Reviewing Special Relativity and Lorentz Trasformations, Relevance to Alternate Cosmologies

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[This is a thread I’m posting to help develop material for my college-level, free-of-charge, unaccredited online buffet style course on ID/Creation.]

As I pondered the various 12 YEC cosmology models and the fact that at least 11 of them must be wrong as a matter of principle, I got interested in building up ideas by starting again from the basics.

In the process, I began suspecting some of the postulates of Einstein’s Special Relativity (SR) may need amendment in light of the fact that the Lorentz transformation at the heart of Einstein’s SR do not mandate Einstein’s SR but admit other possible interpretations. In fact Larmor predicted time dilation before Einstein, but also said time in the ultimate sense time must be absolute.

I don’t know exactly what Lorentz thought, but Lorentz’s equations predicted time dilation even before Einstein.

As I pondered the issue more, the Lorentz transformation may not not rule out an absolute frame of reference, and in fact many of the relativity transformations in classical and Einsteinian physics could be more or less convenience approximations but which could have experimental issues where convenience transformations will not give accurate results since they are transformations of convenience that are only valid approximations under certain conditions.

But before going further, I just want to post how I think I might teach on the basics and I solicit corrections of my understanding of the basics.

My understanding is that Einstein’s SR began with Einstein’s careful study of Maxwell’s of electromagnetic theory. The speed of light is a property of space:

WWVNO%5B1%5D

This velocity is independent of the reference frame whether moving or “stationary”. If the speed is detected to be the same in all moving inertial (un-accelerated frames), then this will result in paradoxes which Einstein’s SR attempted to resolve, and which are encapsulated in the Lorentz’s transformations:

t'= \gamma (t-\frac{vx}{c^2})
x' = \gamma(x-vt)
y'=y
z'=z

where
\gamma = \frac {1}{\sqrt{1-\frac{v^2}{c^2}}}

The Lorentz transformation can be derived by assuming the speed of light is constant in all reference frames and Maxwell’s approximations of classical Electro Dynamics:

maxwells_equations

I will attempt to post my version of the derivation of the Lorentz transformation from Maxwell’s equations in subsequent comments and then post why I think the derivation leads to an opening for alternate cosmologies including YCC/YEC cosmologies. This derivation has already been done in a variety of ways, but I’ll express it in the way that I understand it without resorting to tensor notation which I’m not yet very comfortable with.

From this I will post my criticisms of Einsteinian SR based on the Lorentz transformation which is ironically at the heart of Einsteinian SR.

As an aside, here is a 1927 picture of Lorentz with Einstein (Lorentz is seated a Einstein’s immediate right, our left):

einstein_lorentz
einstein_lorentz.jpg1024×400 144 KB

This picture was from the famous Solvay conference.

Talk about a meeting of GIANTS! WOW!

I hope to provide my version of a well-known derivation of the Lorentz transformation from Maxwell’s equations in the process of this thread since I wish to present it in my class to show that it emerges naturally from the approximations of Maxwell’s equations under certain additional assumptions. It will also be a good exercise to helping re-learn and understand the issues.

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The following is certainly not mine, but I found it summarized on an anonymous powerpoint but which accords with my limited understanding. The Lorentz transformation comes from this bottom line equation derived from Maxwell’s equation for a travelling light wave in a vacuum where there is no charge and no current.

\LARGE \nabla^2E = \mu_0 \epsilon_0 \frac{\partial^2E}{\partial t^2}

That’s the sort of the way I remember it from a homework assignment too (from long ago). This looks the basis for a D’Alambertian with the assumption:

[\nabla^2 - \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2}] E = 0

any way, Lorentz deduced HYPOTHETICALLY:

\large x' = \gamma(x-vt)
\large t' = \gamma (t- \frac{vx}{c^2})

how he arrived at the above hypothesis is probably evidence of his genius!

