Proof Minkowski Spacetime is Poorly Conceived

[danshawen]

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 $$(ct)^2 - x^2 -y^2 -z^2 = (ct')^2 - x'^2 -y'^2 -z'^2$$.

And your answer is, as per usual, perfectly consistent. Thank you.

Translation: "it doesn't matter, because it doesn't matter."

 

[danshawen]

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.

I am not confusing rotation with a dimension.

Remember how I started this thread. If rotation is not a dimension, why did so many folks here object to v = omega x r when I converted both angular velocity and the radius into the equivalent dimensions of light travel time for uniform circular motion?

Actually, this was a cheat, because my intention was to show that a PAIR of photons bound while propagating/spinning in opposite directions was capable of an internal rate of propagation that exceeded c. So what I probably should have wrote was something like:

v1 = +c = omega1 x r1, and
v2 = -c = -omega2 x r2

But the second equation is not limited to a single mode of internal propagation. Within the structure, radial linear propagation at c occurs as well. This is why bulk matter may also "propagate" at relative speeds < c with respect to other matter in any direction. Time doesn't stop outside of a particle of bound energy, any more than it does for a beam coming out of a laser or a flashlight, as viewed from the rest frame.

The photons bind each other into a rotational mode of propagation. Because the relativistic tangential velocity is at right angles to radially propagating energy, this mode propagates internally faster than c, RELATIVE TO ANYTHING THAT IS EXTERNAL TO IT. The vectors do not sum in a Euclidean vector space. The space supports time dilation in the most extreme case imaginable. Time proceeds normally at the geometric center and dilates to infinity at the outside edge. Don't try to make this into a geometry problem until or unless you are ready to explore the geometrical nature of time itself.

 

[danshawen]

So your demand seems ignorant and specious.

I'm pleased you think so.

Whenever something physical, like a meter stick floating in a weightless environment in the cabin of a spacecraft, starts to or spin or rotate about any axis AT ANY RATE, it tends to continue to do so until and unless acted upon by another balanced force that halts the rotation.

But Minkowski 4D hyperbolic rotation of a relativistic projectile into another physical dimension is evidently nothing like that. It appears to rotate, and the observed 3D axis and direction of rotation is dependent upon the position of the observer and the geometry of the thing rotating relative to the position of the observer, and after it rotates by a fixed amount that is dependent upon its velocity relative to the observer, evidently SOMETHING STOPS IT FROM ROTATING ANY FURTHER. It is no secret that Minkowski never bothered to explain this effect in any significant detail, mathematically or otherwise. THIS SEEMS IGNORANT AND SPECIOUS AND ALSO INTELLECTUALLY DISHONEST TO ME.

The "proton pancakes" that circulate in opposing beams in the LHC undergo REAL, ACTUAL, PHYSICAL length contraction, just as predicted by Lorentz and Einstein. If they underwent a rotation too, this would not be surprising, since they are forced to follow a circular path before colliding with the other beam. The .05 mm beams are continuously refocused by means of superconducting quadrupole magnets, and are steered in circular paths by means of superconducting dipole magnets.

You are the one who taught me that the relativistic Doppler shifts of EM wavelengths were not the same effect as Lorentz contraction, and in principle I agree that they are not. For one thing, the Lorentz contraction does not change into a Lorentz expansion depending on whether it is approaching or receding from the observer, and time dilation does not abruptly change into time compression in the same situation either.

Of course it does not. The situation is a bit more finessed than that. On the one hand, you have the bound energy of a proton pancake composed of spaces between protons, and the physical manifestations of protons themselves, evidently composed of quarks, gluons, and color charge exchanges. The masses of the protons increase as they are accelerated. We know from Planck's relation that this mass increase corresponds to an increase in the internal frequency of any energy that is bound particles within the proton, and/or increases in the energy of the color charge exchanges between the quarks. How much of the added energy goes into the internal energy of the protons, and how much is left to contract the spaces between photons is currently anyone's guess.

Why don't you try calculating something like that, instead of showing us all what kind of a pedantic and intellectually dishonest mathematical ass Minkowski really was? Minkowski is not someone I would care to emulate, and I for one don't care if he is relativistically spinning in his too early grave right now.

 

[origin]

Danshawen, I understand better your vitrol towards your professor. Leaving school and going to Vietnam is horrible. I guess in looking at your life your have found this particular professor to be the focal point of where the train went off the tracks. But more specifically you have even identified the specific subject that the one professor was teaching that resulted in your issues. Since that one subject in your mind is responsible for your woes you have made it your mission to prove that the subject is wrong.

First of all there is rarely ONE thing that is responsible for our lot in life, and it is certainly not one subject in one course in college. Secondly why be so pissed off at Minkowski space? Why not just leave it that your professor sucked at teaching it and learn the ins and outs of what Minkowski space is in spite the evil professor?

