Mordred

Agreed one other thought is will BaS coordinates for a Minkowsii or De-Sitter/anti-Desitter spacetime preserve the maximal symmetry relations ? The standard polar to Cartesian coordinate transformations do so without loss of maximal symmetry. However that's simply a consideration that may or may not be affected.

Funny I was also thinking of renormalization issues cropping up. The cosmological constant itself hadn't considered as of yet as as been focusing on the gauge langrangians later in the article. Which in itself is tricky as I'm more used to the QFT formalism as opposed to QM.

We also need to look at your mass gap statements in terms of Yang Mills. The mass gap is to predict the least massive possible particle predicted by Yang Mills and I don't believe that's your intention in the article. If it is your intention then some serious additions need to be added in terms of the energy momentum relations etc. Though if you actually do so I understand there is still a million dollar prize available lol

Excellent glad to hear that +1 I am still going through your mathematics etc

Of course all the above is under the assumption your wanting ways to improve the theory in regards to this article or subsequent articles. For the record I've seen worse articles on researchgate but there's always room for improvements to broaden interest etc.

that is where the clarity is needed I should be able to take what you have and immediately apply it without the need to ask questions. I should also be able to add another coordinate for 3d Euclidean coordinates. I should be able to extract the x,y and z components from r and the angle. I should be able to use your relation and know the transformation rules and apply vectors, spinors and tensors to it even when the geometry is scewed such as when v approaches c. In essence I should be able to take what you have and perform any trigonometric function without confusion from everyday usage of r or confusion with regards to cdot. Let alone adding another scaling function s as you have for your reflection. When the standard method simply has the symmetry relations under a change of signature (+,-). Those are some of the improvements I'm recommending. The other improvement is to figure out how your method is more advantageous that the standard methods (Occams razer). Show how it would improve our understanding outside of simply declaring it may be more advantageous or revealing. For example how does one use the time dependent vs the time independent Schrodinger equation under Bas when the differential denominator has \(d\theta\) instead of dt ? remember the vast majority of physics is kinematics where we need to account for time to handle key relations ie velocity vs acceleration referring to first order and second order differentials. (little side note sometimes its useful to play the dummy, particularly when examining a paper and the goal is ways to improve the paper ) so I'm hitting you with questions that posters not terribly familiar with mathematics will ask. On a practical sidenote when it comes to any modern physics we still have to get to how to apply observer effects to your Bas coordinates. As far as symmetry relations between wavefunctions in differing quadrants physics already has the relevant mathematics in regards to wavefunctions in differing quadrants and the symmetries between them as well as those observer effects etc and they work well with the trig functions I posted. So establishing where there may be a gain by your method will invariably require some comparisons between the standard method as opposed to your proposed method in terms of practicality, gain of data etc. This is where I recommend better detail on the vector, spinor relations under the Bas geometry and compare for advantage using Bas vs Standard trig functions for Cartesian to polar transformations. In particular regards to the other theories and equations inclusive in your article. Mainly the preliminary transformations prior to jumping into say Yang mills for example establishing a transformation matrix for correlating to kinematics and observer effects with regards to BaS would be useful early on as well as having a vector commutation table. Just my thoughts there is some syntax choices you may also consider for example under BaS for your gauge field Langrangian your choice to have BaS in both the subscript then in superscript could lend to confusion with Einstein summations.

great so lets look at your Bas statement given what you just described with cdot being the inner product two vectors and not multiplication \[Bas(\theta;r)=r\cdot(r\cdot \theta)\] recall what I stated concerning cross products and dot products then look at the statement • r is a scaling parameter that modifies both the amplitude and the frequency of the cosine wave. as that is a 2 d graph x,y so \(P(x,y)=P(r,\theta)\) notice I don't have any confusion with vector dot products \[x=r cos\theta\] \[y=r sin\theta\] so \(r^2=x^2+y^2\) therefore \(tan\theta=\frac{y}{x}\) 1)how are you going from this to the top equation ? 2) what advantage does your equation offer as opposed to those simple trigonometric identities I already know work with the entirety of physics ?

