Mordred

No its weird as it is poorly understood. However if you understand superposition as a probability distribution function. That when you make a measurement even if the measurement doesn't cause interference limits the probabilities. Nothing weird about that at all. This occurs in numerous statistical situations. Take a particle it has a statistical probabiliy of being at a given location on a waveform. That wave form is the probability wave. Its amplitude is determined by the percentage chance of the particle being on the peak of the amplitude. Say 75 % chance but the particle has a chance of being anywhere on the probability wave. Once you measure the particles position. You now know the location. So you have reduced the particle position probabilities to 1. Your not interfering with its position. You interfere with the probability of being in any other position.

Think of superposition as the sum of all possibilities. All possible positions and quantum waveforms. When you make a measurement you narrow the possibilities to 1.

When v=c the ds^2 line element =zero. Ie the photon is everywhere at once. This is precisely why a v=c frame is not a valid inertial frame. But you don't want the math and if your understanding of metaphysics is ignore the math then I have no interest. Quite frankly if you ignore the math and definitions of both physics and metaphysics your not discussing physics. (little hint the v-c and v+c can be used to establish the speed limit.) with or without light. Have fun. I have zero interest if were ignoring the math and subsequent definitions To quote David Hume. "If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion". Oh one last detail, against an ether frame medium wise or otherwise. It is the only frame considered as invarient. It is strictly at rest (Non inertial) All other frames are inertial, with arbitrary choice of rest frame. Materialistic or not, undetectable or not. Which isn't the case in SR nor GR. All frames are variant under the same transformations. All frames are inertial.

A measured rate of change. I certainly don't need anything more than that to define kinematic motion. With regards to time.

Gotcha but I too don't want to distract this thread from the OP lol. Sounds like a good paper though. For the benefict of others the equation I gave is Gibb's phase rule. https://en.m.wikipedia.org/wiki/Phase_rule Which gives the number of degrees of freedom (well according to the understanding of particles at the time period lol) the general principle still applies. Today its far more accurate to use the Bose-Einstein, Fermi-Dirac or Maxwell Boltzmann statistics. These correlate the quantum numbers as additional degrees of freedom. Gibbs laws are good stepping stones though. Its still accurate on everyday gases. The difference's comes into play when dealing with elementary particles.

The SI units for a watt is [latex] kg*m^2*s^{-3}[/latex] You use this relation to convert the units you get from that equation. I can't see the link you posted. So I have no idea what example they use. However knowing how to get the watt unit out of the above equation's units should help. By the way you asked a good question, if your not familiar with 1 joule/sec = 1 watt. [latex]Joule=\frac{kg*m^2}{s^2}= watt*sec[/latex]

Well you have a few mixed up. Inertial velocity is due to f=ma. Key note definition of inertia. "Inertia is the resistance of any physical object to any change in its state of motion; this includes changes to its speed, direction or state of rest. It is the tendency of objects to keep moving in a straight line at constant velocity" Peculiar velocity has two definitions depending on application. In cosmology however. "In physical cosmology, the term peculiar velocity (or peculiar motion) refers to the components of a receding galaxy's velocity that cannot be explained by Hubble's law." GR treats it under the first definition on this link. https://en.m.wikipedia.org/wiki/Peculiar_velocity Recessive velocity is a consequence of Hubbles law v=HD. Commoving distance and proper distance https://en.m.wikipedia.org/wiki/Comoving_distance. Details on the particle horizon and conformal time here. https://en.m.wikipedia.org/wiki/Particle_horizon Don't worry about getting all these correct right away. They become clearer when you study the equations involved for each. Which takes time. However be aware of them when reading various papers. Many authors assume you already know these terms and don't show the corresponding metrics. Particularly in arxiv articles, so if your not careful not being familiar with these terms can throw you off and mislead you when reading technical papers. Sean Carroll has a nice write up of some of these hazards. http://www.preposterousuniverse.com/blog/2015/10/13/the-universe-never-expands-faster-than-the-speed-of-light/comment-page-2/

I like what you have so far. Yes I can see the direction your heading on 5. Just so I don't give it away but looks likes your heading to f=p-c+2 (after constraints are applied). Good approach if I'm correct.