 

[el es]

From post#142:

"Time proceeds normally at the geometric center and dilates to infinity at the outside edge."

I thought Wheeler determined that geons would be unstable.

 

[danshawen]

My impression from this discussion is that this revelation (Minkowski was wrong) is not something that is likely to shake physics to its core. It shouldn't. We only wish to remove the principle roadblock that has kept relativity from harmony and reconciliation with quantum physics for 100 years.

I think you will all find, it will be worth the effort, and I think you will also find, any math that does not derive of Minkowski will support any necessary changes.

 

[rpenner]

Tell me: when are you going to post some mathematical arguments that specify or support your claims?

Exactly. You are using "energy" in a sense that might make sense in a children's cartoon, but seem unable to explain your terms and claims in a way that would improve the practice of physics.

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

You have misunderstood the subject matter of the analogy.

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.

Exactly. Physics outsiders opinions rarely matter to how physics is done and taught because their opinions are not informed opinions and not opinions which have had the benefit of being demonstrated to be useful.

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.

[ ... Clear demonstration of some aspects of analogy ... ]

$$\Lambda(\rho \hat{x})$$ "rotates" $$(ct = \textrm{sech} \, \rho, x=0, y=0, z=0)$$ to $$(ct' = 1, x'= \tanh \rho, y'=0, z'=0)$$ in a manner [ analogous ] 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 $$(ct)^2 - x^2 -y^2 -z^2 = (ct')^2 - x'^2 -y'^2 -z'^2$$.

Repaired missing word of the last paragraph, lost in power outage.

And your answer is, as per usual, perfectly consistent.

Consistent with Special Relativity? Yes.
Consistent with the geometry of Minkowski space? Yes.

You didn't address the analogy, especially what remaining issues you might have with it.

Just to be clear:
$$\Lambda(\vec{\zeta}) = e^{A(\vec{\zeta})} = I + \frac{ \sinh \sqrt{ \zeta^2 } }{ \sqrt{ \zeta^2 } } A(\vec{\zeta}) + \frac{ \cosh \sqrt{ \zeta^2 } - 1 }{ \zeta^2} A(\vec{\zeta})^2
\\ R(\vec{\theta}) = e^{B(\vec{\theta})} = I + \frac{ \sin \sqrt{ \theta^2 } }{ \sqrt{ \theta^2 } } B(\vec{\theta}) + \frac{ 1 - \cos \sqrt{ \theta^2 } }{ \theta^2} B(\vec{\theta})^2
\\ \quad \quad \quad = I + \frac{ \sinh \sqrt{ -\theta^2 } }{ \sqrt{ -\theta^2 } } B(\vec{\theta}) + \frac{ \cosh \sqrt{ -\theta^2 } - 1}{ -\theta^2} B(\vec{\theta})^2$$
And A and B are both trace-less matrices with three linear degrees of freedom.

Translation: "it doesn't matter, because it doesn't matter."

Unclear antecedent.
If by "it" you mean "your claims that Minkowski space is not a good model for local space-time", you are correct. Your claims are baseless and so don't matter to physics.
If by "it" you mean "your claims that Minkowski space is not a good model for Special Relativity", you are incorrect. Your claims are intrinsically mathematical in nature and so being wrong matters of itself.

 

[danshawen]

Exactly. You are using "energy" in a sense that might make sense in a children's cartoon, but seem unable to explain your terms and claims in a way that would improve the practice of physics.
You have misunderstood the subject matter of the analogy.
Exactly. Physics outsiders opinions rarely matter to how physics is done and taught because their opinions are not informed opinions and not opinions which have had the benefit of being demonstrated to be useful.
Repaired missing word of the last paragraph, lost in power outage.
Consistent with Special Relativity? Yes.
Consistent with the geometry of Minkowski space? Yes.

You didn't address the analogy, especially what remaining issues you might have with it.

Just to be clear:
$$\Lambda(\vec{\zeta}) = e^{A(\vec{\zeta})} = I + \frac{ \sinh \sqrt{ \zeta^2 } }{ \sqrt{ \zeta^2 } } A(\vec{\zeta}) + \frac{ \cosh \sqrt{ \zeta^2 } - 1 }{ \zeta^2} A(\vec{\zeta})^2
\\ R(\vec{\theta}) = e^{B(\vec{\theta})} = I + \frac{ \sin \sqrt{ \theta^2 } }{ \sqrt{ \theta^2 } } B(\vec{\theta}) + \frac{ 1 - \cos \sqrt{ \theta^2 } }{ \theta^2} B(\vec{\theta})^2
\\ \quad \quad \quad = I + \frac{ \sinh \sqrt{ -\theta^2 } }{ \sqrt{ -\theta^2 } } B(\vec{\theta}) + \frac{ \cosh \sqrt{ -\theta^2 } - 1}{ -\theta^2} B(\vec{\theta})^2$$
And A and B are both trace-less matrices with three linear degrees of freedom.

