Mordred

Might help if you look at the time aspect imsteas of writing \[a=\frac{dv}{dt}\] Write \[a(t)=\frac{dv}{dt}\] Secondly momentum includes mass via \[p=m*v\] So where is the issue ? Others have tried explaining this to you in the older thread

No worries hopefully you resolve your PC issues.

I like that article nice simple approach

This is more for fun but it also demonstrates another aid. Lets say you have a 2D vector field. We can graph this vector field as a function for simplicity lets do a 2D center of mass. I happen to know the function for this \[F(x,y)=(-x,-y)\] now here is a neat trick there is a handy tool Wolframalpha.com its entries can be tricky but the above is https://www.wolframalpha.com/input?i2d=true&i=plot+F\(40)x\(44)y\(41)%3D<-x\(44)-y> now lets say we want the curl of a magnetic field in 2D. \[F(x,y)=(-y,x)\] https://www.wolframalpha.com/input?i2d=true&i=plot+F\(40)x\(44)y\(41)%3D<y\(44)-x> this is just to demonstrate the usefulness of functions Here is what Function of sin(x) looks like see link https://www.wolframalpha.com/input?i2d=true&i=plot+sin\(40)x\(41) here is cos(x) https://www.wolframalpha.com/input?i2d=true&i=plot+cos\(40)x\(41) Now you can do the same with tan(x) and it will look completely different. However the main goal is to point out the WolframAlpha has some handy plotting capabilities as well as numerous others to help check your math or get a better feel for some of the more complex equations. The first graph is a converging field example gravity converging to a center of mass If I switch the sign of x I will type this in as WolframAlpha wants the format Plot F(x,y)=<( -y,x)> the field will be diverging from the center outward. Just copy and paste that line and it should work. Graph 2 is an example of a non diverging curl (rotationally symmetric) good example application is the magnetic field as opposed to the electric field which will be this example. I will let you enter that. However that depends on charge the opposite charge will be example 1. Plot F(x,y)=<( -y,x)> Hope that helps better visualize what functions do in terms of fields One particular handy use will come into play to better understand matrix mathematic for example \[\begin{pmatrix}a & b\\c&d \end{pmatrix}*\begin{pmatrix}e&f\\g&h \end{pmatrix}\] https://www.wolframalpha.com/input?i=[[a%2Cb]%2C[c%2Cd]]*[[e%2Cf]%2C[g%2Ch]] this will solve that operation for you and give a step by step (though you get far greater detail if you pay for membership) the details it does supply to non members is often as useful. Just an additional training aid to help you along

won't particularly matter when you consider absorption distance section. The quoted section makes no sense ALL frequencies are time dependent. The time element is determined via the frequencies in question. So that quoted section will need more than just some handwave statement specifically some form of mathematical proof. You cannot have the same time for all frequencies that is impossible by the very definition of frequency I also hate that terminology " inside time" sorry but that terminology doesn't work and gives the visualization of little matter balls for particles instead of field excitations which is something modern physics now teaches example under QFT I would assume you have some mathematics to your conjecture as its been on your books the past 6 years if not longer and there is absolutely no mathematics for your 2018 thread nothing more than blanket statements. Have you not done any mathematical development in the past 6 years ???? Without the related mathematics you literally have nothing of any substantial worth. You can't even prove to yourself mathematical viability let alone anyone else.