The detail were both describing is directly related to invariance. The coordinate choice should not make any difference. For example choosing Cartesian vs spherical or cylindrical coordinates does not alter any physics nor observer effects. This one reason why for example one requires use of covectors (covariant and contravariant vectors in SR/GR as you require a minimal of a covector and vector to establish Lorentz invariance. Hence why I asked specifically on the cdot as this in typical higher physics applications such as the aforementioned refers to the inner product of two vectors which returns a scalar. For example with the EFE equation you have in your article you need to identify those vector products. If your using it as straight multiply then your not getting the needed relations to work with the EFE. In point of detail you would get the wrong answers completely. For example \[\mu \cdot \nu=\nu \cdot \mu \] is the inner product of two vectors and this statement tells us the inner product is commutative. This applies directly to the metric tensor and it's symmetry relations. Now that statement describes the linear relations however the cross product \[\mu × \nu\] would describe relations involving spinors such as torque or waveforms ie curvature terms. So if your not applying these relations then your not looking at the equations you have involving the EFE Fourier transformations nor the Schrodinger equation correctly as those involve these terms. ask yourself the following will what you have work under spherical polar coordinates \[(x^0,x^1,x^2,x^3)=(\tau,r,\theta,\phi)\] \[ G_{a,b} =\begin{pmatrix}-1+\frac{2M}{r}& 0 & 0& 0 \\ 0 &1+\frac{2M}{r}^{-1}& 0 & 0 \\0 & 0& r^2 & 0 \\0 & 0 &0& r^2sin^2\theta\end{pmatrix}\] line element \[ds^2=-(1-\frac{2M}{r}dt)^2+(1-\frac{2M}{r})^{-1}+dr^2+r^2(d \phi^2 sin^2\phi d\theta^2)\] as well as \[ds^2=-ct^2+x^2+y^2+z^2\] \[\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}\] along with the transformation matrix of SO(3) Poincare group [\Lambda^\mu_\nu=\begin{pmatrix}1&0&0&0\\0&\cos\theta&\sin\theta&0\\0&\sin\theta&\cos\theta&0\\0&0&0&1\end{pmatrix}\] generator along z axis \[k_z=\frac{1\partial\phi}{i\partial\phi}|_{\phi=0}\] generator of boost along x axis:: \[k_x=\frac{1\partial\phi}{i\partial\phi}|_{\phi=0}=-i\begin{pmatrix}0&1&0&0\\1&0&0&0\\0&0&0&0\\0&0&0&0 \end{pmatrix}\] boost along y axis\ \[k_y=-i\begin{pmatrix}0&0&1&0\\0&0&0&0\\1&0&0&0\\0&0&0&0 \end{pmatrix}\] generator of boost along z direction \[k_z=-i\begin{pmatrix}0&0&0&1\\0&0&0&0\\0&0&0&0\\1&0&0&0 \end{pmatrix}\] the above is the generator of boosts below is the generator of rotations. \[J_z=\frac{1\partial\Lambda}{i\partial\theta}|_{\theta=0}\] \[J_x=-i\begin{pmatrix}0&0&0&0\\0&0&0&0\\0&0&0&1\\0&0&-1&0 \end{pmatrix}\] \[J_y=-i\begin{pmatrix}0&0&0&0\\0&0&0&-1\\0&0&1&0\\0&0&0&0 \end{pmatrix}\] \[J_z=-i\begin{pmatrix}0&0&0&0\\0&0&1&0\\0&-1&0&0\\0&0&0&0 \end{pmatrix}\] there is the boosts and rotations we will need and they obey commutations \[[A,B]=AB-BA\] SO(3) Rotations list set x,y,z rotation as \[\varphi,\Phi\phi\] \[R_x(\varphi)=\begin{pmatrix}1&0&0\\0&\cos\varphi&\sin\varphi\\o&-sin\varphi&cos\varphi \end{pmatrix}\] \[R_y(\phi)=\begin{pmatrix}cos\Phi&0&\sin\Phi\\0&1&0\\-sin\Phi&0&cos\Phi\end{pmatrix}\] \[R_z(\phi)=\begin{pmatrix}cos\theta&sin\theta&0\\-sin\theta&\cos\theta&o\\o&0&1 \end{pmatrix}\] Generators for each non commutative group. \[J_x=-i\frac{dR_x}{d\varphi}|_{\varphi=0}=\begin{pmatrix}0&0&0\\0&0&-i\\o&i&0\end{pmatrix}\] \[J_y=-i\frac{dR_y}{d\Phi}|_{\Phi=0}=\begin{pmatrix}0&0&-i\\0&0&0\\i&i&0\end{pmatrix}\] \[J_z=-i\frac{dR_z}{d\phi}|_{\phi=0}=\begin{pmatrix}0&-i&0\\i&0&0\\0&0&0\end{pmatrix}\] with angular momentum operator \[{J_i,J_J}=i\epsilon_{ijk}J_k\] with Levi-Civita \[\varepsilon_{123}=\varepsilon_{312}=\varepsilon_{231}=+1\] \[\varepsilon_{123}=\varepsilon_{321}=\varepsilon_{213}=-1\]