Unclear antecedent.
If by "it" you mean "your claims that Minkowski space is not a good model for local space-time", you are correct. Your claims are baseless and so don't matter to physics.
If by "it" you mean "your claims that Minkowski space is not a good model for Special Relativity", you are incorrect. Your claims are intrinsically mathematical in nature and so being wrong matters of itself.

If a mathematical model is perfectly consistent for 80% of the cases it is used to analyze and 20% inconsistent with explaining the quantitative nature of new science, is that really good enough?

 

[Schneibster]

I am not confusing rotation with a dimension.

I didn't say you were. I said you were confusing an axis of rotation with a dimension.

 

[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.

I have shown that the framework of which you speak is neither consistent nor extensible

No you haven't. You've shown only that you don't understand what Minkowski's framework is, since you keep denying things that it doesn't claim.

Your claim about consistency is unjustified. You've scarcely engaged in any mathematics at all in this thread. Your claim about extensibility is historically false since Minkowski's framework has been extended in at least two independent ways: first, by no less than Einstein himself in his formulation of general relativity and, second, to accommodate spin vectors used in relativistic quantum physics.

and is based upon an inconsistent spacetime geometry that posits inertia as well as absolute space and time where none exists.

Minkowski's framework doesn't posit these things, so you're ranting against nothing here.

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.

Most of this is an ad hominem attack, since you're attacking Minkowski instead of his framework. Your accusations about Minkowski's motivations are also completely unsubstantiated.

The invariance of the spacetime interval and light cone are, as others have already told you, directly derivable from the Lorentz transformation which Einstein had already rederived in his 1905 paper. Einstein himself pointed out, as a consistency check, that a spherical wave expanding at the speed of light (a.k.a. "light cone") is left invariant by a Lorentz transformation of the coordinates:

At the time $$t = \tau = 0$$, when the origin of the co-ordinates is common to the two systems, let a spherical wave be emitted therefrom, and be propagated with the velocity $$c$$ in system K. If $$(x, y, z)$$ be a point just attained by this wave, then

$$x^{2} + y^{2} + z^{2} = c^{2} t^{2} \,.$$​

Transforming this equation with the aid of our equations of transformation we obtain after a simple calculation

$$\xi^{2} + \eta^{2} + \zeta^{2} = c^{2} \tau^{2} \,.$$​

The wave under consideration is therefore no less a spherical wave with velocity of propagation $$c$$ when viewed in the moving system. This shows that our two fundamental principles are compatible.

This is from page 8 of this translation of Einstein's 1905 paper "On the electrodynamics of moving bodies", so you can hardly continue to pretend this was something made up by Minkowski.

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.

Minkowski's framework does not eliminate time, so this is another rant about nothing.

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 find Minkowski's math obscure then that's your opinion which you are entitled to. Your opinion does not negate the opinion of everyone else who has found it very useful, especially for a type of problem that you have failed to even mention in this thread.

I'll only add that Minkowski's math (vector and tensor math in four dimensions) is about as easy as mathematics gets in theoretical physics. It is no more difficult than the math used in much of classical physics or in quantum mechanics (which can be vector and tensor math in infinite dimensions in some cases) and is certainly much easier than the math used in quantum field theory and general relativity. So if you think Minkowski's math is difficult, you are pretty much exposing that you can't have learned much physics beyond highschool level.

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.

Energy and momentum are state functions defined to be conserved quantities. Noether's theorem gives a theory-independent definition of these as conserved quantities associated respectively with time and spatial translation symmetry. This is not specifically addressed by Minkowski mainly because Minkowski's framework doesn't directly concern dynamics and also because it has nothing specifically to do with relativity: nonrelativistic theories can have energy and momentum conservation laws just as easily as relativistic ones can.

You are repeatedly failing to acknowledge theories' and frameworks' scopes and domains of applicability. Minkowski's framework is a tool meant to help with proving that theories are consistent with the relativity principle and little more. Complaining that Minkowski geometry doesn't explain energy and such is like complaining that your fridge won't cook a turkey: that's not what it's for.

 

[danshawen]

Most of this is an ad hominem attack, since you're attacking Minkowski instead of his framework. Your accusations about Minkowski's motivations are also completely unsubstantiated.

Alright. Let's talk about "a certain aspect of relativity theory" without reference to whose idea it was.

If someone has proposed that:

1) There exists a 4D entity called the interval that is as invariant as the speed of light in a vacuum, and which combines time and space into a single Pythagorean complex quantity. No particular reason or derivation for this mathematical construct, other than the ideas that Pythagorus and quadratics and complex numbers are somehow simply divine, like manifest destiny or some such.

