Mordred

OK let's examine it. Let's assume the signal is sent by the lead train. Each engine will receive that signal progressively later than the previous engine. Do you consider that simulateneous ? The speed limit of c will always apply it doesn't matter if the signal is through EM frequencies, or transmitted via particle to particle interactions through the train body (which actually transmits less than c) vibration travels at the speed of sound however a hypothetical perfect rigid rod the speed of sound can be treated at the speed of light. So do this assign an event at each box car or engine in your train. Assign any engine or box car as the transmitter. At no point will every event receive the signal simultaneous. That would require instantaneous communication.

How much GR have you studied ? Under GR coordinate time is the time at each event. The proper time follows the worldline. https://en.m.wikipedia.org/wiki/Proper_time What I stated earlier stands

Proper time would follow the wordline between engines so you still have the same problem

The communication between every engine would also be affected so you still wouldn't have simultaneous acceleration not under rigorous treatment with GR being applied.

Unfortunately a simulataneous acceleration of a train would impossible taking into consideration the speed limit of information exchange. This thought experiment would be accurately described via the Rigid Rod under GR. In essence let's make your train one light year hypothetically. If the force for acceleration starts at say the engine. The tail end would not accelerate until one year later. Thats assuming the medium is ideal enough to allow the signal to propagate at c. Which is your speed limit.

Well covered Markus I was going you reply many of the details you have above however you covered everything I was going to say. Along with additional detail +1

Yeah looks like a typing error will have to double check that but yes any divergence would lead to a curvature divergents. Hence it's still viable our universe has a slight curvature. That's still viable for both Plus or minus curvature.

\[\frac{1}{2}\]

There is little to no reason for the density parameter to change as one can accurately treat expansion as a closed adiabatic perfect fluid. lets put some math to that using The FLRW metric. the GR form of the FLRW equation is \[(\frac{\dot{a}}{a})^2=\frac{8\pi G}{3}\frac{\epsilon(t)}{c^2}-\frac{k c^2}{R^2_0}\frac{1}{a^2(t)}\] k=0 , curvature \[\frac{\epsilon(t)}{c^2}\] is the energy density in the Babera Ryden notation as opposed to mass density \[\rho\] the reason will become clear later on \[\rho_c(t)=\frac{\epsilon(t)}{c^2}=\frac{3H^2(t)}{8\pi G}\] \[H=\frac{\dot{a}}{a}\] critical density value present day value approx 70 km/sec/Mpc \[\rho_c]+\frac{\epsilon_c}{c^2}=\frac{3H_0^2}{8\pi G}=9.2*10^3 g cm^3\]using the 70 km/sec/Mpc \[H^2=\Omega H^2-\frac{kc^2}{R^2_0a^2(t)}\Rightarrow1-\Omega(t)=\frac{kc^2}{H^2(t)a^2(t)R^2_0}\] if \[\Omega=1\] then it equals one at all times since the RHS of the last equation always vanishes for the flat case for the \[\Omega>1,\Omega<1\] the value may change however never change sign ie positive curvature will change but never become negative curvature Now for adiabatic fluid first law of thermodynamics \[dE-PDV+DQ\] the change in internal energy equates to the sum of PDV work and added heat/energy however there is no place for heat/energy to come from or leave the system therefore\[DE+pdV=0\Rightarrow \dot{E}+p\dot{V}=0\] for a commoving sphere \[V=\frac{4\pi}{3}r^3_sa^3{t}\] \[\dot{V}=\frac{4\pi}{3} r^3_s(3a^2\dot{a})=V \frac{\dot{a}}{a}\] \[E=V_\epsilon\] \[\dot{E}=V\dot{\epsilon}+\dot{V_{\epsilon}}\]\[=V\dot{\epsilon}+3\frac{\dot{a}}{a}\epsilon\] with \[\dot{E}+P\dot{V}=0 \]we get \[V\dot{\epsilon}+3\frac{\dot{a}}{a}\epsilon+3\frac{\dot{a}}{a}P=0\] thus \[\dot{\epsilon}+3\frac{\dot{a}}{a}(\epsilon+P)=0\] which is the same as the fluid equation standard notation \[\dot{\rho}+3\frac{\dot{a}}{a}(\rho+P)=0\] there's the first law of thermodynamics as its a closed system according to this examination conservation of energy would apply however this doesn't examine quantum fluctuations or the cosmological constant.

Hrrm interesting thought. Technically the Langrangian paths of the particle interactions will follow the path of least action. So there may very well be some truth in that statement.

Interesting read will have to study it later. Thanks for sharing

Position and momentum are the operators in QM. Klien Gordon equation uses potential and kinetic energy (QFT)

I give up this is the 4th time this got screwed up the last time was when i tried inserting the url for an image

The Schrodinger equation gives a probability wavefunction one that shows the particles dynamics over time. It will work regardless if you treat the particle as a particle or as a state. The thing is on a fundamental level one also has to keep in mind that a field is simply a set of values in a geometric descriptive. A field in essence is merely a descriptive. However it could be argued that the same applies to a particle. A common bad practice is to think of particles as energy packets. The reason is the very definition of energy is the Property of an object or state to perform work. Particles also have no corpuscular (material like composition) one can accurately consider solid as an illusion. I've been studying physics for over 30 years. Although the field excitation is popular and gaining momentum that doesn't mean there is equal validity in the particle view. Both have their applicability, where one better describes an interaction than the other.

Why 2) if your thinking entanglement then there is no superluminal action, communication or hidden variable involved.

