# New article shows a fatal math error in SR

No, it doesn't, because it is based on a false assumption.

Let's use another example. Let's say you take two atoms of hydrogen and two atoms of antihydrogen. What would you have once they combined? You might correctly think they would annihilate each other and produce energy.

"Wrong!" a dolt could say. "2+2=4. The math PROVES that if you combine them you just get more hydrogen!"

Is his math wrong? No. Are his assumptions? Yes.

Specifically, if it's matter and anti-matter entities, then it should be "(+2H) + (-2H) = (zeroH) + (energy equivalent to 4H).

Take care not to sound like you put personal ridicule before obnjective answers to the article's mathematics and conclusions as posted by chinglu, else he will win the debate on this OP by default. Good luck, and enjoy friendly objective on-topic discussion, everyone. Bye.

The article proves SR results in a contradiction.

The "article" is wrong, you are a crank, so what else is new?

Therefore, some other theory is responsible for GPS.

Therefore , you are an ignorant crackpot, the functionality of GPS is based on GR.

It is that simple.

Yes, you suffer from the same knd of mental illness that affects Motor Daddy, the illness is called " I cannot understand relativity, therefore it must be wrong".

The "article" is wrong, you are a crank, so what else is new?

Therefore , you are an ignorant crackpot, the functionality of GPS is based on GR.

Yes, you suffer from the same knd of mental illness that affects Motor Daddy, the illness is called " I cannot understand relativity, therefore it must be wrong".

The simple math of the OP proves SR, which is a subset of GR, results in a mathematical contradiction.

Therefore, since a theory in contradiction does not work, some other theory is responsible for GPS.

Why don't you understand this simple logic?

Andrew Banks said:
Mirrors in Special Relativity
Andrew Banks
A name which is now [post=2949024]synonymous with ignorant, arrogant and wrong[/POST].

See also: http://vixra.org/pdf/1307.0073v1.pdf which I do not refer to -- the copy I quote is exclusively from chinglu's web site for a fake scientific journal. See also http://nongeometric.files.wordpress.com/2011/10/sr2.pdf where Andrew has been shown to be [thread=110037]wrong before[/THREAD].

Andrew Banks said:
Abstract.
This is not an abstract in any conventional sense which demonstrates that this paper has not been subjected to even cursory editorial review an that the publisher is a sham scientific journal -- in short a poetry vanity press masquerading as a scientific journal to fleece gullible pseudo-scientists and skeptics. An abstract should be exactly long enough to know what a paper is about and what the main conclusions are. Here Andrew Banks begins his exposition, leaving the article without an abstract.

Andrew Banks said:
To develop the Lorentz transformations (LT), Einstein placed a mirror in the primed frame at some location (x’,0).
A bold claim, supported by nothing. Also, this would be an excellent place to cite or quote the single Einstein references Andrew Banks lists, but instead he cites it nowhere. What Einstein actually did in part I, section 1, is to establish a system of synchronized clocks in a single stationary frame. Here the use of primed coordinates merely refers to a different time on the same clock (A) as the earlier unprimed coordinate value.
Albert Einstein (translated) said:
If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an “A time” and a “B time.” We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A. Let a ray of light start at the “A time” $$t_{\rm A}$$ from A towards B, let it at the “B time” $$t_{\rm B}$$ be reflected at B in the direction of A, and arrive again at A at the “A time” $$t'_{\rm A}$$.

In accordance with definition the two clocks synchronize if
$$t_{\rm B}-t_{\rm A}=t'_{\rm A}-t_{\rm B}.$$

We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:—
1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.

Thus with the help of certain imaginary physical experiments we have settled what is to be understood by synchronous stationary clocks located at different places, and have evidently obtained a definition of “simultaneous,” or “synchronous,” and of “time.” The “time” of an event is that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.

In agreement with experience we further assume the quantity
$$\frac{2{\rm AB}}{t'_A-t_A}=c,$$
to be a universal constant—the velocity of light in empty space.

It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it “the time of the stationary system.”
At the bottom of section 2, the relativity of simultaneity is introduced, but again the primed coordinates do not refer to the choice of coordinate system.
Albert Einstein (translated) said:
We imagine further that at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the “time of the stationary system” at the places where they happen to be. These clocks are therefore “synchronous in the stationary system.”

