Mordred

This would induce different expansion/contraction rates. Expansion/contraction is a combination of thermodynamics and GR.

Ah gotcha, the cross post. Ok anyways one of the problems that you haven't been looking at closely enough on the BH and WH dynamics is the differences inherent between a homogenous and isotropic expansion/contraction compared to an inhomogenous and anistropic expansion/contraction that a BH or WH would generate.

Ok now we can start toy model building without risk of confusion to Student readers. Lets start with question 1 how do you propose to maintain a homogeneous and isotropic expansion from a white or black hole when that dynamic is anistropic and inhomogeneous? If you prefer we can lock it but its probably not necessary now that its in the forum designed to allow this sort of model building

! Moderator Note Evidently we are in agreement so lets correct this now. Thank you for agreeing with my assessment

I suggest as you are definetely trying your own modelling in a manner that is not found in any mainstream textbook that this thread should be moved to the Speculation forum. The OP of this thread was already pushing the limits to mainstream physics but now you two are model developing. Mainstream physics is the section reserved for textbook answers or peer reviewed papers. Our Soeculation forum is a better choice for this style of model building. As it is poor form to moderate a thread I have participated in previously I will let one of the other moderator staff make the decision to move the thread or not

Interesting request I am surprised no one replied to this thread. So lets get started, as you stated conputer science is an incredibly broad field of study. Most tend to think it involves the PC, your laptop or phone. Yet nothing is further from the truth. The reality is that every circuit in existence relies on conputer science which can be described most accurately as the science of computation. This would include such devices as an abacus. We today tend to think of it as just electronic devices but those are just modern examples where the art of computing is applied. A more accurate descriptive is that computer science is the study of information processing. This encompasses a huge history of aids to information processing that far exceeds the modern electronic era. So first we start with A process is a sequence processes of steps. Each step changes the state of the world in some small way, and the result of all the steps produces some goal state. A procedure is a descriptive application of a process. The steps required to produce the desired outcome. The outcome can be literally anything including baking a cake or manufacturing of any item. Any complex problem can under information processing be broken down into smaller easier to accomplish tasks to get the final result. Boolean logic is a good example of such a process. Indeed in order to develop a program one must take a very complex task and break that task down into smaller steps. This should provide a direction for your report. While I wouldn't consider my diploma in Computer science as being an expert on the field. I apply the lessons taught in computer science (the information processing, procedures to arrive at an outcome) fundamental to every task I perform in everyday existence. This list includes getting dressed in the morning. One may think its a simple matter to get dressed but that task requires numerous steps to complete. It does one no good to put on your pants before you put on your underwear lol. This is really the art taught in computer science, the breakdown of a task into smaller tasks to accomplish a goal. In essence it is the study of algorithms. So what is an algorithm? Informal definition: a step-by-step procedure which solves (all instances of) some specific problem. This should be the focus of your report. ps my Resident expert status applies to topics of physics, though arguably mathematics and lanquage itself can be thought of as an algorithm and information processing. They certainly involve a series of steps to solve a specific problem even if the problem is information exchange. (Hope that helps)

Funny how I don't see any Ether in these equations. Did you forget that the M and M showed a null result for the Ether in the first place?

One of my favourite references hence its been a link on my website ever since I first read that lecture note. One can learn a ton on GR as well as how it applies to cosmology in its later chapters.