2) There exists a kind of relativistic rotation in 4D (although also evident in part in 3D). This rotation is ANALOGOUS to Lorentz contraction, and furthermore:

a) it has no specified axis of rotation because it also has no specified coordinate in any inertial reference frame on which two observers can agree
b) it has no specified rate of rotation, OR ROTATIONAL INERTIA OF ANY KIND, and stops rotating when a constant velocity / FoR is achieved
c) it is a hyperbolic rotation, which means that the angle over which it can rotate is limited
d) it may appear to be a rotation about a different axis, or occur in a different direction, depending on the position of the observer, and
e) all of this is perfectly consistent and has been specified with great mathematical precision, so therefore it should be accepted by all as scientific canon

It should be noted that none of the other results of Special Relativity theory are in doubt or questioned in this thread or any other I have started. Lorentz contraction, time dilation, and the rest are perfectly consistent with Maxwell's equations and with the rest of science with the sole and notable exception of Newton's ideas of absolute time and space. This is not a ad hominem attack on Lorentz, Maxwell, or Newton.

General Relativity maintains some aspects of Newton's absolute time and space, under the influence of the same individual who gave us these flawed ideas about relativistic rotation. Evidently, the field equations work anyway, so I don't care to examine how they got there as closely as this flaw, which as far as physics goes, stands out like blood on vanilla ice cream. It is true that GR's "spacetime curvature" is part of the same very warped wheel.

Is that really different than a certain Papal edict:

1) The Sun (and everything else in heaven) orbits the Earth
2) There are loops known as Epicycles for certain planets which can be predicted with great mathematical precision and confidence
3) Anyone who speaks against this idea is a blasphemer, and will be placed under house arrest, their books burned and their teaching limited
4) The teachings of Aristotle are supreme and cannot be challenged by a mere human scientist like this Italian citizen

Both posit an eccentric view of a rotation and a proposed center of rotation. Both have the support of math. Both flawed ideas impeded the sciences of physics and astronomy for a lot longer than they should have. Landing on the moon in the 19th century might have been problematic, I freely admit.

"Whatever goes around comes around." --unknown author Karma quote

The Earth orbits the Sun. This is not a mathematical fact, but it is a physical one, and it does reduce the complexity of the math as well. Epicycles go away.

Space is not covariant with time. Relativistic movement through space does not rotate time into a physical dimension. Space IS time. Time IS a physical dimension. ALL of them. Combine it with FTL rotation, and it all makes perfect sense.

Why did Galileo launch such vicious ad hominem attacks on Ptolemy, Aristotle, and Pope Urban? Probably figured it was time for the ignorance of their teachings to come to an end. No doubt, his students brought up the subject to him many, many times.

Galileo was no Newton. He had only managed to work out the t^2 dependence of gravitational acceleration. Newton had problems with religious authority as well, but no one heard anything about it until his writings on the subject were uncovered posthumously. But he was a brilliant individual, and it probably also helped that he left "a divine hand" to guide falling objects without the benefit of higher math or instruments to the geometrical center of the Earth. No doubt, the Pope probably liked that.

 

[danshawen]

The math will get MUCH easier this way. You'll just have to trust me on that assertion. Sometimes, as much as I used to obsess about them, the Pythagorean theorem and complex numbers just get in the way.

The speed of light and the rest frame that makes it invariant is enough. A third invariant like the interval just gets in the way.

Understanding the nature of time and time dilation is enough. Spacetime curvature just gets in the way.

If G-d him/her/itself or math stands between you and an understanding of the physical universe, kindly request that he/her/it get out of the way. G-d made us, but if the math holds us back, we really have no one to blame for that but ourselves. Certainly not Minkowski.

 

[James R]

danshawen:

Alright. Let's talk about "a certain aspect of relativity theory" without reference to whose idea it was.

If someone has proposed that:

1) There exists a 4D entity called the interval that is as invariant as the speed of light in a vacuum, and which combines time and space into a single Pythagorean complex quantity. No particular reason or derivation for this mathematical construct, other than the ideas that Pythagorus and quadratics and complex numbers are somehow simply divine, like manifest destiny or some such.

The invariance of the interval is proved by considering the spacetime interval between two events in two different reference frames. Thus it is completely false that "no particular reason or derivation for this ... construct" exists. The interval is, in fact, just one of many invariant quantities in relativity.