We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established in § 1 for the synchronization of two clocks. Let a ray of light depart from A at the time [[“Time” here denotes “time of the stationary system” and also “position of hands of the moving clock situated at the place under discussion.”]] $$t_{\rm A}$$, let it be reflected at B at the time $$t_{\rm B}$$, and reach A again at the time $$t'_{\rm A}$$. Taking into consideration the principle of the constancy of the velocity of light we find that
$$t_{\rm B}-t_{\rm A}=\frac{r_{\rm AB}}{c-v}\ {\rm and} t'_{\rm A}-t_{\rm B}=\frac{r_{\rm AB}}{c+v}$$

where $$r_{\rm AB}$$ denotes the length of the moving rod—measured in the stationary system. Observers moving with the moving rod would thus find that the two clocks were not synchronous, while observers in the stationary system would declare the clocks to be synchronous.

So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.

So where is this mirror at location (x',0). Well in section 3, Einstein finally derives the Lorentz transformation, but does not use x' coordinates like Andrew Banks claims.
Albert Einstein (translated) said:
To any system of values x, y, z, t, which completely defines the place and time of an event in the stationary system, there belongs a system of values $$\xi$$, $$\eta$$, $$\zeta$$, $$\tau$$, determining that event relatively to the system k, and our task is now to find the system of equations connecting these quantities.

In the first place it is clear that the equations must be linear on account of the properties of homogeneity which we attribute to space and time.

If we place $$x' = x - v t$$, it is clear that a point at rest in the system k must have a system of values x', y, z, independent of time. We first define $$\tau$$ as a function of x', y, z, and t. To do this we have to express in equations that $$\tau$$ is nothing else than the summary of the data of clocks at rest in system k, which have been synchronized according to the rule given in § 1.

From the origin of system k let a ray be emitted at the time $$\tau_0$$ along the X-axis to x', and at the time $$\tau_1$$ be reflected thence to the origin of the co-ordinates, arriving there at the time $$\tau_2$$; we then must have $$\frac{1}{2}(\tau_0+\tau_2)=\tau_1$$, or, by inserting the arguments of the function $$\tau$$ and applying the principle of the constancy of the velocity of light in the stationary system:—
$$\frac{1}{2}\left[\tau(0,0,0,t)+\tau\left(0,0,0,t+\frac{x'}{c-v} + \frac{x'}{c+v}\right)\right]= \tau\left(x',0,0,t+\frac{x'}{c-v}\right)$$.
Hence, if x' be chosen infinitesimally small,
$$\frac{1}{2}\left(\frac{1}{c-v}+\frac{1}{c+v}\right)\frac{\partial \tau}{\partial t} = \frac{\partial \tau}{\partial x'}+\frac{1}{c-v}\frac{\partial\tau}{\partial t}$$,
or
$$\frac{\partial\tau}{\partial x'}+\frac{v}{c^2-v^2}\frac{\partial\tau}{\partial t}=0$$.

It is to be noted that instead of the origin of the co-ordinates we might have chosen any other point for the point of origin of the ray, and the equation just obtained is therefore valid for all values of x', y, z.
As you see x and x' are in the same coordinate system, the system K which is called "stationary." Basically, Einstein is saying for a particular object moving with constant speed (the same velocity as system k), then it has coordinates in the stationary system as $$x(t) = x' + v t, \; y(t) = y + 0 t, z(t) = z + 0 t$$ so that while x is a function of time, x', y and z are constants of motion in coordinate system K. And since the object moves at the same velocity as coordinate system k, it follows that the linear motion of the object in K must translated to linear non-motion in system k or $$\xi(t) = \xi + 0 \tau, \; \eta(t) = \eta + 0 \tau, \zeta(t) = \zeta + 0 \tau$$. To figure this out, Einstein made $$\tau$$ a function of the constants of motion of this particular object, moving in stationary system K and motionless in stationary system k, and x' is one of those K-system coordinates corresponding to the stationary system X-position of the object at stationary system time t=0.

So already in sentence one, Andrew Banks has botched it by misunderstanding the 108-year-old paper that every physics baccalaureate understands the conclusions of. Einstein was not using primes to distinguish different coordinate systems as is common in relativity textbooks today. He used Latin letters for one system (K) and Greek letters for the other system (k).

Andrew Banks said:
Then, when the origins of the primed and unprimed frames are common, a light pulse is emitted from the common origin location.
Actually Einstein considers a ray of light in the Latin and Greek coordinate systems. Light is used in various ways in Einstein's paper because the whole point was that the Lorentz Transformation could be derived from basic assumptions and the consistency of the speed of light. Then he does the larger part by showing that this coordinate equivalence was also an equivalence of Maxwell's electodynamics and (within then-current experimental limits) Newton's physics. Thus the 1905 paper was an important unification.

