Is time Lorentz invariant? It is the same interval of proper time. It also follows from the relation between Δs and that c²Δτ that because Δs is Lorentz invariant, the proper time is also Lorentz invariant.
Proper time Δτ, by definition, is the time measured by an observer in their own rest frame, we can say Δτ = Δt and therefore Δs² = c²Δt² = c²Δτ².
All observers in all inertial frames agree on the proper time intervals between the same two events.
So, how come time dilation t' possible when proper time t is Lorentz invariant? It cannot.
1. Considering t<t', where t' is not in the same scale of t, because of enlagement in t.
Note: t' is not t+x or t-x, but it is t<t', where x is Δt. The Δt is infinitisimally small t.
2. The general rule is frequency represents time in inversed relationship f = 1/T = 1/λ, and wavelength equivalents period of time λ∝T.
So wavelength λ cannot be invariant but only T.
Due to Relativistic effects, phase shift in frequencies distort wavelength. So wavelength is not invariant but we know time is invariant because Δs is Lorentz invariant too.
3. Time dilation equation t' = t/√(1 - v²/c²)
The equation attempts to modify t through the influence of velocity v. This is illegal operation in mathematics, as none can modify invariant t with the effect of velocity v or speed..
4. Experiment made on piezoelectric oscillator show that speed or gravity influence wavelength λ, and wavelength corresponds to period of time, so error occurs in T, as in the relationship λ∝T.
Conclusion so called time dilation is relativistic error and not change in T, in order to get time dilation t'.
There is no dilation in time but in wavelength.
Time dilation is wrong and it's equation too.
