Proof Minkowski Spacetime is Poorly Conceived

[przyk]

danshawen, nobody is taking you very seriously here because you keep ranting about things that have little or nothing directly to with special relativity, let alone Minkowski's framework.

Einstein's theory of special relativity claims that the Lorentz transformation is a symmetry of the laws of physics. This is analogous to how coordinate rotations ("no preferred spatial orientation") and translations ("no preferred position") are known symmetries of physics. At it's core, that's really all there is to relativity. Your various comments concerning photon/electron interactions, the Higgs mechanism, etc., are generally irrelevant because relativity isn't itself directly concerned with them. It's the (unspecified) "laws of physics" that are responsible for modelling specific physical processes like these. Relativity just claims that these "laws of physics", whatever they may be, should be Lorentz symmetric.

To understand what Minkowski did, you need to think about what relativity means for physics as a practice undertaken by human researchers. If we take relativity seriously then we need to be able to prove that the various theories that we come up with are symmetric under Lorentz coordinate transformations, as relativity claims they should be. The practical problem with this is that there's a whole soup of physical quantities that we're interested in that we'd like to have theories about. Some of these (like, say, the electric charge of a particle) are invariants, but many quantities are reference-frame dependent (for instance, velocity, momentum, energy, frequency, just about any current or density, the electric and magnetic field components, and on and on), and when we come up with theories about how these quantities are related to each other we need to make sure that we're equating them a consistent way.

What Minkowski did was invent a four-dimensional vector/tensor notation for relativistic physics that makes it much simpler to keep track of this zoo. He introduced a way of classifying physical quantities according to how they depend on the choice of reference frame: basically, represent all physical quantities as either invariants or as the components of four-vectors and tensors, which all share a common transformation rule if you change from one reference frame to another. This makes it almost trivially easy to develop theories that are compatible with the relativity principle: basically, any theory defined in terms of four-vectors and tensors and following a few simple rules is automatically guaranteed to be symmetric under Lorentz transformations. For example, if you have an equation in a theory saying

$$\text{a four vector} = \text{another four vector} \,,$$​

then the components on both sides of the equation change in the same way if you change the reference frame, so the equation is preserved by the change of reference frame.

For a simple example of this, quantum physics says that the energy and momentum of a quantum particle are related to its wavefunction's (angular) frequency and wavevector by the de Broglie relations:

$$\begin{eqnarray}
E &=& \hbar \, \omega \,, \\
\boldsymbol{p} &=& \hbar \, \boldsymbol{k} \,.
\end{eqnarray}$$​

In Minkowski's notation, you can group energy and momentum together into a four-vector called the "four-momentum", defined by $$p^{\mu} = (E/c,\, p_{\mathrm{x}}, p_{\mathrm{y}}, p_{\mathrm{z}})$$, and, like I mentioned earlier in this thread, you can group the frequency and wavevector of a wave into the "four-wavevector" $$k^{\mu} = (\omega/c,\, k_{\mathrm{x}}, k_{\mathrm{y}}, k_{\mathrm{z}})$$. So, in Minkowski's notation, the de Broglie relations would just be expressed as

$$p^{\mu} = \hbar \, k^{\mu} \,.$$​

This is mathematically equivalent to the way the de Broglie relations are written above, but expressing them in this way makes it immediately obvious, to any physicist familiar with Minkowski's framework, that the de Broglie relations are compatible with the relativity principle.

To summarise, Minkowski introduced a mathematical book-keeping tool that makes it trivially easy and systematic to show that theories are consistent with special relativity. This might not be much of a concern to you personally, but it's something we need to do all the time in theoretical physics and it's why Minkowski's framework is as widely used as it is, and your bizarre rants about "19th century mathematics" and such show virtually no understanding or even awareness of this.

 

[Ophiolite]

Thank you pryzk, I just learned more physics in the last five minutes than I did in the last five years. You have given me (pun intended) a reference frame in which to embed all the other snippets I have read that did not make sense at the time.

 

[danshawen]

danshawen, nobody is taking you very seriously here because you keep ranting about things that have little or nothing directly to with special relativity, let alone Minkowski's framework.