Andrew Banks said:
The experiment then considers two-way light travel for both frames such that a light beam strikes the primed frame mirror and is reflected back to the primed frame origin.
Nothing in Einstein's paper can be described as an experiment. Indeed, most of it is an argument from linearity and simple rate equations.

Here, at last, Andrew Bank's butchery of history ends and his beef begins.

Andrew Banks said:
This article proposes locating the mirror in the primed frame at (x’<0, y>0) with the reflective side parallel to and directly facing the primed y -axis. The other side of this mirror is non-reflective. It should be clear that a light pulse emitted from the primed origin will be reflected off the mirror for all y>0.
Horrible syntax. "The article" can propose nothing. "The author proposes" is better but unnecessary. A paragraph break is needed because Andrew Banks has stopped talking about one subject (Misunderstanding Einstein) and began another (Making a Fool of Oneself). The description of the location and orientation of the mirror is nonsensical.
Better: Let a point-like detector exist, stationary in coordinate system k, somewhere to the left of the $$\eta$$-axis and only capable of detecting light to its right (including light originating at the origin of coordinate system k).

Andrew Banks said:
On the other hand, in the context of the unprimed frame, it is also clear given v and x’<0, one can select y large enough such that while a light pulse emitted from the two origins when they are common is expanding, the moving primed mirror crosses the unprimed y-axis before being struck by the light pulse. In this case, the unprimed frame predicts the light pulse strikes the non-reflective side and no light is reflected. So, that means Special Relativity (SR) predicts one light pulse is reflected off the mirror and not reflected, which is a physical impossibility.
Better: Assuming everything stationary in system k moves to the right with velocity v (in the x-direction) in system K, assume the origins of system k and K correspond at their respective zero times. Thus
$$t = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( \tau + \frac{v}{c^2} \xi \right) \\ x = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( \xi + v \tau \right) \\ y = \eta$$
Is it possible that for $$0 < v < c$$ the mirror could have such a large $$\eta$$ value that in the K frame a light flash from the time the origins were at the same position arrives at the detector from the left, preventing detection in one description of reality but not the other, supposedly equivalent one?

Andrew Banks correctly decides that the pulse from $$(\tau, \xi, \eta) = (0,0,0)$$ to $$(\tau_0, -\xi_0, +\eta_0)$$ would be seen in system K as a pulse from $$(t, x, y) = (0,0,0)$$ to $$(t_0, +x_0, +\eta_0)$$ whenever certain geometrical constraints are met, but ignores the question of what "to the right" means in system K.

First, what is the minimum value of v such that in system K the light pulse to the detector in purely in the $$+\eta$$ direction? That would mean $$x_0 = 0$$. Thus

$$v_0 = \frac{c \xi_0}{\sqrt{ \xi_0^2 + \eta_0^2}} < c$$

Then for any v such that $$v_0 < v < c$$ and assuming $$-\xi_0 < 0, \; \eta_0 > 0, \; \tau_0 = \frac{1}{c} \sqrt{\xi_0^2 + \eta_0^2} > 0$$ we have :

$$x_0 = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( -\xi_0 + v \tau_0 \right) = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( -\xi_0 + \frac{v}{c} \sqrt{\xi_0^2 + \eta_0^2} \right) { \Large \quad > \quad } \frac{1}{\sqrt{1-\frac{v_0^2}{c^2}}} \left( -\xi_0 + \frac{v_0}{c} \sqrt{\xi_0^2 + \eta_0^2} \right) = \frac{1}{\sqrt{1-\frac{v_0^2}{c^2}}} \left( -\xi_0 + \frac{\xi_0}{\sqrt{ \xi_0^2 + \eta_0^2}} \sqrt{\xi_0^2 + \eta_0^2} \right) = 0$$

But that, importantly, still doesn't answer if the light comes into the left or the right of the detector, which is answered by the sign of the cross product of the light ray movement and an extension of the detector (finite or infintesimal) in the $$\eta$$ direction.