A lot of people have ideas not theories. The majority of those pet theories aren't theories as they have zero math involved. Their ideas cannot make predictions. Which is required, another requirement being testable. Again you require mathematical predictions

Good question though not one easily answered. In physics a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all dimensions of a system is known as a phase space, and degrees of freedom are sometimes referred to as its dimensions. However this definition may be easier. " the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinitesimal object on the plane might have additional degrees of freedoms related to its orientation." As you can see here there is differences in definition depending on the application. https://en.m.wikipedia.org/wiki/Degrees_of_freedom So to describe a point in 3d I need three values x,y,z. In 4d with time as a vector I now require 4 t,x,y,z. When you spin that object you add another degree of freedom. There is some examples and a decent coverage here. https://en.m.wikipedia.org/wiki/Degrees_of_freedom_(physics_and_chemistry) For example lets deal with a 3d pointlike object under strictly change in position. As each movement must be independant to count as a degree of freedom. The object can change x without changing y or z. Same with y or z. So x,y and z are independant of each other. They are each examples of a degree of freedom. Time is also independant it can change without a change in spatial location. If you add a dynamic that is independant of the x,y,z,t degrees of freedom such as photon polarization you add additional degrees of freedom. PS I'm also hoping Studiot will provide some good mechanical degrees of freedom examples. Hes more practiced on the engineering applications. If not I can use some robotic arm examples lol. So take this object. First ask how how many degrees of freedom is needed to fully desribe this object. To start it has three spatial independant coordinates. x,y,z. If you treat it with time being independant (not dependant) then thats 4. Now the rotations of the total object (both boxes) has been reduced to its independent variables. Yet the inner box can move independant of the outer box. (or at least appears to move independant) lets assume it can. Those independant movements adds additional degrees of freedom. Just watching the object and including time this can be described as a 5 dimensional object. (though it could have more degrees of freedom than I perceive)

or additional degrees of freedom? example Kaluzu-Klien 3 spatial degrees of freedom. One for time, one for electromagnetism=5d. {U(1) guage} The U(1) guage reduces down to one degree of freedom. String theory is similar in that the additional dimensions is describing additional degrees of freedom due to weak, strong and electromagnetic fields. Though it is not strictly additive with guage fixing and can get incredibly complicated with guage fixing lol

Your right I can't see why your ignoring the specifics of what is termed isotropy of light. I'm not specifying models but showing the time isotropy and length isotropy to show you how isotropy of light is determined. Sorry I can't explain it in any simpler terms. I really don't see where you keep misinterpretating my posts. I keep thinking the problem is that you don't stick with the proper terminology. The majority of the terminology used in GR/SR regardless of model is rooted in differential geometry. Yet it seems you don't wish to understand the mathematical basis behind the key terminologies. Your continous use of 3D Lorentz is a prime example. It is mathematically inaccurate. Lorentz ether has 4 degrees of freedom. (four independant variables) 3 spatial one of time. GR/SR is time independant. Galilean relativity is time dependant. Time does not add an additional degree of freedom in Galilean relativity. Answer to this is given above. Your right I am not using metaphysics arguments to answer this but the math behind the physics. Which quite frankly the metaphysics arguments and definitions is BASED upon. Yet you seem to think metaphysics means you can ignore the terminology mathematical or otherwise. As light is invariant to all observers. Then light is obviously symmetric and isotropic. So you answer your question why would think light is anistropic? Maybe you can better define what you mean when you stated light cannot both be anistropic and isotropic. As light is the same for all observers...secondly what two units are used to describe light propogation (length and time) So how light propogation which is invariant be both isotropic and anistropic.? Your right I have no idea how you can even conclude that.

I wasn't defining cause, Nothing doesn't really exist under QM. Doesn't really fit in physics. The closest definition of nothing is the ground state of a vacuum. At least under physics. You always have a quantum vacuum due to the Heisenburg uncertainty principle. Then again does everything require a cause? "In quantum physics, a quantum fluctuation (or quantum vacuum fluctuation or vacuum fluctuation) is the temporary change in the amount of energy in a point in space,[1] as explained in Werner Heisenberg's uncertainty principle." https://en.m.wikipedia.org/wiki/Quantum_fluctuation quantum fluctuations can be simply described as a property of a potential field. As a property they don't necessarily require a cause. "The Heisenburg uncertainty principle is an inherent property of all wavelike systems."

under QM the lowest possible energy state is not nothing but a vacuum condition called zero point energy. https://en.m.wikipedia.org/wiki/Zero-point_energy

permanent membership lol

Wow really had to search and compare to see your reply Janus. I placed in bold

Your looking at dimensions wrong. the number of dimensions is the minimal number of coordinates needed to describe any location. So in 2d x,y two coordinates. 3d x,y,z. For 4d t,x,y,z 3 spatial components plus one of time. This is needed in GR as GR models time as a vector which requires both magnitude and direction.