as I always prefer to include the mathematics for my statements where applicable or I have handy here are the corrections for peculiar velocity (recessive velocity beyond Hubble Horizon Recessive Velocity corrections past Hubble Horizon approx z=1.46 \[E_Z=[\Omega_R(1+z)^4+\Omega_m(1+z)^3+\Omega_k(1+z)^2+\Omega_\Lambda]^{1/2}\] \[v_{r}=\frac{\dot{a}}{a_0}D\] \[\frac{\dot{a}(t_0)}{a_o}=\frac{H(z_0)}{1+z_o)}=\frac{H_0E(z_o)}{1+z_O}\] \[v_r=\frac{cE(z_o)}{1+z_o}\int^{z^{obs}}_0\frac{dz}{1+z_o}\frac{D_c(Z_o,Z_s)}{D_H}\] \(Z_{os}\) is the reduced redshift \[1+z_{os}=\frac{1+z_s}{1+z_o}\] for observerd source redshift z_s present epoch Observer \(z_0=0 ,E(Z_o)/1+(z_o)=1\) \[v_r=(o,z)=c\int^z_o\frac{dz}{E(z)}=c\frac{D_c(z)}{D_H}\] gives redshift as a multiple of speed of light The above is time dilation effects due to expansion and commoving volume to a commoving observer. Below is how to determine the ae of the Universe as a function of redshift the Hubble parameter can be written as \[H=\frac{d}{dt}ln(\frac{a(t)}{a_0}=\frac{d}{dt}ln(\frac{1}{1+z})=\frac{-1}{1+z}\frac{dz}{dt}\] Notice you have a natural logarithmic function in the last statement for scaling look back time given as Ie how to calculate Universe age \[t=\int^{t(a)}_0\frac{d\acute{a}}{\acute{\dot{a}}}\] \[\frac{dt}{dz}=H_0^{-1}\frac{-1}{1+z}\frac{1}{[\Omega_{rad}(1+z^4)+\Omega^0_m(1=z0^3+\Omega^0_k(1+z)^2+\Omega_\Lambda^0]^{1/2}}\] \[t_0-t=h_1\int^z_0\frac{\acute{dz}}{(1+\acute{z})[\Omega^0_{rad}(1+\acute{z})^4+\Omega^0_m(1+\acute{z})^3=\Omega^0_k(1+\acute{z})^2+\Omega^0_\Lambda]^{1/2}}\]

This is more a related FYI and its not something one finds in textbooks. I can pretty much guarantee very few if any members will be aware of this little side detail. As we are all aware our universe is expanding. What is often overlooked when it comes to light propagation in this expanding volume is something called Absorption distance. I will try to keep this as simple as possible however the essence of absorption distance is that the higher the density of a particle ensemble the greater the likely hood of mean free path interference resulting in a reduction in number density of received photons. In order to factor this is will involve the absorption or scattering cross section of the particle population as well as the cross section of photons. Were going to assign X(z) to the absorption distance. \(n_0\) as the number density, \(\sigma_0\) as the cross section. Latter two being present epoch density. The evolution of number density as a function of redshift is \[n(z)=n_o(1+z)^3\] I won't get into the mathematical proof of the above it will invariably involve the density evolution of matter and radiation via the FLRW metric. We will be using the proper distance increment \( dl\) (take a ruler and keep the number of divisions on that ruler the same but as you go further back in time the spacing between each division decreases) \[dl=\frac{a(t)}{a_0}D_c=\frac{D_c}{1+z}\] where D_c is the commoving distance unfortunately the cross section of a photon beam is not consistent with redshift however we can choose to ignore geometric effects of orientation and orientation of gas structures for simplicity. In a commoving cosmic volume along the proper distance increment centered on the Z beam the probable number of targets (absorption/ scatterings)that can potentially interact with the beam is \[DN_t)=n_z\sigma_b(z)dl=n_o\sigma_b(z)(1+z)^3dl\] where \[dl=cdt=\frac{c}{H_o}\frac{d_z}{(1+z)}{(E(z)}=D_H\frac{dz}{(1+z)E(z)}\] \[DN=dn_t(z)[\frac{\sigma_o}{\sigma_b(z)}]\] where \[\frac{\sigma_o}{\sigma_b(z)}\] is the fractional area per structure the redshift dependence of DN/dz can be written as a dimensionless quantity \[\frac{DX}{Dz}=\frac{1+z^2}{E_z}\] upon integration we get the Absorption distance \[X_z=\int^z_o\frac{DX}{d_z}dz\] Now consider the above if for example DM was interacting with the photon beam the entire time of flight travel. Would we ever get the signal at say z=1100 ? conditions affecting the mean free path of photons after surface of last scattering is relatively clear and we are all aware of the opacity previous to last scattering on the mean free path of light. Just for consideration of a likely side effect should photons interact with DM along the mean free path via absorption/emission @DanMP this is the side effect I am referring to should DM interact with photons along the mean free flight path though the only cross section I have atm for DM would be under assumption of sterile neutrinos being DM. As that is part of my current research I have been doing in my Nucleosynthesis thread.