Andrew Banks said:
REFERENCES
[1] Einstein A., in The Principle of Relativity (Dover, New York) 1952, p. 37.
This is proof that this paper has not been through ay sort of scientific review. This "book" is a collection of scientific papers published in real scientific journals and therefore cannot be cited as an original source.
What is actual being cited, according to the page numbers I have is "On the Electrodynamics of Moving Bodies" which is a translation of "Zur Elektrodynamik bewegter Körper" by Albert Einstein published in Annalen der Physik, Volume 17, pages 891-921 in 1905. Moreover, as a note in a different translation shows, this book was a Dover reprint of a 1923 Methuen and Company translation by W. Perrett and G.B. Jeffery of the 1922 Teubner-published collection Das Relativatsprinzip, 4th Edition.

http://users.physik.fu-berlin.de/~kleinert/files/1905_17_891-921.pdf
http://www.fourmilab.ch/etexts/einstein/specrel/www/

Further, the reference was not actually referred to anywhere in the paper.

All assumptions and all math in the article have been flushed out in this thread and proven to be correct.

That is all that is needed.

It is time for you to face the facts.

Quit trolling us with nonsense dummy. Your assertions are meaningless bullshit from a scientific illiterate crank. IE everything you think about your result is bullshit round filed nonsense. It doesn't even deserve a 'roundfile' because it was irrelevant unscientific nonsense before you wrote it down.

A name which is now [post=2949024]synonymous with ignorant, arrogant and wrong[/POST].

See also: http://vixra.org/pdf/1307.0073v1.pdf which I do not refer to -- the copy I quote is exclusively from chinglu's web site for a fake scientific journal. See also http://nongeometric.files.wordpress.com/2011/10/sr2.pdf where Andrew has been shown to be [thread=110037]wrong before[/THREAD].

This is not an abstract in any conventional sense which demonstrates that this paper has not been subjected to even cursory editorial review an that the publisher is a sham scientific journal -- in short a poetry vanity press masquerading as a scientific journal to fleece gullible pseudo-scientists and skeptics. An abstract should be exactly long enough to know what a paper is about and what the main conclusions are. Here Andrew Banks begins his exposition, leaving the article without an abstract.

A bold claim, supported by nothing. Also, this would be an excellent place to cite or quote the single Einstein references Andrew Banks lists, but instead he cites it nowhere. What Einstein actually did in part I, section 1, is to establish a system of synchronized clocks in a single stationary frame. Here the use of primed coordinates merely refers to a different time on the same clock (A) as the earlier unprimed coordinate value.
At the bottom of section 2, the relativity of simultaneity is introduced, but again the primed coordinates do not refer to the choice of coordinate system.

So where is this mirror at location (x',0). Well in section 3, Einstein finally derives the Lorentz transformation, but does not use x' coordinates like Andrew Banks claims.
As you see x and x' are in the same coordinate system, the system K which is called "stationary." Basically, Einstein is saying for a particular object moving with constant speed (the same velocity as system k), then it has coordinates in the stationary system as $$x(t) = x' + v t, \; y(t) = y + 0 t, z(t) = z + 0 t$$ so that while x is a function of time, x', y and z are constants of motion in coordinate system K. And since the object moves at the same velocity as coordinate system k, it follows that the linear motion of the object in K must translated to linear non-motion in system k or $$\xi(t) = \xi + 0 \tau, \; \eta(t) = \eta + 0 \tau, \zeta(t) = \zeta + 0 \tau$$. To figure this out, Einstein made $$\tau$$ a function of the constants of motion of this particular object, moving in stationary system K and motionless in stationary system k, and x' is one of those K-system coordinates corresponding to the stationary system X-position of the object at stationary system time t=0.

So already in sentence one, Andrew Banks has botched it by misunderstanding the 108-year-old paper that every physics baccalaureate understands the conclusions of. Einstein was not using primes to distinguish different coordinate systems as is common in relativity textbooks today. He used Latin letters for one system (K) and Greek letters for the other system (k).

Actually Einstein considers a ray of light in the Latin and Greek coordinate systems. Light is used in various ways in Einstein's paper because the whole point was that the Lorentz Transformation could be derived from basic assumptions and the consistency of the speed of light. Then he does the larger part by showing that this coordinate equivalence was also an equivalence of Maxwell's electodynamics and (within then-current experimental limits) Newton's physics. Thus the 1905 paper was an important unification.

Nothing in Einstein's paper can be described as an experiment. Indeed, most of it is an argument from linearity and simple rate equations.

Here, at last, Andrew Bank's butchery of history ends and his beef begins.

