Mordred

abc \[ G^{\mu\nu}\] test abc \(G^{\mu\nu}\) trst

At one time we could keep small latex such as \[G^{\mu\nu}\] inline without requiring a separate line. This aided readability and allowed a cleaner presentation when simply designating variables or values etc. I have been using the \[ command structure. Is there anyway to get the example above inline ?

future references with regards to Einstein-Hilbert action one loop integrals and two loop integrals. https://arxiv.org/pdf/1706.02622.pdf https://cds.cern.ch/record/261104/files/CM-P00049196.pdf https://arxiv.org/abs/1207.2302 https://arxiv.org/pdf/hep-th/9605057.pdf Quantum geometrodynamics https://arxiv.org/abs/0812.0295 loop quantum gravity https://arxiv.org/abs/1201.4598 https://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf

That's useful info, the other method and not positive on the compound used was a mix of water and sodium bicarbonate (if I recall been a few years ) setup in a water fall type scenario with air pushed through it. One problem was what to do with the captured CO2 the article years ago suggested placing it in old oil wells lol. I do know lithium hydroxide can be used to filter co2. I was close sodium bicarbonate was one of the byproducts. Used sodium hydroxide. https://www.eeer.org/upload/eer-21-3-297.pdf Lol can you imagine telling China or one of the other world major producers. " were going to fire a bunch of nukes to clean your atmosphere "........

I can think of several far more practical ways to remove CO2 from the atmosphere. The methodology I read that seems far more practical and safer to boot is to use long tunes attached to a flotation device with a one way flap. This pumps nutrients from the sea floor enhancing algea growth in the immediate region. Algea like plants filter co2 and return oxygen to the atmosphere. The added advantage is that it also aids in fish production.

IQ is meaningless without the required education and research

You may be referring to the Alcubierre drive though poorly described as it doesn't involve antigravity.

Reminder notes Curl of a vector field definition if vector F equals P,Q,R as a vector field in R^3 and \[P_x,Q_y, R_z\] all exists the the curl F is defined as curl \[\vec{F}=(R_y-Q_z)\hat{i}+(P_z-R_x)\hat{J}+(Q_x-P_y)\hat{k}=(\frac{\partial R}{\partial y}-\frac{\partial Q}{\partial z})\hat{i}+(\frac{\partial P}{\partial z}-\frac{\partial R}{\partial x})\hat{J}+(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y})\hat{k}\] the curl of a vector is a vector field in contrast to divergence given as \[div \vec{F}=\vec{\nabla}\cdot\vec{F}\] \[\vec{\nabla}x\vec{F}\] \[\begin{pmatrix}\hat{i}&\hat{j}&\hat{k}\\\frac{\partial}{\partial x}&\frac{\partial}{\partial y}&\frac{\partial}{\partial z}\\P&Q&R\end{pmatrix}\] with determinant loosely defined as \[(R_y-Q_z)\hat{i}-(R_x-P_z)\hat{j}-(Q_z-P_y)\hat{j}=(R_y-Q_z)\hat{i}+(R_x-P_z)\hat{j}+(Q_z-P_y)\hat{j}=curl \vec{F}\] above definitions from https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/16%3A_Vector_Calculus/16.05%3A_Divergence_and_Curl pursuant next study gravity is divergent free on one loop integrals but divergent on 2 loop

If I ever give you a recipe for baking (any) you would want to throw it into the nearest blackhole and count the information loss a blessing.

