Mordred

Oh I speak nonsense now, good luck with that. What do you believe the term Invariance means ?

We have been but anytime we bring up the required examples you stated your not interested or you don't accept it. The biggest pieces of evidence for c being constant isn't the mathematics but the observational evidence and precision tests. You expect us to use classical mechanics to describe something that requires a deviation from classical mechanics using nothing more than classical physics. Which quite frankly I take your meaning to be strictly Newtonian mechanics. no time dilation, no geometry changes, c being additive with velocity. Those are the deviations from classical Newtonian mathematics. However you refuse to examine the evidence supporting those deviations.

The only way to mathematically keep c constant would require the geometry changes set up via the Lorentz transformations. You do not wish to include those. The mathematics involving Maxwell would be needed as a validation Specifically the polarity shift between the electric and magnetic field. However none of that truly matters. Why not its simple. Observational evidence trumps any mathematics of any theory. Observational evidence takes precedence. You chose not to examine the Observational evidence. So I cannot help you if you have shut your mind down to other researches and tests of the invariance of c or other massless particles. The reason you cannot accept the statement classical mechanics is in error is your refusal to accept the evidence of time dilation, constancy of c and length contraction which go hand in hand with each other. You cannot keep c constant without the length contraction and time dilation which requires a 4 dimensional universe as opposed to the 3 dimensional Euclidean geometry. (dimension describes independent variables or effective degrees of freedom in math speak which is also employed by physics).

Its not my job to prove anything to you. that isn't why I visit this forum. I visit this forum to help people that want to learn physics not force them to believe in something they choose not to accept. I offered numerous literature showing c as constant you chose to ignore those.

Slow Roll single scalar field perturbation \[[\delta\frac{\tilde{p}}{\rho}]^2=\frac{k^3}{2\pi^3}\int d^3 xe^{i\vec{k}\cdot \vec{x}}\langle \frac{\partial \rho}{\rho}\vec{x},t \frac{\partial \rho}{\rho}\vec{O},t\rangle\] \[[\delta\tilde{t}(\vec{k})]^2=\frac{k^3}{(2\pi)^3}\int d^3xe^{i\vec{k}\cdot\vec{x}}\langle \partial t\vec{x}\partial{t}\vec{O}\rangle\]

In your opinion, however you also choose to ignore relevant sections and materials for c being constant.

No the mainstream sections is specifically for mainstream sciences as taught in textbooks and professional peer reviewed literature. It is not the place to examine personal theories. That belongs in our Speculation forum.

I see well its up to you if your going to accept c as being constant. That entails also time dilation and length contraction. As I mentioned before its not really our goal to force posters to believe in something.

Really he doesn't mention Lorentz funny he specifically notes the Lorentz transformations and even has a footnote directly referring to it on the bottom of page 8. he even goes through the related mathematics directly applying the Lorentz transformations in that paper. "The equations of the Lorentz transformation may be more simply deduced directly from the condition that in virtue of those equations the relation x2 + y2 + z2 = c2t2 shall have as its consequence the second relation "

Unfortunately your incorrect regarding the researches by Lorentz and Maxwell. The easiest way to show that is to compare the transforms That Lorentz developed that Einstein used in section 3. Galilean transformations. the important 2 is time and travel along the x axis. \[\acute{x}=x-vt, \acute{T}=T\] no time time dilation Lorentz transformations \[ \acute{x}=x\gamma(x-vt),\acute{t}=t-\gamma \frac{vx}{c^2}, \] time dilation and length contraction

It also applies to the statement the laws of physics are the same regardless of observer. The stationary system is a replacement from an absolute rest frame. Which Einstein also states isn't necessary. A simple example take observer A being stationary. Now observer B moves towards Observer A. You already know how to mathematically describe that. Now switch observers Observer B is now stationary while Observer A moves towards observer B. The equation will be identical. ( symmetric). If a relation is symmetric it is also commutative.

Your essentially correct so far. However as I mentioned showing light as constant he refers to two works by other physicists. Lorentz and Maxwell. In section 3 he applies the Lorentz transformations. In later sections he applies the Maxwell equations, which at this time has already been shown by other research papers to follow Lorentz invariance and not Galilean invariance. In essence he refers to other research papers that have already shown light being constant. One of those tests being the null results of the M and M experiment for Luminiferous Eather. In that test it also showed zero deviation from c due to velocity of emitter or observer.

Just a side, more for other readers but its also useful. You recall I stated that often the mathematics are more important than the words spoken. This is a good example. in the first equation where he is defining synchronization he uses the equation \(T_a-T_b=\acute{T}_b-\acute{T}_a\) this immediately tells me that not only does this describe synchronization, it also shows the relation is commutative, and symmetric. What this means is the choice of observer A or observer B doesn't change the mathematics. Either observer A or observer B can be treated as at rest or alternatively the inertial frame of reference. (it tells me far more than that in terms of related mathematics but that's outside the scope of the discussion)

Fair enough we will stick to section 2. Let's express what section two does not describe. 1) it does not describe time dilation. 2) it does not describe length contraction. 3) it does not describe the ticks from the face of the clock as being slower or faster. What does it describe ? It describes classical physics and Galilean invariance using relativity of simulaneaity. Which existed since the late 1600's section two does not present any new physics for the time period. He does use c as a constant but that's one of the postulates of the paper. However the relevant math showing how that applies comes later in the paper. It is not contained in section 2. Section 2 in essence shows that one does not require an eather to describe Galilean relativity. Nor relativity of simultaneaityThe end of section 2 covers what he showed in the section. "So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system " We already covered the math where you see that in the stationary setup. The synchronous readings of clock A and Clock B was right in the middle between them. We also covered that in the moving system this is no longer true. That is what that quoted section is referring to.