Horrible syntax. "The article" can propose nothing. "The author proposes" is better but unnecessary. A paragraph break is needed because Andrew Banks has stopped talking about one subject (Misunderstanding Einstein) and began another (Making a Fool of Oneself). The description of the location and orientation of the mirror is nonsensical.
Better: Let a point-like detector exist, stationary in coordinate system k, somewhere to the left of the $$\eta$$-axis and only capable of detecting light to its right (including light originating at the origin of coordinate system k).

Better: Assuming everything stationary in system k moves to the right with velocity v (in the x-direction) in system K, assume the origins of system k and K correspond at their respective zero times. Thus
$$t = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( \tau + \frac{v}{c^2} \xi \right) \\ x = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( \xi + v \tau \right) \\ y = \eta$$
Is it possible that for $$0 < v < c$$ the mirror could have such a large $$\eta$$ value that in the K frame a light flash from the time the origins were at the same position arrives at the detector from the left, preventing detection in one description of reality but not the other, supposedly equivalent one?

Andrew Banks correctly decides that the pulse from $$(\tau, \xi, \eta) = (0,0,0)$$ to $$(\tau_0, -\xi_0, +\eta_0)$$ would be seen in system K as a pulse from $$(t, x, y) = (0,0,0)$$ to $$(t_0, +x_0, +\eta_0)$$ whenever certain geometrical constraints are met, but ignores the question of what "to the right" means in system K.

First, what is the minimum value of v such that in system K the light pulse to the detector in purely in the $$+\eta$$ direction? That would mean $$x_0 = 0$$. Thus

$$v_0 = \frac{c \xi_0}{\sqrt{ \xi_0^2 + \eta_0^2}} < c$$

Then for any v such that $$v_0 < v < c$$ and assuming $$-\xi_0 < 0, \; \eta_0 > 0, \; \tau_0 = \frac{1}{c} \sqrt{\xi_0^2 + \eta_0^2} > 0$$ we have :

$$x_0 = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( -\xi_0 + v \tau_0 \right) = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( -\xi_0 + \frac{v}{c} \sqrt{\xi_0^2 + \eta_0^2} \right) { \Large \quad > \quad } \frac{1}{\sqrt{1-\frac{v_0^2}{c^2}}} \left( -\xi_0 + \frac{v_0}{c} \sqrt{\xi_0^2 + \eta_0^2} \right) = \frac{1}{\sqrt{1-\frac{v_0^2}{c^2}}} \left( -\xi_0 + \frac{\xi_0}{\sqrt{ \xi_0^2 + \eta_0^2}} \sqrt{\xi_0^2 + \eta_0^2} \right) = 0$$

But that, importantly, still doesn't answer if the light comes into the left or the right of the detector, which is answered by the sign of the cross product of the light ray movement and the finite extension of the detector.

This is proof that this paper has not been through ay sort of scientific review. This "book" is a collection of scientific papers published in real scientific journals and therefore cannot be cited as an original source.
What is actual being cited, according to the page numbers I have is "On the Electrodynamics of Moving Bodies" which is a translation of "Zur Elektrodynamik bewegter Körper" by Albert Einstein published in Annalen der Physik, Volume 17, pages 891-921 in 1905. Moreover, as a note in a different translation shows, this book was a Dover reprint of a 1923 Methuen and Company translation by W. Perrett and G.B. Jeffery of the 1922 Teubner-published collection Das Relativatsprinzip, 4th Edition.

http://users.physik.fu-berlin.de/~kleinert/files/1905_17_891-921.pdf
http://www.fourmilab.ch/etexts/einstein/specrel/www/

Further, the reference was not actually referred to anywhere in the paper.

Chinglu is probably going to give the 'read my nonsense' and weep response. Great post from you.

The simple math of the OP proves SR, which is a subset of GR, results in a mathematical contradiction.

...only for a crank like you, not for the millions of people who understand the theory.

Therefore, since a theory in contradiction does not work, some other theory is responsible for GPS.

Yet, GPS is built entirely on the formalism of GR. You are a nutter.

The article proves SR results in a contradiction. No one can refute that.
It's already been refuted and killed, dead on arrival. GPS refutes it posthumously, proving that Andrew Banks is a crank.

So, some other theory explains current experiments. What is so hard to understand about that?

That's pretty moronic considering the fact that GPS is flying at sufficient speed to set up the conditions to test Andrew Banks' claims, and then reveals that those claims are false.