seesaw mechanism righthand neutrino states with Higgs coupling \[f^v \varepsilon_{ab}\overline{L}^aH^bV_r\] which gives rise to Dirac mass term \[M_D(\overline{V_L}V_R+\overline{V}_RV_L\] Majorona mass terms \[M_{m1}\overline{V_L}V^c_L+M_{2}M^{-c}_RV_R+c.c\] \[\begin{pmatrix}\overline{V_L}\\\overline{V^c_R}\end{pmatrix}\begin{pmatrix}M_{m1}&M_D\\M_D&M_{M12}\end{pmatrix}(V^c_LV_R)\] eugenvalues \[\lambda^2=(M_{m1}+M_{M2})\lambda(M_{M1}M_{M2}-M_D^2)=0\] solution \[\lambda=\frac{(M_{M1}+M_{M2}\pm\sqrt{M_{(M1}-M_{M2}^2+4M_D^2}}{2}\] as one eugenvalue increases the other decreases. set \[M_{M1}=0,,,,M_{M2}>>M_D\] gives \[\lambda=M_{M2}(\frac{1\pm\sqrt{1+4}(\frac{M_D}{M_{M2}^2})}{2})\] \[\lambda_1\approx M_{M2},\lambda_2\approx \frac{M^2_D}{M_M^2}\]

I sincerely hope you never rely on AI. There is an expression garbage in equals garbage out. If you do not have a strong understanding of physics you won't be able to ask the AI the correct questions with the correct terminology. Without strong skills you won't be able to recognize when the AI makes mistakes. Or be able to correct the AI so it can improve the quality of the answer.

yes to blazars the difference between the two is the orientation As you described. Try thinking of it this way the infalling material is the shared material of the surroundings. you have two BH in a region does not increase the available material. That material must be already available in that region. Lets say you have a solar mass of available plasma of material in a 1 light year radius. In the center you have a single BH. In the other scenario you have 2 BH of the same mass. Which scenario would produce the most luminous accretion jet ?

lets take an example the geodesic equation used to describe the path of a particle. \[\frac{d^2x^\mu}{ds^2}+\Gamma^\mu_{\alpha\beta}\frac{dx^\alpha}{ds}\frac{ds^\beta}{ds}=0\] most texbooks and articles will simply describe this as I did the spacetime path of a particle. However someone who understands calculus and the mathematics will know it actually describes the extrenum of the function. In this case the minumum. {shortest path}. Another good example is entanglement. Anyone well versed in statistical mechanics will know that particle {Alice} entangled with particle {Bob} does not mean A affects Bob or vise versa there is no cause and effect. You can simply make probability predictions of Bob by what happens to Alice and vise versa through the Probability function called the correlation function. Yet poor quality papers verbally describe otherwise. The mathematics itself tells the real story. Anyone that truly desires to understand a physics theory requires understanding the math. Anyone no matter how knowledgeable that doesn't understand the math will always be a victim of verbal descriptions that often mis imply or is merely one of many interpretations

Try articles that show the related mathematics. Far too often confusion occurs more from verbal descriptions than it would in the related math. A good quality paper should be 75% math. I've seen far too much confusion by laymen reading simply the verbal descriptions and simply seeking key words they recognize rather than understanding the paper itself. They then mistakenly believe that paper supports their ideas when it doesn't even come close. Size for Particles for example isn't really applicable. Here try these for particle related physics http://arxiv.org/abs/0810.3328 http://arxiv.org/abs/0908.1395 Although this article deals specifically with BH accretion disks its earlier sections cover the major formulas with regards to rge BH.. http://arxiv.org/abs/1104.5499 Though if you want the essential tools to learn any physics theory. Differential geometry Kinematics Calculus Statistical mechanics.

Never try to learn physics via pop media style articles. They tend to never accurately describe any given scenario.

Found the paper I was looking for. Bunn and Hogg examines cosmological redshift in context of both gravitational redshift (would thus include time dilation) and Doppler shift. (Only involves time dilation in the relativistic scenario). He concludes that as free fall observers and emitters apply, then the latter case is more accurate than the previous. https://arxiv.org/abs/0808.1081 One of the problems with the former and latter case is that you end up applying a large number of infinitesimal calculations between observer and emitter.

I do recall Bunn and Hoggs years ago wrote a paper examining cosmological redshift as a possible time dilation. He also wrote one specifically on gravitational redshift equating to time dilation. So it's been examined, I can see if I can track that paper down.