lol greatest training aid graph paper

I can live with bad terminology so now that is addressed we can move on. DM assuming it is a particle is considered professionally as being very stable so no issue there. The issue however still remains that even via absorption and emission of a photon your still involving medium like properties so time of flight for the photon beam is being additionally delayed. The other problem that makes this interaction distinct from redshift is accordingly via Snell's law the refraction angles (emission of photons will be frequency dependent on an equivalent refraction index. This leads to diffusion or divergence of the waveforms which is not the case with redshift. The redshift relation has no refraction index redshift has no frequency dependence on refraction. As redshift equates to time dilation ie gravitational time dilation, relativistic Doppler shift or even cosmological shift (with corrections beyond Hubble horizon) this is relevant and shouldn't be ignored. Granted the other detail I hadn't mentioned is such an interaction would also affect the KE terms so there should be a temperature increase/decrease

night and its great your starting to understand scalars and vectors keep at it. Here is an assistant article just on units and vectors for physicists https://www2.tntech.edu/leap/murdock/books/v1chap1.pdf in particular \[A\times B=\begin{pmatrix}i&j&k\\a_x&a_y&a_z\\b_x&b_y&b_z\end{pmatrix}\] which in other notation equals \[A\times B=(a_yb_z-a_zb_y)i+(a_zb_x-a_x b_z)J+(a_xb_y-a_yb_x)k\] this will correspond to that right hand rule I mentioned quite a while back also those matrix you have been looking at for the 2*2 matrix drop the k terms. You can project a 2d plane in any orientation in 3d. The 3*3 case is two complex planes where as the first case is one complex plane (first case SU(2) second case SU(3). Those are two fundamental particle physics groups which is where this lesson becomes valuable. For spin you need the SU(2) gauge group those vectors above are applied under all unitary groups U(1), SU(2),SU(3). for higher dimensions we will need higher vector commutations. we can only fill a matrix entry with scalar values so we need to get scalar values from vectors. That is why this lesson is so important. By the way once you understand the above you will have the necessary tools to understand Special Relativity and the Minkowskii metric. We can step into SR quite readily once you are comfortable with the above. Were literally on the edge of stepping you into electromagnetism via Maxwell equations

lets start with this statement an observable is any measurable quantity that includes time so how can an observable which we can measure lies outside of time when most observables are time dependent via the time dependent Schrodinger equations or velocity and acceleration. That statement alone goes against all modern physics

that is understandable it gave me trouble as well when I first learned this but if you figured out the 2d case your on the right track and doing well. Just a side note that plane your moving around is a complex plane and you may have noticed you can orient it in 3d. The entries for i and j had previous math operations done to it for the linearization they are complex conjugates denoted by the \[\hat{i}\] hat on top when it comes to quantum spin we will have to calculate these as the vertical will be imaginary numbers and the horizontal will be real numbers. ( we will need those for charge conjugation ie CPT charge, parity and time symmetry) later on hint your boundaries is the edges of the parallelogram for spin its the edges of the possible values ie the edges of the shaded area of the spin graph https://en.wikipedia.org/wiki/Spin_quantum_number the shaded area on that graph are the range of possible values ie the quantization which we have to cover specifically the math in this link https://en.wikipedia.org/wiki/Azimuthal_quantum_number hopefully though this will take considerable time we can get you to understand this link https://en.wikipedia.org/wiki/Angular_momentum_diagrams_(quantum_mechanics)#Inner_product but we need to sharpen your classical physics before taking on the challenges of QM

Yes the 4 entry box is a matrix. That matrix has entries those entries don't worry about just yet but they are derived by the inner products of the i,j vectors. ( part of the linear algebra that the link doesn't show so don't fret of the entries itself as I have taught you how to fill those entries for the determinant you are performing a math exercise using the entries \[\begin{pmatrix} a&b\\c&d\end{pmatrix}\] so lets set the entry values a=2 b=3 c=4 d=5 the formula for determinant is \[ad-bc\] so the determinant is (2* 5)-(3*4)\] so 10-12=-2 which if you look at the descriptive's in the link if the sign changes from a positive to negative determinant the orientation of the parallelogram is flipped over but also the value (2) is greater than 1 so it is stretched out. that is the general purpose of the determinant its to provide a means of scaling For quantum spin the main focus is the sign reversal itself specifically spin up and spin down. The entries for that matrix in the third link will be using a specific set of linear equations that will be determinant from linearizing the spin angular momentum operators. Which we haven't covered yet.

