Mordred

Yes I understand your under L^2 Euclidean norm by the p=2 Cauchy inequality value. Which if memory serves satisfies the inner space products, have you worked out the Minkowskii inequality? I'm a bit rusty on Young's I see from the last established a boundary cutoff except to the operator functions themselves fair enough. Going through your metrics atm I take it you never looked ar at the Functions for the Feyman S-matrix diagrams? Your verbal descriptive above tells me no. VP are described under propogators for intent and purpose (internal legs) external legs are operators... Real particle or states ie observable. minimal 1 quanta of action is required. So once again where iz your effective Hilbert boundaries to address VP? You have your observable operators but no boundaries to distinquish an excitation from a fluctuation expect via Hamiltonian action under R^n

So if I'm following correct your in essence breaking the SO(3) group into two unitary Hilbert spaces. You mentioned finite spaces, which is part of the issue with renormalization. How are you setting the effective cutoffs ? ie the UV cutoff? The notations above are all in the realm of operators, but part of the issue directly relating is the propogators. I don't doubt the math above as being correct, LQC does a similar technique in principle but uses a Wicks rotation ( Wilson loop, to quantize units of spacetime) The only cutoffs I see in the above, is the standard QFT operator IR/UV cutoffs.

Depends on the asteroid composition, asteroids of largely ice and conglomerate stones tend to explode more readily in the upper atmosphere compared to the solid metals asteroids.

and what medium is present where yoy have lensing in regions with average density less than 15 protons per cubic metre? Perhaps you should actually study a dataset taken from a radio telescope that records the different frequencies via a spectrum analyzer. Its quite easy to distinquish diffraction due to Weins displacement law and that due to gravity. In the intergalactic medium the refractive index is effectively zero, NOT ENOUGH DENSITY

Sounds like he is ignoring the changes in path length and the differences in rotational vs translational velocities under SR. Did he strengthen his argument with actual counter mathematics? All you provided is his statements. After all the first paper does not prove Sagnac wrong. It is a highly cited paper that shows that linear motion does not affect the speed of light. For one thing light is only constant in a vacuum, this is a fibre optic cable so one should not expect constancy of c in the first place

If you ever truly studied both GR and the LCDM model under the FLRW metric. One of the first thing one notices is that the FLRW metric employs a fundamental observer. Ie an observer in the same frame of reference as the background metric in the observer frame. The emitter frame is also a fundamental observer being at the same frame as its moment in time/background metric. In Cosmology we use these observers as we are comparing the geometry changes (Specifically). We are not concerned with observers on gravitational bodies nor accelerated observers. We are setting the geometry of each moment as the observer. This however does not mean that it does not examine the affects of time dilation, indeed it does but that is a different redshift formula. Gravitational redshift, this uses the SR metric everyone is familiar Cosmological redshift however is a different formula (For good reason, different cause). While both are involved, cosmology with its fundamental observers are interested in the latter formula, as stated it is the changes in geometry we are specifically modelling. (comparing global change, not local) We include the former only when required for localized effects. and only for localized effects. Now here is an advanced tip: Anyone reading a dataset, such as from Planck , WMAP etc. The majority of those papers are calibrations ( removal of unwanted data influence such as those due to localized influences). This includes dipole anistrophy due to the Earths and satellite movement. It is the comparison of global change we are interested in Cosmology.....

Incorrect dynamics, charged fields has specific dynamics that are easily detectable. The observations of our universe is homogeneous and isotropic which does not match the dynamics of a charged field. Granted without any mathematics, I am only guessing at your descriptive.

Ah ok that is a different scenario then, as the lens equation stops at the Schwartzchild radius. Kruskal may work for you I will have to dig a bit at the different coordinate systems. I believe what you need is Bozzas technique for the weak field/strong field multiple image. https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/gr-qc/0102068&ved=0ahUKEwja8M6Qo6LWAhVhr1QKHYtCDNgQFggfMAA&usg=AFQjCNFRwiIbOVQOAqG1GaKJJ-ITTK3qNg often described as Bozzas technique in numerous strong lensing papers. Beyond that I am not aware of any solutions. At the very least you can get a direction on the weak field/strong field image strength boundaries for multiple images due to the strong field. However that is a region just outside the photon sphere to the single image weak field.

