Proof Minkowski Spacetime is Poorly Conceived

[danshawen]

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

 

[exchemist]

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

Sounds like "Alternative Theories" to me. "Faster than light rotation of bound matter"?? How is that not alternative? Do you have references for this concept (apart from vixra)?

 

[Dr_Toad]

It doesn't work if c = 1, does it?

 

[origin]

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
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

I 've gone ahead and requested that mods move this to the appropriate section for you.

 

[danshawen]

I 've gone ahead and requested that mods move this to the appropriate section for you.

I hope you were specific about what parts offended you. Science isn't pseudoscience JUST BECAUSE SOMEONE SAYS IT IS. I have been very specific. Follow the example.

Thanks for you opinion, at least.

 

[danshawen]

It doesn't work if c = 1, does it?

Relativity does work if c=1, Dr_Toad. In fact, it is a time honored mathematical tradition in relativity theory.

 

[danshawen]

Sounds like "Alternative Theories" to me. "Faster than light rotation of bound matter"?? How is that not alternative? Do you have references for this concept (apart from vixra)?

This time, exchemist, I have actually derived that result mathematically using only simple algebra and a determination that space is equivalent to light travel time. The technological consequences of this are manifest and far reaching, starting with NIST's standard of length.

 

[arfa brane]

The rotational one (and also quantum entanglement) is much faster than c, and science already knows this for certain.

You have yet to show that anything propagates between entangled states.

You will need to demonstrate conclusively that entanglement is not an artifact of measurement and that entangled particles do actually communicate "something" at faster than c. I don't know that anyone has managed to do this.

Also, suppose a beam of light is circularly polarized. Does the rate of rotation of the polarization vector exceed c?

Finally, science, in particular physics, is based on measurement. You will need to "invent" some method of measuring speeds that exceed c. I think that's the showstopper right there.

 

[Ophiolite]

The technological consequences of this are manifest

Obviously my inadequate knowledge of physics, limited logical skills, poor critical thinking and impoverished IQ have combined to cloud my perception. Please share a couple of these technological consequences, so apparent to yourself and, doubtless, trios of others.

 

[Dr_Toad]

Relativity does work if c=1, Dr_Toad. In fact, it is a time honored mathematical tradition in relativity theory.

Not if you're taking the square of c as some magical new thing, since it is still 1.

Rotational propagation of energy must occur at c x c = c^2.

 

[przyk]

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?

Huh? First, the components of four vectors in different reference frames are not related by rotations. They are related by Lorentz transformations. These are analogous to rotations in some ways but they are not the same. For instance, Lorentz transformations preserve the Minkowski "norm" $$(x^{0})^{2} - (x^{1})^{2} - (x^{2})^{2} - (x^{3})^{2}$$ of a four vector $$x^{\mu} = (x^{0},\, x^{1},\, x^{2},\, x^{3})$$, while 4D rotations preserve the Euclidean norm $$(x^{0})^{2} + (x^{1})^{2} + (x^{2})^{2} + (x^{3})^{2}$$.

Second, you can represent the frequency, wavelength, and direction of propagation of a sinusoidal wave by a wave four vector $$k^{\mu} = \bigl( \omega/c,\, \boldsymbol{k} \bigr)$$, where $$\omega$$ is the angular frequency (related to the frequency $$f$$ by $$\omega = 2 \pi f$$) and $$\boldsymbol{k} = (k_{\mathrm{x}}, k_{\mathrm{y}}, k_{\mathrm{z}})$$ is the (3D) wave vector (this is a vector that points in the direction the wave is propagating in and its norm is related to the wavelength by $$\lVert \boldsymbol{k} \rVert = 2 \pi / \lambda$$). In terms of these a (e.g., complex wave of amplitude $$A$$) might be given by

$$\phi(x^{\mu}) = A e^{- i k_{\mu} x^{\mu}} \,.$$​

Setting $$x^{\mu} = (ct,\, \boldsymbol{x})$$, the Minkowski product inside the exponential above expands to $$- k_{\mu} x^{\mu} = \boldsymbol{k} \cdot \boldsymbol{x} - \omega t$$.