And what do you mean experiments - GPS is a done deal. This baby is flying, unlike the piss-poor Andrew Banks crash-and-burn denial pseudomath anti-Geometry antirelativity pseudotechnoscreed.

GPS proves SR and GR, both as coupled and independent effects. Here you have the transverse SR producing 7 us of error per day for the stationary and slow moving ground receivers, plus all of the combinations of SR effects for aircraft and sats that use it. It works per the LT, per SR, but only because the premise of GPS is correct. No games are played like the moron Andrew Banks has done by pretending to have a peer reviewed proof.

It's quite simple actually. Andrew Banks is a dolt, and you are either him or his gullible minion. What's so hard about that? Nothing. That's why everyone here nailed you from the get-go.

Specifically, if it's matter and anti-matter entities, then it should be "(+2H) + (-2H) = (zeroH) + (energy equivalent to 4H).

Take care not to sound like you put personal ridicule before obnjective answers to the article's mathematics and conclusions as posted by chinglu, else he will win the debate on this OP by default. Good luck, and enjoy friendly objective on-topic discussion, everyone. Bye.

Birds of a feather.

A name which is now [post=2949024]synonymous with ignorant, arrogant and wrong[/POST].

See also: http://vixra.org/pdf/1307.0073v1.pdf which I do not refer to -- the copy I quote is exclusively from chinglu's web site for a fake scientific journal. See also http://nongeometric.files.wordpress.com/2011/10/sr2.pdf where Andrew has been shown to be [thread=110037]wrong before[/THREAD].

This is not an abstract in any conventional sense which demonstrates that this paper has not been subjected to even cursory editorial review an that the publisher is a sham scientific journal -- in short a poetry vanity press masquerading as a scientific journal to fleece gullible pseudo-scientists and skeptics. An abstract should be exactly long enough to know what a paper is about and what the main conclusions are. Here Andrew Banks begins his exposition, leaving the article without an abstract.

A bold claim, supported by nothing. Also, this would be an excellent place to cite or quote the single Einstein references Andrew Banks lists, but instead he cites it nowhere. What Einstein actually did in part I, section 1, is to establish a system of synchronized clocks in a single stationary frame. Here the use of primed coordinates merely refers to a different time on the same clock (A) as the earlier unprimed coordinate value.
At the bottom of section 2, the relativity of simultaneity is introduced, but again the primed coordinates do not refer to the choice of coordinate system.

So where is this mirror at location (x',0). Well in section 3, Einstein finally derives the Lorentz transformation, but does not use x' coordinates like Andrew Banks claims.
As you see x and x' are in the same coordinate system, the system K which is called "stationary." Basically, Einstein is saying for a particular object moving with constant speed (the same velocity as system k), then it has coordinates in the stationary system as $$x(t) = x' + v t, \; y(t) = y + 0 t, z(t) = z + 0 t$$ so that while x is a function of time, x', y and z are constants of motion in coordinate system K. And since the object moves at the same velocity as coordinate system k, it follows that the linear motion of the object in K must translated to linear non-motion in system k or $$\xi(t) = \xi + 0 \tau, \; \eta(t) = \eta + 0 \tau, \zeta(t) = \zeta + 0 \tau$$. To figure this out, Einstein made $$\tau$$ a function of the constants of motion of this particular object, moving in stationary system K and motionless in stationary system k, and x' is one of those K-system coordinates corresponding to the stationary system X-position of the object at stationary system time t=0.

So already in sentence one, Andrew Banks has botched it by misunderstanding the 108-year-old paper that every physics baccalaureate understands the conclusions of. Einstein was not using primes to distinguish different coordinate systems as is common in relativity textbooks today. He used Latin letters for one system (K) and Greek letters for the other system (k).

Actually Einstein considers a ray of light in the Latin and Greek coordinate systems. Light is used in various ways in Einstein's paper because the whole point was that the Lorentz Transformation could be derived from basic assumptions and the consistency of the speed of light. Then he does the larger part by showing that this coordinate equivalence was also an equivalence of Maxwell's electodynamics and (within then-current experimental limits) Newton's physics. Thus the 1905 paper was an important unification.

Nothing in Einstein's paper can be described as an experiment. Indeed, most of it is an argument from linearity and simple rate equations.

Here, at last, Andrew Bank's butchery of history ends and his beef begins.