The particle view doesn't particularly work well. A primary reason is one such as spin of an electron. In order to consider an electron spinning via its angular momentum in the particle view the electron would have to exceed the speed of light by a factor of 10. This obviously alerted physicist that an electron cannot be spinning such as a ball. However under the field excitation spin is addressable due to the increased radius of the applicable interactions. Numerous interactions and measurements are making the field excitation view far more likely. Factors such as quantum tunneling, Bose-Einstein condensate state and in particular the Higgs field interactions are far easier to explain under the excitation view. The pointlike and wavelike characteristics of a particle becomes readily addressable as the pointlike characteristics as an excitation is simply another wavefunction that is readily localized . The article below explains waveparticle duality via the excitation view "There are no particles only fields" https://arxiv.org/abs/1204.4616

The anti Desitter metric itself works for any case where the geometry is a negative curvature. The conformal portion applies to the string theory portion of the metric. The positive curvature is covered via the De-Sitter spacetime. The metric is particularly useful to allow string theory flexibility in regions of strong couplings such as the EH of a blackhole.

Electroweak Langrangian L=−14WαμνWμνα−14BμνBμν+Ψ¯¯¯¯iγμDμΨ W1,2,3μ and Bμ Covariant Derivative Dμ=∂μ+igWμτ2−ig´2Bμ mass eigenstates observed in experiments are linear combinations of the electroweak eigenstates. Hence W− and W+ W±μ=12−−√(W1μW2μ) γ and Z are\ Aμ=BmucosθW+W3μsinθW Zμ=BmusinθW+W3μcosθW Cabibbo-Kobayashi-Maskawa matrix ⎛⎝⎜⎜d´s´b´⎞⎠⎟⎟⎛⎝⎜VudVcdVtdVusVcsVtsVubVcbVtb⎞⎠⎟⎛⎝⎜dsb⎞⎠⎟ symmtric massless SU(2)L⊗U(1)γ −LW=g2√UIL¯¯¯¯¯¯γμ1DiLW+μ+hc UIL and DIL is a vector in generation space of the up/down quark interaction-eigenstates. while 1 is a unit-matrix in generation space. Symmetry break (weak) LY−UIL¯¯¯¯¯¯FUIRH0∗+DILGDIRH0+hc VeV 〈H0〉=v/2–√ F and G are Yukawa matrices. quark mass terms MU=Fν2–√::MD=Gν2–√ Gauge Interaction LW=gsqrt2UL¯¯¯¯¯¯γV†LDLW+μ+hc where V†L is the mixing matrix for quarks giving n generations (n*n unitary matrix) with n2 parameters, in which n(n-1)/2 can be chosen as real angles and n(n+1)/2 are phases subsequent transformation v=PUV†LP∗D v=⎛⎝⎜VudVcdVtdVusVcsVtsVubVcbVtb⎞⎠⎟ for 3 generations of quarks THE CKM QUARK-MIXING MATRIX 1) https://escholarship.org/content/qt1jt6c151/qt1jt6c151_noSplash_4cb0f722c2c328730fbac6c5d0971db9.pdf Feymann Integrals by Stefan Weinzierl 2) https://arxiv.org/abs/2201.03593 PMNS mixing matrix https://pdg.lbl.gov/2020/reviews/rpp2020-rev-neutrino-mixing.pdf

Unfortunately it dropped the math structure in the fractions and dropped the superscript to subscripts etc. I will simply redo it. At least the Electroweak section and just reference the statements for the Feymann Integrals I want to explore. Maybe a few days though. The reference is one I just recently found and is extremely informative.

Why did all the math symbols and structures dissappear? Will have to redo this from scratch

Feymann Integrals set c=ℏ =1, (D-1), momentum o particle p as D dimensional vector D(00) =E/c with D-1 remainder spatial components Minkowskii scalar product of pa,pb pa⋅pb=pμagμνpμb set propogator of a scalar particle momentum p and mass m 1p2+m2 consider graph G with Next external edges, Nint internal edges and L=loop number for connected graphs page 16 forwards on Feymann graph rules Feymann Integrals by Stefan Weinzierl https://arxiv.org/abs/2201.03593 project goal examination of the gauge group langrangians with above reference and applying the QFT creation and annihilation operators and QFT propogators Electroweak Lanqrangian L−14WαμνWμνα−14Wμνμν+Ψ¯¯¯¯iγμDμΨ W1,2,3μ[ and Bμ are the 4 spin 1 fields Covariant derivative D2=∂μ+igWτ2−ig´2Bμ W+ andW− bosons are expressed as W±μ=12−−√W1μ∓iW2μ) γ and Z as Aμ=Bμ cosθw+W3μ sinθW Zμ=−Bμ sinθw+W3μ cosθW The Cabibbo-Kobayashi-Maskawa matrix

bump I would like to get back to this took a break

Thanks for the link. Nice to see additional validation for the cosmological principle. Will study in more detail

Sounds like a bad scene in men in black lol

Text books are about the next best thing to formal training. I never pay attention to anything YouTube unless I can quarantee the poster is a well accredited physicist in the field of his or her expertise. ( The field of physics is highly diverse. I can quarantee someone like Swansont far beats my skills in his specialty. While I have my own specialty (cosmology)). So research on a topic should never be blind faith. If you cannot find numerous support on a theory by different professional opinions then be wary. Lol though I give credits to Studiot for applied engineering physics, Marcus for relativity and Janus for astrophysics. The information in this thread does not meet any criteria to question the second law in thermodynamics in any cosmology related studies I am familiar with including QFT related applications. You are absolutely correct to question the above. So +1 for that.