2) There exists a kind of relativistic rotation in 4D (although also evident in part in 3D). This rotation is ANALOGOUS to Lorentz contraction, and furthermore:

a) it has no specified axis of rotation because it also has no specified coordinate in any inertial reference frame on which two observers can agree
b) it has no specified rate of rotation, OR ROTATIONAL INERTIA OF ANY KIND, and stops rotating when a constant velocity / FoR is achieved
c) it is a hyperbolic rotation, which means that the angle over which it can rotate is limited
d) it may appear to be a rotation about a different axis, or occur in a different direction, depending on the position of the observer, and
e) all of this is perfectly consistent and has been specified with great mathematical precision, so therefore it should be accepted by all as scientific canon

I think you're confused about the use of the word "rotation". That word, when used in reference to a Lorentz tranformation, is used in a more general sense than when it is used to describe a "normal" rotation in a 3 dimensional space.

You can describe a "normal" rotation as the action of a 3 by 3 matrix operating on one vector (with 3 spatial components) in order to transform it into another vector. Analogously, a Lorentz "rotation" is the action of a 4 by 4 matrix operating on a vector (with 4 components that can be described, very roughly, as 1 time component and 3 spatial components) to transform it into another vector.

(a) Notice that the 3 by 3 matrix that describes a "normal" rotation doesn't specify an axis or a coordinate system, either.
(b) Notice that the 3 by 3 matrix that describes a "normal" rotation doesn't specify a rate of rotation or ROTATIONAL INERTIA OF ANY KIND etc.
(c) Notice that the 3 by 3 matrix that described a "normal" rotation can only rotate things from 0 to 360 and to get a "different result". Rotating a vector by 720 degrees, for example, is indistinguishable in its result from rotating it by 360 degrees.
(d) Notice that the orientation of a "normal" rotational axis changes depending on the observer.
(e) All of this is perfectly consistent and should be accepted by all as scientific canon.

It should be noted that none of the other results of Special Relativity theory are in doubt or questioned in this thread or any other I have started.

If you question the Lorentz transformation, you also necessarily question length contraction, time dilation and the rest. Those things are just special cases of a more general Lorentz tranformation.

General Relativity maintains some aspects of Newton's absolute time and space, under the influence of the same individual who gave us these flawed ideas about relativistic rotation. Evidently, the field equations work anyway, so I don't care to examine how they got there as closely as this flaw, which as far as physics goes, stands out like blood on vanilla ice cream. It is true that GR's "spacetime curvature" is part of the same very warped wheel.

GR incorporates Lorentz tranformations. GR, recall, is the general theory, whereas SR is a special case of the general theory. GR can't be right if the Lorentz transformations are wrong. Thus, if GR's field equations "work" then the Lorentz transformations must "work" too.

Is that really different than a certain Papal edict:

1) The Sun (and everything else in heaven) orbits the Earth
2) There are loops known as Epicycles for certain planets which can be predicted with great mathematical precision and confidence
3) Anyone who speaks against this idea is a blasphemer, and will be placed under house arrest, their books burned and their teaching limited
4) The teachings of Aristotle are supreme and cannot be challenged by a mere human scientist like this Italian citizen

If you believe that part or all of relativity is incorrect dogma, you should post a disproof of those parts you disagree with.

Why have you never done that?

Show me the maths!

Space is not covariant with time.

I don't even know what you mean by that. Explain.

Relativistic movement through space does not rotate time into a physical dimension.

Or that.

Space IS time.

Take a walk across your room. Now walk backwards to where you were. Are you back in the past now? If not, then maybe there's something different about space compared to time.

Come to think of it, why can't you walk backwards or forwards in time, if space and time are the same, like you say they are? And what would it mean to walk "sideways" in time? Can you do that?

Time IS a physical dimension.

Yes. Time is part of physics, and can be described as a dimension.

ALL of them. Combine it with FTL rotation, and it all makes perfect sense.

Great! Show me the maths! Show me how your maths of FTL rotation all makes perfect sense. I can't wait!

Why did Galileo launch such vicious ad hominem attacks on Ptolemy, Aristotle, and Pope Urban?

He certainly never launched a vicious attack on Pope Urban. That would have put his life and/or freedom in peril. He wasn't dumb.

As for Ptolemy and Aristotle ... they were wrong about a lot of stuff.

Galileo was no Newton.

Newton mentioned something about standing on the shoulders of giants, if I recall correctly. Guess who died in the same year Newton was born.

He had only managed to work out the t^2 dependence of gravitational acceleration.

What? Gravitational acceleration near the Earth's surface is a approximately constant. It has no time dependence. Galileo knew that. How about you?

Newton had problems with religious authority as well, but no one heard anything about it until his writings on the subject were uncovered posthumously. But he was a brilliant individual, and it probably also helped that he left "a divine hand" to guide falling objects without the benefit of higher math or instruments to the geometrical center of the Earth. No doubt, the Pope probably liked that.

What is this "divine hand" you believe Newton left? Explain.

 

[danshawen]

danshawen:


The invariance of the interval is proved by considering the spacetime interval between two events in two different reference frames. Thus it is completely false that "no particular reason or derivation for this ... construct" exists. The interval is, in fact, just one of many invariant quantities in relativity.