Horrible syntax. "The article" can propose nothing. "The author proposes" is better but unnecessary. A paragraph break is needed because Andrew Banks has stopped talking about one subject (Misunderstanding Einstein) and began another (Making a Fool of Oneself). The description of the location and orientation of the mirror is nonsensical.
Better: Let a point-like detector exist, stationary in coordinate system k, somewhere to the left of the $$\eta$$-axis and only capable of detecting light to its right (including light originating at the origin of coordinate system k).

Better: Assuming everything stationary in system k moves to the right with velocity v (in the x-direction) in system K, assume the origins of system k and K correspond at their respective zero times. Thus
$$t = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( \tau + \frac{v}{c^2} \xi \right) \\ x = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( \xi + v \tau \right) \\ y = \eta$$
Is it possible that for $$0 < v < c$$ the mirror could have such a large $$\eta$$ value that in the K frame a light flash from the time the origins were at the same position arrives at the detector from the left, preventing detection in one description of reality but not the other, supposedly equivalent one?

Andrew Banks correctly decides that the pulse from $$(\tau, \xi, \eta) = (0,0,0)$$ to $$(\tau_0, -\xi_0, +\eta_0)$$ would be seen in system K as a pulse from $$(t, x, y) = (0,0,0)$$ to $$(t_0, +x_0, +\eta_0)$$ whenever certain geometrical constraints are met, but ignores the question of what "to the right" means in system K.

First, what is the minimum value of v such that in system K the light pulse to the detector in purely in the $$+\eta$$ direction? That would mean $$x_0 = 0$$. Thus

$$v_0 = \frac{c \xi_0}{\sqrt{ \xi_0^2 + \eta_0^2}} < c$$

Then for any v such that $$v_0 < v < c$$ and assuming $$-\xi_0 < 0, \; \eta_0 > 0, \; \tau_0 = \frac{1}{c} \sqrt{\xi_0^2 + \eta_0^2} > 0$$ we have :

$$x_0 = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( -\xi_0 + v \tau_0 \right) = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( -\xi_0 + \frac{v}{c} \sqrt{\xi_0^2 + \eta_0^2} \right) { \Large \quad > \quad } \frac{1}{\sqrt{1-\frac{v_0^2}{c^2}}} \left( -\xi_0 + \frac{v_0}{c} \sqrt{\xi_0^2 + \eta_0^2} \right) = \frac{1}{\sqrt{1-\frac{v_0^2}{c^2}}} \left( -\xi_0 + \frac{\xi_0}{\sqrt{ \xi_0^2 + \eta_0^2}} \sqrt{\xi_0^2 + \eta_0^2} \right) = 0$$

But that, importantly, still doesn't answer if the light comes into the left or the right of the detector, which is answered by the sign of the cross product of the light ray movement and an extension of the detector (finite or infintesimal) in the $$\eta$$ direction.

This is proof that this paper has not been through ay sort of scientific review. This "book" is a collection of scientific papers published in real scientific journals and therefore cannot be cited as an original source.
What is actual being cited, according to the page numbers I have is "On the Electrodynamics of Moving Bodies" which is a translation of "Zur Elektrodynamik bewegter Körper" by Albert Einstein published in Annalen der Physik, Volume 17, pages 891-921 in 1905. Moreover, as a note in a different translation shows, this book was a Dover reprint of a 1923 Methuen and Company translation by W. Perrett and G.B. Jeffery of the 1922 Teubner-published collection Das Relativatsprinzip, 4th Edition.

http://users.physik.fu-berlin.de/~kleinert/files/1905_17_891-921.pdf
http://www.fourmilab.ch/etexts/einstein/specrel/www/

Further, the reference was not actually referred to anywhere in the paper.

First off, let's correct rpenner on the experiment proposed by Einstein.

The article claimed Einstein used (x',0) in the context of the moving frame for his LT equations.

Let us quote Einstein.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

"To any time of the stationary system K"

So, capital K is the stationary system.

Then we have,

"From the origin of system k let a ray be emitted at the time t'0 along the X-axis to x', and at the time be reflected thence to the origin of the co-ordinates, arriving there at t'1"

So, we have lower case k as the moving system as indicated in the article. Then, in the moving system k, a light pulse is emitted from the origin of k along the X axis to x' which means (x',0) just as the article says, and there is a mirror there which reflects back to the origin of the k moving system.

This is exactly what the article says and this is exactly what Einstein says.

This proves rpenner is in absolute error.