Einstein's theory of special relativity claims that the Lorentz transformation is a symmetry of the laws of physics. This is analogous to how coordinate rotations ("no preferred spatial orientation") and translations ("no preferred position") are known symmetries of physics. At it's core, that's really all there is to relativity. Your various comments concerning photon/electron interactions, the Higgs mechanism, etc., are generally irrelevant because relativity isn't itself directly concerned with them. It's the (unspecified) "laws of physics" that are responsible for modelling specific physical processes like these. Relativity just claims that these "laws of physics", whatever they may be, should be Lorentz symmetric.

To understand what Minkowski did, you need to think about what relativity means for physics as a practice undertaken by human researchers. If we take relativity seriously then we need to be able to prove that the various theories that we come up with are symmetric under Lorentz coordinate transformations, as relativity claims they should be. The practical problem with this is that there's a whole soup of physical quantities that we're interested in that we'd like to have theories about. Some of these (like, say, the electric charge of a particle) are invariants, but many quantities are reference-frame dependent (for instance, velocity, momentum, energy, frequency, just about any current or density, the electric and magnetic field components, and on and on), and when we come up with theories about how these quantities are related to each other we need to make sure that we're equating them a consistent way.

What Minkowski did was invent a four-dimensional vector/tensor notation for relativistic physics that makes it much simpler to keep track of this zoo. He introduced a way of classifying physical quantities according to how they depend on the choice of reference frame: basically, represent all physical quantities as either invariants or as the components of four-vectors and tensors, which all share a common transformation rule if you change from one reference frame to another. This makes it almost trivially easy to develop theories that are compatible with the relativity principle: basically, any theory defined in terms of four-vectors and tensors and following a few simple rules is automatically guaranteed to be symmetric under Lorentz transformations. For example, if you have an equation in a theory saying

$$\text{a four vector} = \text{another four vector} \,,$$​

then the components on both sides of the equation change in the same way if you change the reference frame, so the equation is preserved by the change of reference frame.

For a simple example of this, quantum physics says that the energy and momentum of a quantum particle are related to its wavefunction's (angular) frequency and wavevector by the de Broglie relations:

$$\begin{eqnarray}
E &=& \hbar \, \omega \,, \\
\boldsymbol{p} &=& \hbar \, \boldsymbol{k} \,.
\end{eqnarray}$$​

In Minkowski's notation, you can group energy and momentum together into a four-vector called the "four-momentum", defined by $$p^{\mu} = (E/c,\, p_{\mathrm{x}}, p_{\mathrm{y}}, p_{\mathrm{z}})$$, and, like I mentioned earlier in this thread, you can group the frequency and wavevector of a wave into the "four-wavevector" $$k^{\mu} = (\omega/c,\, k_{\mathrm{x}}, k_{\mathrm{y}}, k_{\mathrm{z}})$$. So, in Minkowski's notation, the de Broglie relations would just be expressed as

$$p^{\mu} = \hbar \, k^{\mu} \,.$$​

This is mathematically equivalent to the way the de Broglie relations are written above, but expressing them in this way makes it immediately obvious, to any physicist familiar with Minkowski's framework, that the de Broglie relations are compatible with the relativity principle.

To summarise, Minkowski introduced a mathematical book-keeping tool that makes it trivially easy and systematic to show that theories are consistent with special relativity. This might not be much of a concern to you personally, but it's something we need to do all the time in theoretical physics and it's why Minkowski's framework is as widely used as it is, and your bizarre rants about "19th century mathematics" and such show virtually no understanding or even awareness of this.

I have shown that the framework of which you speak is neither consistent nor extensible, and is based upon an inconsistent spacetime geometry that posits inertia as well as absolute space and time where none exists.

The aether theory of the 19th century seemed to them to be trivially easy to understand and to apply as well. Perhaps that complacency is part of the problem. It took someone as brilliant as Einstein to disrupt it even briefly. I'm no Einstein, but I know when I have been conned. Minkowsi understood quadratics and tried for all he was worth to see them everywhere he looked. That's why his theory of spacetime is Pythagorean. That's why he proposed a 4D interval to replace an invariant speed of light when he had no conception of what time was. Perhaps he believed that light cones shaped like little hour glasses would make up for his ignorance. That isn't how physics works. That isn't how anything works.

