Mordred

It gets worse than that as ds^2=0 for null geodesics which is another reason for a photon frame being invalid as a reference frame. Its nonsensical answers such as time stopping or the photon existing everywhere at once that makes it obvious on the photon frames invalidity.

Sounds good I will wait on your next installment and work with the math you post to limit added confusion

I can work with this and tie it into system states. I will have time to work out a format to include Correspondance Principle.

Here is a couple of lists http://www.cmat.uni-halle.de/~hsl/PoM-files/Symbols.pdf https://archive2.iupap.org/wp-content/uploads/2014/05/A4.pdf In the last article it mentions two symbols used in multiplication however when it comes to vectors those same symbols has another usage. \[\vec{a}\cdot \vec{b}\] The dot in this case isn't multiply but is the dot or inner product of two vectors (used for linear relations.) \[\vec{a}\times \vec{b}\] This is the cross product of two vectors (will involve angles and rotations) A simplified link showing the dot and cross product. https://www.mathsisfun.com/algebra/vectors-dot-product.html Of essential importance is that the dot product of two vectors give the magnitude (scalar) while the cross product of two vectors returns a new vector. Magnitude and direction

It's not uncommon 99 percent of posts in Speculations result in efforts to in essence reinventing physics as the OP never understood the physics involved. In your case you weren't attempting to reinvent but simply lacked the knowledge I will see what I can dig up

You will have a number density of virtual particles when mediating a scattering event. You cannot measure a virtual particle directly you can only determine their existence and involvement through indirect evidence via an ensemble of virtual particles that sum up to a quanta of action. https://en.m.wikipedia.org/wiki/Action_principles A short time in the quantum regime is far less than 1 second they exist just long enough to mediate a process. The range of a force is determined by the momentum of the mediator boson for that force and it's lifetime. As the real photon is stable with high momentum c. The range of the EM field is infinite. However the Strong force mediator is incredibly short lived so it's range is far more limited 10^{-15} meters

Let's put it this way right from your Opening post what you attempted to describe is already covered in physics treatments and Studiot and I have been trying to teach you how that OP would be formally described in different scenarios.

Rudimentary lead up for the Correspondance Principle ? I've been trying to figure out how to keep that simplified so if so then I may be able to work with your upcoming example. No the event horizon is an observer limit due to spacetime curvature. In essence it shows the point of no return for any infalling outfalling massive and massless particles. You don't require the quantum regime to determine that boundary just GR.

In this case you can do the calculation with an everyday calculator. \[R_s=\frac{2GM}{c^2}\] https://www.omnicalculator.com/physics/schwarzschild-radius. For zero point energy it's typical to treat that field as the Propogator which I've only detailed the Operator action. There is an expression "The propogator, propogates the Operator and the Operator operates on the Propogator." https://en.m.wikipedia.org/wiki/Propagator so from this wiki it mentions virtual particles. Some detail is needed a photon for example can be real or virtual. Real photons have 1 quanta of energy and are individually measurable. However when mediating the EM field they are offshell meaning they can have any energy level required to mediate (off shell) and have less than a quanta of action/energy. So are not measurable in this state hence the term (virtual). They propogate (Mediate the Operators ) on Feymann integrals they are the wavy internal lines. While the operators form the external lines for the real on shell particles as opposed to the virtual mediator or Guage particles. https://arxiv.org/pdf/1602.04182 See example 6 the link does include the relevant mathematics but shows primarily the essential basic equations in simplified form (though it won't seem that way)

Lol if you recall I essentially asked that same question in regards to first equation it's why I mentioned the decay being acausal. It's also one of the reasons for mentioning the choice of examples in the article. In regards to gauge theories all Gauge theories must have symmetry invariance for both global and local symmetries. This includes Lorentz invariance under SO(3.1) Poincare group. Those details are inclusive in the covariant derivative for each gauge group. Edit forgot to add that you may find other review turn downs as a result of the first equation. I would consider eliminating that example altogether but that's just my advise. As the purpose of the paper also isn't to show a deterministic universe as a fundamental reality that example isn't really needed

All gauge theories are Lorentz invariant so yes they all are in accordance with Observer effects factored in. From what I've seen thus far on your mathematics I don't see how your hypothesis complies under Lorentz invariants from what I've read of your article. Obviously under group theory all gauge theories must meet specific criteria which I don't see included in your article.

