Mordred

In essence yes that a succinct way to describe it.

Oh now I'm a gang leader, did it never occur to you that everyone posting in this thread literally has their own opinion ? Anyways I would advise you to take into consideration the mod note in the post prior to this one. Quit wasting time with fruitless accusations

Think of it this way the applications in that paper don't describe encrypted messages. They describe means of detecting security breaches. It's something on the order of error detection methods used by computers today. Older examples being checksum or Cyclic redundancy checks.

Well said...+1

Not if you send numerous entangled photons. When Alice examines her photon stream Bob also examines his. If the photons are not opposite to one another on every pair then you would know you had corruption or a security breach Here is some of the encryption methods that have been suggested. https://arxiv.org/pdf/2003.07907 The easiest example the paper gives is through parametric down conversion. You will know the initial frequencies but once the beam passes through the beam splitter you wouldn't know which polarity is sent until you examine. From this you can apply the conservation laws and expect the opposite polarity at end. If you font have the opposite polarity at each end then you know something occurred to interfere with the signal.

Why wait ? It's very common to show what a model states with the relevant equations. Then apply the corrections or improvements. If you want to show you truly know what you talking about you might want to get the real meat of your analysis. Lol you have no idea how often we hear grandiose claims that A poster cannot mathematically support it would be a nice change to hear a good solid mathematical argument.

You know it seems to me your only argument is to judge the posters involved in this thread. You certainly haven't applied a single equation showing SR as being wrong.. So far the only mathematics has been posted by myself. SR and GR are mathematical models might help if you actually focused on the math for a change.

Really I know what mathematics works I certainly will not randomly believe your unproven claims over a well established and well tested theory. You have done absolutely nothing to prove SR is incorrect. I'm not about to willy nilly believe you simply because you claim your ideas are correct over well established models

No I grew tired of your antics. I showed mathematically what is described as the laws of physics are the same to all observers. If you cant figure out how invariant quantities apply and how the transforms apply to mathematically defining that postulate that isn't my hangup. Hint it also applies to conservation laws which also directly apply to invariant quantities.. Those details were further shown in the link I provided by the way. Tell me something does not the fact that SR has length contraction and time dilation not mean that this doesn't describe curved spacetime ? Spacetime curvature occurs when you have both

Don't believe the physics of SR stopped in 1905. Work continued on SR Long after that date. The term geodesic also existed prior to both SR and GR. For that matter

Did you not catch the part where I mentioned in either form of relativity? 3 forms Gallilean, SR, GR. Though geodesics certainly do apply in SR as well. Geodesics don't exist in just curved spacetime they also exist in flat spacetime. Would you like the Christoffel connections for flat spacetime? Or are you not aware the the line element describes the worldline of a metric. Given by ds^2 for separation distance ? A worldline is a type of geodesic

Great glad to hear that. Then you should have no problem mathematically showing where SR is incorrect.

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.