Mordred

The equation of state w=-1 for the cosmological constant is valid and agrees with observational evidence thus far. What is not mentioned is that it is the same equation of state for an incomparable fluid which can be mathematically defined under the Euler hydrostatic equations. ( Though few textbooks will mention this either). An equation of state in essence gives us a dimensionless value for the energy density to in essence, pressure influence. Via the ideal gas laws. Later tonight I will try to find the mathematical proof for the W=-1 with regards to Lambda. They can be tricky to find.

Ego is best left at the door on Mordred's couch . Lol no place for it in science.

I have a far more complex way of thinking of geodesics. It is the sum of all infinitisimal deviations between two seperation points due to the local infinitisimal field interaction at each coordinate and immediate surrounding infinitisimals within infinitisimal causality units. Whats real fun is understanding and applying the above under lattice gauge treatments. Here is a thought experiment to understand local. "What is the radius of a field that can interact with a particle, bofore the particle moves " Now obviously the above has no easy answer, as numerous factors will need to be known. However it demonstrates the principle of local under motion and causality.

Right and read your OP again, then compare that to the quality of post your presenting now... Anyways enough said about that. With regards to your questions above this will take a bit to put together. Give me a bit of time on it. How much do you understand on spin connections with regards to superconductor materials? Its an arena that actively applies the required mathematics.

To add to this, we can also infer from the above the luminosity to mass relations, accounting for the above Doppler shifts influences upon spectral index measurements. This is in regards to understanding how Zwicky determined the missing mass problem. The mass to luminosity correspondance to rotation curves showed a considerable amount of missing mass.

You don't measure the talent of a forum by being scattering a few key terms into a post. For example you claimed Maxwell theory cannot describe the above, yet the entire field of superconductors does well in describing the above. Is there perhaps something wrong with those treatments that you disagree with or what is it that you find doesn't work about them to claim they cannot describe Block? where is your mathematical proof that Maxwell cannot describe the relations your after in this post? Your images are utterly useless, this is physics. Not drawing class.... You imply requiring an ether in them yet have posted zero zip on mathematics. So don't presume to lecture us. here is an example http://www.physics.rutgers.edu/~dhv/pubs/local_copy/mt_fdw.pdf isn't it funny that there is literally 100's of examples of using Maxwell to model Bloch domain walls and its part of the MIT lessons? yet you come here with extremely poor terminology on your OP, and don't address that issue itself??? What is wrong with these equations in regards to your claims? https://conservancy.umn.edu/bitstream/handle/11299/3947/1936.pdf;sequence=1

exactly, another way to think of it is spatial infinity via equation 2 of this article. http://export.arxiv.org/pdf/1704.06223 though hadn't read the article for quality etc, the formula is accurate.

Don't think of it as a single worldline but all possible worldlines between event and observer. ie killing vectors of a metric. This is where the debate drops in on your different coordinate systems involved in information loss. Some killing vectors are artifacts of the metric, ie a horizon is an apparent horizon. The majority of this article discusses the killing vectors and touches on Hawking radiation etc http://arxiv.org/abs/1104.5499 :''Black hole Accretion Disk'' -Handy article on accretion disk measurements provides a technical compilation of measurements involving the disk itself. http://arxiv.org/abs/1104.5499 :

Particles can and do change worldlines all the time. Remember GR is a freefall geometry freefall is a constant velocity. So anytime the velocity of a particle alters regardless of cause. It will follow a new worldline. Ie New worldlines must be calculated via rapidity boosts and rotations. A barrier tunnelling would certainly qualify

Under rotation via rapidity ( ie accleration) the particle no longer follows the same worldline. A worldline is under constant velocity, a change in velocity via acceleration causes new worldlines so I would think quantum tunneling would cause a similar affect as it will cause a change in velocity ie no longer constant under freefall. sounds like this is describing all possible worldlines to a specified observer ie at rest and maximum redshift.

hrmm that is an excellent question, I would have to say yes in similar manner that an acceleration causes new world lines.