Also can we apply any of thee correct equations that actually apply to a GW wave. IE the superposition state of the transverse and traceless guage under the Einstein field equations specifically that correspond to the calculations involved in determining the length of the arms required to detect the quarter wave of the GW wave frequency? If your going to argue against something it might help if you actually study the correct mathematics that correspond the the h+ and hx polarities which is precisely why the wave is a quadrupole (spin 2) and not dipolar spin 1 as per the electromagnetic. All too often we see posters argue that science is stupid yet those same posters don't even know the correct formulas. So by all means lets see the correct formulas being examined in this case please lets start with the the correct equation [math]A^{\mu\nu}=h_+e^{\mu\nu}_++h_x e^{\mu\nu}_x[/math] there is your two polarizations which arises from [math] h_{\mu\nu}-A_{\mu\nu}e^{ik_ax^a}[/math] via the wave equation [math](\frac{\partial^2}{\partial t^2}-\nabla^2)h_{\mu\nu}=\Box h_{\mu\nu}=0[/math] the box is the D'Alemburtion operator from the Einstein field equation [math]g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}+\mathcal{O}h^2_{\mu\nu}[/math] now show you can calculate the wavelength hint the geodetic deviation equation to the above...though you will also require the correct flux formula...to derive the arm sensitivity... SO use the above to prove LIGO is lying to us. After all these formulas is how LIGO derived the required arm length and design in the first place.... by the way a quick google search will give you the wrong geodetic deviation equation.. [math]\frac{D^2\,\delta x^{\alpha}}{D\tau^2}\ =\ -\,R^{\alpha}_{\ \mu\beta\sigma}\,V^{\mu}\,V^{\sigma}\,\delta x^{\beta}[/math] you will need to derive the correct one. You might start with learning how the quadrupole formula is derived from the above https://en.m.wikipedia.org/wiki/Quadrupole_formula A good GR textbook will have the proof of the equation in the wiki link.

OK you are absolutely correct that the waveform you often see in textbooks isn't precisely telling the full story. The reality is that no waveform is ever singular. They never have just 1 frequency and wavelength. In fact there is always a small spread of frequencies. Most textbooks of a frequency is usually referring to the superposition state of these frequencies. So the localized wave packet is a superposition of many wave functions in the same localized region. One must decompose a wave packet into the sine and cosine waves via Fourier analysis of which there is two broad categories 1) periodic 2) non periodic and non repeating the latter is the localized wave packet. (little side note probably why the packet term is used) The function A(k) is the Fourier transform of f(x) it gives the weighting of cosine functions with different values of k that make up the wave packet via [latex] f(x)=\int A(k)cos(kx)dk[/latex] an easy way to understand the above is A(k) gives the distribution of wave numbers k that make up the localized wave packet. so Heisenburg [math]\Delta x\Delta p\ge\frac{\hbar}{2}[/math] this tells us we cannot precisely know the the position and momentum De-Broglie tells us [math]p=\frac{h}{\lambda}=\hbar k[/math] the uncertainty (range of values of the momentum) [math]\Delta p=\hbar\Delta k [/math] where [math]\Delta k[/math] is the spread in k values in a wave packet that represent a particle. So in terms of the uncertainty the above becomes in terms of k as [math]\Delta x\Delta k\ge\frac{1}{2}[/math] see for the above formulas etc the reference I used for the above https://www.google.ca/url?sa=t&source=web&rct=j&url=https://ps.uci.edu/~cyu/p51A/LectureNotes/Chapter6/Chapter6_wf.pdf&ved=0ahUKEwiA67HWmszXAhUpxlQKHdasAPMQFgggMAE&usg=AOvVaw3EJ1PhBYQbEOvkZgKVgrga The above being a quick brief from the reference. Its been a while since I last thought of this in terms of the HUP lol

Yes that has the precise mathematical details to my post

A GW wave is a superposition of 10 waves, the only two waves are the Tranverse and traceless wave components. Hence GW waves being in the transverse traceless gauge. These two waves have a 45 degree phase shift from each other. This corresponds to the H positive and cross polarizations in image above. Also the quadrupole moment. spin 2 characteristic

Dark energy being a scalar uniform distribution by itself no. Distortions arise from density anistrophies (including those caused by thermal hydrodynamics) Gravity wells can cause localized distortions via the same mannerism above as gravity affects the mean density of particles in a given overdense region. DE the mean average in voids where it has measurable influence is constant. This also sets s boundary we use to place a limit to the size of a galaxy. When the mean density due to a gravity falls less than 200 times the critical density is the galaxy boundary. Ie this is the point Lambda has measurable influence the expansion of the universe only applies to regions not gravitationally bound. They are in collapsing states via Jeans instability. The boundary see above quote.(x-post) Higher than above value a LSS is collapsing, same value applies to LSS as a galaxy though obviously applicable distances will vary. (this boundary includes DM distribution) due to formation distribution.