Agreed the one way light can however be used to detect DM hasn't been mentioned yet. Though c is still invariant nor is light interacting with DM. Via gravitational lensing and its relation to mass luminosity.

Yes but there is still no such thing as a quasi absorption not to my knowledge. Absorptions I can accept quasi-absorptions not so much lol. However irrelevant as absorption still amounts to light slowing down and absorptions still requires DM to interact with photons.

No such thing as a quasi or failed absortion. Nice try the rest is nothing more than random hand waving assertions based on WAG guess work. You have two types of scattering and all particle based interactions are described by scatterings inelastic and elastic. No scattering equals no particle to particle interaction. Scatterrings involve particles not just atoms see Feymann diagrams those interactions are also scattering events and detectable. When particles collide in a cyclotron those are scattering events

So what is known as scattering which is detectable using spectography. So as scatterring events are detectable why do we not see any evidence of such scatterrings? We can certainly measure such events with regards to photons and regular matter why do we not see any such events with photons and DM ? Photon scattering events are readily detectable Did you forget photons only travel at c ina vacuum when photons travel through some medium such as ordinary matter ie plasma the propagation speed is no longer c ? That is precisely why photons only travel at c in a vacuum. See previous comment I already mentioned scatterings. For the record I do in actuality perform spectographic research its part of my professional formal training and a large part of my internships directly involved studying spectroscopic data. This is also true with @swansont as the same physics applies with neutron interferometry which I know @swansont has professionaly been involved with. Specifically Braggs law, Moseley law, Shells law, which you learn that there is a frequency dependency on scattering angles as well as the medium refractive index. Scatterrings are very distinctive from redshift just an FYI. You might also note I included related articles above which involve such scatterrings with ordinary matter.

All the time that's usually when I usually take a mental break and sit back to figure out what detail I'm missing. It's very common, the trick is to not stress about it and go back and few steps to look for the missing details or look for other references that may have a different writing style, examples or different math treatments and look for the elements common to both treatments. There are various equations common to all physics example the energy momentum relation, scalar, vectors and spinors This is also why I keep dropping reminders to learn vectors and vector addition. Every physics theory involves them and once you master vector particularly in vector field treatment the vast majority of physics becomes far easier to understand regardless of theory. Example spin is angular momentum so I automatically know I will need cross products of vectors. Linear relations only requires the inner product of vectors. Conserved systems are systems where no force is applied example freefall condition under GR or Newtons laws of inertia. An object will maintain a constant velocity until acted upon by a force=acceleration. Acceleration is not conserved but velocity is. For another example if no force acts upon a particle you can describe the particle as a conserved system. When a force acts upon that particle its no longer conserved. Invariant properties (same to all observers are conserved systems ) All conserved systems are closed as you are describing the system or state without any outside influence. Closed systems must also be finite in extent. The inner product of 2 vectors returns a scalar how convenient we now have the magnitude. The cross product of two vectors returns a new vector so now we have the change in direction. How convenient. It's so convenient it's common to all physics theories. Hence also why I pointed out similarities that QM has with classical physics. Classical physics provides a solid foundation to understand more complex physics. If you ever want to understand how it is I can make sense out the most complicated physics treatments the above describes precisely how I so. I find where classical physics can be applied and then study where more complex examinations becomes required and why they are required.

The x is a placeholder for any relation being compared example a vector or spinor or even some geometry or object. Yes the comma is just seperation for legibility. Protons are simply tightly packed and Pauli exclusion applies to protons as well. RHS is right hand side In those graphs think of the determinant as the volume distortion but it can have different meaning in other systems or more accurately how much the linear transformation will affect the volume

DM doesn't interact with the electromagnetic spectrum so doesn't interfere with photons That's well known so how would it affect c in regards to any test using photons ? In rhst regards any far field test using stellar objects would have intervening DM and we do not see any evidence of scattering due to DM. So any link I included using any methodology of far field stellar object examination is also testing any intervening DM. Believe me I wish DM would scatter or influence photon path it would be far easier to detect

Well then the thought experiment in essence has already been performed if you look through I provided you would find improved yet equivalent style experiments. Or did you not notice for an example the experiment done in space and quite frankly if you do a Google search you would find related equivalence principle experiment done on the moon. So don't tell me the effort I took is uncalled for or does the simple detail experiments are constantly being performed in dozens of different methodologies elude you.

