### Time Dilation

Nobody applies the kinetic energy equation to a body at rest. Nobody applies the gravitational acceleration law to a body on a table. Nobody expects a chemical reaction by mixing sugar and water: there only is a dilution process.

The theme is the same: it is only possible to apply an equation if the phenomenon is real. And the opposite is also true: a mathematical equation does not justify a phenomenon being real simply because an equation exists. It is only possible to apply a mathematical formula to a phenomenon if the phenomenon is observed.

Such is the case of time dilation.

### Lorentz’s Coefficient

It should be commented here that the coefficient that appears in the classical kinetic energy equation was discussed over the period of 50 long years. It took many decades and many long battles for the scientific world to come to agree that the value of this coefficient should be 1/2.

Lorentz’s coefficient 1/(1- v^2/c^2)^1/2 is nothing more than a simple coefficient like the classical 1/2. But unlike the classical kinetic energy coefficient, the Lorentz coefficient is not static or invariable. It is instead a function of velocity where velocity is **inside** the coefficient, not **outside** as in the classic case.

Lorentz’s coefficient in SR or AD’s relativity, is also nothing more than a simple coefficient like the 1/2 coefficient in the classic kinetic energy equation. The Lorentz’s coefficient is more complete and more complex than the classic one because it involves the body velocity v, which is not the case in the classical 1/2 coefficient. But it is important to remember that the first approximation of the square root is precisely the 1/2 value, applicable to low velocities. The velocity in this case varies independently of 1/2 as a coefficient. But this doesn’t change the principle concept.

Everyone is familiar with automatism as it applies to Lorentz’s coefficient in special relativity theory. Einstein himself introduced automatism and the inexorability of its action in his theory.

In the Lorentz’s expression, the 1/2 coefficient and velocity v are put together in a unique expression. But this doesn’t change the physical concept neither does it effect automatism or inexorability.

### Autodynamics

In AD’s relativity theory, concepts about automatism and inexorability don’t exist. In AD, the equation is only applied if the phenomenon exists. The contrary is false: that is if the phenomenon doesn’t exist then AD cannot be applied. If it were, it would introduce strange concepts into AD itself.

In AD, there is an equation for charge variation which only exists in the AD relativity theory. This doesn’t mean that an electron in motion has charge variation. This only means that the equation will be applied if the electron is going through a decay process. Until now this phenomenon has not been observed for electrons in motion. But this phenomenon **does** occur when a muon decays into electrons, or more precisely, in a two step process: into an intermediate particle called an electro-muon and later into a particle decaying to electrons.

In AD, Lorentz’s coefficient is found in the equation t’= t/(1- v^2/c^2)^1/2. But this doesn’t mean that we introduce automatism or inexorability in time variation as a general time dilatation concept. This equation will be applied only when a phenomenon exists: muon decay time dilatation when it is traveling at high speed (acceleration involved) inside accelerators. If the phenomenon is real, time will be calculated using the time dilatation equation.

### More…

AD replaces the classical Lorentz equations:

x’ = (x – v t) / (1-B^2)^1/2 (1)

t’ = (t – (v x)/c^2) / (1-B^2)^1/2 (2)

by the Lorentz simplified equations, which really are Carezani’s equations

x’ = (v t) / (1-B^2)^1/2 (3)

t’ = t / (1-B^2)^1/2 (4)

Both equations for t’ represent the “time dilation” found by Lorentz and Carezani. The difference is visible: the Lorentz equations includes distance (position (, x), Carezani’s does not.

Technically speaking, as was pointed out by Ulysses J. Balis from the University of Utah, “time dilation” is only a question of semantics.

“I agree though, dilation may be more of a semantic issue in that the interpretation of the phenomenon is more of an issue than the phenomenon itself.”

Two very interesting practical points will be presented here: The Atomic Clock, and Muon Decay

### TIME DILATION – The Atomic Clock

Also from U. J. Balis:

“How does one account for the vast compendium of experimental data showing traveling atomic clocks to lag in the predicted SR interval as compared to stationary atomic clocks. The data seem to support time dilation.”

The data seem to support time calculated with the equation

t’ = t /(1-B^2)^1/2 (4).