What I have proposed to replace it requires no static geometry or elimination of the variable we call time which Minowski and those who carried on the fight to retain Euclidean space in a relativistic universe put forth in the decades after his death in 1908. It makes quantum FTL and astrophysical processes as well as relativity as easily understood as you seem to think Minkowski accomplished with his conglomeration of obtuse and obscure geometry involving tensors where there should only be light travel time, and curvature of space where there should only be time dilation.

If you really had understanding of what momentum and energy is, you should be able to relate both fundamentally to time itself and also to inertia, both rotational and linear, for both bound and unbound energy. There seems to be a gaping hole or three in your self-consistent math. I'm sure you don't care. Minkowsi, even if he had lived to see part of the atomic age like his students did, probably wouldn't either.

There was no unified field theory in 1908, and thanks to thinking like 19th century mathematicians like him, there still isn't.

 

[The God]

First, this is NOT an alternative theory.

It is well KNOWN AND APPLIED science that physical standard lengths are defined by NIST as a number of wavelengths of a hyperfine transition of a cesium atom, and that one of the reasons it is so defined is due to relativity's determination that the speed of light is a strong invariant.

While it would be impossible to actually disprove any of the analysis of Minkowski relating to Lorentz covariance (spatial relationship to time), a recent discussion with Q-reeus about maximal photon energy has suggested a means to motivate a more careful consideration about exactly what was lost when Minkowski decided to create another invariant called the interval, along with inconsistent expressions for 4D rotations and the relativity of simultanaeity which does not include descriptions of things like quantum entanglement or FTL phenomena which are also NOT ALTERNATIVE SCIENCE, even though it lacks a solid base of mathematics to help us understand how it works. Also, Minkowski provided a version of length contaction that involved physical rotations in 4 dimensions for matter, and then completely ignored the possibility of providing a similar 4D rotational template for explaining relativistic Doppler shifts of propagating light. Why the omission? Why would the bound energy that is matter undergo Minkowski rotation when propagating unbound energy did not? At last, I have found a partial definitive answer.

I have often pointed out that space may be expressed as light travel time. This is not alternative science either. Light years and light nanoseconds alike have well defined physical meaning.

Consider the expression of a velocity as a ratio of how fast something moves (space or light travel time) vs how fast something else moves. The something else could be the hands of a stopwatch or a beam of light traveling at c.

So for linear velocities, the speed of light can be used to define any 3D (or even 4D) length. Add the element of rotation in an infinitude of possible directions and it is just possible that space and time are more simply related than Minkowski ever believed.

With light propagation used as a ruler, the measure of the speed of light becomes unity, a concept often used by Einstein himself.

Let's take that idea a little deeper. The expression for tangential velocity for uniform circular motion is given by v = omega x r, where omega is the angular velocity and r is the radius. What an extraordinary concept this is when light travel times are substituted for physical lengths. Rotational propagation of energy must occur at c x c = c^2. Where have we seen this term before? This makes perfect physical sense. If your intention is to make something relativistic (a particle or a wave) trace a relativistic circular trajectory, you will need to push it tangentially at c while it is propagating at c. The vectors may not add as they do in Euclidean space, but on the other hand, this actually is a geometrically unique case, and I think it just might work.

While a beam of photons traverses the known universe at c with no passage of time from the photon's point of view, the c^2 rate of propagation of relativistic rotation assures that the bound energy that is matter may persist in time, and that time itself is a superposition of both linear and rotational propagation modes. The rotational one (and also quantum entanglement) is much faster than c, and science already knows this for certain. We have just provided the math to support why this is the case. Any discussion of simultanaeity without a consideration of processes which occur >c would seem ludicrous to anyone other than Minkowski.

Something that is science is scaffolded and extrapolated from existing science in an inductive manner that pseudoscience can never match. We know pseudoscience because it can be falsified. I have just falsified Minkowski 4D rotation and his ideas about simultaneity. I have explained faster than light rotation of bound matter in what some would term classical physics. I have a different working definition of what classical physics means, and Minkowski's work does not even qualify for that description. It has impeded progress in relativity physics for about 100 years too long

This thread is in all directions. Can you please put your theory or propositions in 2-3 two liners. I am confident and It will be proved (very soon) that both SR and GR are incomplete, you will be shocked (in time to come) to realise that GR maths holds the key along with emission of light at c by any source irrespective of source motion.

