Mordred

The above is completely wrong. The first paragraph is a common misconception of not recognizing the reference frame relations. The second part isnt inapplicable in that gravity doesn't behave in the same manner as the EM field ie the coulomb force isn't involved.

The processes of transition whatever you mean by that has nothing to do with lepton numbers. The lepton numbers go as follows non lepton =0. Positive lepton +1, antiparticle lepton -1. For any particle decay the lepton number on the right must equal the lepton number on the left of the equal sign. (Conservation of lepton law) so let's look at your claim. 6 photons =1 electron. (6×0) does not equal 1. Equals violation.

I have a theory that addresses all the mass terms and principle quantum numbers of all elementary particles. The lepton mass mixing angles are described by the PMNS matrix. That incorporates the Higgs field and Yukawa couplings. The CKMS matrix with the above matrix handles all the elementary particles. They do so without the violations I mentioned that you need to mathematically prove you do not. Not simply assert. If you like I will show you the difference between how bosons behave compared to fermions with regards to the Pauli exclusion principle. By the way elementary particles are not comprised of other particles. They would not be elementary if they did. The electron has no internal structure it is not composed of other particles.

I believe you meant inertia mass not inert mass in the above. You might want to kick yourself Strange as to gravitational mass. You are right GR does handle gravitational mass but there is a straightforward explanation. GR applies the principle of equivalence the gravitational mass is the same as the inertial mass. [math] m_i=m_g [/math] this is oft described by the Einstein elevator. The four vectors of GR however will preserve the invariant (rest mass)

Nope your not being a pain in pointing those out. The four vectors differ from Euclidean vectors. The magnitude of the four vector invariance is preserved through the Lorentz transformations. I should have been a bit more clear on that. I've been trying to figure out how to introduce one forms and why they are used in tensors. However how to introduce them in a simple manner is a bit daunting. Particularly since you need the components of a vector and vector basis.

What happens when you square a negative number ? Then consider energy density is always positive. In essence all particles has positive energy. Secondly all particles will have positive mass. The positive norm also applies to particle states hence squaring the wavefunction [math]|\psi^2\rangle [/math] for its probability amplitudes and density functions.

Informative side note on local diffeomorphism in GR which is diffeomorphic invariant through its use of one forms and a vector. (This also results in the invariance under coordinate change) vectors are not invariant under coordinate change however one forms are. A one form being a covector. The principle of covariance is preserved through the local diffeomorphism of the [math]g_{\mu\nu}[/math] metric by the push forward of the Minkowskii tensor [math]\eta[/math] with the Poincare group SO(3.1) being the ISO group for the Minkowskii tensor. ISO(n). The above will also apply to the killing vectors of causality connected fields. (Localization)

Yes it is a mass term. Any mass term must satisfy that definition under kinematics and the laws of inertia. The total mass (both types) is given by the energy momentum equation. E=mc^2 only describes the invariant mass of a particle. [math]E^2=\overbrace{(pc)^2}^{kinetic-energy}+\overbrace{(m_0c^2)^2)}^{potential-energy}[/math] It is the momentum term in the above formula that allows photons to provide thrust to a solar sail. Little trivia side note the reason to square the energy term is to denote positive norm. Ie no negative energy allowed.

Well there is the problem it is the particle spin that is involved in the Pauli exclusion. It is also the spin that invalidates your theory with regards to the conservation of spin. Other violations include conservation of charge, conservation of lepton number. If I go through the complete conservation laws of particle physics it's likely your violating every one of them. To put it bluntly your proposal has zero chance of being correct for the reasons myself and others have identified. For example bosons due to their quantum number symmetry relations can be stacked to an infinite particle number density in the same space and will not suddenly form a particle with anti symmetric quantum number wavefunctions as is the case with fermions which comprise the matter particles. (That would be a conservation violation. Accordingly due to those assymetric wavefunction relations fermions of the same wavefunction state cannot reside in the same localized space. Hence matter particles take up space which the behavior of a matter particle. While bosons do not. Lastly your not applying any of the correct formulas to describe the particle states. This detail is required to define all particle interactions given by the Feymann path integrals. Your model will not work with those integrals either... The other problem is your model cannot describe the family generations of the Leptons. So will not work under electroweak symmetry breaking of the family generations.

That confusion is one of the reasons why the current terminology is the invariant mass for rest mass and variant mass for the relativistic mass. I wouldn't describe the relativistic mass as an energy term without describing the energy type. It's better to use the kinetic energy term for its association to the momentum term. Photons having no invariant mass tells us that it does not couple with its fields of interaction. It is the coupling strength that gives rise to the invariant/rest mass. This is the potential energy terms. If the photon did have invariant mass then the range of the EM force would not be infinite. That confusion is one of the reasons why the current terminology is the invariant mass for rest mass and variant mass for the relativistic mass.

