Light speed is constant when acceleration does not have to be considered. The traveler has a dilation of time and distance compared to the origin. In SR the approximation for a traveler can be made where v is relative to the frame in which co was measured.
c2 = co2 / ( 1 - v2/c2 )
This is probably not true when high energy density bends space and SR is not used. A variety of assumption can be made. Most convenient is the case of GR which means h the Planck constant does not vary with acceleration. The usual integration is done for acceleration in the direction of v.
dE2 = c2 dp2
2c/co - c2/co2 = Eo2 (1 - v2/c2 )( 1 + (v2/c2)/(c2/co2) )
The implication is that in GR the light speed measured by a traveler can not exceed two times the standard value.
For higher light speed quantum mechanics must become relevant and h must become variable with acceleration. These are the extreme high energy cases where QM can not be ignored. Scale relativity and squeezed quantum states lead to a method for variable h and additional predictions, but not light speed ever reaching three times the standard value. A worm hole is predicted to open around the vehicle if kinetic energy ever reaches such extreme high range. Conventional technology will not do this.
At such speed the ability of a traveler to make measurements is in doubt.
What Light Speed Will A Traveler Measure Under Acceleration At High Speed?
A traveler under acceleration at high speed will observe frequency shift of the approaching light and it will be blue shifted, which means its frequency will increase. With the change in the frequency, the wavelength and period of the wave will also change. In case of light, the velocity of the phase of the wave is equal to the velocity of the particle (photon). This velocity is given by the ratio of the wavelength to its period. In case of light, this ratio is always constant and equal to the velocity of light, no matter how much frequency shift occur. Period is inversely proportional to frequency. Therefore frequency shift due to the motion of the traveler under acceleration at high speed does not alter the ratio of the wavelength to its period. It is always constant.
This is a proof that time is periodic in nature.
https://www.researchgate.net/publication/225712819_Periodic_relativity_basic_framework_of_the_theory?ev=prf_pub
https://arxiv.org/abs/0707.4539
By integration
dE2 = c2 dp2
Constant c results in constant mass and this is the range of Special Relativity.
In General Relativity both c and m may change when locally measured, but h is constant.
Beyond GR in the highest energy cases h also becomes variable.
Local limitations apply that are taken to represent energies and speeds at which near by vacuum space time changes from one quantum state to another.
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