I think you're confused about the use of the word "rotation". That word, when used in reference to a Lorentz tranformation, is used in a more general sense than when it is used to describe a "normal" rotation in a 3 dimensional space.

You can describe a "normal" rotation as the action of a 3 by 3 matrix operating on one vector (with 3 spatial components) in order to transform it into another vector. Analogously, a Lorentz "rotation" is the action of a 4 by 4 matrix operating on a vector (with 4 components that can be described, very roughly, as 1 time component and 3 spatial components) to transform it into another vector.

(a) Notice that the 3 by 3 matrix that describes a "normal" rotation doesn't specify an axis or a coordinate system, either.
(b) Notice that the 3 by 3 matrix that describes a "normal" rotation doesn't specify a rate of rotation or ROTATIONAL INERTIA OF ANY KIND etc.
(c) Notice that the 3 by 3 matrix that described a "normal" rotation can only rotate things from 0 to 360 and to get a "different result". Rotating a vector by 720 degrees, for example, is indistinguishable in its result from rotating it by 360 degrees.
(d) Notice that the orientation of a "normal" rotational axis changes depending on the observer.
(e) All of this is perfectly consistent and should be accepted by all as scientific canon.


If you question the Lorentz transformation, you also necessarily question length contraction, time dilation and the rest. Those things are just special cases of a more general Lorentz tranformation.


GR incorporates Lorentz tranformations. GR, recall, is the general theory, whereas SR is a special case of the general theory. GR can't be right if the Lorentz transformations are wrong. Thus, if GR's field equations "work" then the Lorentz transformations must "work" too.


If you believe that part or all of relativity is incorrect dogma, you should post a disproof of those parts you disagree with.

Why have you never done that?

Show me the maths!


I don't even know what you mean by that. Explain.


Or that.


Take a walk across your room. Now walk backwards to where you were. Are you back in the past now? If not, then maybe there's something different about space compared to time.

Come to think of it, why can't you walk backwards or forwards in time, if space and time are the same, like you say they are? And what would it mean to walk "sideways" in time? Can you do that?


Yes. Time is part of physics, and can be described as a dimension.


Great! Show me the maths! Show me how your maths of FTL rotation all makes perfect sense. I can't wait!


He certainly never launched a vicious attack on Pope Urban. That would have put his life and/or freedom in peril. He wasn't dumb.

As for Ptolemy and Aristotle ... they were wrong about a lot of stuff.


Newton mentioned something about standing on the shoulders of giants, if I recall correctly. Guess who died in the same year Newton was born.


What? Gravitational acceleration near the Earth's surface is a approximately constant. It has no time dependence. Galileo knew that. How about you?


What is this "divine hand" you believe Newton left? Explain.

Can you make energy, in any of its forms, spontaneously PROPAGATE BACKWARDS from the way it originated?

This is literally all there is to the arrow of time. That room you backed up in is spinning and moving in a half dozen astrophysical ways involving undreamt of amounts of energy exchanges. No, you won't be able to reverse the process, halt, or reset it in any real sense.

Can matter or energy be directed to propagate in the direction from which it propagated? Yes, with nothing more complex than a plane mirror. Is this the same thing as having all of the energy in the universe retrace its path? No. No mystery here, James R. Energy can propagate in any direction you wish. That's a dynamic of light travel time and no fictitious space with different properties is necessary to explain anything else, other than FTL rotation, which is both bound energy and inertia. Time only exists at their geometric centers. This is the only absolute space/time in the universe, and even that point is subject to relativity's time dilation.

Newton's "divine hand" is between the lines in his theory of gravitation. The magnitude is explained. The direction isn't other than "towards the center". How does a stone without Newton's knowledge of geometry know where the center of the Earth is? It doesn't. Something which permeates the space around gravitating bodies causes it to choose a particular direction. Calling it a gravitational field does not require detailed structural knowledge of what is in the vacuum either. Don't pretend that it does.

 

[danshawen]

Minkowski:

"I have seen the fourth dimension, AND it is Pythagorean. Solids are Pythagorean, and all I know is invested in a study of solid geometry, so spacetime MUST be Pythagorean." QED

Your responses to his proof here.

Be sure and explain why you believe that if any side of a right triangle can be expressed as light travel time, the side longitudinal to its direction of motion should be treated any differently than the other two. Check your math.

 

[przyk]

1) There exists a 4D entity called the interval that is as invariant as the speed of light in a vacuum, and which combines time and space into a single Pythagorean complex quantity. No particular reason or derivation for this mathematical construct, other than the ideas that Pythagorus and quadratics and complex numbers are somehow simply divine, like manifest destiny or some such.

No. It is an easy mathematical exercise to prove that the spacetime interval $$c^{2} \Delta t^{2} - \Delta x^{2} - \Delta y^{2} - \Delta z^{2}$$ is invariant under a Lorentz boost. It has nothing to with liking quadratics or "manifest destiny".