Use order \[ test \,] just remove the comma on last statement

good night unfortunately Physics is all about math and you wont learn physics properly without the math. Trust me its a challenge keeping the math as simple as possible. I certainly wouldn't be able to show you the entire math contained in say a single textbook on a forum lol. ( though some may feel I have thrown the textbook at their heads ). For example you would require mathematics to describe how state A affects state B with any predictive and testable accuracy. However in order to even describe the interaction via math one must also mathematically define the states themselves. a little hint on the math. If you study the difference between how scalar quantities ie magnitude only examples being temperature and speed. When you require force you need a direction of force or motion as well so vectors. The other key math study is spinors (rotations) example torque, vorticity, flux will involve both vectors and spinors as will any wavefunction or waveform. These are fundamental relations to any and all physics formulas without these skills you never really understand any physics formula. Lets use that last equation as an example. Someone knowledgeable in the mathematics involved will automatically recognize that this expression \[\frac{d}{dt}\langle\psi|\hat{A}\psi\rangle=\frac{i}{\hbar}\langle \psi|[\hat{H}\hat{A}]\psi\rangle\] describes a particle field that includes the harmonic action, which describes the fluctuations using the symmetry relations between the fluctuations and the equations of motion for a Spring but you a spring at every coordinate.... Here is a well recommended site Professor Matt Strassler has a lot of good simpified articles on his site. With regards to his article on the harmonic oscillator https://profmattstrassler.com/articles-and-posts/particle-physics-basics/quantum-fluctuations-and-their-energy/zero-point-motion/ here is the link to his other articles it will be a huge recommendation to read them as he does an excellent job on any of his articles. https://profmattstrassler.com/articles-and-posts/

Overall not bad a descriptive far better improved. Lets start here you have two states that are well defined with well defined boundary conditions. Now here is where things get tricky, we haven't defined the states themselves to be able to determine what occurs when those two states interact however we can ignore that for the moment. Under QFT treatment the region between the two states simply describe as quantum fields. This is where the interaction between the two states is mediated. So if for example your two states are two separate EM fields. The region between the two will still be an EM field which is good as the EM field is mediated by photons. However we still want a term to describe that region between states. However this becomes problematic as the interactions between two states can vary so its best to simply treat this region as some relevant field or assign it to the type of interaction itself between states. That interaction can be widely varied so its best to allow for all possibilities and simply keep that as an interaction region via the relevant fields. Now here is an important distinction in QFT/QM states are mediated by Operators (they have a minimal of one quanta of action) An operator is a function that maps of one state vector into another a simple expression is Dirac notation \(|\psi\rangle\) is the initial state \(\langle\psi|\) is the final state .\( A\) is some Observable (Minimal 1 quanta of action for any observable) \(\hat{A}\) is some linear operator. So we have some state \(\psi\) the expectation value of A between the initial and final state can be defined as \[\langle\psi|\hat{A}|\psi\rangle\] so for example you have an initial state followed by a final state and for this example we want a time evolution between the initial state and the final state that last expression therefore becomes \[\frac{d}{dt}\langle\psi|\hat{A}|\psi\rangle\] so if we take the time dependent Schrodinger equation https://en.wikipedia.org/wiki/Schrödinger_equation Yes I'm going to skip a few steps but those steps involve defining the different Operators such time evolution, projection, momentum, position Operators \[\frac{d}{dt}\langle\psi|\hat{A}\psi\rangle=\frac{i}{\hbar}\langle \psi|[\hat{H}\hat{A}]\psi\rangle\] \(\hat{H}\) is the Hamilton operator. https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics) the expression above directly applies the quantum uncertainty to the initial and final state via the quantum harmonic action of the quantum field.

Lol interesting role reversal

lets address this as well in greater detail. Expansion of the universe does not affect everything equally. In terms of any gravitationally bound object, expansion does not affect. Nor does it affect particles themselves nor atoms. The local binding forces due to those interactions overpowers what drives expansion. Today the primary driving term is the cosmological constant. In redshift it isn't the photons being stretched. It is the wavelength of a light ray. That wavelength will correspond to a number density of photons received. This is true for all forms of Doppler shift This can be applied in terms of photon flux.... The energy of a single photon is hv or \(\hbar\omega=\frac{h}{2\pi}\omega\) where 'h' is the planck constant \(6.626*10^{-34}\) Joules-sec. One photon is roughly \( 10^{-19}\) joule photon flux \(\phi\) and P as beam power ( in Watts) gives \[\phi=\frac{P}{hv}\] this will give you the photons per sec photon/\(s/m^2 \) for bright sunlight it will be roughly on the order of\( 10^{18}\) photons per second lol if you want to play around here is a calculator for it to give you some feel the numbers and relations involved https://www.pveducation.org/pvcdrom/properties-of-sunlight/photon-flux