I'm still trying to figure out why your ignoring spatial direction in one case but not the others. Its the same as the twins paradox. Especially since you know There is no possible way to distinquish Lorentz ether from GR If the twin is moving towards his twin he will recieve signals faster. So why would you think this isn't true for Lorentz ether? as well as Minkowskii and full GR? The time symmetry relation just applies to the transform and is implicity shown via [latex]\acute{t}=\gamma (t-v^2/c_2)[/latex] [latex]t=\gamma (\acute{t}-v^2/c_2)[/latex] So event a measures the time dilation and event b measures the same dilation. Both observers get the same value for the magnitude the clock slows down when looking at the other reference frame. This is symmetric and isotropic. Length contraction symmetry does not apply to the Worldline path. It applies to the object not the path. The Worldline path itself being invariant. Doesn't matter if the twin is moving away or towards the other twin the symmetry follows the same rules as above. [latex]\acute{x}=\gamma(x-vt)[/latex] with reverse being identical upon calculation. [latex]x=\gamma (x-vt)[/latex] It is only those relations that are symmetric and isotropic. This amounts to both twins will get the same value for the amount of length contraction and time dilation The spatial seperation however is not symmetric and isotropic as an observer moving away from an emitter will recieve signals slower than moving towards the emitter. The symmetric and isotropy literally applies to strictly the transforms I've posted it does not apply to direction and the subsequent different signal rates. ie series of signal pulses. The observer moving away from the emitter recieves pulses slower than moving towards. That isn't due to the transformations themself but to the spatial seperation with direction. This is true for all cases. Put simply if given a value for gamma. Event a and b will have identical length contraction and time dilation values when looking at the emitter. This is the isotropy relation. In the pulse rate scenario both will measure the same rate of pulses. It does not mean the outgoing observer will recieve the pulses at the same rate incoming. Wiki has a slightly different way to describe the symmetry but it amounts to the above. "which shows much more clearly the symmetry in the transformation. From the allowed ranges of v and the definition of β, it follows −1 < β < 1. The use of β and γ is standard throughout the literature." https://en.m.wikipedia.org/wiki/Lorentz_transformation Now the preferred frame in Lorentz ether itself presents a problem with isotropy in time. The preferred frame is the only one that is at rest. So here you do have time anistropy. Which follows by the following. Alice is the Lorentz ether frame. Bob is on the inertial frame. Bob sees himself as inertial so does Alice as Alice IF is the true rest frame. Alice's reference never undergoes transformations While Bob's frame does regardless if you switch observer and emitter. Which is different from comparing two inertial frames. Alice sees Bobs as the frame being transformed. If you switch emitter/observer the opposite is true.( time symmetry) Neither Alice or Bobs frame has higher priority or accuracy. On the preferred frame case Alice reference is always at rest and never transforms. It is the only accurate frame.(this is a t-assymetry) Yet ignoring the preferred frame itself the time isotropy applies between two inertial frames but not to the preferred frame. This is precisely why I stated the Preferred Lorentz ether is incompatible with the Principle of relativity "There is no preferred frame "

After reading that paper I'd like you to read the section on proper distance in particular this section. "Comoving and proper distances are not the same concept of distance as the concept of distance in special relativity. " https://en.m.wikipedia.org/wiki/Comoving_distance That quote is under proper distance. This is something you have to be careful of is learning the different classes of observers, time treatments etc. For time proper time, conformal time, coordinate time, commoving time, cosmological time. length coordinate distance, proper distance, commoving conformal etc. velocity can be apparent, peculiar or inertial. (notice this distinction). The Lineweaver Davies and Hoggs papers I previously linked to you goes into these details. SR uses proper observer and coordinate observer. Which is distinct from a commoving or cosmological observer. Brian Powell adds some key details here. http://tangentspace.info/docs/horizon.pdf

Sorry had that link before accidentally deleted it when I did edit. To include the wiki link. Phone is acting up lol

