Mordred

Well quite frankly if you don't understand the very basis of relativity, that it is a model that describes particle kinematics which entails addition of velocities under graph aka coordinate system. in essence the space or spacetime paths. Which is described by geodesics. Then its pointless to go any further. That is precisely what Relativity in either form is designed to do.

what do you think the transformation are for ? they directly apply to transforming from one geometry to the other. That is the very essence of the laws of physics are the same in all inertial frames of reference. That includes velocities from 0 to c. Regardless of geometry or regardless of observer all observers will agree on invariant quantities. c itself is an example of an invariant quantity. so to maintain that invariance you need the relevant transformation rules. Here this will save me tons of having to type in the basis of the kinematics and how it relates to the addition of velocities. It will start with the basics of Galilean relativity to Lorentz. Including highlighting Covariance and invariants. https://www.seas.upenn.edu/~amyers/SpecRel.pdf in particular note section 8 with regards to c Maxwell equations starting with "8. Electrodynamics and Lorentz symmetry" The article highlights the essence of invariant quantities (an invariant quantity is the same to all observers) under both Galilean relativity and SR,GR.

So you want me to teach you basic calculus is that it? Did you not learn basic kinematics in school ? Why should I waste time teaching you that if your here questioning relativity itself ? I showed you how the transforms preserves those lessons you should have been taught in high school physics If you dont understand basic kinematics under geometry treatment in Euclidean level mathematics You should start there. Prior to trying to understand and question SR and GR. Those basic lessons are essential.

start with the Galilean transforms (t´=t),(x´=x−vt),(y´=y),(z´=z) with Pythagorus theorem \(a^2+b^2=c^2\) we all know the relevant trigonometry rules regarding the Euclidean Geometry. however those Trig rules can be applied using Euler coordinates. Further we need to preserve f=ma. Which we all know from basic geometry we can apply vector notation towards. Those kinematics you had an issue with. I'm not about to teach an entire course on differential geometry. So lets skip ahead and look at Euler angles these are given here https://phas.ubc.ca/~berciu/TEACHING/PHYS206/LECTURES/FILES/euler.pdf Now due to length contraction these Euler angles are no longer preserved so we need transformation rules The Lorentz transforms are \(\acute{t}=(\gamma\frac{vx}{c^2}), \acute{x}=\gamma(x-vt), \acute{y}=y,\acute{z}=z\) In general relativity, the metric tensor below may loosely be thought of as a generalization of the gravitational potential familiar from Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as distance, volume, curvature, angle, future and past. [latex]dx^2=(dx^0)^2+(dx^1)^2+(dx^3)^2[/latex] [latex]G_{\mu\nu}=\begin{pmatrix}g_{0,0}&g_{0,1}&g_{0,2}&g_{0,3}\\g_{1,0}&g_{1,1}&g_{1,2}&g_{1,3}\\g_{2,0}&g_{2,1}&g_{2,2}&g_{2,3}\\g_{3,0}&g_{3,1}&g_{3,2}&g_{3,3}\end{pmatrix}=\begin{pmatrix}-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/latex] Which corresponds to [latex]\frac{dx^\alpha}{dy^{\mu}}=\frac{dx^\beta}{dy^{\nu}}=\begin{pmatrix}\frac{dx^0}{dy^0}&\frac{dx^1}{dy^0}&\frac{dx^2}{dy^0}&\frac{dx^3}{dy^0}\\\frac{dx^0}{dy^1}&\frac{dx^1}{dy^1}&\frac{dx^2}{dy^1}&\frac{dx^3}{dy^1}\\\frac{dx^0}{dy^2}&\frac{dx^1}{dy^2}&\frac{dx^2}{dy^2}&\frac{dx^3}{dy^2}\\\frac{dx^0}{dy^3}&\frac{dx^1}{dy^3}&\frac{dx^2}{dy^3}&\frac{dx^3}{dy^3}\end{pmatrix}[/latex] The simplest transform is the Minkowskii metric, Euclidean space or flat space. This is denoted by [latex]\eta[[/latex] Flat space [latex]\mathbb{R}^4 [/latex] with Coordinates (t,x,y,z) or alternatively (ct,x,y,z) flat space is done in Cartesian coordinates. In this metric space time is defined as [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] the boosts and rotations of the Lorentz group are as follows Lorentz group Lorentz transformations list spherical coordinates (rotation along the z axis through an angle ) \[\theta\] \[(x^0,x^1,x^2,x^3)=(ct,r,\theta\\phi)\] \[(x_0,x_1,x_2,x_3)=(-ct,r,r^2,\theta,[r^2\sin^2\theta]\phi)\] \[\acute{x}=x\cos\theta+y\sin\theta,,,\acute{y}=-x\sin\theta+y \cos\theta\] \[\Lambda^\mu_\nu=\begin{pmatrix}1&0&0&0\\0&\cos\theta&\sin\theta&0\\0&\sin\theta&\cos\theta&0\\0&0&0&1\end{pmatrix}\] generator along z axis \[k_z=\frac{1\partial\phi}{i\partial\phi}|_{\phi=0}\] generator of boost along x axis:: \[k_x=\frac{1\partial\phi}{i\partial\phi}|_{\phi=0}=-i\begin{pmatrix}0&1&0&0\\1&0&0&0\\0&0&0&0\\0&0&0&0 \end{pmatrix}\] boost along y axis\ \[k_y=-i\begin{pmatrix}0&0&1&0\\0&0&0&0\\1&0&0&0\\0&0&0&0 \end{pmatrix}\] generator of boost along z direction \[k_z=-i\begin{pmatrix}0&0&0&1\\0&0&0&0\\0&0&0&0\\1&0&0&0 \end{pmatrix}\] the above is the generator of boosts below is the generator of rotations. \[J_z=\frac{1\partial\Lambda}{i\partial\theta}|_{\theta=0}\] \[J_x=-i\begin{pmatrix}0&0&0&0\\0&0&0&0\\0&0&0&1\\0&0&-1&0 \end{pmatrix}\] \[J_y=-i\begin{pmatrix}0&0&0&0\\0&0&0&-1\\0&0&1&0\\0&0&0&0 \end{pmatrix}\] \[J_z=-i\begin{pmatrix}0&0&0&0\\0&0&1&0\\0&-1&0&0\\0&0&0&0 \end{pmatrix}\] there is the boosts and rotations we will need and they obey commutations \[[A,B]=AB-BA\] the symmetry statement \(\mu\cdot\nu=\nu\cdot \mu\) tells us the Minkowskii metric inner product of those two vectors are covariant hence symmetric that the choice of who is the observer or emitter is irrelevant. ( the laws of physics are the same for all observers. Which is the more common notation. So in essence we have the transformations to regain Pythagoras theorem as well as Newtonian kinematics. The point of all those mathematics is the Principle of General Covariance in a nutshell. We is easiest to describe as we know Newton physics works at slow velocities. So why not include them. We simply need the corrections for when we reach relativistic velocities. The principle in equivalence tells us the inertial mass is equivalent to the gravitational mass. \(m_i=m_g\) So in that Einstein paper he didn't waste time teaching Euclidean differential geometry rules. He extended them by adding the necessary corrections. It is those corrections that are being shown in that paper we have been examining. He isn't going to waste time going over 3d Euclidean and Newtonian physics.