The only next relevant claim by rpenner is that the unprimed frame claims that the moving mirror strikes the light sphere on the front side so that reflection occurs for both frames even though the mirror is on the positive side of the unprimed frame x-axis when light strikes it and the back side is the non-reflective side is facing the unprimed origin.

This means, along any y-line, a sphere is above that line before the mirror strikes it so that it runs into it. That would mean there is a light beam along a y line that is in front of any other light beam on that line.

Therefore, this beam would exceed c and contradict SR.

So, rpenner's proposal contradicts SR and that would mean SR people would call him a crank and crackpot.

So, rpenner's post does nothing to refute the OP link

Quit trolling us with nonsense dummy. Your assertions are meaningless bullshit from a scientific illiterate crank. IE everything you think about your result is bullshit round filed nonsense. It doesn't even deserve a 'roundfile' because it was irrelevant unscientific nonsense before you wrote it down.

The OP stands without any logical challenge.

What is it like living on a flat earth?

It's already been refuted and killed, dead on arrival. GPS refutes it posthumously, proving that Andrew Banks is a crank.

That's pretty moronic considering the fact that GPS is flying at sufficient speed to set up the conditions to test Andrew Banks' claims, and then reveals that those claims are false.

And what do you mean experiments - GPS is a done deal. This baby is flying, unlike the piss-poor Andrew Banks crash-and-burn denial pseudomath anti-Geometry antirelativity pseudotechnoscreed.

GPS proves SR and GR, both as coupled and independent effects. Here you have the transverse SR producing 7 us of error per day for the stationary and slow moving ground receivers, plus all of the combinations of SR effects for aircraft and sats that use it. It works per the LT, per SR, but only because the premise of GPS is correct. No games are played like the moron Andrew Banks has done by pretending to have a peer reviewed proof.

It's quite simple actually. Andrew Banks is a dolt, and you are either him or his gullible minion. What's so hard about that? Nothing. That's why everyone here nailed you from the get-go.

I agree, GPS refutes SR.

Try to take your GPS unit with the sagnac correction and hold it over an MMX experiment. What do your get?

The article also prove SR results in a contradiction.

I agree, GPS refutes SR.

Try to take your GPS unit with the sagnac correction and hold it over an MMX experiment. What do your get?

The article also prove SR results in a contradiction.

Unrepenting crank, the theory of GPS includes the Sagnac effect.

I agree, GPS refutes SR.
Only a blind moron would say that. Ok, a person in a psyche ward or intellectually disabled.

Try to take your GPS unit with the sagnac correction and hold it over an MMX experiment. What do your get?
No, try and add 7us/day in keeping with bonehard Andrew Banks and see if you're still in Bugtussle when the hangover wears off in the morning.

The article also prove SR results in a contradiction.
GPS proves the premise of the article is fraudulent.

You are simply proving that your anti-science denialism, naivete and narcissism has no bounds. Other than that, your bogus claims are DOA.

The OP stands without any logical challenge.

What is it like living on a flat earth?

The OP fell as soon as billvon called you out, and rpenner just carried out the trash and nuked it in a colossal incinerator. The rest of the folks were just sweeping up the crumbs.

GPS declared it dead on arrival.

Unrepenting crank, the theory of GPS includes the Sagnac effect.

OK,
so hold your GPS unit over an MMX experiment and tell me what you get.

I feel like I am talking to an ape.

The OP fell as soon as billvon called you out, and rpenner just carried out the trash and nuked in a colossal incinerator. The rest of the folks were just sweeping up the crumbs.

GPS declared it dead on arrival.

rpenner was refuted.

if not, simply point out exactly where he refuted the OP.

OK,
so hold your GPS unit over an MMX experiment and tell me what you get.

I am getting that you are insane. But we knew that for years.

Only a blind moron would say that. Ok, a person in a psyche ward or intellectually disabled.

No, try and add 7us/day in keeping with bonehard Andrew Banks and see if you're still in Bugtussle when the hangover wears off in the morning.

GPS proves the premise of the article is fraudulent.

You are simply proving that your anti-science denialism, naivete and narcissism has no bounds. Other than that, your bogus claims are DOA.

The article proves SR results in a contradiction.

That means all experimental evidence prove some other theory.

Why is that so hard for you to understand?

I am getting that you are insane. But we knew that for years.

Oh, what do you get if you hold your GPS device with sagnac over MMX, you did not say.

Do you actually FALL OFF A FLAT EARTH?