Yes, it's known as global Lorentz invariance and its generalization is known as diffeomorphism invariance.

Stam Nicolis Thank you for your response! I agree that global Lorentz invariance and diffeomorphism invariance describe the symmetry properties of space-time in special and general relativity. However, in my research on the Electron Approach Theory, I explore the idea that time may have an oscillatory and absolute nature, which could imply a deviation from strict Lorentz invariance in specific conditions.

If time undergoes periodic inversions during quantum transitions (as suggested by the imaginary Lorentz factor in my model), could this mean that the standard assumptions about time symmetry need to be reconsidered?

Furthermore, if an absolute time exists as a fundamental background, would it challenge the full diffeomorphism invariance assumed in general relativity? I would love to hear thoughts on this!

Violation of global Lorentz invariance is studied as a matter of course, cf. https://lorentz.sitehost.iu.edu/kostelecky/lv.html for establishing backgrounds for experiments.

Violation of diffeomorphism invariance is, also, studied, in order to establish

backgrounds for experiments. However any oscillation of the time coordinate is nothing but an example of a diffeomorphism, so it can't affect anything, regarding general relativity.

Stam Nicolis I agree that Lorentz violations and diffeomorphism invariance are actively studied and appreciate the reference.

However, in my model, the oscillation of the time coordinate is not simply a coordinate transformation, but a physical effect related to quantum transitions. The imaginary Lorentz factor introduces a dynamical oscillation that affects the energy states and motion of electrons, which means that it is not just a mathematical diffeomorphism, but something that could, in principle, have measurable consequences.

If the time oscillations lead to real variations in energy decay rates or quantum transitions, could this imply a departure from standard diffeomorphism invariance in a more physical sense? This is obviously a rhetorical question. But what do you think?

To explore possible experimental implications, I have been investigating high-voltage, high-frequency electromagnetic fields generated by Tesla coils as a possible way to induce and observe electron capture dynamics under controlled conditions. The idea is that strong oscillating fields might amplify space-time feedback effects at the quantum level, potentially influencing the way electrons transition between energy states.

Would you consider that such an approach could offer new insights into deviations from standard relativistic symmetry?

Once more, t->t+f(t), is an example of a diffeomorphism. Of course f(t) must be a real function of t, otherwise the transformation simply doesn’t make sense. Coordinates are real numbers and their transformations are real-valued functions of these numbers.

Electrons in coils, of ``small" size, are affected only by electromagnetic forces, all other forces are irrelevant. In ``larger" coils, e.g. for the LHC, tidal effects of the Earth start to become relevant. https://www.quantumdiaries.org/2012/06/07/is-the-moon-full-just-ask-the-lhc-operators/

Stam Nicolis I appreciate your clarification on diffeomorphisms. However, in my model, the transformation t → t + f(t) is not a mere coordinate change, but an effect induced by the imaginary Lorentz factor, which alters the physical energy states of the system rather than just reparametrizing time.

Regarding Tesla coils, I fully agree that their primary effect is electromagnetic. However, the idea I am exploring is whether strong, high-frequency oscillations in the electromagnetic field could lead to space-time feedback effects at small scales, particularly in electron capture dynamics. If such feedback influences energy decay rates, it could suggest that time oscillations are not merely a mathematical redefinition, but a measurable physical phenomenon.

Would you agree that if an electromagnetic system exhibits energy shifts beyond what standard quantum electrodynamics predicts, this could hint at a deeper interaction between time and energy states?

It doesn't matter what the origin of the transformation is; that it is a diffeomorphism only matters. And the change from t to t + f(t) is a coordinate change. The statement that it changes the energy of the system is wrong, because energy is the conserved charge of time translation and, when the translation is local-as is the case here-not global, then conservation laws are local, not global and it's known what happens.

(Classical) Gravitational effects on electromagnetic phenomena can be consistently described.

If there is a preferred background then time oscillations represent a measurable physical effect; if there is no preferred background, then a time oscillation is a diffeomorphism, that can't have any measurable physical effect.

What QED predicts is known and any claim of something new must pass tests about backgrounds, like any other effects.

Stam Nicolis Fair point. I agree that any new approach must ultimately be tested against experimental evidence. That’s exactly the direction I’m exploring. Thanks for the insightful discussion!

You're welcome!

Dear all, to delve deeper into the theoretical framework I presented in The Electron Approach Theory (https://www.researchgate.net/publication/389871123_Electron_Approach_Theory_A_Damped_Oscillation_Model_Based_on_Relativistic_Effects_and_Space-Time_Feedback) and in the questions and answers presented in these chats, I invite you to read the entire text of my book, The Mechanics of Time, now available in its entirety in the "Book" section of my profile (https://www.researchgate.net/publication/394013969_The_Mechanics_of_Time_A_Damped_Oscillation_Model_Based_on_Relativistic_Effects_and_Space-Time_Feedback). Thank you for your time, and I remain available for any questions on the topics covered.

“...Open question to the community:

How can we experimentally test the concept of absolute time in modern physics?.....”

- really there is no any necessity in the concept of absolute time experimental tests. The phenomenon/coordinate/dimension “Time” – as that the space phenomenon/coordinates/dimensions fundamentally are also – is fundamentally absolute. Though this contradicts with the standard in mainstream physics SR theory, where it is postulated that the absolute Matter’s spacetime doesn’t exist, and so all/every inertial reference frames are absolutely completely equivalent and legitimate,

- however from these postulates any number of really senseless consequences follow; say, the Dingle objection to the SR: if there are two relatively moving frames, then every observer in both frames simultaneously ages simultaneously faster [in own frame] and slower [in opposite frame], what is evident biological absurdity.

So by the completely rigorous Proof by contradiction Matter’s spacetime – i.e. space and time dimensions is/are absolute.

Cheers