Mordred

Yep sockpuppet reported

It doesn't if you actually understand the paper is examining the different possibilities. Then later on provides the reasons why SR or GR alone is insufficient as neither account for the observer nor the equations of state. This is beginning to sound much like another sockpuppet attempt quite frankly. It doesn't if you actually understand the paper is examining the different possibilities. Then later on provides the reasons why SR or GR alone is insufficient as neither account for the observer nor the equations of state. This is beginning to sound much like another sockpuppet attempt quite frankly. So I'm not going to waste my time if that's the case.

If your referring to the screenshot from. The Lineweaver and Davies article. Once you read the full article and examine the mathematics the article itself will tell you precisely what I described. Never rely on part of any article without examining the full article.

Which screenshot ?

One of my favorite articles regarding GUT (grand unification) which is oft described as a TOE if one can complete the GUT including gravity is by John Beaz. It's an interesting and informative reading I highly recommend it. http://arxiv.org/pdf/0904.1556.pdf

Yeah that was annoying to say the least. What is tricky about the FLRW metric is that proper time is effectively tied to the scale factor for determination of Cosmic time. The Cosmic time being to the commoving observer. Hence the scale factor connection. Unfortunately it's easy to mistakenly think that the time dilation formulas work with cosmological redshift but the truth is once you get recessive velocity that exceeds c. One should instantly recognize something is wrong. Unfortunately in nearly every argument I have ever had on this topic. The posters pushing their personal theories typically wish to ignore that relevant detail. Let alone any math involving GR which quite frankly the stress energy momentum yemsor components will tell one that there is no gravitational time dilation involved. (The only entry being the energy density at T_{00}.) Unfortunately too often posters rely on verbal descriptives and seek statements from articles to support their beliefs but don't recognize the math shows a different story from the verbal descriptives. Spacetime being another common misconception with the fabric descripitives. Once one studies the mathematics one recognizes there is no spacetime fabric and spacetime is simply a volume where time is given dimensionality of length via the Interval.

Yeah that's the one lol needless to say it's far more convenient to extract the terms and relations needed lol.

You would never be able to account on a single theory cover everything. The most one can reasonably expect under physics is as described above by Joigus, myself and Migl. In essence every fundamental particle interaction encapsulated under the groups of the irrep equation I posted above with the addition of a renormalization for gravity. Even with that irrep equation one doesn't calculate from it. It encapsulates numerous formulas under each group irrep including numerous tensors too many to list.

Graphs added where most useful.

One further recommendation this is more on how to order the paper to the other gauge fields. Start classical then do weak field limit under Minkowskii. This will aid integration into any strong equivalence principle conditions under GR or curvature terms. For progressive steps into the Langrangian formalism do a quick intro. Then apply the minimally coupled scalar langrangian. Then step unto U(1) natural progression Then add fermionic fields including Dirac under SU(2) Then for quarks etc step into SU(3) Set the various couplings such as Yukawa Dirac Higgs in the relevant gauge sections. That should provide a natural progression of complexity simple to more complex Graphs added where most useful.

Yes however I will note most papers involving bubble universes in terms of bubble nucleation ignore don't add any terms for magnetic monopoles. Primarily for the reason of none ever being detected.

On a different angle in line with the parameters involved as per the title lol. You would need all the parameters of the standard model, those parameters directly involve any coupling constants of the different fields in question in direct relation to any momentum terms. Couplings such as Higgs couplings, Dirac and Yukawa couplings as they pertain to groups U(1), SU(2),SU(3). For gravity the SO(3.1) group. In covariant derivative form a representation can be expressed as follows. \[\mathcal{L}=\underbrace{\mathbb{R}}_{GR}-\overbrace{\underbrace{\frac{1}{4}F_{\mu\nu}F^{\mu\nu}}_{Yang-Mills}}^{Maxwell}+\underbrace{i\overline{\psi}\gamma^\mu D_\mu \psi}_{Dirac}+\underbrace{|D_\mu h|^2-V(|h|)}_{Higgs}+\underbrace{h\overline{\psi}\psi}_{Yukawa}\] At higher energy levels each field will decouple from the fields involved. This is oft described for example John Baez as running of the coupling constants. At these higher temperatures all particle interactions of the different fields have symmetry to each other and become indistinguishable from each other. Gravity may or may not involve a graviton. Just to make that clear. Also one can include a covarisnt derivative form under current SO(3.1) in the above. Leaving it out is intentional as the other fields involved are all renormalizable.

Yeah they make universes look like soap bubbles which is extremely unrealistic. The math and relevant equations of state for the boundary conditions tell a completely different story. The boundary conditions are determined as a region where the expansion rate can be reasonably described by a specific value of Hubbles constant value using the FLRW metric Just as those bubbles universes are formed by anistropic expansion rates there is no physical surface. For analogy think of a river flowing into an ocean. You have water of a certain salinity separated by water of a different salinity. The boundary is the region where mixing occurs. There is no surface. Now apply that analogy using the equations of state for a scalar field as per inflation. You have one region with a different inflationary expansion as opposed to another region. This leads to differing phase transitions at differing times involving electroweak symmetry breaking and is described by false vacuum to true vacuum phase transitions. If it's easier one can think of it as region of different blackbody temperature as the blackbody temperature of our universe evolves in proportion to the inverse of the scale factor. However that wouldn't provide any detail on what causes the differing inflationary rates

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.

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