View Full Version : On the generation and existence of tachyons (S. Kalimuthu)

johannes

09-25-2010, 03:34 PM

Remarks on On the generation and existence of tachyons (S. Kalimuthu)

I refer to the document published on www.mrelativity.net; On the generation and existence of tachyons (http://www.mrelativity.net/Papers/40/FTLphenomenon%20_1_.pdf)

This document contains an error and therefore an incorrect conclusion is drawn.

Given is equation (4) as

a² + 2ca − c²/m² = 0

The author then derives equation (5) as

c / m²a + 1 = ±√(1 + 1/m²)

this is however not correct.

The simplest test would be to put in numbers. Say c=1, a=1/4 and m=4/3. Then for equation (4) we get

(1/4)² + 2(1/4) − 1/(4/3)² = 1/16 + 8/16 − 9/16 = 0.

However put these numbers in the original equation (5) and we get

1 / (4/3)² 1/4 + 1 = ±√(1 + 1/(4/3)²)

thus

9/4 + 1 = ±5/4

which is not correct.

Given is equation (4) as a² + 2ca − c²/m² = 0 then

a² + 2ca − c²/m² = 0

c² − 2cam² = a²m²

(c − am²)² = (am²)² (1 + 1/m²)

(c/am² − 1)² = (1 + 1/m²)

c/am² − 1 = √(1 + 1/m²)

The correct equation (5) should be

c / m²a − 1 = ±√(1 + 1/m²)

The number test now gives 9/4 − 1 = ±5/4 which is correct for the positive root. Equation (5) in this document is not correct and the part after equation (5) is based on this equation and is also not correct.

- Johannes

cincirob

09-25-2010, 04:09 PM

cinci: The article concludes that tachyons don't exist. Are you taking issue that position?

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johannes

09-25-2010, 04:22 PM

cinci: The article concludes that tachyons don't exist. Are you taking issue that position?

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Cinci, the authors draws that conclusion (tachyons don't exist) based on contradiction - which itself is based on an incorrect equations. I have only shown that the equation is not correct and therefore the conclusion is not correct as done in the document. That tachyons do exists or not requires more analysis (and what does the word "exist" mean). I have once calculated the effect of observing faster then light particles (not questioning imaginary mass or infinite energies) - and they behave then like their antiparticle; an electron moving faster then light behaves like a positron and so on.

- Johannes.

qupta

09-26-2010, 02:46 PM

Remarks on On the generation and existence of tachyons (S. Kalimuthu)

I refer to the document published on www.mrelativity.net; On the generation and existence of tachyons (http://www.mrelativity.net/Papers/40/FTLphenomenon%20_1_.pdf)

This document contains an error and therefore an incorrect conclusion is drawn.

Given is equation (4) as

a² + 2ca − c²/m² = 0

The author then derives equation (5) as

c / m²a + 1 = ±√(1 + 1/m²)

this is however not correct.

The simplest test would be to put in numbers. Say c=1, a=1/4 and m=4/3. Then for equation (4) we get

(1/4)² + 2(1/4) − 1/(4/3)² = 1/16 + 8/16 − 9/16 = 0.

However put these numbers in the original equation (5) and we get

1 / (4/3)² 1/4 + 1 = ±√(1 + 1/(4/3)²)

thus

9/4 + 1 = ±5/4

which is not correct.

Given is equation (4) as a² + 2ca − c²/m² = 0 then

a² + 2ca − c²/m² = 0

c² − 2cam² = a²m²

(c − am²)² = (am²)² (1 + 1/m²)

(c/am² − 1)² = (1 + 1/m²)

c/am² − 1 = √(1 + 1/m²)

The correct equation (5) should be

c / m²a − 1 = ±√(1 + 1/m²)

The number test now gives 9/4 − 1 = ±5/4 which is correct for the positive root. Equation (5) in this document is not correct and the part after equation (5) is based on this equation and is also not correct.

- Johannes

Nice catch.

Mitch

09-27-2010, 06:13 AM

Cinci, the authors draws that conclusion (tachyons don't exist) based on contradiction - which itself is based on an incorrect equations. I have only shown that the equation is not correct and therefore the conclusion is not correct as done in the document. That tachyons do exists or not requires more analysis (and what does the word "exist" mean). I have once calculated the effect of observing faster then light particles (not questioning imaginary mass or infinite energies) - and they behave then like their antiparticle; an electron moving faster then light behaves like a positron and so on.

- Johannes.

Mitch: Johannes, just out of curiosity, were those particles also going 180 degree in respect to time ? ! !

Mitch

09-27-2010, 07:07 AM

The author then derives equation (5) as

c / m²a + 1 = ±√(1 + 1/m²)

this is however not correct.

- Johannes[/QUOTE]

Mitch: It also does not look correct from a dimensional point of view: on the left side of (5) we have kg^-2 while we have kg^-1 on the right side. One must also assign compatible dimensions to each 1 of the equation.

ps : and there is a typo on Equ.(3), m0 = ? ?

cincirob

09-27-2010, 09:57 AM

Johannes: Cinci, the authors draws that conclusion (tachyons don't exist) based on contradiction - which itself is based on an incorrect equations. I have only shown that the equation is not correct and therefore the conclusion is not correct as done in the document. That tachyons do exists or not requires more analysis (and what does the word "exist" mean). I have once calculated the effect of observing faster then light particles (not questioning imaginary mass or infinite energies) - and they behave then like their antiparticle; an electron moving faster then light behaves like a positron and so on.

cinci: Sounds a bit like mirror symmetry with the speed of light being the mirror. What branch of mathematics do you use to do this kind of analysis?

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johannes

09-27-2010, 02:57 PM

Hello Cinci

cinci: Sounds a bit like mirror symmetry with the speed of light being the mirror. What branch of mathematics do you use to do this kind of analysis?

******************************

yes - it looks indead like mirror symmetry. That is because faster then light behaves as if time goes backwards (thus due to quantum symmetries, particles behave like anti-particles). I need to look them up again, but it is simple mathematics.

I will try to do repeat it here again.

Say a light source is moving such that the co-ordinates are given by x=vt and y=y (constant)

The distance between the source and an observer at the origin is given by r²=y²+v²t²

The time at which the observer will see the light source is given by τ=t+Δt where Δt=r/c

Then we have τ²−2τt+t²=Δ²t and Δ²t=y²/c²+β²t² where β=v/c

So using 1−β²=1/γ² we have t²−2γ²τt+γ²τ²=γ²y²/c²

We can solve this and we find that t=γ²T[1 ± √(y²/γ²T²+v²)/c]

Case v<c.

Then we have γ²>0 - a special case would be y/T≈0 then we obtain t≈γ²T[1±β] - so we need to take the negative root, since T>t. The light source is always observable.

Case v>c.

Then we have γ²<0. The argument of the square root can becomes negative. Critical is y²/γ²T²+v²=0 thus T=y√(1/c²−1/v²). In general there are two solutions for T>y√(1/c²−1/v²).

We can write t = T' ± √(y'²+β²T'²) where T'=Tγ² and y'=y/c.

Solutions are: t = T' + √(y'²+β²T'²) and t = T' − √(y'²+β²T'²) - both solutions convert into the other using time reversal.

Time reversal: (−t) = (−T') + √(y'²+β²(−T')²) gives t = T' − √(y'²+β²T'²).

- Johannes

ps. I have tried to reproduce it as best as I can - since I could not find my original

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