the interactive parallelogram for determinant's (khan link above we can assign it as a matrix any assignment will do so lets just call it matrix B so that matrix is the box with two rows and two columns. The rows and columns are equal so it is a square matrix. Adding the \(\hat{i},\hat{j}\) coordinates we can place those coordinates in the (subscript= bottom, superscript=top exponent). \(B_{i,j}\) on subscript, \(B^{i,j}\) where " i " is the row vector," j" is the column vector. Now recall those spin states. Each spin has a limited set of allowed values for the S component. for spin 1/2 particles https://en.wikipedia.org/wiki/Doublet_state In quantum mechanics, a doublet is a composite quantum state of a system with an effective spin of 1/2, such that there are two allowed values of the spin component, −1/2 and +1/2. Quantum systems with two possible states are sometimes called two-level systems. Essentially all occurrences of doublets in nature arise from rotational symmetry; spin 1/2 is associated with the fundamental representation of the Lie group SU(2). for Spin 1 bosons. https://en.wikipedia.org/wiki/Triplet_state In quantum mechanics, a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin S = 1. It has three allowed values of the spin's projection along a given axis mS = −1, 0, or +1, giving the name "triplet". Spin, in the context of quantum mechanics, is not a mechanical rotation but a more abstract concept that characterizes a particle's intrinsic angular momentum hopefully the above helps as a means to see what the math is doing without knowing the math. Going to let you study the above as there is a lot to absorb on the last post https://en.wikipedia.org/wiki/Spin_quantum_number In the last link look at the reflection symmetry for spin up and spin down.