If you're not familiar with the Lorentz transformation, then you can still easily check a special case just from the invariance of the speed of light. You have:

$$c = \text{speed of light} = \frac{\text{distance travelled by light}}{\text{time taken}} = \frac{\sqrt{\Delta x^{2} + \Delta y^{2} + \Delta z^{2}}}{\Delta t} \,.$$
​

Simple highschool algebra then gets you

$$\begin{eqnarray}
c &=& \frac{\sqrt{\Delta x^{2} + \Delta y^{2} + \Delta z^{2}}}{\Delta t} \\
\Rightarrow \qquad c^{2} &=& \frac{\Delta x^{2} + \Delta y^{2} + \Delta z^{2}}{\Delta t^{2}} \\
\Rightarrow \qquad c^{2} \Delta t^{2} &=& \Delta x^{2} + \Delta y^{2} + \Delta z^{2} \\
\Rightarrow \qquad c^{2} \Delta t^{2} - \Delta x^{2} - \Delta y^{2} - \Delta z^{2} &=& 0 \,.
\end{eqnarray}$$​

So claiming that the speed of light is invariant is the same as claiming that lightlike intervals are invariant.

2) There exists a kind of relativistic rotation in 4D (although also evident in part in 3D). This rotation is ANALOGOUS to Lorentz contraction

Not quite. According to special relativity, the coordinates of inertial reference frames are related by Lorentz transformations. For two reference frames arranged so that their $$\mathrm{x}$$, $$\mathrm{y}$$, and $$\mathrm{z}$$ axes are aligned and their origins pass each other at $$t = 0$$, and moving at velocity $$v$$ relative to one another along the $$\mathrm{x}$$ axis, the coordinates of the reference frames would be related by

$$\begin{eqnarray}
t' &=& \gamma (t - \tfrac{v}{c^{2}} x) \,, \\
x' &=& \gamma (x - vt) \,, \\
y' &=& y \,, \\
z' &=& z \,,
\end{eqnarray}$$
​

where $$\gamma = 1 / \sqrt{1 - v^{2} / c^{2}}$$. These transformations were known by the late 19th century to be a symmetry of Maxwell's equations and were rederived starting from the invariance of c postulate by Einstein in his 1905 paper introducing special relativity. They imply that the distance and time measures of one reference frame are mixtures of the distance and time measures of other reference frames. This is, in some ways, analogous to a 3D rotation of the coordinates $$x$$, $$y$$, and $$z$$, but it is not the same thing.

It should be noted that none of the other results of Special Relativity theory are in doubt or questioned in this thread or any other I have started. Lorentz contraction, time dilation, and the rest are perfectly consistent with Maxwell's equations and with the rest of science with the sole and notable exception of Newton's ideas of absolute time and space.

Lorentz length contraction, time dilation, and relativity of simultaneity are special cases of and together equivalent to claiming that the coordinates of inertial reference frames are related by Lorentz coordinate transformations. This in turn is equivalent to claiming that the spacetime interval is invariant. You cannot choose to accept one of these and deny the others because they are all mathematically equivalent to and derivable from each other.

 

[danshawen]

So claiming that the speed of light is invariant is the same as claiming that lightlike intervals are invariant.

No doubt. Good math. It is the same math that I was taught over 40 years ago, in fact.

I said it before, but perhaps it bears repeating. I have no issue with the Lorentz transformations or relativity in general. I'm sure Minkowski took some care to craft his intervals and rotations to be geometrically consistent with them.

The speed of light is an invariant BECAUSE?
What exactly is the speed of light invariant with respect to? Even an invariant speed of light must be an invariant RELATIVE TO something else. What is that something else?

The speed of light is invariant for any inertial reference frame because any inertial reference frame may be considered as the rest frame. The rest frame is defined by the relativistic addition of +c and -c for all inertial reference frames, in any state of relative motion, in any direction. We did not really need the interval to be defined to demonstrate that, did we really?

You should be seeing a symmetry here. The speed of light doesn't just define the speed at which unbound energy propagates. It also defines the rest frame where bound energy in any relative state of motion is at rest. Can Minkowski's invariant interval do anything like that?

An interval is only invariant because it has included the invariant speed of light and it has ignored the effects of time dilation. The delta t in the denominator of the relation you have used to define the interval is a time interval. Time intervals of any may dilate depending on relative motion or position in a gravitational field, and this was not part of Minkowski's calculation of the universal invariance of his interval. We know the speed of light is invariant because we have performed experiments that prove that it is. This is not the case with Minkowski's 4D interval. It is not a working standard the way the speed of light is. It never was.

