2021-11-16 03:43:30 UTC
Critical Theory comes in several flavors: Critical Law Theory, Critical Literature Theory, Critical History Theory, Critical Race Theory. To these we now add Critical Relativity Theory!
In the spirit of Derrida we shall deconstruct the clumsy reasoning of special relativity and separate said reasoning from the algebraic symbols and equations that express it, keeping in mind that mathematics is just another form of rhetorical expression wherein falsity can be expressed every bit as plausibly as the truth.
“There is only the text.”— J. Derrida
According to special relativity two observers in motion with respect to each other will disagree on each other’s length. They will also disagree on the proper flow of time. But they will always agree on the velocity they have with respect to one another. This is exceedingly strange. How can it be that two relative quantities, space and time, combine to produce an absolute quantity called relative velocity? It is true that SR does have a formula for calculating coordinate velocity; just like it has formulas for calculating coordinate space and coordinate time. But the Einstein velocity addition formula ONLY applies to a third object in motion wrt a pair of FoRs. If that third object happens to be at rest wrt one of the FoRs then Einsteinian velocity reduces to Galilean velocity, albeit subject to the speed limit c. Relativists simply assumed without further justification that if FoR-1 measures a velocity v between itself and FoR-2 then FoR-2 must measure the same numerical value v for the velocity between itself and FoR-1. Trivial? Nope. Seemingly trivial assumptions can be monumental when constructing a theory of motion. But a 26 year old would probably not yet have the requisite philosophical sophistication needed to recognize this.
Einstein’s choice to make velocity strictly Galilean when calculating the velocity between pairs of FoRs ( yes, it is a choice because it does not follow from either the first or the second postulates ) can be expressed mathematically as
∆x’/∆t’ = ∆x/∆t = v (1)
I now raise equation (1) to the level of a postulate and declare it to be the third, and heretofore hidden, postulate of special relativity. In recognizing its own structural Galileanism through this new postulate, special relativity can finally claim to be woke.
The problem with the third postulate is that even though it is already assumed in every equation of special relativity, it turns out to be true only when v = c ( the second postulate ) or when v = 0. The third postulate can be demonstrated invalid for all values of v in between. The invalidity of the third postulate causes special relativity fall on it’s algebraic face. Big Bang move over…Not recognizing and acknowledging the third postulate was Einstein’s biggest blunder.
Time for some examples.
DIRK & DONO
Consider two FoRs whose x-axes are parallel and lie very close to one another. The relative velocity between these two FoRs is .866c (γ = 2). Dirk assumes the Lotus position at the origin of one FoR whilst Dono assumes the fetal position at the origin of the other. Both Dirk and Dono and their clocks are glued to the origins of their respective FoRs.
Dirk opens one eye and takes note of the meter marks on Dono’s contracted x-axis as they whiz by. Dirk apprehends that Dono’s meter marks are contracted to only half as long as his own meter marks. Dirk opens the other eye and observes that Dono’s clock is ticking at only half the rate of his own clock. Dirk begins to count Dono’s meter marks as they race past Dirk’s position. After one year (by Dirk’s clock) of counting Dono’s meter marks, Dirk has tallied 1.64e+16 Dono meters ( 9.5e+15 meter marks/Ly x .866Ly x γ ). Dirk has also observed that only 0.5 years have elapsed on Dono’s clock. Dirk now calculates what his coordinate velocity should be according to Dono
( 1.64e+16 Dono meters ) / ( 1.58e+7 Dono seconds ) = 1.04e+9 m/s = 3.5c (2)
[ shortcut: ∆x’/∆t’ = (∆x/∆t)(γ^2) = v(γ^2) ] (3)
“Stop!” You cry, “Dirk’s and Dono’s relative velocity was already stipulated to be an absolute .866c with respect to one another, when measured in either FoR.”
That is true, according to (1). But remember that (1) is an arbitrary choice made by Einstein when he built his theory. It is no more legitimate a choice than the Dolan FoR coordinate velocity transform (3) for determining one’s FoR coordinate velocity. It is also no less inconsistent. For we immediately see by inspection that the Dolan FoR coordinate velocity is always greater than the relative velocity by a factor of γ^2. But Einstein’s choice for requiring Galilean FoR pair velocities clangs with just as much antinomy as Dolan’s transform, as we shall see. Special relativity’s dirty little secret is that it’s hidden third postulate (1) destroys the theory from within.