I like your reference four paper, there is several Langrangians in that paper I will latex later on to have a handy copy of them. I also like what you did with the overbrace and underbrace. I don't see any problems thus far

I don't particularly have a problem with that. Use of three observers with regards to the twin paradox has been presented before. It's nothing particularly new. However to make the OPS scenario complete he should become familiar and apply the transformations. Several of his later posts indicated to me that certain aspects of the Minkowskii symmetry relations with regards to inertial frames vs non inertial frames needed clarification. Particularly since curved spacetime can lead to some surprising results. Though for this thread I've been assuming his solution is restricted to the Minkowskii or at most the weak field limit.

A simple way to look at dimensions under physics is any independent mathematical object such as a variable or group etc. With spacetime any coordinate can vary in value without changing any other coordinate value. If the group etc has an infinite set then you can compactify that dimension as any infinite set contains finite a finite set.

I don't think you realize I replied to his later post which I quoted in my last post. If no acceleration is involved then one can simply apply the equivalence principle. However where would the paradox arise if all observers consider themself as being in an inertial frame as opposed to at rest as per SR. In GR all frames are inertial to begin with.

Did you not read his comment concerning changing inertial reference frames ? That isn't describing a commoving inertial frame. Let's stick to how inertial frames are applied compared to non inertial frames for a turnaround twin. https://en.m.wikipedia.org/wiki/Inertial_frame_of_reference In particular in regards to this post which I was replying to. Now you tell me how a commoving inertial frame handles the turnaround to preserve an inertial frame. Particularly since commoving inertial frames is a technique to specifically handle acceleration. However let's deal with a further issue. There are two quantities called “acceleration”: Three-acceleration and four-acceleration. Three acceleration is defined as the derivative of the coordinate velocity with respect to coordinate time. It is a relative acceleration which can be transformed away. Four-acceleration is defined as the derivative of the four-velocity with respect to proper time. It is an absolute acceleration which cannot be transformed away. Four-acceleration is the acceleration of a particle as measured in an instantaneous inertial rest frame of the particle. Particles falling freely have vanishing four-acceleration. A non-vanishing four-acceleration is due to non-gravitational forces. Centrifugal acceleration has non vanishing four acceleration.

If you have a change in inertial frame then you likely underwent an acceleration. For example the mathematics I posted previously shows that during acceleration the travelling twin is in a non inertial reference frame. When the twin stops accelerating then he is in a new inertial frame than that previous to accelerate. Forces are involved with acceleration in accordance to the laws of inertia ie f=ma

I would suggest you look into the principle of least action and how it applies to the geodesics equation. I would also suggest you look at the Principle of equivalence. [math]m_i=m_g[/math]

! Moderator Note As this is a Speculative article I will move this thread to our Speculation forum. Please take the time to review the Speculation rules in the pinned threads at the top of page one on that forum. Secondary the forum rules require that as much effort as possible be taken to post the material here. So please post relevant sections of your document for discussion here. By the way welcome aboard. Now that is out of the way. I will read this in more detail later on. However one immediate question comes to mind. How do you plan to account for the electron spin 1/2 fermionic statistics and polarity states as per the Pauli exclusion principle with 6 spin 1 bosonic photons ? Each polarity state has identifiable transverse and longitudinal polarity components. With bosons the wavefunctions are symmetric however with electrons you will assymetric wavefunctions as per fermions.

Well truth of the matter is it would be extremely difficult to simplify how tails result from nonlinear aspects of curved spacetime. I've studied a few examples in the past but the mathematics are not trivial. Even if I were to post those mathematics without bring familiar with the quadrupole moments of linearized equations a reader wouldn't understand the nonlinear equations. A good way to understand tails is to think of backscatterring with curved spacetime. The backscatterring causes delays to reach the detector. It's a simplification to describe monopole - monopole - quadrupole interaction moments which isn't the same as interaction with a medium. The interaction is with spacetime itself but only the non linearity conditions such as curved spacetime. Which is different than photons interacting with a medium (though fields can give medium like relations ) it's best to never think of spacetime as a medium. Probably the most accurate analogy I can think of is to use the example of signal propogation delay in electrical signals. If you take a signal wire and lay it parallel to a power line the delay is negligible from the cross talk between the signal wire and power wire. However if you were to lay the signal wire perpendicular to the power wire you can induce a propogator delay due to the EM field crosstalk between the two wire field lines. The tails is very similar to this analogy it is the non linear cross interactions of the GW waves with the local nonlinear spacetime curvature that causes the signal propogation delay of the GW wave. This analogy doesn't require any association with a medium as your simply involving field interactions which is the cases when dealing with spacetime. (It also provides the right direction to apply the relevant mathematics). Those mathematics will involve polarity states Ie a quadrupole has 4 polarity states while the EM field is Dipolar with two polarity states. These states are needed to model tails. (Hence part of the complexity) Now onto the massless graviton. If the the graviton has mass then gravity would not have infinite range. Much like the photon as the propogator for the EM field. The effective range of a force is a function of the mass term of the mediator boson. For example the mass term of the W and Z bosons limit the range of the weak force. In order for a force to have infinite range it's mediator boson must be massless. [latex] ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/latex] [latex]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/latex] Now the above is an example of linearized spacetime. We haven't got any curvature terms so you wouldn't get tails from the above. The above is also how GW waves are derived. Those two above equations are where the polarizations [math]h_+[/math] and [math]h_x[/math] are derived from. However let's look at a rotating Neutron star (we will get nonlinear terms from the Sagnac effect.) Spacetime in a rotating frame would look like this. [latex]g_{\mu\nu}=\begin{pmatrix}1-\frac{w^2r^2}{c^2}&0&\frac{wr^2}{c^2}&0\\0&1&0&0\\\frac{w^2r^2}{c^2}&0&r^2&0\\0&0&0&1\end{pmatrix}[/latex] So in this spacetime the relation between worldtime and proper time (tau for proper) [math]d\tau=\sqrt{1-\frac{w^2r^2}{c^2}dt}[/math] in essence time goes slower in a rotating frame. This situation can lead to tails. Hope that helps