It takes time to latex mathematics in place mate.

Ok well maybe you should ask yourself which laws are being preserved and what is their mathematical definition. Let's start with Pythagoras theorem and the other law involves Newtons laws of inertia. If you hsve length contraction and time dilation with time being given dimensionality of length via the interval ct. It becomes readily apparent that a 4d geometry needs transformations to restore Pythagoras theorem as well as the Galilean transformations that have so well tested in everyday situations. (Principle of General Covariance for further detail)

Let me ask you a question. Would you trust an engineer that couldn't calculate the structural integrity of a bridge to build one ? Would you trust a professional physicist to tell you how the physical world interacts without mathematics? I certainly wouldn't I never trust any claim that cannot be shown and tested with the relevant mathematics regardless of who states it. This includes other professional physicists. I could easily show you what the first postulate means in terms of the mathematics. However that would a waste of time as you would ignore any math based answer

That's a very weak argument, it's essentially stating all test methods are simply duplications. How else do you validate any theory in any science without rigorous testing ? I performed my own measurements I performed my own examination of the test methodology I chose. 30 years ago you didn't have the easily obtainable information available on the internet you have today. Lol we were still using those clunky dialup modems

That's my statement, not Swansont's my position always prioritizes the math over verbal.

For the record I received high marks for my efforts. I learned a lot more about redshift and spectography than you will find in textbooks lol. Most textbooks only give you the most commonly used formulas. They rarely provide the formulas to get a higher degree of accuracy ones that account for other influences such as light pollution atmospheric distortions or temperature variations.

My main focus was using Proximus Centauri. Though not the only star I used. I had picked a list of 30 different nearby stars. As objects close enough but far enough away to validate its distance using a non redshift related method parallax. This required waiting for certain seasons of the Earths orbit relative to those stars. Then using the common spectral data to each I compared the hydrogen spectral lines at different time periods as the Earth orbited our sun. If c were not constant then the gravitational redshift calculations would also be in error. I could find no error even with a range of frequencies to work from. Granted gravitational redshift is small for Earth but it is still a measurable influence. Cosmological redshift didn't need to account for as all the objects I used are in essence gravitationally bound and not influenced by universe expansion

No I took my own measurements using the equipment available. It took me 2 years to get my own datasets to work from.

