Jump to content

Mordred

Resident Experts
  • Content Count

    7463
  • Joined

  • Last visited

  • Days Won

    20

Everything posted by Mordred

  1. 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
  2. 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]
  3. The EM field itself being used is Dipolar. Magnetic Monopoles as MigL noted would change our physics understanding. This would require far greater evidence than a YouTube video. Magnetic Monopoles are a hypothesized quanta of magnetic charge with a mass term roughly [math]10^16 [/math] GeV/c^2. If they did exist they would exist prior to electroweak symmetry breaking. Our current particle accelerators do not come close to the energy requirements to produce one. Hence I am 100 percent certain that no arrangement of magnetics can produce one.
  4. ! 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.
  5. I can state with 100 percent certainty that isn't a monopole magnet.
  6. 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
  7. 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
  8. 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.
  9. 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.
  10. 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.
  11. 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]
  12. 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.
  13. Sure now apply the turnaround acceleration. However your missing the point behind the request for the OP to look directly at the formulas. It isn't a shut up and calculate reason but to have the OP look directly at the symmetry relations between emitter and observer reference frames Axiom there is no frame preference.
  14. You should do this with the relevant formulas. A simple description is insufficient. Once you sit down with the formulas you would then realize the twin paradox doesn't depend on the measurement device but upon the symmetry relations between the two events and the solution involves the stages where that symmetry is removed. Ie the acceleration stages (rapidity)
  15. No symmetry breaking isn't a fancy word for a paradox. In actuality symmetry is a fundamental aspect in particle physics. Bosons are symmetric while fermions aren't for one example. The Higgs field doesn't combine all of quantum theory in point of detail it's only 2 of the 18 coupling constants. There is far more involved in QFT that has nothing to do with the Higgs field. If you understood anything about symmetry in physics you would never think of it a some form of paradox (spacetime or not) Let's start with am easy example. The inner product of two vectors used in the Minkowskii (spacetime metric) are symmetric and orthogonal [math]\mu\cdot\nu=\nu\cdot\mu [/math] Now where is the spacetime paradox in that statement which is fundamental to the SR (Minkowskii metric) ? Very little in this makes sense however the one detail that is correct is that wave particle duality always exists and must be considered. However I will note that the pointlike property that we associate as the localized particle is defined by the particles Compton or DeBroglie wavelength. Where do you think the meaning of " a particle is a field excitation" comes about ?
  16. The fundamental mistake your making is assuming fundamental particles are made up of other particles. It's a common mistake and error, a large part of that error is thinking particles are corpuscular solids. The SM particles are field excitations. Lets take an example to prove the error on thinking. Take two protons and accelerate them to near c, then have a scattering collision. Now ask yourself the following question, if the rest mass of both protons is 938 MeV, how did this collision form a Higgs boson or in other reactions a top quark ? The Higgs boson isn't part of the proton as it is comprised of quarks and gluons, Secondly the mass of the Higgs boson far exceeds the rest mass of the two protons. Thinking that your colliding solid balls of matter particles and ending up with pieces of different types of matter particles is incorrect. What you really need is their wavefunctions and how those wavefunctions interfere either in constructive or destructive interference for both elastic and inelastic collisions of the particles wavefunctions. While your at it consider how it's possible for one type of particle and not others are capable of passing through solid matter while other particles do not. This can also occur with particles that would either get absorbed or reflected by that barrier of the same type. Ie quantum tunnelling. A little side note. The only way I have found to understand thermal equilibrium of particle states is by throwing away any matter like view point. Toss any corpuscular visualizations away and deal strictly through the QFT wavefunctions. (Also done in String theory) In thermal equilibrium different particle species cannot be distinguished from one another their Compton or DeBroglie wavelength becomes identical etc. (Ie they are symmetric to each other in any measurable quantity. (Hint symmetry breaking occurs as the particle species drop out of equilibrium) Bose Einstein or Fermi condensate is the same process. In this state all particles lose their identity from another. Hard to explain those with a little billiard ball point of view.
  17. A string is a vibration mode of a wavefunction. A string in and of itself isn't a particle. Rather each particle will have its own vibration mode.
  18. Quite honestly using mass terms derived by the mass of other particles doesn't determine why the Higgs field or Higgs boson has the coupling constants that it does. Comparing the mass term cross sections allows one to calculate the mass of the Higgs boson. However does nothing to determine why the VeV for example is 246 Gev. Secondly the Higgs mechanism is not a step toward unifying gravity with QM. The step to do that requires a theory with zero renormalization divergences. The Higgs field will not solve that issue but provides some clues as to how some of the mass terms come about.
  19. No they are charge neutral bosons which can be it's own antiparticle another is the Z boson. Higgs boson as well.
  20. The Higgs boson mass can be derived through those mixing angles. There is advantages to using normalized units hence the mixing angles to establish the correlation. The factor that the above also accounts for is helicity of particles under the right hand rule. Example photon has two polarity states. As well as being its own antiparticle.
  21. The above isn't quite accurate what your referring to is the numerous indpendent unitary triangles of the CKM and PMNS mass mixing matrixes https://en.m.wikipedia.org/wiki/Cabibbo–Kobayashi–Maskawa_matrix There are six independent triangles in the CKM. Through those mixing we also correlate particle generations. Yes you get a correlation to the Higgs mass value by the bosons you mentioned however I needed to show you what is meant by triangle. Your descriptive above lacked that clarity for other readers./posters. Ie needs that detail so everyone recognizes your describing a unitary triangle.
  22. I can name several gauge bosons with mass. You might want to consider the w+ and w- gauge bosons. There is no criteria that all gauge bosons must be massless. It is literally the neutrino mass terms that required the SM model to become extended. The mass term also correlates the range of a force. Ever wonder why the EM field is infinite in extent while the weak or strong force are not ? To answer that you need the gauge boson mass terms.
  23. No it the inner product between Lambda and g. Your dealing with vectors. Here is cross product. https://www.mathsisfun.com/algebra/vectors-cross-product.html I don't know if your familiar with the right hand rule in EM theory https://en.m.wikipedia.org/wiki/Right-hand_rule You can from those links how the cross product equates to the right hand rule. The dot product returns a scalar however the cross product returns a vector. So here is a question how can one claim that the EM field and the cosmological constant are related when the latter has no cross product of two vectors and is described strictly via the inner or dot product ?
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.