Like other four vectors, the wave four vector is defined in such a way that its components in different inertial reference frames are related by Lorentz transformations. For the simple case of a wave propagating in the $$\mathrm{x}$$ direction (i.e., taking $$k_{\mathrm{x}} = k$$ and $$k_{\mathrm{y}} = k_{\mathrm{z}} = 0$$) and considering a Lorentz boost of speed $$v$$ in the $$\mathrm{x}$$ direction, the components of the wave vector in the reference frames related by the boost would be related by

$$\begin{bmatrix} \tfrac{\omega'}{c} \\ k' \end{bmatrix} = \begin{bmatrix} \gamma & - \gamma \tfrac{v}{c} \\ -\gamma \tfrac{v}{c} & \gamma \end{bmatrix} \begin{bmatrix} \tfrac{\omega}{c} \\ k \end{bmatrix} \,,$$​

with $$\gamma = 1 / \sqrt{1 - v^{2} / c^{2}}$$. The first row of this matrix equation says that $$\omega'$$, $$\omega$$, and $$k$$ are related by

$$\frac{\omega'}{c} = \gamma \frac{\omega}{c} - \gamma \frac{v}{c} k \,,$$​

or just

$$\omega' = \gamma \omega - \gamma v k \,.$$​

Finally, if the wave is moving with speed $$c$$, then $$\omega$$ and $$k$$ are related by $$\omega / k = c$$, which rearranges to $$k = \omega / c$$, so that

$$\begin{eqnarray}
\omega' &=& \gamma \bigl(1 - \frac{v}{c} \bigr) \omega \\
&=& \frac{1 - \tfrac{v}{c}}{\sqrt{1 - \tfrac{v^{2}}{c^{2}}}} \, \omega \\
&=& \frac{1 - \tfrac{v}{c}}{\sqrt{1 + \tfrac{v}{c}} \sqrt{1 - \tfrac{v}{c}}} \, \omega \\
&=& \frac{\sqrt{1 - \tfrac{v}{c}}}{\sqrt{1 + \tfrac{v}{c}}} \, \omega \,,
\end{eqnarray}$$​

which is one way to derive the relativistic Doppler relation for a Lorentz boost in the direction of wave propagation.

 

[danshawen]

Not if you're taking the square of c as some magical new thing, since it is still 1.

You are still thinking of v = omega x r in terms of Euclidean vectors. This evidently was Minkowski's mistake as well. I have no doubt that even if he knew this, he could not reconcile it with any of the 19th century math he knew.

The dynamics of this mode of propagation is very likely much more complex in terms of composite rotations than the simple 2D model I have proposed, but now it is clear that it must propagate faster than the speed of light in the linear mode and also why this is the case.

 

[danshawen]

Also, suppose a beam of light is circularly polarized. Does the rate of rotation of the polarization vector exceed c?

No. Circular polarization of a light wave or energy may have some aggregate effect on composite rotation, but I don't claim to understand what that is. Electroweak bosons evidently obtain an extra degree of polarization freedom (compared to photons) that allows a sort of rolling.

I haven't a clue what sort of particle this mode of rotational propagation I am describing would produce, its charge, or anything else about it. All I have shown so far is that the rotational mode must be quite considerably faster than the linear mode. The expression derived is a strong hint that this is the fundamental process that provides inertial mass to particles of matter.

You will need to "invent" some method of measuring speeds that exceed c. I think that's the showstopper right there.

I actually don't think that will be much of a show stopper. But it does require a bit more thought.

 

[danshawen]

Obviously my inadequate knowledge of physics, limited logical skills, poor critical thinking and impoverished IQ have combined to cloud my perception. Please share a couple of these technological consequences, so apparent to yourself and, doubtless, trios of others.

Don't sell yourself short, Ophiolite. You are most welcome in the discussion.

The trio to which you refer disbanded long ago, but thanks for paying attention. This thread was instigated by a 30 year old Usenet discussion, and Q-reeus pushing me to finally finish it.

 

[Ophiolite]

Don't sell yourself short, Ophiolite. You are most welcome in the discussion.

The trio to which you refer disbanded long ago, but thanks for paying attention. This thread was instigated by a 30 year old Usenet discussion, and Q-reeus pushing me to finally finish it.

Excellent news. Now, as far as I can tell, and I grant you that's not very far, you don't seem to have answered my question. Perhaps you overlooked it, or perhaps you are - even now - constructing something that, on the face of it, would be a bombastic cornucopia of concatenated word salad, yet conceals an insightful explication of foundational import.

Either way - answer the frigging question.