lol you can relax on this one symmetry is in actuality easily understood its learning which mathematical relations are symmetric that tends to get confusion. lets first take a simple everyday example. One of my favorite examples is to use fan blades.. Each blade is identical so they are symmetric to each other. As the fan rotates those blades are unaltered this is called rotational symmetry. if you move the fan around the room the blades remain unaltered. this is called translational symmetry. if you look at an image of the blades in a mirror they look identical (reflection symmetry) if you combine both translation symmetry and reflection symmetry this is called glide symmetry. Now on the mathematics side. if you add a set of numbers or values and the order of operation doesn't change the resultant the equation is commutative https://en.wikipedia.org/wiki/Commutative_property if an equation is commutative then its relations are symmetric. so for example with states this can be expressed as \[|\psi\rangle_{c}=|\psi_a\rangle +|\psi_b\rangle\] the above tells us the order you add the states doesn't matter. So it is a symmetric relation if on the other hand you have \[|\psi\rangle_{c}=|\psi_a\rangle -|\psi_b\rangle\] the order of operations does change the result this is an antisymmetric relation. it is common nomenclature to place the negative sign as the first term on the RHS of the equal sign \[|\psi\rangle_{c}=|-\psi_a\rangle +|\psi_b\rangle\] multiplication is commutative (symmetric) however division is not (antisymmetric) Now consider spin. Boson spin is an integer 1 most common zero in Higgs. You can add or subtract bosons in any sequence and the order of operation doesn't but also other than total energy and number of bosons in the system no other change occurs as a result. This isn't true for fermions with half integer spins ie 1/2 the order of operations does matter . It is also this detail that leads to the Pauli exclusion principle. https://en.wikipedia.org/wiki/Pauli_exclusion_principle In bosonic systems, all wavefunction must be symmetric under particle exchange. for bosons \[\psi(x_1,x_2)=\psi(x_2,x_1)\] the above is a commutative expression (symmetric) for fermions \[\psi(x_1,x_2)=-\psi(x_2,x_1)\] this is an anticommutative expression (antisymmetric) Last two expressions are called Slater determinants https://en.wikipedia.org/wiki/Slater_determinant the matrix in that link can readily be understood here https://www.khanacademy.org/math/multivariable-calculus/thinking-about-multivariable-function/x786f2022:vectors-and-matrices/a/determinants-mvc that link has an interactive graph you can play around with ( Pay close attention to how the parallelogram changes shape as you interact with it this will become important to understand spin later on.) but also a link to 3d Determinants https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-of-matrices/v/linear-algebra-3x3-determinant This should also help better understand that with vector addition the inner product of two vectors \[\vec{a}\cdot \vec{b}=\vec{b}\cdot \vec{a}\] is symmetric (commutes) the order of inner product of two vectors doesn't matter where as the cross product of two vectors anticommute \[\vec{a}\times\vec{b}=-\vec{b}\times \vec{a}\] now some instant recognition rules with matrix/tensors \[\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}\] this matrix is symmetric and orthogonal https://en.wikipedia.org/wiki/Orthogonality the only non vanishing terms are on the diagonal given as 1 in each entry any non vanishing term not on the diagonal above is antisymmetric For QM if all diagonal terms are a real number (set or reals) that matrix is a also Hermitean https://en.wikipedia.org/wiki/Hermitian_matrix as you can see in the above a Hermitean matrix need not be symmetric but all diagonal terms must be a real number. this will help when it comes to spin statistics under QM example a preliminary lesson to understand https://en.wikipedia.org/wiki/Conjugate_transpose but before we deal with the complex conjugate under QM treatments lets familiarize you with what a complex number is. as You learn best from videos https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:complex-num/v/complex-number-intro now recall that interactive video where I asked you to pay attention to the parallelogram. ? replace the two axis as one axis imaginary numbers the other axis Real numbers. Just like the complex number wiki link images and make further note that the parallelogram in the interactive map is identical to the parallelogram in that same link and that we can add two complex numbers using the parallelogram. this will become important later on when we assign operators as those complex numbers as well. (under QM two spinors which are also complex number for what is called a bi-spinor giving us 4 complex numbers in total needed for Dirac matrices later on). This will also apply to linearization of non linear systems. Take your time on this as it will become incredibly useful for a great many different physics treatments including GR/QFT etc. @studiot will also recognize the above applies to classical physics as well as engineering applications. further consideration as your looking at the parallelogram I want you to also consider the following (eigenvectors and eigenvalues) https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. if you look at the interactive graph on that last wiki link you can see the connection. to the Khan University interative map. the below will also help for those last two terms https://www.mathsisfun.com/algebra/eigenvalue.html note from last link 1 means no change, 2 means doubling in length, −1 means pointing backwards along the eigenvector's direction now look back at the values in top left corner of the first khan interactive map on determinants. The box with the changing numerical values in matrix form (2 by 2 matrix) All the above is called skew symmetry. As you stretch the eugenvector the parellelogram becomes scewed/stressed. (will apply to all energy momentum stress tensors). Further a skew symmetric geometry can be Hermitean (assign real values only on the eugenvector) while the geometry is not orthogonal (its now skewed) (you may also want to notice that the interactive determinant graph is showing rotation and reflection symmetry ie when i axis is in line with j axis. They have reflection symmetry with one another. Vectors where the only change is direction have rotational symmetry.

Lets start with a couple of statements Physicforum doesn't allow any form of speculation or any physics that isn't concordance or found in Peer reviewed literature. However that is irrelevant. DM has little or nothing to do with the isotropy of the speed of light or its constancy. Both isotropy and constancy is a large part of Lorentz invariance tests. The tests you have above are far too behind the times of modern day tests of c constancy or Lorentz invariance. Those precision tests place the error margin at roughly 1 part in 10^15 for any error margin. That is well beyond the tests you have proposed. for example you second proposed test takes what you have into far greater precision. https://arxiv.org/abs/physics/0510169 here is the usage of stellar objects and time of flight https://arxiv.org/pdf/2409.05838 we also use microwave interferometers, laser interferometers, rotating mirrors, to name a few other tests commonly done. here are some Lorentz invariance constraints https://arxiv.org/abs/2406.07140 here is one example using gravity waves https://arxiv.org/abs/1906.05933 here is a small listing of modern methods https://arxiv.org/abs/gr-qc/0502097 https://arxiv.org/pdf/1304.5795 model independent tests https://arxiv.org/abs/1707.06367 tests done in space New Test of Lorentz Invariance Using the MICROSCOPE Space Mission https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.231102 All the above clearly show that we are constantly testing c and Lorentz invariance those tests never stop and were constantly seeking higher precision tests. So nothing you have suggested above is new or hasn't been thought of already. In point of detail Modern tests have far far greater precision than what you have above

Lets tackle symmetry before spin as symmetry can be easily shown and I will work up an easy way of understanding symmetry