But on that hypothetical assumption, then if we evaluate the Laplacian only along the X-axis:

\large \nabla^2E = \frac {\partial^2 E}{\partial^2 x} + 0 + 0

and

\large \frac{\partial x'}{\partial x}= \gamma

\large \frac{\partial x'}{\partial t}= -\gamma v

\large \frac{\partial t'}{\partial t} = \gamma

\large \frac{\partial t'}{\partial x} = -\gamma \frac{v}{c^2}

Now under this hypothesis, then after some basic calculus, and the fact we’re using a simplified Laplaican:

\large \frac {\partial^2E}{\partial x^2}=

\large \gamma^2\frac{\partial^2E}{\partial x^{'2}}-\frac{2v}{c^2}\gamma^2\frac{\partial E}{\partial t' \partial x'} + \gamma^2 \frac{v ^2}{c^4}\frac{\partial^2E}{\partial t^{'2}}

I have yet to evaluate:

\large \mu_0 \epsilon_0 \frac{\partial^2E}{\partial t^2}

in terms of transformed coordinates, but then comparing it with

\large \frac {\partial^2E}{\partial x^2}

it’s supposed to demonstrate the invariance of the Lorentz transformation which demonstrates relativity (not necessarily Einsteinian) just based on 2 assumptions:
Maxwell’s equations and the assumption of the constancy of the MEASURED speed of light in various reference frames.

I’ll have to take some time to do this calculation:

\large \mu_0 \epsilon_0 \frac{\partial^2E}{\partial t^2}

But I think it’s supposed to yield:
\large \gamma^2\frac{\partial^2E}{\partial x^{'2}}-\frac{2v}{c^2}\gamma^2\frac{\partial E}{\partial t' \partial x'} + \gamma^2 \frac{v ^2}{c^4}\frac{\partial^2E}{\partial t^{'2}}

EDIT!!! ERROR:
see my correction here:

Reviewing Special Relativity and Lorentz Trasformations, Relevance to Alternate Cosmologies - #17 by stcordova

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Ok, so you aren’t sure you’ve got the basics right, but that doesn’t stop you amending relativity theory.

Clearly an impeccable source.

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No assumption of the constancy of the speed of light, it comes out of Maxwell’s equations and the wave equation.

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The starting point I asserted earlier:
\LARGE \nabla^2E = \mu_0 \epsilon_0 \frac{\partial^2E}{\partial t^2}

and the D’Alamberian form which can be derived by simple algebra is described here:

So far what I’ve said is in agreement with the mainstream. I will also cite accepted experiments and derivations from the Lorentz transformation and point out contradictions with the interpretations of SR, and argue it is the CLOCKS that are slowed down, not that real time is actually dilated. Time dilation is a misnomer.

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To get to this (which is the wave equation of light travelling through a vacuum):

\LARGE \nabla^2E = \mu_0 \epsilon_0 \frac{\partial^2E}{\partial t^2}

one has to take “the curl of the curl” on Maxwell’s equations. I have to dig up the justification of that. I no longer remember the justification for doing that.

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No justification for that is needed, Sal - it’s just a mathematical manipulation to draw out an implication of Maxwell’s equations.

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In the spirit of this thread, for anyone interested, here’s a great video series introducing SR:

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OK, after searching hard, I found the derivation stated nicely the way I want, I might have to rework it to make it clearer, but it required some nasty algebra tricks. UGH!

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I was asking so I could understand, not skeptically questioning. Finding solutions to differential equations with one variable/dimension – not so bad, but with 4 variable x,y,z, t under the constraints of Maxwell’s equations, not so clear. I mean yeah:

\nabla \times (\nabla \times \vec{\Psi}) = \nabla (\nabla \cdot \vec{\Psi}) - \nabla^2\vec{\Psi}

which leads to

\nabla^2 E = \mu_0 \epsilon_0 \frac {\partial^2 E}{\partial t}

where we can put B or E in place of \Psi

but where does

\nabla \times (\nabla \times \vec{\Psi})

come from in the first place. I can dig it up, but I was asking in case anyone knew off the top of their head.

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Since many Creationists are Engineers, and a few are Electrical Engineers, the question of derivation of relativity will invariably come up. Since most Electrical Engineers, especially the antenna and motor engineers are acquainted with Maxwell’s equations of electro magnetism (since Maxwell is one of the founding fathers of Electrical Engineering), I thought it would be good to show how Lorentzian relativity arises naturally out of Electromagnetism. But there are a few catches to all this as I pondered it.

At issue, since the days of Lorentz and Larmor is whether there is absolute time and maybe the clocks in moving frames slow down, or whether time actually flows differently depending on velocity. The Lorentz transformations that make Maxwell’s equations invariant, as I’ve clumsily tried to show (and finally had to provide a link that had been searching for on and off for two years), does not actually say whether time flows differently or if the clocks merely slow down!