Lets look at the difference between an explosion vs an expansion. Yes we can distinguish mathematically and through observation the difference between the two. Here is how. take a triangle This triangle will be any three reference points such as 3 different galaxies. Label each point of the triangle 1,2,3. Between 1 and 2 label \(R_{12}\) between 2 and 3 \(R_{23}\) and between 3 and 1 \(R_{31}\). The R is for the length of each side of the triangle. Now think back to the balloon analogy I posted earlier as the universe expands The length of each R changes equally and the shape of the triangle is preserved with zero changes in any of the triangles angles. so we can describe this mathematically as \[r_{12}(t)=a(t)R_{12}(t_0)\] \[r_{23}(t)=a(t)R_{23}(t_0)\] \[r_{31}(t)=a(t)R_{31}(t_0)\] where \(t_0\) is the time now (today) and a{t} is the scale factor. The scale factor is very easy to understand for example \[a=\frac{R_{then}}{R_{now}}\] radius then of the universe compared to radius now using scale factor gives \[H=\frac{a}{a_{now}}=\frac{0.5}{1}\] where we set \(a_{now}=1\) so when a=0.5 at some previous time and setting a{now} to 1 we can see that the universe was half the volume it is today. That expansion has no inherent direction as shown by the triangle above. The rate of change on all 3 sides remain identical to each other. H is the Hubble parameter. Now with an explosion if you place the point labelled 1 closest to the explosion source then sides \(R_{12}\) and \( R_{31}\) will expand at the same rate but side \(R_{23}\) will not its expansion would be at a different rate than the other two sides. This in turn will cause a change in angles between the three different sides. The first case is a method to prove a homogeneous and isotropic expansion. (homogeneous=no preferred location, Isotropic= no preferred direction). in the explosion case we have a preferred location ( BB source) and a preferred direction galaxy movement radiating outward from the source. ( unfortunately if I tried to include an image the latex above will get messed up its some forum software glitch ). However the first case above is described as the Cosmological Principle. this link isn't bad as it includes another piece of evidence (Olber's paradox) https://pages.uoregon.edu/jschombe/cosmo/lectures/lec05.html Now as the universe expands its temperature reduces this is in accordance with the ideal gas law https://en.wikipedia.org/wiki/Ideal_gas_law as a volume of gas increases the density and temperature decreases. Now an interesting relation arises above with this and the scale factor. If you take the inverse of the scale factor you will get the CMB temperature at any value of the scale factor compared to the temperature today. )2.73 Kelvin today. This isn't accidental but a consequence of the ideal gas laws and how matter, radiation and Lambda (Dark energy aka cosmological constant) relate to the changes in volume. Let stop there and see if you understand the above as its extremely important to any other equations involved.

Th If your referring the portion of the quote that you highlighted and underlined. "Any system or state will typically have a boundary condition if it's finite. There is no boundary condition of an infinite system or state however when one renormalizes we remove infinite quantities for the finite portion as every infinite quantity or set of values etc has a finite portion. " Lets push your understanding of boundary conditions can oft also be referred to as a constraint. Now as you likely do understand is that the language of physics is mathematics so lets mathematically describe how a boundary condition works with regards to the quote. ( without overwhelming you with mathematics lol) Lets take the the x axis for simplicity. Now this set has an infinite range of values however we can limit this set to have a minimum or maximum range of values. Whatever the reason for the constraint or boundary we now have a finite set. The set is made finite by the boundary condition of the set. That is a straightforward example of an infinite set showing a finite portion and how boundary condition applies to that set. Now that's a very simple example the set can be a group under group theory or some formula with a limited range being finite. On graphs the Neumann and Dirichlet boundary conditions are commonly used. https://en.wikipedia.org/wiki/Dirichlet_boundary_condition https://en.wikipedia.org/wiki/Neumann_boundary_condition from those links they also mention other types of boundary conditions. In QFT they use the IR (infrared and Ultraviolet ) boundary conditions Now it gets worse because some boundary conditions can apply to reflection or region of some interaction. say for example your describing a wave bouncing off a mirror. You have a limit on the range of values (the surface of the mirror) but the interaction with the mirror can alter the waveform direction etc. Thats a rough and dirty simplified descriptive mathematically it is far moer rigidly defined. Good examples where boundary conditions apply is fluid hydrodynamics container walls, regions where you have an average density different than another, or different properties such as temperature than another region With regards to your OP the gap

No I'm not a professor but I do help teach at our local university. I have a Masters in Cosmology and a Bachelors in particle physics. Swansont has a Ph.D. Early universe processes are my specialty focus from BB to CMB primarily. The only reason I come to forums is to help others like yourself learn so it's pleasant to have someone willing to learn.