There are three different problems or issues here:

What equation is this: SR’s or AD’s?

Why is “time dilation” calculated with equation (4), if the SR (Lorentz) equation is equation number (2) t’ = (t+ v x)/c^2) / (1-B^2)^1/2

Why is this called “time dilation”, rather than “calculated time,” “time-interval” or the time that the phenomenon consumed?

Here are the concise answers:

– there is no doubt that the equation is the AD equation.

– because this equation possesses the position term (v x) / c^2, it is not useful

– the issue is related to the mistaken SR solution, rather than to physical reality.

In describing the radioactive processes, we are not speaking about time dilation but rather about “time-interval” or “time average” taken by the phenomenon to emit the energetic particle or photon (lifetime).

AD does not reject the apparent confirmation that the motion changes atomic rhythm. AD does not reject “time dilation” in Muon decay or similar phenomena.

Whereas AD is concerned, this phenomenon could be “time dilation” or “time-interval”, longer or shorter, but as a natural physical process.

We need to be very sharp to see the phenomenon as a “time dilation” or “time-interval, the time that the phenomenon needs to start. With present knowledge of this natural phenomena we cannot decide what really is happening.

### TIME DILATION – Muon Decay

A physicist from the University of Michigan Physics Department gave us the following interesting example. We selected this particular example from many similar ones because it seems to reflect the most common opinion of the scientific community.

“It gives rise to time dilation t = t_o * gamma. Which has been verified by many experiments around the world. Particles that decay follow an exponential decay law which is easily derived from

dn/dt = -P * n

Where dn/dt are the number of decays in a given interval of time. n is the initial number of particles and P is the probability per unit time. Integrating this you get the wonderful formula

n(t) = exp(-p*t)

We now let p = 1/Tau and call Tau the lifetime of the particle. If we have some particle (say some muons that we can create at a particle accelerator) and do an experiment of looking at the spatial distribution of the decays. That is count how many decays occur at 1cm from the production target, 2cm from the production target, etc. We also can also detect these particles easily since they are charged. Now if we also put them in a magnetic field we can determine their momentum. Knowing that they are a muon we can calculated their relativistic gamma. Gamma = E/m. Where E^2 = P^2 + M^2. (The magnetic field gives us the value of P). Now we then calculate the flight time in the frame of reference of the muon which is given by: t = Distance / velocity in lab / gamma. Now we histogram this value and watch as the histogram is filled with an exponential with a decay constant of 1/tau.”

The equation dn/dt = -P*n is correct. A question arises: what is the relationship between this equation and SR or AD? It is an EMPIRICAL equation taken from past experience. It is related to SR or AD through

t = t_o * gamma

Where does t come from? In SR (really, the Lorentz equation)

t = (t_o + (v x)/c^2) / (1-B^2)^1/2

(equation (2) already mentioned above).

Gamma is equal to t = t_o /(1-B^2)^1/2, that is to say, it is necessary to eliminate the position term (v x) / c^2 from expression (2). The term (v x) / c^2 simply disappears! When we only need the Lorentz coefficient, we surreptitiously eliminate the term (v x) / c^2 ! Unfortunately, SR is full of this kind of magic, as pointed out many times by Carezani.

AD doesn’t have this problem. In AD, t = to / (1-B^2)^1/2 and everything is correct. No magic, and the experimental result is explained. As was espoused before, the equation does not automatically represent “time dilation.” The term 1/ (1-B^2)^1/2 is only a coefficient like many others. Time is only the time that the process spends to perform the action.

### Conclusion

For AD, there is no such thing as automatic clock time dilatation. And unlike SR, in AD there is no twin paradox since “all systems” in relative motion are equivalent (i.e., in AD, there is only one system).

Time dilatation does not exist as a physical phenomena in and of itself. There is no inexorability or automatism in time dilatation as long as the phenomenon is not real.

Finally, in AD, a coefficient has the property of a coefficient just like the 1/2 coefficient in the classic kinetic energy equation, even though in AD the 1/2 and v are also includes in the same expression: Lorentz’s coefficient 1/(1- v^2/c^2)^1/2 or AD’s coefficient (1- v^2/c^2)^1/2.