That has been looked into, if you run the time dilation calculations using cosmological redshift as gravitational redshift. You will hit infinity at the Hubble horizon as that is also the point where recessive velocity which is an apparent but not actual kinetic velocity will exceed c. It may help to consider that the other major evidence of expansion isn't simply redshift. The most important evidence is the temperature decrease due to an increasing volume. The other detail to consider is extreme efforts have been made from all the steady state supporters that didn't Like the idea of the BB. Nearly every possible effort to find counter arguments have been tried. They all failed. Time dilation aspects included. If your really looking into an aspect of expansion with a time dilation effect. Look into the integrated Sache Wolfe effect. It should give you some indication of some of the time dilation aspects many aren't fully aware of. It directly involves the stages where the universe switched from radiation dominant to matter to Lambda dominant and the surface of last scattering (CMB) Another detail is the typical cosmological redshift equation ie the one I posted earlier in the article isn't the one a professional cosmologist uses It doesn't take into consideration the evolution of radiation, matter and Lambda

Observational evidence tested further by the CMB itself. If you had curvature the CMB would appear fuzzy not clear. It was the COBE dataset itself that gave clear confirmation. Later confirmed to higher degrees of accuracy through WMAP and Planck. We can readily detect curvature by how we receive light. Curvature will involve lensing effects.

No all field variations will propagate at c as the maximum. To date their has been no exceptions to the speed of information exchange limit.

You don't have time dilation due to the homogeneous and isotropic mass distribution. At time of the emitter the universe mass distribution is uniform. At time of observer the same applies. During any point in time between the two the same applies. In essence you don't have time dilation when spacetime is flat at any point in travel time of the null geodesic worldline. Edit a simple analogy that might help. Take an elastic band stretch it just enough to be straight. There is your null geodesic of the photon path. Stretch it further the density decreases but it will still remain straight.

If you do the math you will likely find the images don't work as well as you believe they do. For example define the mathematics for consciousness hue whatever that's suppose to mean. The Feymann integrals has precise rules for their Dynkan diagrams with regards to virtual particles vs real particles those rules are exact and precise. In every vertex their is a mathematical equation supplying the details. Every representation shape has the same.

Sterile Neutrino related research papers Next decade of sterile neutrino studies by Alexey Boyarsky, Dmytro Iakubovskyi, Oleg Ruchayskiy https://arxiv.org/pdf/1306.4954.pdf Detection of An Unidentified Emission Line in the Stacked X-ray spectrum of Galaxy Clusters Esra Bulbul, Maxim Markevitch, Adam Foster, Randall K. Smith, Michael Loewenstein, Scott W. Randall https://arxiv.org/abs/1402.2301 Neutrino Masses, Mixing, and Oscillations Revised October 2021 by M.C. Gonzalez-Garcia (YITP, Stony Brook; ICREA, Barcelona; ICC, U. of Barcelona) and M. Yokoyama (UTokyo; Kavli IPMU (WPI), UTokyo). https://pdg.lbl.gov/2022/reviews/rpp2022-rev-neutrino-mixing.pdf

science isn't pictures and verbal descriptions. It is making testable predictions using mathematics of cause and effect. At least in any physics related topic. A picture or verbal description doesn't make a testable prediction. a very simple example I have a mass if I accelerate that mass to such and such it will deliver a measurable force. \[f=ma\] it is testable it makes predictions used in nearly every aspect of modern engineering as well as applying in every modern theory in physics.

Tricky as much of the details are in the mathematics however some textbooks are geared to those without a strong background in mathematics. Sean Carroll has a decent free article which does include the relevant math but he does an excellent job stepping one into it. https://arxiv.org/abs/gr-qc/9712019 If you don't mind buying textbooks then I recommend Introductory to General relativity by Lewis Ryder. https://www.amazon.ca/Introduction-General-Relativity-Lewis-Ryder/dp/1108798373 some online video lectures are also helpful https://ocw.mit.edu/courses/8-962-general-relativity-spring-2020/video_galleries/video-lectures/