The geodesic equations for the Schwartzchild is the valid equations from at rest, to EH. So I fail to see why you cannot use them. Are you trying to model beyond EH, if so then your observer location will be an issue. Not to mention infinite redshifts beyond the photon sphere. Why do you feel the Schwartzchild won't work outside the EH cutoff? The ds^2 line element of the Schwartzchild is the Worldline path from observer at rest to EH boundary. Well assuming a static non rotating BH. If rotating charged or uncharged use the Kerr metric, If you want to confirm the above look specifically at the strong field geodesic equations of the strong field lensing papers. (They use the same ds^2 line element worldline)

The last paper is your best approach, start with the more standard QFT approaches under group. Then look at degree freedom reductions, after that with higher dimensional symmetries exc. I hadn't had much time, to look much further than what I already posted, though you have found a non wick rotation method, that avoids the conformal divergence issues.

While your at it, think about "Observer limits and range of validity within a given metric or function. Then think about observer limits to different observers, when it comes to BH's and if you understand particles as field excitations. Think about observer limits/range of validity of the metric. A model is only accurate within its range of validity, with field treatments observer limits is the effective cutoffs of a given metric. ( the above is needed to understand Hawking properly under different coordinate systems. (also applies to semiconductors in the emitter/observer limits)

excellently appropriate approach. Look forward to this developing on this thread. Also +1 to Strange's reply

Lol,

the above involving those killing vectors. ( For other readers, invluding OP. Migl already knows the above) she is ( if I recall correctly) too consistent with her posts in related threads, not to understand anything I posted above.

I agree however the FLRW metric treats the Conservation laws as valud under the ideal fluid, adiabatic and isentropic expansion system. The universe from Nothing model also treats the universe at any moment under the same definitions. This is a common misconception to the Universe from Nothing model, that it violates the Conservation laws, however within its mathematics it is constructed to preserve those laws. The thing is we cannot measure "An absolute/true energy state." Hopefully this descriptive doesn't cause sphincters to compress, but lanquage has its limits. We can only measure energy, relative to another arbitrary field coordinate. So we can only measure the potential differences in a field as your energy values. aka the definition of potential energy. (Energy due to an objects position within some field ) You often see this described roughly in numerous QFT literature. The "absolute true" energy value is beyond any viable means to determine and can literally be any arbitrary value. We can never know orherwise. Under math [latex] F_e=0[/latex] (field energy) is literally the potential energy difference to the observer from the emitter. Change the coordinates of either and your energy value also changes. However to any observers in the reference frame of emitter. No change occurs in the emitter. ( just like voltage we require a potential difference to measure) So one must be careful how one defines a conservation law under observations via relativity. Which quite frankly cannot decide if the conservation laws are applicable under relativity. Think of it this way, all possible "Observers" are Within the system. Measuring a true energy field value requires an Observer outside the system, not one within. The above also applies to "fundamental vs absolute observers. A fundamental observer in LCDM is not an absolute observer. We have no viable absolute observers. No an Ether based absolute frame doesn't count, its still part of the system. (assuming there is an ether, which we know there is no evidence supporting such). It was a hopeful idea of finding a an "invariant reference frame, within our system". Under GR all reference frames are inertial (variant). Lol if you include the above with the understanding that particles are field excitations. Then particles arise due to potential differences. ( quite frankly that is an obvious statement) once you accept the field excitation definition of a particle. The "rest mass" being an invariant quantity. Invariant to all observers quantity. The relativistic mass being the variant quantity. A good way to explore the above is look at what happens to the number of particles within a box to different observers, where you get a different quantity of photons ( quanta) to different observers. Important caveat. One often sees the statement "The universe at any given time has roughly 10^90 particles" That is only true to fundamental observers... (The Nothing in the model literally means to an observer in the same field potential. The universe arises from anistophy regions and how they evolve in our field potentials. (Potential energy). Far too often the observer limitations of any given model is a missed detail in understanding those models. Lets take an example. QED, look specifically at the IR/UV cutoffs, those cutoffs are specifically chosen, as they are defined by the killing vectors to a specified type of observer. Every field treatnent theory is defined by the limits of the observer killing vectors of that system state.

