Mordred

I would highly recommend you look into independence in particular for planar and spherical waves. You should also be able to match up to the relevant logarithmic functions as they apply to acoustics. If your not it indicative of an error or some missed factor. Once you get into more than one wave you will definitely need to factor in your wave equations primarily in amplitude and phase angles. In essence constructive and destructive interference factors.

let me guess your adding two waves of opposite phase and seeing c_o disappear ? still going through your math but I'm glad to see you got the displacement phase lag that showed in the reference I posted though the graph in the article isn't very clear. here is a decent article to use for comparision https://hal.archives-ouvertes.fr/hal-03188302/document

That just leads to a whole range of misconceptions. It's better and more accurate to simply point out that anything moving at c isn't an inertial frame of reference. Hence follows a null geodesic.

Lmao now there's an expression to deflate one's ego lmao

I like your example it also does an excellent job of showing degrees of freedom with the rotations etc. +1

A dimension is a mathematical term for a degree of freedom or some indepenendent variable. The spatial dimensions x,y,z can each vary without the other variables varying. Time we give dimension of length by the interval (ct) the distance light travels in one second.

In essence yes though the methods vary. I can't recall the theorem name but any infinite set has a finite portion. All gauge groups are finite

No its actually very easy think of a graph. Now set the max value at 1 (max value for a normalized unit. Now take the bell curve as it trends to 0 and 1 on that graph. Lets use the infrared end, divide 1 by a 1/2 with each result being further divided by 1/2 until you reach 0. You will never reach 0 that is an example of diverging to infinity. You have an infinite number of 1/2 divisions. So you apply some cutoff. (reqularization

In math language normalized units such as c=h=k=g=1. If you have a field such as the EM field you have the normalization via the quanta given Planck units. That's included in the previous expression. Divergence means diverges to infinity where you typically have two points on a graph that this applies. \[0\leftarrow x \rightarrow\infty\] QFT has a regulator to provide an effective cutoff before those two points apply. The infrared regulator and the ultraviolet regulator. these will vary depending on the theory. The more common is dimensional regularization.

That would still be accurate as a quantum theory would have to be divergence free. In essence normalized. QFT for example has the infrared and ultraviolet cutoffs for the \[SU(3)\otimes SU(2)\otimes U(1)\] gauges of the SM model.

you would still have the same classical effects as per Newtons gravitational laws as well as per the EM field with the photon. Range of force isn't quite the same as strength of force in that regard. Its better thought of as "At what range from the source can the force potentially be given sufficient energy" with the weak field its range is limited regardless of the energy density of the source.

well a graviton could be a stable spin 2 massless particle in that case the range of the force would be infinite as per classical gravity. Assuming that caveat which is also the common hypothesis for the graviton then the answer is yes it can have the same range. As we can only conjecture on what the likely-hood of the graviton properties are that's about as accurate an answer as can be given

yes that would make sense in near field and far field examinations I've come across though acoustics isn't something I often look into. The article I posted hints at that as well if I recall. No problem on trying to supply some direction etc its always nice to see a speculation posting that includes the related mathematics

Well I can understand that, if that's the goal then I would recommend including a planar wave examination and a comparison between the two. here is an example which should help. Though primarily it simply explains that there is a difference between the two but the article is lacking in what those differences entail in acoustics. https://ccrma.stanford.edu/~jay/subpages/Lectures/Lecture1-Acoustics.pdf I didn't spot any mistakes in the first article of equations you applied however still looking it over as I have time

I would like a little clarity on the goal in terms of acoustics. I fully agree that there is distinctions in the behavior of plane waves and spherical waves in terms of the specific acoustic impedence. This is known, the specific acoustic impedence is the relations the calculator that Swansont linked above applies. For plane waves the Z as it's commonly denoted stays relatively constant. However in the spherical wave you will have a 1/r relation. This affects the sound intensity. Is our goal specifically reverberation time as per Sabines equation ?