 

[danshawen]

Excellent news. Now, as far as I can tell, and I grant you that's not very far, you don't seem to have answered my question. Perhaps you overlooked it, or perhaps you are - even now - constructing something that, on the face of it, would be a bombastic cornucopia of concatenated word salad, yet conceals an insightful explication of foundational import. I don't expect the answer is to be found by means of a recount. I doubt a recount would help. Math by itself only gets you so far.


Either way - answer the frigging question.

A deeper fundamental understanding of inertia is still needed. It has been almost four years sine the discovery of the Higgs boson and still there is no explanation forthcoming to reconcile either the idea that imparting inertia BY ANY MECHANISM creates a different kind of inertia than the most remarkable principle of equivalence. If it is different, I want to understand why. The US and Europe spent $6b on the LHC. We deserve a better explanation of why the math has stopped working. Is it incomplete, inconsistent, or merely a little of both?

How about finally unlocking fusion energy or more efficient hydroelectric plants, or perhaps something even more powerful? You should not expect that I have worked out the last detail about the design of something like that. I only found this relationship day before yesterday, and I'm many times Einstein's age when he derived E=mc^2. Previously, the best explanation for the c^2 term was John D. Norton's (University of Pennsylvannia) "world's shortest derivation of E=mc^2" combination of energy and momentum in a single expression. Now we know better. Somehow, I intuited that there was even a simpler way. Now you all know it. Someone should have told poor Minkowski: things should be described mathematically as complex as they need to be, but never more so.

But I do understand your keen interest. I don't plan on patenting anything. If you see a way to do that, you have my permission and endorsement to do so. I don't want your money to develop the idea, and besides, I'm sure there are plenty of scientists and pseudo scientists standing in line to do just that. Maybe that's the problem. I trust you to handle it.

 

[danshawen]

Huh? First, the components of four vectors in different reference frames are not related by rotations. They are related by Lorentz transformations. These are analogous to rotations in some ways but they are not the same. For instance, Lorentz transformations preserve the Minkowski "norm" $$(x^{0})^{2} - (x^{1})^{2} - (x^{2})^{2} - (x^{3})^{2}$$ of a four vector $$x^{\mu} = (x^{0},\, x^{1},\, x^{2},\, x^{3})$$, while 4D rotations preserve the Euclidean norm $$(x^{0})^{2} + (x^{1})^{2} + (x^{2})^{2} + (x^{3})^{2}$$.

Second, you can represent the frequency, wavelength, and direction of propagation of a sinusoidal wave by a wave four vector $$k^{\mu} = \bigl( \omega/c,\, \boldsymbol{k} \bigr)$$, where $$\omega$$ is the angular frequency (related to the frequency $$f$$ by $$\omega = 2 \pi f$$) and $$\boldsymbol{k} = (k_{\mathrm{x}}, k_{\mathrm{y}}, k_{\mathrm{z}})$$ is the (3D) wave vector (this is a vector that points in the direction the wave is propagating in and its norm is related to the wavelength by $$\lVert \boldsymbol{k} \rVert = 2 \pi / \lambda$$). In terms of these a (e.g., complex wave of amplitude $$A$$) might be given by

$$\phi(x^{\mu}) = A e^{- i k_{\mu} x^{\mu}} \,.$$​

Setting $$x^{\mu} = (ct,\, \boldsymbol{x})$$, the Minkowski product inside the exponential above expands to $$- k_{\mu} x^{\mu} = \boldsymbol{k} \cdot \boldsymbol{x} - \omega t$$.

Like other four vectors, the wave four vector is defined in such a way that its components in different inertial reference frames are related by Lorentz transformations. For the simple case of a wave propagating in the $$\mathrm{x}$$ direction (i.e., taking $$k_{\mathrm{x}} = k$$ and $$k_{\mathrm{y}} = k_{\mathrm{z}} = 0$$) and considering a Lorentz boost of speed $$v$$ in the $$\mathrm{x}$$ direction, the components of the wave vector in the reference frames related by the boost would be related by

$$\begin{bmatrix} \tfrac{\omega'}{c} \\ k' \end{bmatrix} = \begin{bmatrix} \gamma & - \gamma \tfrac{v}{c} \\ -\gamma \tfrac{v}{c} & \gamma \end{bmatrix} \begin{bmatrix} \tfrac{\omega}{c} \\ k \end{bmatrix} \,,$$​

with $$\gamma = 1 / \sqrt{1 - v^{2} / c^{2}}$$. The first row of this matrix equation says that $$\omega'$$, $$\omega$$, and $$k$$ are related by