I will argue the clocks slow down, and that there is absolute time, and I will use argument by contradiction using Lorentz transformations.

But I wanted to apply some rigor to show that the Lorentz transformations at the heart of Einstein’s Special Relativity weren’t pulled out of a vacuum (pun intended).

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Is this not Sal just using PS as a handy notepad for his musings? Is that a legitimate use of the web site?

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If is boring, people will ignore it.

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The reason I’m posting this is to showcase some of the forgotten work of Lorentz and others like Fizeau, Fresnel, Hoek, Stokes, Maxwell, Larmor, Miller and other fine physicists who worked on the Aether formulations of relativity.

The experiments on Fresnel drag and the clock slowing (misnamed time dilation) suggest fairly absolute cooridinate systems and that the Aether is related to the zeropoint energy, and variable zeropoint energy implies anisotropic variable light speed, exactly what the YEC/YCC are searching for.

With that in mind, based on the Lorentz transformations derived from Maxwell’s equations above:

\Delta t = \frac{1}{\sqrt(1-\frac{v^2}{c^2}}t_0 = \gamma \Delta t_0

But this needs some clarification from mainstream interpretation, so let me add subscripts

\Delta t_\text{Earth} = \gamma \Delta t_\text{Spaceship} or

\frac{\Delta t_\text{Earth}}{\gamma} = \Delta t_\text{Spaceship}

now there is subtlety that requires some time dilation(clock slowing) due to General Relativity (GR) when the space ship is accelerating and decelerating as well, but that can be accounted for, suffice to say the clock on the space ship will have fewer ticks than the clocks on Earth due to both SR and GR type effects.

No problem, so far, and the Hafele Keating experiments show these effects using cesium beam clocks flown on airplanes:

hk1%5B1%5D
hk1%5B1%5D1863×1468 314 KB

It confirmed that clocks slow down when they travel fast relative to the aether/Zero Point Enegy field.

BUT there is a subtle issue here – the clock that slowed down was the clock on the object that was subject to accelerations and decelerations! This would suggest that there could in principle be an object with a net velocity of zero, based on this integral

\LARGE v(t) = \int {a(t)}

but also the fact that we might infer what the zero velocity point is by firing space ships in opposite directions at various speeds. I suspect Earth is moving close to the zero velocity, but not exactly because of it’s orbit around the sun and the sun’s movement relative to the universal/cosomological frame. Magueijo and the VSL advocates were right to point out the Cosmos itself defines a frame of reference. Surely we can say one object is accelerating relative to another – i.e. You assume when you’re driving and step on the accelerator, that you’re the one accelerating, not the rest of the universe! This leads then to the inference from the above integral that there exists a zero velocity in principle, where the clock from that frame is the reference clock for all other clocks.

Oh, that’s the other thing, if we use the stars and the cosmos to define a frame, we can also define what objects are accelerating relative to this frame, and this will also define absolute velocities which imply privileged frames, and the relativisitic frames are only convenience conceptions.

Further comments will go into other experiments that involve Fresnel drag, which have bearing on re-interpretations of Michelson-Morely and the variable Zero Point hypothesis which could lead to possible solutions to the distant starlight problem of YEC/YCC.

PS
I just discovered this, Lorentz won the Nobel Prize in 1902:

https://www.nobelprize.org/images/lorentz-13546-content-portrait-mobile-tiny.jpg![lorentz-13546-content-portrait-mobile-tiny[1]|232x325](upload://7kMOOMnWHiBAP7KJljsg93u4NyU.jpeg)

The so-called Lorentz transformation (1904) was based on the fact that electromagnetic forces between charges are subject to slight alterations due to their motion, resulting in a minute contraction in the size of moving bodies. It not only adequately explains the apparent absence of the relative motion of the Earth with respect to the ether, as indicated by the experiments of Michelson and Morley, but also paved the way for Einstein’s special theory of relativity.

Yes, the absence is only apparent, and Lorentz and Fresnel and new interferometry experiments suggest this.

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I expect, but cannot tell for sure, that Sal’s excursions into physics are fully as bad as his attempts at biology or geology. Can any of the physicists here confirm?