The basic premises of GR is wrong, but we will have almost the same maths even if premises is corrected, thats the beauty of GR maths, and hat off to tensor guys.....this coupled with emitted light speed always at c...will define the cosmology very soon....Schmelzer has good future. Who knows you too.

So please put your propopsitions pointwise, remove the extra flab of what you think and what Minko thought.[/B][/B]

 

[el es]

From post#1:

"I have often pointed out that space is light travel time."

Light travel time is a measurement of something, not the thing itself.

From post#76;

"Time and energy is all there is."

How do you calculate the value of time dilation with energy alone?

What is it relative to?

 

[danshawen]

From post#1:

"I have often pointed out that space is light travel time."

Light travel time is a measurement of something, not the thing itself.

From post#76;

"Time and energy is all there is."

How do you calculate the value of time dilation with energy alone?

What is it relative to?

From #1:

My point is exactly what I said. A measurement of a velocity is a ratio of how fast something (time) happens compared to how fast something else (time) happens. Quantum entanglement states change faster than anything else, including the propagation of light in a vacuum in an unbounded straight straight trajectory. The mathematical nature of time depends on whichever is faster. Anyone who says that Minkowski nailed this bit of basic physics with equations that cannot even represent FTL other than a complex number is a liar.

From #76:

Time dilation is measured with respect to "at rest" relative to light speed, in the case of bound energy that is matter. Time dilation INSIDE if the bound energy that is matter, is measured relative to the exact physical geometrical centers of bound particles. If there is an absolute 'space' or 'time' in the relativistic universe of energy transfer events, this is the only place you will ever find it.

 

[danshawen]

Mathematics depends on closure in order to remain consistent. Physics cannot support such closure and remain a science.

 

[Schneibster]

If Minkowski rotation exists, what is the specific RATE AND DIRECTION (CW OR CCW) of that rotation, in radians/sec?

I assume you mean to talk about motion, in which case the "rotation" (actually more properly the angle) of the 4-vector is static. There is only a rate of rotation if there is acceleration, as that is change in the angle, as "rate" implies.

The angle of rotation in spacetime is also called "rapidity." "Relativity rapidity lorentz transform" is a pretty good search string. Rapidity links quite closely with the gamma factor which is used in the modern version of the algebraic Lorentz transformation.

Because time has a negative index, it follows mathematically that it is hyperbolic in its relation to the spatial dimensions, whereas the spatial dimensions are circular in their relations to one another. Thus, instead of ordinary circular trigonometry, we must use hyperbolic trig.

The Lorentz transforms are therefore, in hyperbolic terms:

t → (cosh s)t + (sinh s)x
x → (sinh s)t + (cosh s)x
y → y
z → z

for motion in the x direction. The angle is s, also known as I noted above as the rapidity.

This is what physicists mean when they talk about velocity being a rotation in spacetime. It might be a bit better to think of it as an angle in spacetime, and it's also important to remember that the angle is dependent upon what frame of reference it is viewed from.

Go ahead, make that a mathematical convention also, just like 19th century mathematical minds did for the coordinates of the AXIS OF MINKOWSKI ROTATION IN ALL INERTIAL REFERENCE FRAMES.

I can't follow your thinking here. You'll need to be more explicit what you mean by "making <something> a mathematical convention."

 

[danshawen]

I assume you mean to talk about motion, in which case the "rotation" (actually more properly the angle) of the 4-vector is static. There is only a rate of rotation if there is acceleration, as that is change in the angle, as "rate" implies.

The angle of rotation in spacetime is also called "rapidity." "Relativity rapidity lorentz transform" is a pretty good search string. Rapidity links quite closely with the gamma factor which is used in the modern version of the algebraic Lorentz transformation.

Because time has a negative index, it follows mathematically that it is hyperbolic in its relation to the spatial dimensions, whereas the spatial dimensions are circular in their relations to one another. Thus, instead of ordinary circular trigonometry, we must use hyperbolic trig.

The Lorentz transforms are therefore, in hyperbolic terms:

t → (cosh s)t + (sinh s)x
x → (sinh s)t + (cosh s)x
y → y
z → z

for motion in the x direction. The angle is s, also known as I noted above as the rapidity.