Here, this is expansion history CMB forward including future expansion. The H_0/H_Z column is expansion rate today compared to then as a function of redshift [latex]{\small\begin{array}{|c|c|c|c|c|c|}\hline T_{Ho} (Gy) & T_{H\infty} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}[/latex] [latex]{\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&z&T (Gy)&R (Gly)&D_{now} (Gly)&D_{hor}(Gly)&D_{par}(Gly)&H/Ho \\ \hline 0.001&1090.000&1089.000&0.000373&0.000628&45.331596&0.056714&0.000856&22915.263\\ \hline 0.001&739.062&738.062&0.000713&0.001172&45.031283&0.083238&0.001668&12283.974\\ \hline 0.002&501.112&500.112&0.001342&0.002163&44.653685&0.122010&0.003214&6658.325\\ \hline 0.003&339.773&338.773&0.002496&0.003956&44.183524&0.178562&0.006124&3639.803\\ \hline 0.004&230.379&229.379&0.004601&0.007192&43.602350&0.260828&0.011554&2002.235\\ \hline 0.006&156.206&155.206&0.008416&0.013015&42.887747&0.380106&0.021616&1106.404\\ \hline 0.009&105.913&104.913&0.015309&0.023478&42.012463&0.552333&0.040144&613.344\\ \hline 0.014&71.813&70.813&0.027726&0.042257&40.943206&0.799715&0.074095&340.773\\ \hline 0.021&48.692&47.692&0.050056&0.075939&39.639382&1.152677&0.136056&189.626\\ \hline 0.030&33.015&32.015&0.090158&0.136321&38.051665&1.651928&0.248752&105.633\\ \hline 0.045&22.386&21.386&0.162117&0.244527&36.119894&2.350040&0.453165&58.889\\ \hline 0.066&15.178&14.178&0.291145&0.438335&33.771262&3.311204&0.823085&32.852\\ \hline 0.097&10.291&9.291&0.522342&0.785104&30.917756&4.606237&1.491191&18.342\\ \hline 0.143&6.978&5.978&0.936102&1.403692&27.454972&6.297233&2.695518&10.259\\ \hline 0.211&4.731&3.731&1.674119&2.496871&23.266389&8.402147&4.860753&5.767\\ \hline 0.312&3.208&2.208&2.977691&4.373615&18.247534&10.827382&8.733318&3.292\\ \hline 0.460&2.175&1.175&5.215425&7.334123&12.397762&13.279345&15.569626&1.963\\ \hline 0.678&1.475&0.475&8.789420&11.115281&6.042158&15.275613&27.272101&1.296\\ \hline 1.000&1.000&0.000&13.787206&14.399932&0.000000&16.472274&46.278944&1.000\\ \hline 1.468&0.681&-0.319&19.704190&16.201608&4.910267&16.992292&75.113899&0.889\\ \hline 2.154&0.464&-0.536&26.084608&16.928765&8.515267&17.174536&118.018864&0.851\\ \hline 3.162&0.316&-0.684&32.638034&17.180008&11.040250&17.224075&181.212698&0.838\\ \hline 4.642&0.215&-0.785&39.249711&17.261713&12.776339&17.261713&274.042078&0.834\\ \hline 6.813&0.147&-0.853&45.880114&17.287747&13.962589&17.287747&410.320588&0.833\\ \hline 10.000&0.100&-0.900&52.516301&17.296130&14.771503&17.296130&610.357404&0.833\\ \hline 14.678&0.068&-0.932&59.154549&17.298683&15.322788&17.298683&903.973904&0.832\\ \hline 21.544&0.046&-0.954&65.793394&17.299445&15.698407&17.299445&1334.944709&0.832\\ \hline 31.623&0.032&-0.968&72.432255&17.299812&15.954315&17.299812&1967.523376&0.832\\ \hline 46.416&0.022&-0.978&79.071348&17.299828&16.128669&17.299828&2896.022178&0.832\\ \hline 68.129&0.015&-0.985&85.710288&17.299959&16.247453&17.299959&4258.871858&0.832\\ \hline 100.000&0.010&-0.990&92.349407&17.299900&16.328381&17.299900&6259.261851&0.832\\ \hline \end{array}}[/latex] The S=1.000 column is today, you have the three horizons and age of universe with total radius.

Well in less than a second during inflation it expanded 60 e folds. Since then its expansion rate per Mpc has been slowing down. However due to quantity of Mpc. The rate of expansion of the overall volume is accelerating.

One can model GR as a flow of reference frames as per the River model. One can also keep the coordinates static. Analogies are useful, but only to the type of treatment. More often than not they mislead, so your better off not thinking about them to understand GR..Spacetime shrinking, stretching, flowing etc are all descriptives that while useful can be easily miss understood. For example spacetime stretching implies that spacetime is materialistic. Fabric being another problematic analogy. To understand time dilation properly study the transforms themselves in terms of vectors and vector fields. Don't rely on verbal descriptives. They are interpretations of the math.

Replace the need to apply a materialistic analogy. At every coordinate assign a vector. A vector field is converging if its vectors are to a point. Diverging if from a point outward . Now apply that to a freefall field. (converging, central potential CoM.) Of course for dimension (ct) this takes a bit to understand. However don't think about cause, restrict yourself to the pure math relations first. Compare Galilean relativity to SR (Lorentz transform). Study how gamma is a constant of proportionality (scale factor) between two spacetime graphs first. In order to preserve the Euclid (invariant/rest) frame.