Lol you have absolutely no idea the steps I took. Including conducting my own experiments with the available university equipment. Nor do you have any idea how often I have to apply relativity in Cosmology and particle physics datasets. You would be amazed just how often it becomes important. The constant c doesn't just apply to the speed of light. It is the speed limit of all forms of interactions and information exchange. Here are the Galilean transforms \((\acute{t}=t), (\acute{x}=x-vt), (\acute{y}=y),(\acute{z}=z)\) Feel free to try and have a variant c and prove it sufficiently to match observational evidence to the contrary. As for myself I used the university telescope with spectrometry datasets combined with parallax data. To test the constancy of c with bodies that move at the decent velocities of interstellar bodies.

No nothing of the sort. When I first started studying physics I for one hated relativity and didn't agree with the constancy of c. I like a great many others went out of our way to invalidate relativity. However that too is part of the scientific method, so my instructors supported my efforts. Physics isn't based on some popularity contest. In actuality it is based on testable evidence. You might actually be surprised at what kind of transforms it would take to agree with observational evidence with a Lorentz type eather that would agree with the M and M experiments or the far more refined and high experiments for one way/two way speed of light tests

For the record Swansont has a PH.D. So has a very good understanding of physics. Several of our members have similar backgrounds. Many of us have our own accredited backgrounds myself included. So you can bet those of us with various degrees in physics topics will consider mathematics an essential element of physics. Especially if those same mathematics have been extremely well tested against observational evidence. The other detail to consider is the postulates of SR are also mathematically defined. This leads in essence to Lorentz invariant and the various symmetry relations.

The signal will never exceed c there is no ftl communication entangled or not. Hence why entanglement for communication is only practical for encryption.

Just a side note the speed of light was determined prior to Einstein. I own a 1919 physics textbook that shows the same value. The textbook doesn't even mention relativity. It however covers Galilean relativity. The only known particles at the time was the photon, proton and electron.

Typically entanglement will involve a particle to particle interaction the most common method is particle pair creation such as through parametric down conversion using a beam splitter for photons. The probability correlation function can then be determined by applying the various conservation laws such as conservation of charge, energy momentum, lepton number, isospin, color, flavor etc. Entanglement can be used in communication for cryptology. However no communication exceeds c

Your very statements is your opinion. That should be obvious even to you. Secondly the math always comes first in any physics theory. It's the very essence of model building. It is literally the very first test of any hypothesis. It is also a step you should be taking . Mathematically prove the EFE or the Minkowskii field equations is wrong. Not simply declare they are. Show where your Hypothesis gives higher accuracy to explain the literal mountains of observational evidence. As The principles of GR and SR are two of the most rigidly tested theories we have. They have been so rigidly tested that the vast majority of all major Theories incorporate SR and GR. When any professional physicist tests a theory. That physicist isn't testing verbal descriptions. They are testing the mathematics. To see how accurately the mathematics makes predictions of effects from A causes B found in nature. It is literally the very essence of physics. The predictive power of the applied mathematics.

Well regardless of your opinion, the constancy of c is well tested. I'm positive you have heard that before. Seems you would rather ignore the mathematics or recognizing a paper doesn't need to cover commonly applied mathematics in that SR paper in a verbal descriptive. Quite frankly that's your hangup not mine. The resultant time dilation due to the speed limit of information exchange is so well tested that none of our opinions truly matter lmao. So regardless of opinions of any forum or forum members the mathematics of SR and GR obviously work how they are verbally described is simply interpretations. So railing because such and such paper doesn't verbally describe something to conform to your opinion is meaningless. It also seems to me your arguments are more in line with metaphysical arguments and they bore me. Always have always will. If the mathematics accurately describe a theory. I don't bother with verbal descriptives

He didn't need to his use of reference frames was established with Galilean relativity. He incorporated those mathematics in the paper. So he chose not to waste time describing the obvious inherent in the mathematics. Think of it this way papers you read today don't point out every detail not when those details are in established formulas. Galilean relativity was very well established. When you get down to it the gamma terms for the Lorentz transforms are a simple extension.

Well ways to interpret that paragraph. Often doesn't imply always. The convulsion can also prevent you from letting go of a live conductor. AC will cause muscle spasms so your more likely be able to let go. From personal experience of having felt both at 20 and higher Amp services. I'd much rather be hit with AC. Trust me you can feel the difference. Regardless both are highly dangerous. Both can cause serious injury or death if they aren't carefully handled.

Light cone barrier? A light cone doesn't involve its own signals. In the case of the EH the particle undergoes a wide range of inference. Prime example being the gamma ray accretion jets that result from infalling matter.

DC is actually considered more dangerous. High DC amps can literally blow a hole through you. Also with AC you have a chance in letting go of a conductor not so much with DC. Either way it's the AMPS that kills

Think of it this way Hoola, an entangled particle is entangled by a probability function. When one particle changes state it does not cause the other to change state. You can merely make predictions of state of the other particle by measuring the state of one of the pairs. Once a measurement is made the superposition wavefunction collapses. So you cannot measure prior to sending a particle into the Bh. It's also highly unlikely the particle will not lose its entangled state due to the interference from the BH accretion disk.