In a universe composed of energy transfer events, simultaneity means exactly NOTHING that is useful. Phase locked loops are only locked to phase references within the range of a small but easily measurable error signal. The clocks we synchronize in order to implement GPS receive continuous corrections in order to render accurate location data, but NONE OF THEM ARE SIMULTANEOUS FOR MORE THAN AN INSTANT, and even that measure of simultanaeity is not one that is serviceable for Minkowski's purposes. Because Minkowski's conception of simultaneity involved the speed of light, and as it turns out, that is a process much slower than quantum entanglement, his entire reason for creating the interval, besides not being a working standard, will never be even remotely useful to any real purpose.

The interval was just Minkowski's clumsy mathematical attempt to leverage absolute time in order to restore absolute space.

 

[The God]

danshawen:

..

Take a walk across your room. Now walk backwards to where you were. Are you back in the past now? If not, then maybe there's something different about space compared to time.

Come to think of it, why can't you walk backwards or forwards in time, if space and time are the same, like you say they are? And what would it mean to walk "sideways" in time? Can you do that?

..

But then you are not on the same spatial point either ! If by travelling back and forth in a room establishes that you can come back to your original point again (unlike time), then i am afraid you are just playing games within your frame.

 

[James R]

danshawen:

So you're just going to ignore my requests that you show me mathematical disproofs of the parts of relativity you say are flawed?

And you're also going to ignore my request that you show me mathematically how your faster-than-light rotation thingy makes perfect sense?

If you claim you can show these things, why won't you do it?

Why do you ignore all requests for you to put up something solid, rather than unsupported assertions?

I think I know why.

Can you make energy, in any of its forms, spontaneously PROPAGATE BACKWARDS from the way it originated?

You're mistaking energy for a substance again. Energy is not a glowing plasma-like substance. It is more like an accounting system.

This is literally all there is to the arrow of time. That room you backed up in is spinning and moving in a half dozen astrophysical ways involving undreamt of amounts of energy exchanges. No, you won't be able to reverse the process, halt, or reset it in any real sense.

But I can walk across the room and back easily enough. Why can't I just walk forwards and then backwards in time? After all, according to you space and time are the same thing, are they not? You actually say space is "light travel time" - whatever that means. So is time different from space, or the same? Please clarify.

Can matter or energy be directed to propagate in the direction from which it propagated? Yes, with nothing more complex than a plane mirror. Is this the same thing as having all of the energy in the universe retrace its path? No. No mystery here, James R. Energy can propagate in any direction you wish.

Can it propagate in the backwards time direction?

That's a dynamic of light travel time and no fictitious space with different properties is necessary to explain anything else, other than FTL rotation, which is both bound energy and inertia. Time only exists at their geometric centers. This is the only absolute space/time in the universe, and even that point is subject to relativity's time dilation.

Really? Show me the maths, then.

Newton's "divine hand" is between the lines in his theory of gravitation.

You mean you're imagining something that you're calling the "divine hand". I see.

How does a stone without Newton's knowledge of geometry know where the center of the Earth is? It doesn't.

I don't think stones know geometry - Newton's or anybody else's. If fact, last time I check, stones didn't know anything.

Something which permeates the space around gravitating bodies causes it to choose a particular direction.

Curved spacetime?

Calling it a gravitational field does not require detailed structural knowledge of what is in the vacuum either. Don't pretend that it does.

Never fear. I won't pretend that.

 

[danshawen]

But then you are not on the same spatial point either ! If by travelling back and forth in a room establishes that you can come back to your original point again (unlike time), then i am afraid you are just playing games within your frame.

Let's have this mathematical argument out.

Since before Newton's era and apparently even through the 21st century, ABSOLUTE SPACE AND ABSOLUTE TIME ARE 100% COMPATIBLE WITH MATH.

The last poster did it. Rpenner has done it here hundreds of times. It is as easy a mistake to make as dividing by zero, only you will get no check that anything is wrong with your math other than IT CHECKS OUT JUST FINE FOR ONE OBSERVER OR ONE REFERENCE FRAME.

Time dilates (flows at different rates) around an atom of uranium than it does around an atom of hydrogen, or around the vicinity of an electron as opposed to a proton. Yet the speed of light (NOT TIME) remains constant in all cases. But the speed of light is not time itself. It can't be. It ISN'T FAST ENOUGH.

If Minkowski's light cones were used to demonstrate this (they can't, but if they could), each light cone vertex solid angle for every atom or particle in the universe would be different. Time flows at different rates while the speed of light remains the same everywhere except within bound particles of matter.

The derivation of the Lorenz transformations work fine because the math retains time vs space as discrete relativistic vectors and deal with only two frames of reference, one of which "at rest" is invariant. As soon as you combine time and space into a covariant entity, you restore absolute space and absolute time in an unnatural way. Space is light travel time, but time is not the speed of light. Far from it.