This is what physicists mean when they talk about velocity being a rotation in spacetime. It might be a bit better to think of it as an angle in spacetime, and it's also important to remember that the angle is dependent upon what frame of reference it is viewed from.

I can't follow your thinking here. You'll need to be more explicit what you mean by "making <something> a mathematical convention."

And if it hyperbolic rotated in the other direction, what would that mean?

Would it make a difference to the sense of rotation on which SIDE of the relativistic projectile the observer was? Hint: yes. In this respect, the analysis abruptly drops from the 4D world back to 3D, just as your hyperbolic math suggests. Which kind of rotation is it, exactly?

The relativistic 57 Chevy rotates CW as viewed from the driver side, CCW as viewed from the passenger side as it speeds past while you are watching the tail lights.

When you ask a Minkowski indoctrinated person from which end a Lorentz contracted object contracts (assume UNEQUAL DENSITY), or exactly where is the axis of rotation, you will get only mathematical convention for an answer. Why, from its geometrical center of cousrse. This is not science. I'm certain, it is perfectly consistent in terms of the math, so don't bother. This is not about the math. If it was, I would have titled this thread as a mathematical proof, which it isn't. It can't possibly be successfully argued that the math is in error. But the physics is.

 

[Schneibster]

And if it hyperbolic rotated in the other direction, what would that mean?

You mean the motion was in -x, not in +x? Because that's the only way this is meaningful, other than time reversal, which is unphysical.

Would it make a difference to the sense of rotation on which SIDE of the relativistic projectile the observer was? Hint: yes.

Actually, no. If you see an object moving away from you at v, you see the same foreshortening, apparent mass gain, and time dilation as you do if it's moving toward you at v. And we have measured this on the decay times of muons, among many other ways.

In this respect, the analysis abruptly drops from the 4D world back to 3D, just as your hyperbolic math suggests. Which kind of rotation is it, exactly?

It's an angle, not a rotation as you mean it since you're talking about a rate of rotation, and it's an angle in 4D spacetime. You can't just ignore time and hope it goes away; this stuff has been experimentally validated.

The relativistic 57 Chevy rotates CW as viewed from the driver side, CCW as viewed from the passenger side as it speeds past while you are watching the tail lights.

Err, you mean above and below, not one side and the other. And your analogy fails because you haven't taken time into account integrally; you're still trying to separate time from space and that's not going to work in relativity.

When you ask a Minkowski indoctrinated person from which end a Lorentz contracted object contracts (assume UNEQUAL DENSITY), or exactly where is the axis of rotation, you will get only mathematical convention for an answer. Why, from its geometrical center of cousrse. This is not science.

A Lorentz transformed object doesn't contract from an end. It contracts overall, the same at each point along it, and only in the frame of an observer moving at a different velocity than it is.

You are also making a serious mistake in talking about axes of rotation; the proper way to think about rotation is in a plane of rotation. By using axes you are trying to use your intuitive understanding of rotations, which is only valid in 3D. If you think about planes of rotation, then the plane of rotation of an object that rotates to some angle in space is x-y, x-z, or y-z, or some combination of them; and, of course, adding t adds three more planes of rotation, x-t, y-t, and z-t, for a total of six, not four as your intuitive understanding (driven by the fact that in 3D space, the axis of rotation in the x-y plane happens to coincide with the z axis) suggests. This is not as monstrous as it seems; in 2D, rotation is only possible in one plane, the x-y plane, and the axis of rotation points in a direction that does not exist. So it's not meaningful to ask what the axis of rotation is in 4D; your perception that it is meaningful is entirely the result of the coincidence that the axis of rotation in 3D happens to point in the direction of the third dimension for rotation in a plane defined by the other two.

 

[rpenner]

Each and every subatomic particle of matter or antimatter has its very own frame of reference,

Incorrect. Every ponderable classical phenomenon conveying energy and momentum has its own subluminal state of motion. But a frame of reference also needs three spatial directions and a space-time event to serve as the origin of a system of coordinates. These are lacking in the classical view of particles.

Quantum Physics means we cannot pretend to know a particle's momentum and energy both, and this renders the idea more remote from reality.

To explain simultanaeity that occurs FTL

What, in your opinion, needs to be explained about simultaneity? Remote events either happen with a slower-than-light space-time separation, a same-as-light space-time separation or a FTL space-time separation and their is always a valid system of coordinates in which to do physics that renders the third case as simultaneous.