Funny part is, if you use actual physics to toy model systems. You do end up learning far more than from lectures or reading literature or watching videos. However further discussion on the pros and modelling are outside the topic under discussion.

All good simultaneaity is highly important to understand. I certainly don't mind assistance. Sometimes a different angle on any topic opens the light of day.

Energy is simply the ability to perform work. Mass is the resistance to inertia change. Matter has the requirement of "taking up space" so via the Pauli exclusion principle only fermionic particles count as matter. Bosons do not. If you learn mainstream physics you will discover there is an answer to most of your questions. Without invoking personal theories.

Correct I'm still thinking of the easiest way to explain section 3. As section 3 gets more into the Lorentz transforms. Though naturally it will have to wait till after work (RL sux lol)

So now your adding quark generations? That won't work either once you apply the CKMS mass mixing angles. Little hint all particles except electron proton and photon were mathematically predicted before discovery. One might think it's as easy as simply describing some particle to have specific properties and then brute forcing the math to accept it. However it doesn't work that way. Certain relations of Fibonacci are already part of main stream physics so I certainly have no objection to its uses. It can certainly have its applications with wavefunctions but you need a bit more than just Fibonacci. Particularly when the path integrals become important. LOL you also shouldn't need to create new particles to make your theory viable. That sort of thing quickly gets overturned. If you cannot use Fibonacci with existing mathematics pertaining to particles then your theory requires work. Though doing so will require extremely intensive mathematics.

Ok keeping an open, even though you are showing math relations. Albeit primarily on graph. You will find on further examination what you have won't work once you try to incorporate the S matrix. The 3 quarks you have shown is only the valence quarks. In point of detail the proton or neutron etc have a probability function that will project a sea of quarks where valence quarks represent the charge requirement for the overall charge. What you have so far would only amount at best as a first order approximation however doesn't appear to include any reference to the probability function of the Schrodinger now Klein Gordon equations. Secondly simply because we can mathematically describe nature. That does not mean nature cares how we describe or measure it. Absolutely we can mathematically describe nature. However that does not mean nature is mathematical as a fundamental.

The constant velocity of massless particles such as photons regardless of the velocity of the source or receiver is not merely a postulate or math trick. It is observed by every related experiment as highly accurate. Its a tough pill to swallow but its one of the most tested theories in Physics. It is still being tested to higher and higher precision to this day. Course the other pill to swallow will be an equally well tested aspect of SR (time dilation). The two are related but that gets complex and does require remembering the mass definition I provided For the record I will never apply any eather in any physics discussion. SR and GR do not use the Eather in its theory either. anyways its late here Night

No idea on the down point.. any measure is relative to the observer in any physics. Regardless of model. As far as the measurements taken well There is a huge list ranging from observing stellar measurements of extremely fast moving stars. The CMB etc etc. To using extremely high speed cyclotrons, Historicaly though Jupiter was used along with the sun back in 1675 done in Paris by Roemer. He also included Jupiters 4 brightest moons. By knowing their orbit he measured different transition times over a long period of time and used that data to get the value of c. The value he got back then is pretty much the same. 186,000 miles per second. We have taken that to incredibly higher precision using extremely high precision tests. Some of which I posted earlier. Back when I mentioned error margins a few days ago. (one way speed of light/two way speed of light tests. The St Ives test etc etc all involve measuring c). With modern telescopes there are plenty of objects emitting light travelling at near c. We still measure the speed of light from them as invariant c edit just a side note all massless objects will have a velocity c. (mass is resistance to inertia change(or acceleration aka Newtons laws of inertia.). Knowing the definition of mass is essential to understand SR and GR or any physics theory it applies to all physics theories.

Any measurement taken of the speed of light will give the value of c. A measurement is defined as an Observer.

An observer can himself be at near c and still measure the velocity of a light signal as being c even if the ship with the emitter is also going near c. Regardless of the velocity of emitter or observer any measurement of the velocity will equal c. (this is the part where the length contraction and time dilation kicks in of the Lorentz transformations. ) This is also the point where the deviations occur from the classical physics. LOL is typically also the hardest to get people to accept. Hence all the research and studies, this required a huge burden of proof. So far its tested as true to extremely high precision

We cross talked while I was editing your correct in the section you quoted the rest of my above post contains an edit where I added details on the moving train. When the train moves Right down the middle is no longer true and we must now account for the train motion. All events (a term that includes observer-emitter-coordinates-signals ie light etc) are always relative to the observer. Yes an observer will measure the velocity of light at c regardless of the velocity of the emitter. This is an invariant quantity. It never varies regardless of observer Nor how fast the emitter is travelling. If your good up to hear I suggest to better understand the math of SR we cover principle of equivalence next. If you have further questions on this stage ask away. As we can see though there is only limited positions where the two clock are simultaneous and where those point lie will vary.