Well I don't know about anyone else, but I certainly cannot read his images to even attempt to verify the calcs.

And maybe energy is simply the ability to perform work and is an emergent system property. Not something that needs to be created or destroyed as it is a property and not a thing unto itself. Coincidentally mass is the same way. Keep in mind you still have the conservation laws, (the above provides the key to understanding the universe from nothing model)

True however the FLRW metric treats the universe as an adiabatic and isentropic fluid. Which is in essence closed as adiabatic is no net inflow or outflow

Well I don't agree with that, so I will upvote it

This is the lightcone diagram for the FLRW ds^2 worldlines. The image is from Lineweaver and Davies. http://arxiv.org/pdf/astro-ph/0402278v1.pdf[/url This defines your causality to Observer worldlines. This is the basis behind Wrights website. Though under different parameters etc. The paper is a highly recommended read for numerous BB misconceptions. The calculator in my signature conforms to the lightcones produced via the above paper as its basis to programming. It uses the stretch value described in the above article

Compton wavelength is typically the descriptive that applies to pointlike field excitations. Which corresponds to the Planck length as being the minimal measurable volume via the QFT treatments of Observable action. In effect an IR cutoff by analogy to Feyman path integrals. (by analogy which conforms to the Wheeler-Dewitt treatments) just a side note there

So let me get this straight. You don't agree that each sphere of causality under speed of information exchange via GR leads to each "Observable portion"(which is a sphere of causality) would concentrate to a finite pointlike portion under the FLRW metric, which is a simplification of GR when you run the time/expansion backwards? ie turning back the clock and having the universe contract. In reverse to its expansion history.

Your welcome, glad to see you got latex working. I agree the paper is extremely interesting on the pulsation and informative in the confinement of the different scales. Planck, macro and cosmological. The beauty of the paper is that it shows that the old cosmological problem isn't a problem if you examine the limits of the effective action due to the HUP. I am still studying several of the details in the paper myself. As you have noted, its fairly intensive in detail. Not something one can easily understand by simply reading it. The problem of using Wicks rotations on Euclidean space however is still an issue. The issue comes down to renormalization on path divergences when your under significant curvature. The Wicks rotation works well under Euclid space, not so great under curvature. Most of the papers detailing this is intensive in group algebra, so if your weak on QFT will be pointless to include. I will see if I can dig up a more appropriate level. I'm a little busy this weekend but would like to assist you on your modelling approach, so once I get a chance I will probably provide some further details to assist you in moving forward into your approach. In particular we will need to test if your approach gives the equation of state w=-1 for the Lambda term under scalar modelling. Though I see nothing above that shouldn't, one cannot assume that lol.

I usually prefer to latex in the older forum method( old habits being hard to break) lol Enclose your latex with [latex]\Omega[/l$tex] Replace the $ sign in the above. I used it to prevent it from activating. Once you replace the dollar sign above with [/latex] you will get [latex]\Omega[/latex] The new forum software is tricky. Once you type in the [latex] enclosure you must refresh the page to see if you did it correct. The latex doesn't activate until you renew the page. So it can fool you into thinking it didn't work. So refresh the page after your attempts

Its possible and even likely that further density evolution studies will lead to further changes in age estimates. Usually easiest to follow via different Hubble values. Yes that will also influence universe distance measures ie our observable portion. The above redshift to expansion relations above also apply to distance measures.