Yes it is a typo it should have epsilon for energy density as it evolves with cosmological time. Also referred to as commoving time. "The comoving time coordinate is the elapsed time since the Big Bang according to a clock of a comoving observer and is a measure of cosmological time. The comoving spatial coordinates tell where an event occurs while cosmological time tells when an event occurs. Together, they form a complete coordinate system, giving both the location and time of an event." https://en.m.wikipedia.org/wiki/Comoving_distance The commoving observer is also often referred to as "Fundamental observer"

You need to be careful here. The Lorentz transforms by itself without rapidity or tidal forces etc is symmetric. In all cases. Movement is a change in spatial position so yes at first it appears anistropic but becomes isotropic once you remove the added influence of the spatial position change. I would classify Lorentz ether as a 4d view but with a frame preference as it does have a time transformation. Galilean relativity is a 3d view no time transformation. The M$M experiment was looking for an additional aberration due to medium dragging. It already realized the above would hold true if there was no ether. With an ether the above would also be affected. You can do this experiment at home. Take a glass tub with a laser beam. Step one light where the tub is filled with water. Then have the water moving. The two beams will not match. This is the essence of the M and M experiment, it simply used the Earths movement to get ether flow. Unfortunately it wasn't a one way speed of light test but still a two way speed of light test. There is numerous papers showing this flaw. I'm not even sure what apparatus would be needed to have a true one way test. Though I'm sure someone has developed one. I simply haven't researched that line of later tests enough to state this test is a true one way test. I have a decent coverage of M$M showing the transforms but its rather lengthy to post the math. I can show it later on though. Actually there is a simple example. let U be the speed of light in a medium at rest. Primed U medium in motion. V velocity of medium. [latex]U=\acute{U}+kv[/latex] k=1-1/n^2 where k is the drag coefficient. Google Fizeau experiment. therefore [latex]U=\frac{\acute{U}+v}{1+\acute{U}\frac{v}{c^2}}=\acute {U}+U (1-\frac{\acute{U}v}{c^2})=\acute{U}+v(1-\frac{\acute{U}^2}{c^2})=\acute{U}+kv [/latex] The Michelson-Morley experiment was trying to find the value for k. Drag coefficient. Note there is no time transformation in the above. Its a Galilean relativity kinematics.

Heavier metals to the inner planets. Is also fairly typical.

Higg's Field, GR and the FLRW. [latex]R_{\mu\nu}-\frac{1}{2}[/latex] with c=1 here [latex]T_{\mu\nu}[/latex] is the stress energy-momentum tensor. In general one has to consider all contributions from all possible fields. So lets start with the electromagnetic contributions. [latex]T_{\mu\nu}^{em}=(4\pi)^{-1}(-F_\mu^\alpha F_{v\alpha}+\frac{1}{4}g\_{mu\nu}F_{\alpha\beta}F^{\alpha\beta})[/latex] where the electric field tensor [latex]F_{\mu\nu}[/latex] is given by four potential [latex]F_{\mu\nu}=A_\mu-A_{v\mu}[/latex] [latex]A_\mu[/latex] being the four potential. when we introduce the scalar field for Higg's [latex]\phi[/latex] we need to add an additional energy momentum tensor on the RHS. Without going into excessive detail on the Langevians which I will skip. We get the following energy tensor. [latex]\acute{T}_{\mu\nu}=\partial_\mu\phi\partial_v\phi-g_{\mu\nu}L=\partial_\mu\phi\partial_v\phi-g_{\mu\nu}[\frac{1}{2}\partial_\sigma\phi\partial^\sigma\phi-V(\phi)][/latex] we can write the stress tensor [latex]T^v_\mu=diag(\epsilon,-p,-p,-p)[/latex] with the prime tensor [latex]\acute{T}^v_\mu=diag(\acute{\epsilon},-\acute{p},-\acute{p},-\acute{p})[/latex] [latex]\acute{\epsilon}=\frac{1}{2}\dot{\phi}^2+V(\phi);;\acute{p}=\frac{1}{2}\dot{\phi}^2-V\phi;;\\dot{\phi}=\frac{\partial\phi}{\partial t}[/latex] this shows that we can simply replace [latex]\epsilon[/latex] with [latex]\acute{\epsilon}+\epsilon[/latex] and p by [latex] \acute{p}+p[/latex] so the following holds [latex]\frac{\dot{R}}{R}=H^2=(\frac{8\pi}{3})(\epsilon+\acute{\epsilon})[/latex] [latex]2\frac{\dot{R}}{r}+H^2=-8\pi G(p+\acute{p})[/latex] This should be enough detail on how the Higg's field works in regards to expansion contributions. The last two equations provide its influence upon the volume elements. Enjoy lol PS yes the above is math heavy, however we can see how the Higg's field is modelled by the above with its stress tensor contributions. This last section many will find handy as we just added multiple field couplings to gravity. I demonstrated how a spin 1 field (electromagnetic) couples to the spin 2 field (gravity) as well as how a spin (zero) scalar field couples to spin (2) gravity. Not something that is easy to find examples of. Adding SU(3) for the chromodynamics follows similar procedures, (strong force) again its spin 1 but has additional degrees of freedom. Which affects the energy-momentum tensor

