"Doppler effect -- when an observer moves toward a stationary source" https://www.youtube.com/watch?v=bg7O4rtlwEE

"The wavelength is staying the same in this case." https://www.youtube.com/watch?v=MHepfIIsKcE

"Thus, the moving observer sees a wave possessing the same wavelength [...] but a different frequency [...] to that seen by the stationary observer." http://farside.ph.utexas.edu/teaching/315/Waveshtml/node41.html

"Vo is the velocity of an observer moving towards the source. This velocity is independent of the motion of the source. Hence, the velocity of waves relative to the observer is c + Vo. [...] The motion of an observer does not alter the wavelength. The
increase in frequency is a result of the observer encountering more wavelengths in a given time." http://a-levelphysicstutor.com/wav-doppler.php

Since "the motion of an observer does not alter the wavelength", "the velocity of waves relative to the observer is c + Vo." And that's the end of Einstein's relativity.

In this particular scenario (Doppler moving observer) the wavelength of light obviously remains constant. Actually, this constancy is a universal principle valid in ANY scenario. So the fundamental axiom in future (Einstein-free) physics will be:

The wavelength of light is constant.

The fundamental axiom, combined with the formula (frequency)=(speed of light)/(wavelength), entails the following corollaries:

Corollary 1: Any frequency shift is caused by a proportional speed-of-light shift.

Corollary 2: If the emitter and the observer (receiver) travel towards each other with relative speed v, the speed of light as measured by the observer is c' = c+v, as posited by Newton's theory.

Corollary 3: Spacetime and gravitational waves (ripples in spacetime) don't exist.

Corollary 4: Light falls in a gravitational field with the same acceleration as ordinary falling bodies - near Earth's surface the accelerations of falling photons is g = 9.8 m/s^2. Accordingly, there is no gravitational time dilation.

Corollary 5: The Hubble redshift is due to light slowing down as it travels through vacuum. The universe is not expanding.

Corollary 6: The dark sky in the Olbers' paradox can be explained by the fact that very slow light coming from very distant sources (known as CMB) is invisible.

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The concept of variable wavelength of light is so obviously wrong:

Stephen Hawking, "A Brief History of Time", Chapter 3: "Now imagine a source of light at a constant distance from us, such as a star, emitting waves of light at a constant wavelength. Obviously the wavelength of the waves we receive will be the same as
the wavelength at which they are emitted (the gravitational field of the galaxy will not be large enough to have a significant effect). Suppose now that the source starts moving toward us. When the source emits the next wave crest it will be nearer to us,
so the distance between wave crests will be smaller than when the star was stationary." http://www.fisica.net/relatividade/stephen_hawking_a_brief_history_of_time.pdf

So, according to Einsteinian physics, the wavelength at the emitter is a function of the speed of the emitter, or, vice versa, the speed of the emitter is a function of the wavelength at the emitter: https://youtu.be/3mJTRXCMU6o?t=77. But this directly
contradicts the principle of relativity. If the wavelength at the emitter varied, the emitter could regularly measure the variations inside his spaceship - so he would know his spaceship's speed without looking outside. If, for instance, measurements
inside the spaceship show that the wavelength has decreased, the emitter will conclude that his spaceship is now moving faster than before.

The wavelength of light depends only on the nature of the emitting substance and is constant otherwise. In future, Einstein-free physics the wavelength of light will be nothing more than an invariable coefficient in the formula

(speed of light) = (wavelength)(frequency)

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