Looking above looks like the OP attempted to use the correct latex structure but it may be they didn't specify keeping it in plain text and it defaulted to RTF format when they copy pasted from the original article.

I see we're on the same page lol particularly since several of the relations involve vector/ spinor/tensor fields.

No problem glad to see you have the relevant mathematics for our forum latex uses \[ latex\.] For new line latex for inline it's \( I placed a period on the latex closure statement to prevent activation. I will go through your article in more detail later this evening. Quick clarification I assume cdot is being used as the inner product have you checked how your BAS function works with cross and outer products ? If cdot is being used for multiply then please clarify its a common source of confusion. Also you might want to get several of your equations active in the article as some of them didn't expressed in latex form before you send for peer review. The other problem I foresee is several equations require specific trig functions with regards to rotations and boosts particular with regards to covariant and contravariant vectors (complex vectors ) as per vector commutation rules.

The name itself isn't important to whether a sound is relaxing or not. There are studies available on music and how certain types of music are relaxing or not.

The BB theory doesn't actually describe how the universe came into existence. We can only describe how and why it expands from 10^{-43} seconds onward.

You wouldn't see an edge, in the case of bubble universes or Hubble bubbles due to eternal inflation. What you will have is regions of differing expansion rates.

It would certainly help as there are numerous formulas needing good testing related to galaxy rotation curves and the core cusp problem.

Totally your choice however you cannot fault us for trying to teach you the SM as to how a TOE is defined and applied which has nothing to do with spiritualism nor old outdated beliefs. Best of luck

Nothing here is applying physics for starters alchemy Earth, air fire and water has nothing to do with modern physics and nothing to do with quantum gravity or the two slit experiment. Cross posted with Swansont

! Moderator Note Personal theories belong in their own thread in Speculations and must adhere to the Speculation guidelines in the pinned threads at the top of the Speculation forum. When answering questions in other posters threads all answers are required to be mainstream answers. To answer with personal theories amounts to thread hijacking which is just one of the reasons for that rule. That being stated your more than welcome to ask any related questions were happy to help you learn. If your not particularly familiar with DM as understood by current research.

It was and your likely correct on that. It's been quite a few years since I last looked at any TeVeS literature.