Lol yeah quite a bit of a leaning curve for some of those articles. In regards to waves you have two distinct types waveform which is physical ie measurable where the amplitude also relates to the particle number density. Those links in the training section will detail how to determine the number density via the blackbody temperature of the CMB. Though the same formulas are also used under QFT the format is different. Though equivalent with regards to say the EM field as one example. The other case is wavefunctions which is a probability function and the amplitude peak is the highest probability. (This also has a probability current but don't worry about that right now). So in regards to light, the intensity or energy density can be used to calculate the number density of photons. So it's better to think of redshift as a decrease in the number density of photons due to the reduced wavelength rather than mediator wavefunctions being affected. After work I will step you through the basics of Cosmology in terms of the BB (rapid expansion of spacetime not an explosion) different dynamics. The global geometry of spacetime averages as close to flat which I will detail further this evening. Any system or state will typically have a boundary condition if it's finite. There is no boundary condition of an infinite system or state however when one renormalizes we remove infinite quantities for the finite portion as every infinite quantity or set of values etc has a finite portion. http://cosmology101.wikidot.com/redshift-and-expansion http://cosmology101.wikidot.com/universe-geometry http://cosmology101.wikidot.com/geometry-flrw-metric/ These articles I wrote will help.

Thanks nice catch on a recent link +1

Gee didn't know I was bilingual lmao. You can relax on this particular topic lol. Though I'm still studying the paper. I do agree with Swansont's assessment.

The unfortunate part is that the factors are not just a case of funding and curriculum. For example when we went to school we were taught some useful skills that simply are not taught today. One example being finding the square root of a large number say for example 6 digits long without resorting to a calculator using a sequence of division by two. I've also noticed that many recent high school graduates don't even know how to add, subtract, multiply and divide fractions. Those same ppl quickly understood how once I spent a measly 15 to 20 minutes showing them. So had nothing to do with their learning ability. They weren't shown before. They relied on the calculator

In so far as emergent spacetimes I would say you would need a considerable amount of additional details to the article to be useful for showing its applicability to determining an emergent spacetime particularly in regards to incorporation to QM/QFT. I also feel that your article would be far better off if you included the invariant vs variant quantities in regards to causation rather than the verbal descriptive attempts with regards to your IFRs. The other recommendation is to use examples that at least have some viability. You have seen the commentary on the examples you provided by others. Poor examples that have no viability will be counter productive to any further interest in the article or hypothesis. Those are some immediate suggestions granted more work on finding indirect means of testability would go along ways as well. For the record there were numerous points where poor descriptives and examples were extremely distracting from the articles goal. Several of those were already mentioned in this thread. Think of it this way. If you, yourself was reading some paper that is poorly described and included examples with zero viability or has statements that doesn't conform with known physics Do you continue reading it ? Now in the interest of article improvement in one regard I can offer some advise with regards to the causal vs acausal argument involving atoms. Now Swansont may very well have a better treatment for dealing with half life decay but a method I'm familiar with is to treat the atom as a single state via a summation of all amplitudes using the Caasimer trick and then applying Breit Wigner distributions. This will give a reasonable decay rate for neutral atoms as well as ionized atoms. Obviously the formulas will vary between the two cases. Breit Wigner is typically in the CM frame but it does have the Lorentz invariance corrections. However as that isn't the focus of the article whether or not you choose to include those details is up to you. In terms of applying causality regardless of any specific relativity theory. There are essential equations that all physics theories use. Regardless of the theory work with those in particular those relating to the equations of motion for causation. Good example is time ordering of events viewed from different observers (part of the proof for timelike observers as opposed to spacelike). There's nothing incorrect about applying those lessons without involving SR directly.

Yes thanks lol must have gotten distracted. Fermi-Dirac is often used for low density gas in particular the Fermi level (Fermi-energy) however it's not limited to a low density gas. Other factors included being Fermi temperature and Fermi velocity. See here for details https://en.m.wikipedia.org/wiki/Fermi_energy