 

[danshawen]

But a frame of reference also needs three spatial directions and a space-time event to serve as the origin of a system of coordinates.

And you don't think that the geometrical centers of subatomic particles are eligible to be "the origin of a system of coordinates? for an inertial reference frame?"

Please tell us why you think this idea is wrong. What origin would be more suitable?

Come on, rpenner. You have previously stated that such particles are viewed by QM as ideal points. What has changed?

 

[danshawen]

Remote events either happen with a slower-than-light space-time separation, a same-as-light space-time separation or a FTL space-time separation and their is always a valid system of coordinates in which to do physics that renders the third case as simultaneous.

The third case (FTL light travel time separation) is the ONLY system of coordinates that assures true simultaneity of ENERGY TRANSFER events that are not the same event viewed from different perspectives.

SHM in this universe is never perfectly synchronous with any other SHM, and that covers all particles and wave motion. Only entangled events may be simultaneous. This renders all of Minkowski's simultaneity math invalid. Nothing is FTL in his math.

 

[arfa brane]

And you don't think that the geometrical centers of subatomic particles are eligible to be "the origin of a system of coordinates? for an inertial reference frame?"

No, because of the uncertainty principle and being unable to locate the center of any particle.

Come on, rpenner. You have previously stated that such particles are viewed by QM as ideal points. What has changed?

Viewing quantum particles as ideal points doesn't mean the points have definite locations, or energies. That's why QM is about statistics (really).

The third case (FTL light travel time separation) is the ONLY system of coordinates that assures true simultaneity of ENERGY TRANSFER events that are not the same event viewed from different perspectives.

I can't really parse that. But I can say that entanglement has nothing to do with FTL transfer of energy.

Only entangled events may be simultaneous. This renders all of Minkowski's simultaneity math invalid. Nothing is FTL in his math.

Rubbish, two synchronized clocks have synchronous events. There is no FTL travel, communication, or entanglement--entanglement occurs when particles interact and they don't interact at FTL speeds. Entanglement is quite ordinary, but measurement of entangled states isn't.

 

[danshawen]

No, because of the uncertainty principle and being unable to locate the center of any particle.

Dang it.

http://www.sjsu.edu/faculty/watkins/yukawa.htm

Special Relativity works with pi mesons. It works with the center of those particles being inertial reference frames.

It works with the centers of EVERY PARTICLE OR ATOM as a DIFFERENT inertial reference frame, EACH ONE with DIFFERENT RATES OF TIME DILATION.

Even particles of different inertial rest masses experience different rates of time dilation.

The uncertainty principle has very little to do with what I have asserted in terms of every particle having its own inertial reference frame due to relative motion with respect to other particles.

This is actually a physics forum, isn't it?

For Mr. Minkowski's version of simultaneity to work, the two simultaneous events would need to be at the same place at the same time, IN THE EXACT 'PRESENT' VERTEX OF ONE OF HIS LIGHT CONES, not separated from the other 'simultaneous' event by even a single yocktosecond of light travel time. That rules out most events in this universe, other than entangled state changes, as simultaneous unless they are the same event viewed from different perspectives.

Strange ideas coming from a 19th century mathematician who never had a clue about what time is. His geometry was certainly timeless, as are the minds who continue to believe that he knew anything about physics. By that I mean, they aren't likely ever to leave the 19th century.

 

[arfa brane]

Special Relativity works with pi mesons.

Yea. those are relativistic particles is why. You can describe a center-of-mass frame for reasons I can't go into, but it's roughly because "particles" at relativistic velocities do look ballistic, like little projectiles.

It works with the center of those particles being inertial reference frames.

Please justify this claim.

It works with the centers of EVERY PARTICLE OR ATOM as a DIFFERENT inertial reference frame, EACH ONE with DIFFERENT TIME DILATIONS.

Nah.

You should look into what "particle" means in the context of modern physics.

 

[rpenner]

And you don't think that the geometrical centers of subatomic particles are eligible to be "the origin of a system of coordinates? for an inertial reference frame?

For the reason a line may not substitute for a point.