That was over a decade ago it would be tricky to find those earlier comparisons. The bullet cluster and Spiral galaxies were often used in arguments of which is the better treatment between LCDM and MOND. Most of the recent papers are now using later versions of MOND which has undergone numerous changes over the last decade. Some versions of MOND include DM as well. If I recall it tied into the cusp core core problem which MOND required extensions to handle. So nowadays the first question one has to address when doing comparisons is "which version of MOND ?" Though I don't keep up with MOND research I do occasionally examine their articles in the interest of looking for mathematical methodologies. It's one of the primary reasons I examine alternative theories as more often than not one cones across treatments that can be useful in other applications. For example one alternate theory not mentioned yet was Poplowskii BH universe origin papers if I recall he tried addressing both DM and DE using torsion. However the constraints on a torsion component in our universe global metric is nowadays far too stringent. The mathematical techniques come in handy with certain aspects of particle characteristics. Not to mention toy universe modelling Just an aside it took me awhile to recall a MOND treatment involving GR which was one of your earlier questions. One such model is TeVeS it's been considered an alternative possible replacement of GR. Where it stands nowadays I couldn't tell you it does tie into gravitational lensing as part of its examinations

MOND does a better job than LCDM on Bullet cluster galaxies and for a time it did poorly on Spiral galaxies. However that has been dealt with in the case of MOND. What MOND needs to improve is galaxy clusters and early universe LSS formation processes where DM under LCDM is useful for that. AFAIK MOND makes no predictions on lensing.

Very well described +1 thankfully there is a handy trick for summing those amplitudes called the Cassimer trick. The squiggly internal lines are what's referred to as the propogator action. This is also where virtual particles are described. The operator action are the external solid lines. (An operator must have a minimal of a quanta of action.) This is an example of a one loop integral. \[\vec{v}_e+p\longrightarrow n+e^+\] \[\array{ n_e \searrow&&\nearrow n \\&\leadsto &\\p \nearrow && \searrow e^2}\] The internal line in this case is the S-channel described by the earlier link I posted (first one on renormalization). The self interactions of gravity causes ever increasing propogator action so you get unwanted terms in the propogator or S-channel action leading to Faadeev Popoff ghost fields. Though you will typically have some ghost field it's minimal for EM strong force etc. However due to the self interaction Migl mentioned those unwanted terms become infinite. The needed counter term used to normalize is increasing in the gravity case whereas in the EM case the counter term is fixed. In essence the propogator or S Channel is divergent If anyone is interested a way to learn about Faddeev Popoff ghost fields is to study BRST quantization. A couple further hints in case someone wishes to learn the mathematics of renormalization with Pauli Villars and other methods you will also need to perform a Wick rotation. You will encounter two boundaries Dirichlet and Neumann boundaries which collectively is used in the Cauchy Boundaries. Any good Calculus textbook covers these. Those boundaries are also used in String theory as well. Unfortunately true and we do seem to get a lot of those attempts here lol though typically never the related math lmao.

That's not correct by any means.

The term infinitisimal is your pointlike object. We get divergences prior to R=0 that's an extreme case example. https://en.m.wikipedia.org/wiki/Infinitesimal#:~:text=In common speech%2C an infinitesimal,zero by any available means. Here is a little hint every infinite quantity has a finite portion. An effective cutoff is just prior to that quantity becoming infinite. So zero makes a good IR cutoff in the set of Real numbers but the UV cutoff would be infinite-1. That statement would make the set of Real numbers finite from an infinite set. With fields however it's not that simple but the premise is the same. If you have further questions on renormalization I would recommend a new thread so we don't hijack this one from the OP @JohnM29111 I read your article though normally I wouldn't as all material should be posted here in compliance of our forum rules. Quite frankly you have zero chance of getting a peer review level on that article. I sincerely hope your goal is to get it more in tune with modern physics. If your hope is that it will be accepted by the professional physics community you have a ton of revamping to do. That's an honest opinion Earlier I had stopped reading once I recognized you based your premise on the Bohr model. Reading further just made matters worse. Particularly when you include things like spiritual plane, angelic plane and all the spiritualism behind it and trying to include it into a TOE. All I can say is good luck on that in those aspects.

Not sure what you mean but under GR one can have a series of clocks along the null geodesic (proper time). The FLRW metric does something similar except the clocks are viewed by a commoving observer. As INow mentioned one must also specify the observer.