Mordred

Other than confirming the stress energy momentum tensor is valid under the Einstein Field equations which essentially dictates the curvature terms that's the only insight. Once one understands how the stress energy momentum tensor works it becomes rather obvious.

Propogator or S Channel. A one loop integral will have one progogator inner loop with two incoming and two outgoing external lines typically however you can have further interactions on a particular leg.. Here is an example of a loop integral \[\vec{v}_e+p\longrightarrow n+e^+\] \[\array{ n_e \searrow&&\nearrow n \\&\leadsto &\\p \nearrow && \searrow e^2}\] The wavy line in the center to the progogator internal loop

Well described Migl +1

Well Joigus did give a couple of examples of self coupling for gravity. However gravity also can generate its own gravity via the self couplings Let's use gravity waves. \[g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}\] Now the spacetime locally to the gravitational wave is Minkowskii (local not global). The gravity wave being transverse traceless quadrupolar wave has two key polarizations. These fall under the perturbation tensor \(h+\) and \(h\times\) for the plus and cross poalarizations. The remaining polarizations are reducable. (Traceless) They increase the strength of gravity briefly where the perturbation wave is. This is one example gravity requires using a tensor that linearizes a non linear curve. It does so through curvilinear coordinates and via covariant and contravariant vectors and spinars under a tensor field. The requirement of using tensors for gravity is precisely due to the non linear nature of spacetime curvature. Another way to see this is via the stress energy momentum tensor.

As Studiot noted earlier your idea had merit what was lacking was the correct terminology and application. Unlike many we see posting personal hypothesis you show a willingness to learn and adapt so for that were more than willing to work with you to improve your knowledge +1

Lol your welcome

Good article I enjoyed reading it as well though I've always enjoyed anything written by Sean Carroll. +1. In regards to particles being field excitations we have a pinned thread covering @StringJunky has a link to an excellent Sean Caroll In this thread in his first post of the thread it's an excellent lecture you may enjoy. PS you will note the lecture video will coincide with the article posted by Studiot.

My wife would kill me if I got more textbooks, have a bunch in storage already. Otherwise I would jump at the opportunity

One can readily treat deceleration as an acceleration depending on the observer. Yes that is correct. Velocity is the speed plus the direction so it is represented by a vector. This is an important distinction from speed which is a scalar quantity (magnitude only). Momentum is the velocity plus the mass. This will become important when determining the amount of force delivered when an object strikes another object.

I understand that Minkoskii via SR isn't important but where it does become relevant is on how your defining the IFR particularly for causation. Now when I saw the first equation my question that came to mind is what is it about A(t) that is operating on the state that determines the decay rate and try though I might except out of a scattering decay that ionizes the atom I could not think of any possibility. Particularly since a neutral atom is also subjective to radioactive decay. Now its also apparent that your causation doesn't involve the usage of determinism as opposed to the relevant probabilities Am I correct on the last Keep in mind it isn't so much not understanding what's involved but challenging the article to see how well you can answer any issues and points raised. As well as pointing out portions that don't make alot of sense or lends to confusion.

What KJW is referring to is the symmetry under change in sign for different observers. One observer will see a deceleration while another observer at the opposite end of the object being measured will see acceleration. In essence deceleration is symmetric to acceleration Constant velocity is extremely important to master. Study Newtons three laws of inertia. https://en.m.wikipedia.org/wiki/Newton's_laws_of_motion This should help with the lecture your learning. Acceleration cam be in two forms change in velocity or change in direction. This is also important to recognize.

If only renormalization of gravity were that easy. It would have been accomplished long ago. Here is the Hoof.t paper showing one loop divergence renormalization where he further states in the conclusion that it does not renormalize the second order terms. https://bpb-us-e2.wpmucdn.com/websites.umass.edu/dist/e/23826/files/2014/11/thooft-and-veltamn.pdf This might give you some idea of the complexity. For the record there is different types of normalization, Position normalization as well as momentum normalization as two other examples. The equation you have is the position renormalization. The link you got that equation from also has the momentum normalization relation.