I can see by Dono’s tightening fetal position that he still doesn’t believe me. Very well. We shall prove SR’s mathematical inconsistency in the next example.
SPECIAL RELATIVITY COLLAPSES UNDER THE WEIGHT OF ITS ALGEBRAIC ORIGINAL SIN
Consider a pair of FoRs whose relative velocity v is some value other than c and other than zero. This is expressed mathematically as
v = ∆x’/∆t’ = ∆x/∆t != c (4)
v = ∆x’/∆t’ = ∆x/∆t != 0 (5)
The Lorentz transforms allow us to construct the FoR coordinate velocities for pairs of FoRs
∆x’ = γ( ∆x - v∆t )
∆t’ = γ( ∆t - ∆xv/c^2 )
∆x’/∆t’ = [ γ( ∆x - v∆t ) ] / [ γ( ∆t - ∆xv/c^2 ) ] (6)
We now endeavor to solve (6) for v in hopes of demonstrating the internal consistency of special relativity, i.e, that v = v for all pair of FoRs. We saw how this was not the case in DIRK & DONO.
The reader will find that trying to solve for v is hopeless unless we make the substitution
v = ∆x/∆t or v = ∆x’/∆t’
It does not matter which we use—either substitution is permitted by the third postulate (1).
With the substitution made, we eventually arrive at the preposterous results
∆x’/∆t’ = c (7)
∆x’/∆t’ = 0 (8)
The derivation is left as an exercise for the reader. For those needing help with the derivation ( I'm looking at you, Dono ) I will be happy to provide it in another post.
The laughable results (7) and (8) directly contradict our assumptions (4) and (5). Furthermore, the results impose the requirement that v is not even a variable—v turns out to be a constant always equal to c or zero. Absolutely absurd.
Algebraic relativity is thus reduced to ridiculous rubble by means mathematical reductio ad absurdum. The root cause of special relativity’s spectacular algebraic failure lies in the propositional calculus. I am happy to expatiate on that subject in another post if there is interest.
Let’s do one more example—this one ripped from the headlines of experimental physics.
Imagine that you are a hadron in deep space minding your own business when all of a sudden you turn to see a Lorentz-flattened earth coming at you at a velocity of .866c. In the impending collision the first thing to strike you is an air molecule high in the earth’s atmosphere. That molecules knocks the stuffing out of you. What is left of you is now a muon which means that you only have 2.2 microseconds more to live.
It turns out that the surface of the flattened earth is exactly 571.56 meters away from you, according to your own muon FoR. By a remarkable coincidence there is a flattened scintillator and a flattened clock in a flattened laboratory directly below you on the surface of the flattened earth. You note the time on the flattened lab clock. Because you are a muon, you are your own 2.2 microsecond alarm clock.
The surface of the flattened earth continues to speed towards you at .866c. 2.2 microseconds later the flattened earth, lab and scintillator smash into you. Just as you expire in the scintillator you note that only 1.1 microseconds has elapsed on the lab clock. Nothing strange here; the labs clock is traveling at γ=2 with respect to you so it only logs half as much elapsed time as you.
One of the lab scientists now cries out “Just a minute! That’s not how this story goes. First of all, it is the hadron that is Lorentz-flattened, not us. And second of all, that hadron used it’s flattened FoR to determine that is was only 571.56 meters away from our scintillator at the point it became a muon. Our unflattened earth FoR clearly indicated that the hadron was actually 1143.12 meters away when it became a muon. That’s why it took 4.4 microseconds, traveling at .866 c, to reach our scintillator. And that’s what our lab clock shows. Not 1.1 microseconds, like that dumb muon is claiming.”
Special relativity leaves us in a quandary. How much time actually did elapse on the lab clock from the moment of the muon’s inception to the moment of its scintillating demise? Was it 1.1 microseconds? Or was it 4.4 microseconds? It has to be one or the other, it can’t be both. However, different elapsed times on the same lab clock can be calculated by the muon and by the earthbound scientists with equal justification. Special relativity is incapable of providing a unique elapsed time on the lab clock. I challenge anyone to show that special relativity can provide a unique elapsed time in the preceding case.
Special relativity’s greatest experimental confirmation turns out to be it’s second greatest falsification. Gravity has been special relativity’s greatest falsification since 1907 ( check out the author’s brilliant post on special relativity vs. Kepler’s 3rd law ).