Re: [SR] The traveler of Tau Ceti

On 3/28/2024 7:02 AM, Richard Hachel wrote:

Le 27/03/2024 à 17:07, Volney a écrit :

On 3/27/2024 8:25 AM, Paul B. Andersen wrote:

Den 27.03.2024 07:23, skrev Richard Hachel:

 

It appears "Dr." Hachel stumbled across the physics concept of "rapidity". Rapidity is related to speed but isn't a speed. It is related to speed by r = arctanh(v/c) where v is the velocity. The rapidity of light is infinity. AFAIK, rapidity is used sometimes to simplify the math. For example, rapidities of two objects in one dimensional motion can be just added but velocities need the Einstein velocity addition formula.

 Your answer is very interesting, I will just modify it slightly.
You say that for Doctor Hachel the notion of real speed is not a speed.
Of course yes, and it's even the only consistent speed.
This is the usual notion of observable speed Vo which is NOT a speed but a simple decoy.

You have this backwards. The velocity v is real but the rapidity r is not a speed/velocity but instead is a function of speed, specifically r=arctanh(v/c).
At low speeds (v<<c), arctanh(v/c) ~= v/c which is why adding (low) speeds "works" even though doing so technically calculates a rapidity.

You are talking about additions of observable (measurable) speeds, the formula is here:

The observable/measurable speed v is the real speed. Its range is simply -c < v < c. Rapidity can take on any real value, the rapidity of light moving at c is infinite.

 I remind you that physicists who say that real speeds are of no interest are wrong.

The real speed v is of extreme interest, of course. Rapidity, as far as I know, is little used except as a simplifier as it has gamma 'built in'. Perhaps someone more familiar with it can provide details.