As your new to this forum latex on this site uses \.[latex].\ simply remove the periods I used to prevent activation. So previous to the word latex \[ for inline latex \.( latex\.) By the way the reason I was asking on Galilean as opposed to SR/GR is nowhere in your paper do I see any reference to proper time I only see coordinate time. I also don't see any second order time derivatives but we can ignore acceleration for now. Then we have this statement "Some events cannot affect other events, since they are separated by a space-like interval. In quantum physics, this is expressed as the absence of correlation of measurement results at points separated by a space-like interval." true on spacelike separation but I am curious on what your understanding is on a correlation function which doesn't require any causation to begin with

Yes I see problems that are not being addressed so is everyone else seeing the same problems. Let me know when you distinguish between an Observer and a reference frame or for that matter a global metric from a local metric in terms of causality. Ask yourself the following under SR/GR light-cones which of the following does causality apply. Timelike events Spacetime events Null events Past/present/future. Yes I recognize your trying to avoid relativity in particular SR but ignoring invariant quantities, the speed limit of information exchange to different observers which your entire paper mentions while not applying any of the transformation rules (either Galilean or Lorentz ) makes no sense whatsoever. Well I'm simply going to chalk this up to ignore all verbal descriptives and apply strictly the mathematics. lets start with your math statement \[\psi(t+dt)=A\psi(t)\] you state A is some operator, \(\psi) being a state. Which you describe in the following statement "includes the set of values that are necessary to describe the system. For example, to describe a system of objects based on Newton's law of universal gravitation, if we consider objects as material points, the masses, velocities and coordinates of objects are sufficient to describe the state. Accordingly, the value should consist of mass, velocity vector and object coordinates. According to the principle of causality, events without a cause do not exist. Someone might think that, for example, the radioactive decay of the nucleus of an atom has no cause. Let's look at equation 1. The radioactive decay of a nucleus is obviously described by this equation. Therefore, it also corresponds to the principle of causality. The principle of causality does not mean determinism. There are many discussions on this issue. Note that if there were at least one phenomenon that violates the principle of causality, then this would mean a refutation of this principle." so How does the equation one describe radioactive decay of an atom ? Simply by being a state ? what state or system is causing the state above to change ? to give radioactive decay eliminating any uncertainty or probability function in determining its rate of decay ? answer this with the following definition of causation. Particulalry since its been argued radioactive decay is acausal and not causal yet you claim otherwise above with the following statement " According to the principle of causality, events without a cause do not exist." since when ? where is the reference that makes this declaration ? Other than your own Causality is the relationship between causes and effects.[1][2] While causality is also a topic studied from the perspectives of philosophy and physics, it is operationalized so that causes of an event must be in the past light cone of the event and ultimately reducible to fundamental interactions. Similarly, a cause cannot have an effect outside its future light cone. https://en.wikipedia.org/wiki/Causality_(physics)

How ? You haven't included time dependency that I can determine. No where have I seen any reference to the speed limit of information exchange. Nor have you at any point specified a coordinate system. Is your examination strictly Cartesisn with no speed limit of information exchange where time is absolute or are you at some point applying causality in accordance to the lightcones of Minkowskii metric ? In your article you do not have either the Galilean transformations nor the SR transformations so how are you determining causality in accordance to anything applying relativity ?

I noted you haven't addressed my questions yet

Ok try not to think of particles as little solid balls. Solid is an illusion generated by our senses. Under QFT all particles are field excitations so it's not little balls splitting but rather constructive and destructive interference of a waveform. A waveform can also be split off into seperate waveforms such as a monochromatic light beam splitter performing parametric down conversion of a beam into two separate beams each with their own photons. Conservation laws still apply so the two beams will be half each of the original beams waveform. For quarks you have 3 generations the names are simply placeholders denoting the fractional charges. The names aren't particularly important except as a label. It's the particle quantum properties that's relevant not the name. Details here https://en.m.wikipedia.org/wiki/Quark

It may seem confusing but one has to keep in mind these a brief loose descriptions. The real detail is the mathematics. Those mathematics are what's needed to explain experimental results and the truth is the experimental results involve scattering experiments. Such as produced by particle accelerators or other detectors. In essence there are very practical reasons the formulas are designed the way that they are. For example those formulas include probability functions involving scatterings and angles to specific observers.