$$\frac{\omega'}{c} = \gamma \frac{\omega}{c} - \gamma \frac{v}{c} k \,,$$​

or just

$$\omega' = \gamma \omega - \gamma v k \,.$$​

Finally, if the wave is moving with speed $$c$$, then $$\omega$$ and $$k$$ are related by $$\omega / k = c$$, which rearranges to $$k = \omega / c$$, so that

$$\begin{eqnarray}
\omega' &=& \gamma \bigl(1 - \frac{v}{c} \bigr) \omega \\
&=& \frac{1 - \tfrac{v}{c}}{\sqrt{1 - \tfrac{v^{2}}{c^{2}}}} \, \omega \\
&=& \frac{1 - \tfrac{v}{c}}{\sqrt{1 + \tfrac{v}{c}} \sqrt{1 - \tfrac{v}{c}}} \, \omega \\
&=& \frac{\sqrt{1 - \tfrac{v}{c}}}{\sqrt{1 + \tfrac{v}{c}}} \, \omega \,,
\end{eqnarray}$$​

which is one way to derive the relativistic Doppler relation for a Lorentz boost in the direction of wave propagation.

We are not discussing inertial reference frames here, but your confusion is understandable. Inertia comes in many varieties. That much, we have demonstrated.

 

[origin]

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.

OK.

What an extraordinary concept this is when light travel times are substituted for physical lengths.

Why is it extraordinary?

Rotational propagation of energy must occur at c x c = c^2.

Why?

Where have we seen this term before?

c^2 is seen in several equations.

This makes perfect physical sense.

The idea of energy propagating at c^2 makes no physical sense to me.

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.

First of all a particle (a massive particle) cannot travel at c. A photon travels at c but how in the world do you 'push' a photon at c. How do you 'push' a photon AT ALL?

A photon always follows the geodesic, so I do not understand your idea of 'pushing' a photon.

 

[danshawen]

OK.

Why is it extraordinary?

Why?

c^2 is seen in several equations.

The idea of energy propagating at c^2 makes no physical sense to me.

First of all a particle (a massive particle) cannot travel at c. A photon travels at c but how in the world do you 'push' a photon at c. How do you 'push' a photon AT ALL?

A photon always follows the geodesic, so I do not understand your idea of 'pushing' a photon.

This is all done with photons. Two of them, actually. The result is a theoretical particle that has inertial mass, but the mechanism by which that occurs is remarkable. I will attempt to provide a diagram. Very busy today.

Thanks for all of your comments. Please be patient.

 

[danshawen]

Let's formalize this.

I'm saying that v = omega x r
(expression for tangential velocity, classical uniform circular motion),

and also that r = c x t
(radius of a particle expressed in terms of light travel time)

And since omega has the units of angle/t, for a given radius, it follows immediately:

v = c x angle (referred to the radius of a particle),

And BECAUSE THE SPEED OF LIGHT IS INVARIANT EVEN IN THE CASE OF CIRCULAR PROPAGATION, AND ALSO BECAUSE WE ALREADY KNOW THAT PHOTON PARTICLE CREATION REQUIRES TWO PHOTONS, it follows that:

v = c^2

And because we have derived it using omega, this expression would hold REGARDLESS OF THE PHYSICAL DIMENSIONS OF THE PARTICLE.

The internal rate of propagation of energy within a particle of matter or antimatter is the equal to the square of the speed of light. So, incidentally, is the speed of quantum entanglement.

If you are more than a little put the off that a CLASSICAL DYNAMICAL EXPRESSION has been used to derive this result, let me remind you that Einstein used a classical dynamical expression involving the center of mass of a long spacecraft with a photon emission at one end, and something to completely absorb it at the other, to prove his most famous mathematical expression to an audience of Newtonian physicists.

The power of thinking of space in terms of light travel time is manifest here. Lorentz covariance, 4D intervals, and Minkowski rotations are demonstrated to be the frauds they are, and always were. Simultanaeity without entanglement in a universe of energy transfer events means nothing, and since we now understand that it can be no faster than c^2, it means even less, if that is possible.

Relativity has now been extended into the quantum domain, where it always belonged.

Don't bother asking any of my former physics and/or math teachers anything about this idea, nor anything about how brilliant their former student was or wasn't. The teachers who mattered most and who are not long dead are right here.