The initial roll depends on the model which has some variations but roughly 10^{-32} seconds after the big bang. Don't think of it as a particle rolling downhill that would be incorrect. Instead think of it as the potential energy density of the early universe decreases. Today we may or may not be in a metastable state but at lower potential. or we could be close to the minimum. There are competing models on this.

range of force is the particle momentum and mean lifetime of the mediator. So a graviton would need to be stable as per what Migl stated above. The HUP does also apply in the decay rates of particles

I'll look at it in more detail later on but on a quick glance I'm impressed good job so far

@Joigus something to keep in mind in topological spaces you will have connected and disconnected sets. For any topological space dealing with the Feymann path integrals. You will be dealing with connected graphs (sets) where momentum conservation is applied and the graph is oriented. Just an FYI to help better understand path integrals. A way to help is think of any point on a graph or if you prefer manifold/geometry etc. In Feymann path integrals that point is a vertex. In GR its a reference frame, In Feymann Integrals that vertex can be connected to other vertexes or disconnected. If its disconnected its assigned a valency of zero. If its connected to another vertex it will have a valency of 1 or greater depending on the number of connections. so your path integral has a valency of 1 it has 2 vertexes joined by an edge.(the two vertexes are the initial state/event and the final state/event. The edge being the path defined by the Euler Langrangian for the extremum of the action integral which will be the geodesic. Which will also apply the affine connections through the Christoffels with the use of parallel transport. This then gets into the metric connection which that parallel transport of two vectors must stay parallel along a curve in metric space. (covariant derivative of the above gauge groups). Hopefully the correlation for 4d spacetime will help with regards to the various topological space connections. You can readily see how they may apply in degrees of freedom

Well trust me I can relate when I first started studying gauge groups I didn't realize the above and kept getting lost and mislead. Once I realized the reasoning of gauge group axioms life got a whole lot simpler in understanding numerous relations described by the group. In particular the (U(1), SU(2) and SU(3) groups including the corresponding SO(N) groups. As SO(N) groups are a double cover of the SU(N) groups.

You really don't have much here to show a shrinking matter theory. Trying to show shrinking matter and how it supposedly accounts for universe expansion measurements isn't at all viable. For starters if matter shrinks then the fine structure constant itself would vary along with numerous other coupling constants. There is zero evidence this ever occurs. You moon conjecture has absolutely zero relation as the orbitals mathematics as it applies to escape velocity and the conservation laws is sufficient to explain the moons orbit. The paper you posted examines cosmological redshift of quasars vs super nova and shows the two have different redshift relations due to various factors related to luminosity distance relations etc. Unfortunately the paper didn't really do a good job as it doesn't take into account the non linearity past the Hubble horizon of z. However that's just my opinion. However regardless. The paper does nothing to support a shrinking matter case. (your first paper You already admit your second paper doesn't relate Lastly the very scales of change were talking about is like seeing a tiny change at one end to a massive change in the measurements. The two do not equate.... You mentioned in your opening posts concerning constraints . 1) the effect on coupling constants 2) doesn't account for BB nucleosythesis 3) cosmological redhift is a logarithic exponential change it isn't linear 4) the temperature history corresponds to that redshift as being proportional to the scale factor. 5) the cosmic microwave background we can measure infalling and out flows of matter in terms of the corresponding sound wave modes E and B modes why do we not see evidence of an expanded matter field in terms of c ? That's a start

The reference frame is the commoving frame however the FLRW metric uses this to apply commoving time. The commoving frame is set at mean average mass density of the the metric.

Higgs cross sections partial width's \[\Gamma(H\rightarrow f\bar{f})=\frac{G_Fm_f^2m_HN_c}{4\pi \sqrt{2}}(1-4m^2_f/m^2_H)^{3/2}\] \[\Gamma(H\rightarrow W^+ W^-)=\frac{GF M^3_H\beta_W}{32\pi\sqrt{2}}(4-4a_w+3a_W^2)\] \[\Gamma(H\rightarrow ZZ)=\frac{GF M^3_H\beta_z}{64\pi\sqrt{2}}(4-4a_Z+3a_Z^2)\]

as this subject is on Dm being the sterile neutrino here is some useful tidbits to chew on. In the standard model model SU(3) gauge used to describe neutrinos. The left hand (particle) is a doublet. However the right hand neutrino is a singlet. This has consequence which takes quite a bit of math to explain However let me know if anyone would like to see the related formulas. I will gladly post them. Anyways this has consequences in the weak mixing angles of the CKM matrix via the Higgs seesaw mechanism will have a higher mass term than the left hand neutrino ( a massive partner.) hence cold dark matter (vs warm or hot). so as matter doesn't generate pressure p=0 equation of state. While neutrinos do w=1/3

right DM can readily pass by other particles in the galaxy without interaction while baryonic matter will interact and those baryonic particles are more likely to join the galaxy as you described