I find it remarkable that not once has the speed limit of information exchange hasn't once been included in regards to causality. why ? Perhaps you should include relativity as its obviously not being applied correctly if at all. You should also learn what is meant by invariant vs variant quantities. As others have already noted. Further more there is causality between an event and a non inertial frame of reference. So stating that causality only occurs with inertial reference frames is false. Take for example all Observers regardless of being inertial or non inertial will record the same velocity for massless particles that being c. How does that work under your hypothesis ? there is obvious causation when you take a measurement. Information exchange counts Nor does causation even require observers. Causation simply requires sufficient time for exchange between two events. This can occur even without any observers. Primary example the BB and all processes prior to any lifeforms that could observe or make measurements. So how are you defining an observer ? Under QM its the act of measurement which includes interference obvious causation in that regard. Or perhaps your only discussing local causality defined by c to an observer in regards to the Observers past, present and future light-cones. None of which has been mentioned yet. One could readily argue that everything in our Observable universe has a past causal connection. That is what defines our Observable universe to begin with. However I assume you wish to keep this under SR in which case all time-like separated events are in causal connection while space-like separated events are not. All Observers will agree on the ordering of events to all time-like separated Observers. For observers that are accelerating one can preserve time-like separation via the relevant proper time transformations. a simple treatment using instantaneous velocities in time ordering \[\tau=\int_{t1}^{t2}\frac{dt}{\gamma(t)}\] for varying \(\gamma\). Now without downloading your paper I bet dollars to donuts you don't have any spacetime treatment and is strictly looking at Euclidean Geometry instead of Minkowskii ? Ie your not applying the Lorentz transforms \[\acute{(ct)}=\gamma(ct)-\beta x\] \[\acute{(x)}=\gamma(x-\beta (ct))\] am I correct in that ?

Good question lets try a very simplistic example. take a lake and the air above it. The boundary is the surface of the lake. So in this instance the EM field is what holds atoms together to make up solids, liquids and gases. So what makes up the boundary condition is the water molecules and the air molecules at the point of intersection between the two. In this case what holds the boundary condition is the EM field. that last example should answer that question and no the Higgs field only gives mass to certain particles. W,Z boson, leptons and quarks it only accounts for 1 % the mass of protons and neutrons. The remainder of the mass is the strong force and EM force. These are handled via the Dirac, Yukawa and Higgs couplings. the quarks that make up the protons and neutrons are mediated by quarks. To bind neutrons to protons for the atom requires the photon for the EM mediator. part of the mass term for quarks being the Higgs field the Higgs boson is the mediator. So yes you can have several mediator particles involved with particles that interact with multiple fields. Don't treat time as anything other than the property describing rate of change or duration. Too often ppl want to make time into some substance or allow it to exist on its own. It doesn't its a property of systems, states, objects etc. Much like color doesn't exist on its own. It too is a property. Other physical properties include mass and energy. They too do not exist on their own but are properties. here is a short list of physical properties. https://en.wikipedia.org/wiki/Physical_property as noted in that link a physical property must be measurable.

Lol 😆 yes dealing with the mathematics of quantum fields is evil 😈. I also noted you found where I got my callsign image from lol. Time is best understood as the property describing rate of change not a self existing entity. Ok if you want a force between a table and paper or chair you couldn't use the strong force. That force is within protons and neutrons etc. For everyday objects they are held together by the EM force. So make two systems or states. State A is the table State B is the paper Each State is describable by a field ( condensed matter lattice network for an official treatment) however let's keep it simple an EM field for each. Each State has a boundary condition (edges) Now there is interactions between State Table and state paper ( two EM fields interacting.) These interactions are mediated by the EM mediator the photon. Example the force between chair and paper where applicable (repulsion/attraction). It is much the same with quantum states or quantum particle states. Each particle is described as a state via wavefunctions. Those states also have boundary conditions determined by their interaction cross sections. (Your not ready for bare mass vs mass due to field couplings just yet.) The states interact with one another via mediator bosons such as the photon for the EM field, gluons for the strong force, W and Z bosons for the weak force. For gravity it's possibly the graviton we haven't detected any yet to confirm. So I recommend you switch your terminology to states with the edges being the boundary conditions. Hint when answering one of Studiots questions involving least energy. Apply that to each State. Studiot has been stepping you into a very specific interaction between two states (with two different energy potentials).

More an indication that we do not have a means to test for a limit for gravity aka curvature.

A field is renormalized when you have eliminated all infinities. For gravity we have not found an effective cutoff for the high energy end (UV cutoff) IR cutoff is the low energy end. Example g=0 is an effective IR cutoff.

No it doesn't quarks make up all hadrons which includes mesons, tetraquarks, protons and neutrons https://en.m.wikipedia.org/wiki/Hadron

Mu Must be distracted at work lmao. Those diodes have been around over 15 years when I first heard about them. If memory serves correct. Given the silly mistakes above lmao I wouldn't put too much faith in that timeline.