Well that's good as spacetime isn't some fabric like substance lol. I always find it most accurate to think of it as the freefall paths that bend. Example the worldlines

I really don't understand the issue of ensuring experimental validation as a step. Particularly when you wish to ensure accuracy. You want to quarantee that the 4 years you mentioned is as accurate as possible. The worldline could be 3.5 years but the clock error could give a result of 4 years.

It's a validation that the clocks give consistent time with other. In order to eliminate the possibility one clock runs slower than the other for reasons other than that due to relativity.

Anyways I will finish the proof behind the hyperbolic angle tonight for completeness. The reason I wanted the OP to study the symmetry vs antisymmetric relations is as follows. By changing the observer emitter from twin A to B B to A respectively we have mathematically defined The symmetric and identical relations [math]\acute{\tau}=\gamma(\tau-\frac{vx}{c^2})[/math] [math]\acute{x}=\gamma (x-vt)[/math] Hence we cannot from those equations show a priveleged frame nor prove which twin is the inertial twin to identify which twin will age slower. During the acceleration the travelling twin will be in a non inertial frame flowing the spacetime coordinates of the hyperbolic angle which is also antisymmetric. [math]x2-ct^2=\frac{c^4}{g^2}[/math] The above is the result of change from v+ to v-. If the turnaround is sufficiently long enough to model as a rotationary body however brief then we can incorporate the Sagnac effect which I will show that tensor tonight. In essence we can mathematically show where the aging becomes antisymmetric.

I've thought about how to go about this so I decided to take a few posts to the four momentum form. (I will need that for the four acceleration) First let's get the symmetry relations behind the (supposed paradox). We will obviously be applying the Lorentz transformations [math]\acute{\tau}=\gamma(\tau-\frac{vx}{c^2})[/math] [math]\acute{x}=\gamma (x-vt)[/math] Y and Z coordinates are equivalent respectively. [math] \gamma=(\sqrt{1-\frac{v^2}{c^2}})[/math] The inverse of each is simply switching the observer frame ie [math]x= \gamma(\acute{x}-vt)[/math] Now you can see under math the symmetry between frames. This being under constant velocity. Using coordinates [math]x^\mu={x^o,x^1,x^2,x^3}={ct,x,y,z}[/math] Now let's see how acceleration gets involved under the Minkowskii metric. We will need the four momentum and four acceleration. Four velocity [math]\mu^\mu=\frac{dx^\mu}{d\tau}=(c\frac{dt}{d\gamma},\frac{dx}{d\gamma},\frac{dy}{d\gamma},\frac{d}{dz\gamma})[/math] The invariant distance or seperation between two events in Cartesian coordinates. [math]ds^2=-c^2dt^2+dx^2+dy^2+dz^2[/math] [math]ds^2=\eta_{\mu\nu}dx^\mu dx^\nu[/math] [math]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/math] for the Minkowskii tensor. Proper time defined as [math]ds^2=-c^2dt^2[/math] Four acceleration [math]a^\mu=\dot{\mu}^{\mu}[/math] [math]\eta_{\mu\nu}a^\mu\mu^\nu=a^\mu\mu_\nu=0[/math] Now consider a ship in x direction with constant acceleration g the velocity and acceleration four vectors are [math]c\frac{dt}{d\tau}=\mu^0, \frac{dx^1}{d\tau}=\mu^1[/math] [math]\frac{d\mu^0}{d\tau}=a^0,\frac{d\mu^1}{d\tau}=a^1[/math] [math]-(\mu^0)^2+(\mu^1)^2=-c^2[/math] [math]a^\mu a_\mu=-(a^0)^2+(a^1)^2=g^2[/math] As it's getting late will finish this tomorrow to arrive at the hyperbolic turnaround [math]x2-ct^2=\frac{c^4}{g^2}[/math]

I will post the mathematics when I get time tonight though I will not complete the scenario for the third reference. It should be trivial enough for the OP to implement.