 

[Schneibster]

danshawen, let me put that thing about planes of rotation another way: you are confusing an axis of rotation with a dimension. Maybe that will help. In fact, this is a general rule: in spaces of an even number of dimensions, the axis is always pointing outside of those dimensions, that is, in a direction they cannot define, whereas in spaces of odd dimension, the axis always points in a direction defined within them.

 

[rpenner]

If Minkowski rotation exists, what is the specific RATE AND DIRECTION (CW OR CCW) of that rotation, in radians/sec?

The analogy between hyperbolic rotations and rotations in three dimensions in space is an analogy between two types transformations between geometrically equivalent coordinate systems. There is no concept of motion or rate with the latter and therefore no analogy with rate with the former.

So your demand seems ignorant and specious.

$$\vec{\zeta} \to A(\vec{\zeta}) = \begin{pmatrix}0 & \zeta_x & \zeta_y & \zeta_z \\ \zeta_x & 0 & 0 & 0 \\ \zeta_y & 0 & 0 & 0 \\ \zeta_z & 0 & 0 & 0 \end{pmatrix}
\\ A(\vec{\zeta})^2 = \begin{pmatrix}\zeta^2 & 0 & 0 & 0 \\ 0 & \zeta_x^2 & \zeta_x \zeta_y & \zeta_x \zeta_z \\ 0 & \zeta_x \zeta_y & \zeta_y^2 & \zeta_y \zeta_z \\ 0 & \zeta_x \zeta_z & \zeta_y \zeta_z & \zeta_z^2 \end{pmatrix}
\\ A(\vec{\zeta})^3 = \zeta^2 A(\vec{\zeta})
\\ A(\vec{\zeta})^4 = \zeta^2 A(\vec{\zeta})^2
\\ \Lambda(\vec{\zeta}) = e^{A(\vec{\zeta})} = I + \frac{ \sinh \sqrt{ \zeta^2 } }{ \sqrt{ \zeta^2 } } A(\vec{\zeta}) + \frac{ \cosh \sqrt{ \zeta^2 } - 1 }{ \zeta^2} A(\vec{\zeta})^2
\\ \Lambda(-\vec{\zeta}) = I - \frac{ \sinh \sqrt{ \zeta^2 } }{ \sqrt{ \zeta^2 } } A(\vec{\zeta}) + \frac{ \cosh \sqrt{ \zeta^2 } - 1 }{ \zeta^2} A(\vec{\zeta})^2
\\ \Lambda(\vec{\zeta}) \Lambda(-\vec{\zeta}) = \left( I + \frac{ \sinh \sqrt{ \zeta^2 } }{ \sqrt{ \zeta^2 } } A(\vec{\zeta}) + \frac{ \cosh \sqrt{ \zeta^2 } - 1 }{ \zeta^2} A(\vec{\zeta})^2 \right) \left( I - \frac{ \sinh \sqrt{ \zeta^2 } }{ \sqrt{ \zeta^2 } } A(\vec{\zeta}) + \frac{ \cosh \sqrt{ \zeta^2 } - 1 }{ \zeta^2} A(\vec{\zeta})^2 \right)
\\ \quad \quad \quad = I + \frac{ 2 \cosh \sqrt{ \zeta^2 } - 2 - \sinh^2 \sqrt{ \zeta^2 } + \cosh^2 \sqrt{ \zeta^2 } - 2 \cosh \sqrt{ \zeta^2 } + 1}{ \zeta^2} A(\vec{\zeta})^2
\\ \quad \quad \quad = I
$$
$$\vec{\theta} \to B(\vec{\theta}) = \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & -\theta_z & \theta_y \\ 0 & \theta_z & 0 & - \theta_x \\ 0 & -\theta_y & \theta_x & 0 \end{pmatrix}
\\ B(\vec{\theta})^2 = \begin{pmatrix}0 & 0 & 0 & 0 \\ 0 & \theta_x^2 - \theta^2 & \theta_x \theta_y & \theta_x \theta_z \\ 0 & \theta_x \theta_y & \theta_y^2 - \theta^2 & \theta_y \theta_z \\ 0 & \theta_x \theta_z & \theta_y \theta_z & \theta_z^2 - \theta^2\end{pmatrix}
\\ B(\vec{\theta})^3 = -\theta^2 B(\vec{\theta})
\\ B(\vec{\theta})^4 = -\theta^2 B(\vec{\theta})^2
\\ R(\vec{\theta}) = e^{B(\vec{\theta})} = I + \frac{ \sin \sqrt{ \theta^2 } }{ \sqrt{ \theta^2 } } B(\vec{\theta}) + \frac{ 1 - \cos \sqrt{ \theta^2 } }{ \theta^2} B(\vec{\theta})^2
\\ R(-\vec{\theta}) = I - \frac{ \sin \sqrt{ \theta^2 } }{ \sqrt{ \theta^2 } } B(\vec{\theta}) + \frac{ 1 - \cos \sqrt{ \theta^2 } }{ \theta^2} B(\vec{\theta})^2
\\ R(\vec{\theta}) R(-\vec{\theta}) = \left( I + \frac{ \sin \sqrt{ \theta^2 } }{ \sqrt{ \theta^2 } } B(\vec{\theta}) + \frac{ 1 - \cos \sqrt{ \theta^2 } }{ \theta^2} B(\vec{\theta})^2 \right) \left( I - \frac{ \sin \sqrt{ \theta^2 } }{ \sqrt{ \theta^2 } } B(\vec{\theta}) + \frac{ 1 - \cos \sqrt{ \theta^2 } }{ \theta^2} B(\vec{\theta})^2 \right)
\\ \quad \quad \quad = I + \frac{ 2 - 2 \cos \sqrt{ \theta^2 } - \sin^ \sqrt{ \theta^2 } - 1 + 2 \cos \sqrt{ \theta^2 } - \cos^2 \sqrt{ \theta^2 } }{ \theta^2} B(\vec{\theta})^2
\\ \quad \quad \quad = I
$$