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first things firdst. Is there a speed of light? if gravity waves go the same speed as light why is not the Speed of light just the speed of gravity waves? unlikely both go the same speed so they must be speeding THROUGH something else. Then go from there to anything can speed that fast THEN why say light is speeding vas opposed to a provocation in a light field is what is speeding?
This also Einstein probably messed up.

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ERRATA:

The above claim is incorrect!!!

I finally found the correct way to demonstrate invariance. I had done the derivation from scratch once as a homework assignment, but that was 12 years ago. I lost my notes, but I found a comparable derivation on the net and have to adapt the notation and symbols and conventions. Using the symbol conventions above, what I need to show is that under the Lorentz transformation is that assuming:

\LARGE \frac{\partial E}{\partial^2x} = \mu_o \epsilon_0 \frac{\partial^2}{\partial t^2}

under the Lorentz transformation

\LARGE \frac{\partial E}{\partial^2x'} = \mu_o \epsilon_0 \frac{\partial^2 E}{\partial t'^2}

Apologies to the reader. I will put an edit in the original comment to point to this correction.

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The issue is whether Maxwell’s equations must assume a reference frame for them to valid, the answer is “no”, but that does not necessarily mean there is no preferred frame, it could also mean t-prime is measuring time with a slowed down clock, not that time is actually moving slower.

So going from Maxwell’s equations, we can show they hold for a frame where clock-time is defined by t or a frame where clock-time is defined by t-prime. Clock time isn’t necessarily actual/reference time. I’ve suggested evidence that there is an actual preferred/reference clock rate, and that is where:

\large v(t) = \int a(t) = 0

We can deduce if our clock is at or close to absolute zero velocity, v = 0, by accelerating clocks in opposite directions and measuring how many ticks they lose.

For example, if we accelerate one clock in one direction and let it fly for a while, and then accelerate another clock in exact opposite direction and the two clocks end up losing the same amount of clock ticks relative the the lab reference clock, then we know the lab reference clock is at v=0 in the absolute sense. If we get an unbalanced result where one clock loses more ticks than another, or even one clock even gains ticks, then one knows the lab reference clock is not at v = 0.

The reason I wanted to go through the derivation above is that my claim doesn’t violate Lorentz invariance of Maxwell’s equations. There is an absolute speed of light for a given segment of space, but the clocks that measure the speed of light are affected by their absolute speed. If that were not the case, we couldn’t have the results of the Hafele-Keating experiment which had clocks slow down after being accelerated to a certain velocity.

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This was from a respected Physcis journal. The full paper is behind a paywall, and the language in the abstract apparently was deliberately obtuse since the results were favorable to the Aether interpretation by Krisher:

Reginald Cahill showed the significance of the paper along with other experiments including the Michelson-Morely experiment that had Fresnel Dragging (aka the one that had AIR as a medium for light to travel) and other experiments with Fresnel Dragging. Cahill comments here:

We combine data from two high precision NASA/JPL experiments: (i) the
one-way speed of light experiment using optical fibers: Krisher T.P., Maleki
L., Lutes G.F., Primas L.E., Logan R.T., Anderson J.D. and Will C.M., Phys.
Rev. D, vol 42, 731-734, 1990, and (ii) the spacecraft earth-flyby doppler shift
data: Anderson J.D., Campbell J.K., Ekelund J.E., Ellis J. and Jordan J.F.,
Phys. Rev. Lett., vol 100, 091102, 2008, to give the solar-system galactic
3-space average speed of 486km/s in the direction RA=4.29h
, Dec=-75.0◦. Turbulence effects (gravitational waves) are also evident. Data also reveals
the 30km/s orbital speed of the earth and the sun inflow component at 1AU
of 42km/s and also 615km/s near the sun, and for the first time, experimental
measurement of the 3-space 11.2km/s inflow of the earth. The NASA/JPL
data is in remarkable agreement with that determined in other light speed
anisotropy experiments, such as Michelson-Morley (1887), Miller (1933), DeWitte (1991), Torr and Kolen (1981), Cahill (2006), Munera (2007), Cahill
and Stokes (2008) and Cahill (2009).

The Kicher experiment was done by multiple researchers and published in a very respected journal Physical Review Letters D. The other experiment Cahill and Stokes (2008) I attempted to replicate but was unsuccessful. I still have the laser parts from Thor Labs in my basement!