Lets try and fill in some details on Inflation. The particular example I will use is one I believe most strongly in out of the 73+ viable inflation models. Higg's inflation. Higg's field. Is a complex scalar field [latex]SU(2)_w[/latex] doublet. [latex]\phi=(\begin{matrix}\phi_1 & \phi_2 \\ \phi_3& \phi_4 \end{matrix})[/latex] the vector bosons (guage bosons) interact with the four real components [latex]\phi_i[/latex] of the [latex]SU(2)_{w^-}[/latex] symmetric field [latex]\phi[/latex] false vacuum corresponds to [latex]\phi=0 or \phi_1=\phi_2=\phi_3=\phi_4=0[/latex] the true vacuum corresponds to [latex]\phi_1=\phi_2,,,\phi_3^2=\phi_4^2=constant>0[/latex] assign V on the Y axis, [latex]\phi_3[/latex] on the x axis, [latex]\phi_4[/latex] on a 45 degree between the x and Z axis. when you have conditions [latex]\phi_4=0,\phi_3>0[/latex] then the rotational symmetry is spontaneously broken. The Higg's boson becomes massive as well as the vector bosons W+,W-Z and photons the two neutral fields [latex]B^0 and W^0[/latex] form the linear combinations [latex]\gamma=B^0 cos\theta_w+W^0sin\theta_w[/latex] [latex]Z^0=-B^0sin\theta_w+W^0cos\theta_w[/latex] where Z becomes massive. whee as our ordinary photon [latex]\gamma[/latex] remains massless as the photon does not interact with the electro-weak Higg's field. It is electro-weak neutral. The electroweak symmetry is given by [latex]SU(2)_w\otimes U(1)_{b-L}[/latex] as time decreases the vacuum expectation value [latex]\theta_0[/latex] decreases. (expansion in reverse) the true minimal of the potential is [latex] \phi=0[/latex] this occurs above the critical temperature [latex]T_c=\frac{2\mu}{\sqrt{\lambda}}[/latex] at this point the field interactions take on in essence superconductivity properties. Scalar field Dynamics here we need to couple the scalar field to gravitation. [latex]\frac{1}{2}\dot{\phi}^2+\frac{1}{2}(\triangledown\phi^2)+V(\phi)[/latex] and the dynamics can be described by two equations. ::Friedmann equations [latex]H^2+\frac{k}{a^2}=\frac{8\pi}{3M^2_P}(\frac{1}{2}(\dot{\phi})^2+V(\phi)[/latex] and the Klein Gordon equation obeys the scalar fields [latex]\ddot{\phi}+3H\dot{\phi}+\acute{V}(\phi)=0[/latex] if the [latex]\phi_a[/latex] is large we have [latex](\triangledown \phi_a^2)<<V(\phi_2)[/latex] the speed of expansion [latex]H=\frac{\dot{a}}{a}[/latex] is dominated by the potential [latex]V(\phi_a)[/latex] in equation [latex]H^2+\frac{k}{a^2}=\frac{8\pi}{3M^2_P}(\frac{1}{2}(\dot{\phi})^2+V(\phi)[/latex] the advantage of Higg's inflation is that inflation is readily modelled using just the standard model of particles. We do not need k-Fields, inflatons, curvatons, Quintessence or any other quasi particle or field. Secondly we can model inflation as a symmetry phase transistion which is extremely important as we tie inflation with the electro-weak symmetry breaking itself