Distortion would arise if there is curvature, this is literally the fundamental aspect behind GR and the FRW on curvature is how it affects lightpaths via null geodesics. A flat universe light rays don't diverge nor converge. A curved universe they will diverge on negative curvature, converge on positive. The CMB measurements uses this principle to test for curvature (specifically looking for such distortions). Another example being lensing (in this instance the curvature is such to cause magnification). A little side note Hubble uses these lenses to extend its range. ie those earliest galaxies or more often than not found via Hubble using a gravitational lens Don't confuse this with redshift, this alters the frequency not the path specifically.

yeah never worked with Berry curvature. Also didn't have time to examine it glad you found the difference

Yeah I forgot much of their published survey is the local. Anyways there are more recent studies.

Well both these articles are prior to the Planck datasets and the Sloan sky survey so it may be appropriate to look at more recent studies. A lot has changed since these articles.

yeppers it takes a considerable amount of time also we cross posted before I finished the latex see above for additional details

sigh I knew I went too heuristic. Ok I don't have time tonight but a GW wave is a supetposition of waves. The two independent waves are 1) transverse 2) traceless these are your two independant polarizations that is the two independent waves of the original 10 waves. a pure + polarization [math]e^{xy}=0[/math] will give a metric [math]ds^2=-dt^2+(1+h_+)dx^2+(1-h_+)dy^2+dz^2[/math] where [math]H_+=Ae^{xx}exp[-iw(t-z)][/math] the cross polarization is identical but under a 45 degree rotation simultaneously. the linear combination of the two polarization tensors is [math]e_r=\frac{1}{\sqrt{2}}(e_x+ie_x), e_l=\frac{1}{\sqrt{2}}(e_x+ie_x)[/math] where [math]e_+[/math] and [math]e_x[/math] are the two linear polarization tensors and [math]e_r, e_L[/math] are polarizations that rotate in the right and left handed directions.

It would radiate as a quadrupole even under those conditions for example supernovas through gravitational collapse generate GW waves. If you have a copy of General Relativity a first course by Schultz it is described in his book.

That moron friendly enough lol ?

