Omega_{m,0} }{a} + \Omega_{\Lambda,0} a^2 \right)}}}
with \Omega_{k, 0} = 1 - \Omega_{m,0} - \Omega_{\Lambda,0}...
Ok, so far at our level of discussion I agree with you that if the relation between electrostatic repulsion and gravity remains unchanged at small scales then gravity will never become strong enough to make electrons collapse into a black hole.
Do you expect this arguments to hold at very short distances regardless of the running of the coupling constants? I expect they will not hold. In any case, I still think that the formation of a black hole is possible in principle if gravity is strong enough. Whether gravity is strong enough or...
jonmtkisco, how do you explain the formation of a black hole from the collapse of a neutron star or a quark star? The same mechanism would apply for your electron cloud.
I think that for point 1 you are not right and the cloud should collapse into a black hole.
Consider the usual collapse steps or levels in stars. At every of the levels you have some fermions that determine a degeneracy pressure. If gravity overcomes the degeneracy pressure, the fermions...
For B) I would say that the change of coordinates must be possible, but I understand your skepticism until we do not write down the transformation or find a reference that explains this. For A) it seems to me quite clear that an empty universe must have a flat spacetime solution, since spacetime...
Ok, I may be wrong but this seems not to be right, does it? The transformation only changes the r coordinate appropriately. With t \rightarrow a \, t and r=sinh (\chi) we would reach ds^2 = a \, (-dt^2 + d\chi^2 + \sinh^2(\chi) \, d\Omega^2), but what we need is ds^2 = a \, (-d\tau^2 + d\xi^2 +...
I was sloppy when I wrote that the line element ds^2 = a^2 \, (- c^2 dt^2 + dr^2 + \dots)[/tex] can be obtained from the standard one by t \rightarrow at. You are right that you need also to change r to get rid of the factor 1/1-kr^2. You have probably read about the fact that all FRW metrics...