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As I mentioned, I wanted to show the Lorentz transformation of arises from something a tad more down to Earth, namely Maxwell’s equations which are the foundation of electrical engineering. Antenna Engineers and Motor designers are acquainted with these equations. The Lorentzian interpretation of the Lorentz transformation rather than the Einstein interpretation of the Lorentz transformation is friendly to variable speed of light.

I’ve been combing the net to find the derivation explicitly stated, and have had to cobble and rederive it piecemeal, and I’m getting closer to having it ready for my ID/Creation class.

Anyway, I said this earlier, this is one solution to Maxwell’s differential equations for a lightwave travelling through a vacuum, namely in terms of the ELECTRIC field:

\LARGE \nabla^2E = \mu_0 \epsilon_0 \frac{\partial^2E}{\partial t^2}

I’m going to change the form and amend the symbols as I will try to make this more rigorous. To emphasize the E is vector

\LARGE \nabla^2 \vec{E} = \mu_0 \epsilon_0 \frac{\partial^2E}{\partial t^2}

note that E is function of x,y,z,t, that is

\vec{E}=\vec{E}(x,y,z,t)

but for brevity I simply state \vec{E}(x,y,z,t) as \vec{E}

I had to shake off a lot of cobb webbs upstairs to remember how to do the derivation I did 12 years ago for a homework assignment, and the way I did specifically isn’t on the net anywhere and I had to reconstruct my version of the derivation since I think it’s the most accessible to the un-initiated.

Expanding the Laplacian:

\LARGE \nabla^2E = \frac{\partial^2 \vec{E}}{\partial x^2}+\frac{\partial^2 \vec{E}}{\partial y^2}+\frac{\partial^2 \vec{E}}{\partial z^2} = \mu_0 \epsilon_0 \frac{\partial^2\vec{E}}{\partial t^2}

thus

\LARGE \frac{\partial^2 \vec{E}}{\partial x^2}+\frac{\partial^2 \vec{E}}{\partial y^2}+\frac{\partial^2 \vec{E}}{\partial z^2} = \mu_0 \epsilon_0 \frac{\partial^2\vec{E}}{\partial t^2}

noting that \mu_0 \epsilon_0 = \frac{1}{c^2}

\LARGE \frac{\partial^2 \vec{E}}{\partial x^2}+\frac{\partial^2 \vec{E}}{\partial y^2}+\frac{\partial^2 \vec{E}}{\partial z^2} =\frac{1}{c^2} \frac{\partial^2\vec{E}}{\partial t^2}

subtracting \frac{1}{c^2} \frac{\partial^2\vec{E}}{\partial t^2} from both sides yield the familiar d’Alamberitan form:

\LARGE \frac{\partial^2 \vec{E}}{\partial x^2}+\frac{\partial^2 \vec{E}}{\partial y^2}+\frac{\partial^2 \vec{E}}{\partial z^2} -\frac{1}{c^2} \frac{\partial^2\vec{E}}{\partial t^2}=0

another solution to Maxwell’s equation for a light wave travelling through a vacuum can be stated in term of the MAGNETIC field, where B is the vector of magnetic field intensity and direction, and it yields a d’Alambertian of similar form:

\LARGE \frac{\partial^2 \vec{B}}{\partial x^2}+\frac{\partial^2 \vec{B}}{\partial y^2}+\frac{\partial^2 \vec{B}}{\partial z^2} -\frac{1}{c^2} \frac{\partial^2\vec{B}}{\partial t^2}=0

since one could express the the d’Alambertian with the letter E (for the Electric field) or B (for the Magnetic field) I’ll use \Psi as a generalization for either:

\LARGE \frac{\partial^2 \vec{\Psi}}{\partial x^2}+\frac{\partial^2 \vec{\Psi}}{\partial y^2}+\frac{\partial^2 \vec{\Psi}}{\partial z^2} - \frac{1}{c^2} \frac{\partial^2 \vec{\Psi}}{\partial t^2}=0

This sets the stage now for a more rigorous and accessible demonstration of Invariance of Maxwell’s equations under the Lorentz Transformations at the heart of special relativity (be it the Lorentz Aether version or the Einstein version).