Pole= polarity. mono-pole 1 polarity ie single charge dipolar =2 polarity, quadupole 4 polarity states. Dipolar is spin 1 with two polarity states |+1/2> and |-1/2> quadrupole spin 2 for GW waves, as GW waves is changes to spacetime geometry we apply a coordinate basis. As it is convenient to graph changes on amplitude with an x, y graph. Both the x and y axis both undergo changes. So it is convenient to state this as a plane wave travelling in the z direction. We can then preserve the z axis. So now we have at any time interval change 2 simultaneous changes to both the x and y axis on both the positive and negative axis on each. So as both x+ and x- contract, the y+ and y- axis expands as t_1 then at 1/2 a cycle they switch x expands while y contracts. However the GW wave radiates in all directions. Just as an everyday antenna radiates in all directions (for omnidirectional antennas lol) (all of physics uses graphs, with which we can use to apply geometry to describe.) Now to describe the above under GR/SR (more accurately for the formulas I will use (SR) though under GR the Newton limit. I believe everyone currently reading this thread attempted to understand Dubblesix mathematics but failed to follow the Dirac notation he is using. Well Dirac developed a method to better understand and represent vector and vector addition using symbology. (long and short of it) You have three types of vector products the inner, the outer and the cross product. [math] a\bullet b[/math] denoted as the dot product. The inner product is the product of two parallel vectors. This will return a scalar value. Oft denoted A||B. As they are parallel we only require the difference in magnitude. The cross product is used when two vectors are not parallel example angular momentum. L=R×P. The symbol is the same "x". If they are orthogonal they are parallel. A×B. If not then we need to apply Trig to restore to perpendicular. So obviously the cross product requires the direction as well as the magnitude. The cross product of two vectors is a vector. Now a Hilbert space is a 2 dimensional object ie the x,y graph. Now obviously I cannot give an entire course of Vector calculus, GR, QM and GR. lol however I can provide some assist. Dirac notation Bra and ket. [math] | A\rangle [/math] is ket which is the initial state. Ie can be the particle itself eg electron in its polarity state [math] \langle A|[/math] bra the final or conjugate state. [math] \langle |A|\rangle[/math] the transpose between the ket to the bra. [math]|\langle +|\varphi\rangle^2|[/math] probability Now without going through a full course the Kronecker delta has two indices i and j with values 1 to 3. See chapter 1 in particular the Kronecker Delta which in essence shows that your coordinate basis of all 3 coordinates x,y,z are symmetric and normalized to unity. http://physics.csusb.edu/~prenteln/notes/vc_notes.pdf this is the equivalent to the Kronecker under relativity and is used specifically under the Minkowskii tensor [math]\eta_{\mu\nu}[/math] Now part of Dubblesix proofs were specifically using thee Cauchy inequality to prove the triangle inequality to show that pythagorous theorem still applies as per Euclid geometry. Ie Galilean relativity (no time dilation or curvature) Euclidean geometry. now there is a trick to identify any orthogonal matrix any matrix with only the diagonal components being irreducible is orthogonal. [math]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/math] in this Minkowskii tesnor the coordinates are [math]ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/math] so under SR this is time symmetric (under constant velocity that is) once you undergo an acceleration you undergo a rotation and it becomes skew symmetric. Now how can we apply a vector to describe curvature as the above is Euclidean flat? well recall that relativity models freefall under constant velocity. So use two vectors to freefall, if the freefall paths remain parallel then your geometry is Euclidean. (Principle of equivalence) If the paths start to diverge or converge then the spacetime geometry is curved. (ie tidal force) Principle of covariance. so now we need to add another vector k. See the same link above for the Levi-Cevita. this system under GR is [math]G_{\mu\nu}[/math] for this you will need the polar or spherical coordinates where the previous is in Cartesian coordinates. Now our three coordinate axis are no longer symmetric but is antisymmetric. See 1.8 page 24. Now unfortunately there in't any easy way to describe the wave equation and the transverse traceless guage.( I would literally have to skip numerous chapters in a standard texbook on GR. However there is a key fundamental difference between how the polarization's differ from the electromagnetic guage. In the latter the two polarizations have a 90 degree phase shift between the magnetic field and the electric field. However in the case of the GW waves the [math]H_+[/math] and [math] H_x[/math] is a 45 degree polarization difference. The main relevant formulas is included below and saves me tons of latex and explanation. http://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/NS.BH.GW_files/GW_Physics.pdf this has the necessary metrics including the 3d wave equation... see the images for the plus and cross polarizations https://en.wikipedia.org/wiki/Gravitational_wave seeing as everyone likes images lol.... Anyways let me know which areas you want on further details on the above as I went fairly quick and extremely heuristic on the above (too much ground to cover in one post) A little side note despite the fact that LIGO has two arms in an L fashion that act as a detection antenna the polarizations above confirm the spin 2 statistics described above. The detector wouldn't work on dipolar waves which includes mechanical vibrations. Also the reason each arm is 7 km is to catch 1/4 of each polarity. Just like the length of an antenna is designed to catch a quarter wave. This determines what frequency range the antenna can detect. If it catches a 1/2 wave it will not pick up the signal. (the polarities will cancel out)... (should help weed out all the crank papers arguing against the detection lol)

Lol those images are merely representations to assist people with zero math skills get a concept across. The first image is is dipolar and not a quadrupole wave but good luck explaining the difference without math. I will have to work up the math tonight as I will need to cover a lot of preliminary ground work to properly describe a quadupole wave as well as what a transverse traceless gauge is. I will also properly describe spin 2 as well.

No that isn't how GW waves propogate.

Ok give me a bit and I will post how GW waves behave under four momemtum including the H+ and H× polarization states. This will correspond to the spin 2 statistics as well.