Roflmao, the makers of the forum software evidentally don't often use forums if they never encountered the mere convenience of "See post 34 above" Thanks for trying though, can't do what the forum software isn't programmed to allow.

The car in garage paradox with regards to the length contraction.

! Moderator Note Welcome to SFN Moved to Speculation, the mainstream forums are reserved for mainstream physics only. Please review the rules in the Speculation forum http://www.scienceforums.net/topic/86720-guidelines-for-participating-in-speculations-discussions/ Please show how you derived the equation below as it does not account for spin helicity of the two polarity states for a single particle, let alone the combination of baryons and DM. Which indicates you substituted values into a known formula, as opposed to deriving the formula. All baryons are not spin 1/2 particles. The above is invalidated by that alone.

There is a better way to look at this [math]<\psi|\mathcal{U}^{\dagger}\ R_{ij}\ \mathcal{U}|\psi> = <\psi'|R_{ij}|\psi> = <\psi'|\psi'> = 1[/math] try the Heisenburg picture using the [latex]\mathcal{H}[/latex] for the Hamilton. [latex]\langle A\rangle_\tau=\langle\psi(0)|e^{+\mathcal{H}\tau/\hbar} Ae^{-\mathcal{H}\tau/\hbar}|\psi(0)\rangle[/latex] where [latex]\tau[/latex] denotes proper time. use the Langrene density and Hamiltons. You will have a far easier time understanding the path integrals. https://en.wikipedia.org/wiki/Heisenberg_picture

Even if he/she does, this is a key detail to fully understand. +1

Not sure, don't recall ever running into Hestenes. However I cannot see why not. You now know any orthogonal group can be made unitary, which is hermitean. Hermitean being symmetric. You also now know how to define length preservation. So any vector is also hermitean and length bound via above. Also you know how the projector operators are derived via the above. (Though their is several other operators that do not follow the above ie trace operator). Its a short hop to unitary operators, but the trace operator also involves the above. So I don't see why Hestenes cannot be treated under Hilbert spaces. (That's the advantage of learning the above mathematics, you can now look at applying it to any physics theory). Lol gives you a major advantage over a vast majority of posters, laypersons etc, The above applies to any QM topic naturally but can also be applied to classical, though for relativity the renormalization issue. ( you can better understand that via the above) Think curve form fitting using discrete units vs curve fitting without discrete units. ( ie divergences of path integrals)

Excellent, will double check em but don't see any errors. Here is the thing once you established your operators you have effectively quantized a vector and correspondantly your vector field treatments. You have established the above to a coordinate basis, deviations from the coordinate basis has transforms we can employ. You have closed (including boundary confinement) your Hilbert space, checked orthogonality via Cauchy, thus establishing the Kronecker delta affine connections. The groups these metrics follow all follow the right hand rule via Hilbert, This must be preserved throughout your metrics. Also understanding how the projection operators is defined is always a plus plus. Which you have defined in the above... I would study Euler Langrene, and Hamiltons under the above before worrying about 4d. Lets make sure you understand how the above works under path integrals. In particular at the quanta level, in terms of coupling to range of force relations. I have an older thread on this to save time. http://www.scienceforums.net/topic/106004-useful-fundamental-formulas-of-qft/ Though I haven't gotten to the path integrals yet (too many projects :P). (Once again +1 for your diligence in seeking the proper understanding. No amount of heuristic treatments/ descriptives will get you there. The only path that will is under math). You will also find it won't matter what physics topic your reading. Your understanding improves exponentially to all physics by understanding the mathematics.) Mathematics is universal even in theories. I might need to check you hermitean conjugates, but will have to wait till I can focus on it. edit: no its fine, notation caught me for a second. With regards to last article and thread, a unitary group that preserves the length also preserves the particle changes with regards to conservation. (recommended study, skew Hermitean) to above

Precisely, though the above stress tensor is also modified to include the additional dimension for the time component. (Under 4 velocity treatments). Other than that is identical, you more commonly see this format with the Raychaudhuri equations.

Yes super gravity is still viable today. No matter what treatment under physics your working with. Never treat space itself void of all particles as anything other than volume. Space has no particle nor will ever need one. The Prof site Strange linked covers bosons ie VP.

The related articles to the standard model extensions can be started here. https://arxiv.org/abs/hep-ph/0405097 in essence the minimal standard model extensions applies the right hand rule to all rotations. Further can be found SO(10) via the Pati-Salam groups. Yes Higgs is extended for same reasons above. It is more complexely a quaturnion field. Each quaturnion is modelled as a seperate field as well and has its specific interactions to the particles you listed. Wiki link has a bit ( lol page is rather lacking) https://en.m.wikipedia.org/wiki/Standard-Model_Extension The CPT violations in and of itself is a large topic.