$$\Lambda(\rho \hat{x})$$ "rotates" $$(ct = \textrm{sech} \, \rho, x=0, y=0, z=0)$$ to $$(ct' = 1, x'= \tanh \rho, y'=0, z'=0)$$ in a manner to how $$R(t \hat{z})$$ rotates $$(ct = 0, x= \sec t, y=0, z=0)$$ to $$(ct' = 0, x'= 1, y'= \tan t, z'=0)$$. Both are linear transformations, preserve colinearity of trajectories and preserve $$(ct)^2 - x^2 -y^2 -z^2 = (ct')^2 - x'^2 -y'^2 -z'^2$$.

 

[danshawen]

Yea. those are relativistic particles is why. You can describe a center-of-mass frame for reasons I can't go into, but it's roughly because "particles" at relativistic velocities do look ballistic, like little projectiles.
Please justify this claim.Nah.

You should look into what "particle" means in the context of modern physics.

Not only do I understand wave-particle duality; I also understand how pairs of waves of energy combine in FTL rotationally propagating energy configurations, and also why these energy knots can persist indefinitely in time without loss.

This understanding comes at the discount price of an understanding that it doesn't work with Euclidean geometry, coordinate systems, absolute space or absolute time in any form contemplated since 1908.

Anything that moves or rotates relative to something else are the only coordinate systems you will ever need to understand and explain a universe of energy transfer events. That they (rotation vs translation of propagating energy) occur at vastly different rates is going to surprise a great many people, and this is unavoidable.

To clear up simultanaeity once and for all:

There really are two categories of simultanaeity.

One variety, Minkowski's brand, is the simultanaeity of the photonics beam splitter or interferometer. This is not true simultanaeity because time has a much finer granularity than the linear propagation of photons. It physically has to. Those EM FIELDS VARY WITH TIME. Minkowski's simultanaeity is limited by the speed of light, relative to the frame that is at rest with respect to bound energy.

The other variety of simultanaeity is associated with the bound energy that is matter and quantum entanglement. It is not limited by the linear propagation rate of c because particles of matter are bound PAIRS of energy propagating in a rotational mode IN OPPOSITE DIRECTIONS. Entanglement simultanaeity is associated with the inertial reference frame AT REST with respect to the bound energy that is matter.

ONLY ONE of these categories is true simultanaeity, and here's a hint: it IS DECIDEDLY NOT the one conceived of by Minkowski. It cannot be so. The vertices of his light cones are separated by simple linear light travel time between 'at rest' points in space separated by simple linear light travel time. Entanglement is faster. Now you also understand why.