Relativity is used when speed is high enough. Quantum mechanics is used at subatomic scales. Thus, relativity and quantum mechanics are complimentary, depend on different variables, and should follow the law of identity: https://www.researchgate.net/publication/381469939_Critical_Rationalist_Physics
The formalism is called relativistic quantum mechanics. A nice course on the subject can be found here: https://arxiv.org/abs/1110.5013
Relativivistic effects aren't relevant only at high velocities, but, also, at high energies, i.e. when the typical energy exceeds mc^2, where m is the typical mass.
Combining relativity with quantum mechanics involves reconciling general relativity, which describes gravity and the large-scale structure of the universe, with quantum mechanics, which governs the behavior of particles at microscopic scales. Quantum Field Theory (QFT) successfully merges special relativity with quantum mechanics, forming the basis of the Standard Model of particle physics, but it doesn't include gravity. Efforts to unify general relativity and quantum mechanics include approaches like string theory, which posits that particles are one-dimensional strings, and loop quantum gravity, which quantizes spacetime itself. These theories face significant mathematical and experimental challenges, and while high-energy physics experiments and astrophysical observations offer potential insights, a complete and experimentally verifiable theory of quantum gravity remains an open and active area of research.
Prof. Solomon Budnik
We've united quantum gravity and quantum mechanics. See on the internet: Prof. Solomon Budnik, United Matter Theory, and Loop Quantum Gravity in Superstrings
Alexander Ohnemus
Quantum Field Theory (QFT) combines special relativity and quantum mechanics, forming the basis of the Standard Model of particle physics.
General Relativity (GR) is hard to reconcile with quantum mechanics, necessitating quantum gravity theories.
String Theory and Loop Quantum Gravity (LQG) are key approaches to unifying GR and quantum mechanics.
Experimental Evidence for quantum gravity is indirect, coming from studies of black holes and gravitational waves.
Relativity and quantum mechanics are complementary, addressing different physical realms and maintaining consistency within their scopes.
Unifying these theories remains a significant goal in physics, requiring further theoretical and experimental progress.
(gamma)^2 = n/2 (alpha_G)^-1
(7) (PDF) Particles from Gravity (May 30, 2024) (researchgate.net)
Turns out it is surprisingly simple to unify Relativity theories with Quantum Mechanics. Those who have been "indoctrinated" into the "flat spacetime" mindset, "think" that Planck units of length & time are fixed throughout time -- for them it is impossible to reconcile QM with Relativity.
Cosmological Relativity successfully unifies Special and General Relativity with QFT by consciously mixing quantum and emergent metrics in the same equations, thus making relativistic math compatible with quantum-scale metrics.
From a higher perspective all we need is to realize that our "here & now" local reference frame experiences Space~Time expansion. This means that all atoms, meter sticks, pendulums, people, planets & galaxies expand with time. Suddenly, the math becomes so simple that it will boggle the minds of many physicists who think that unification has to be made so complex that is needs mathematical notations so abstract it becomes impossible to relate the math to actual measurements.
Many equations contain the speed of light squared, c² [m²/s²] this becomes [Δ area]/[(Δ Planck times)/second] - this describes the local reference frame spreading forth its surface area while the number of Planck seconds -- per each passing second -- increases linearly with the age of the universe. Thus, the Speed of Light, c = l_P/t_P remains constant because (Number of Planck Lengths/second) grows in lockstep with the number of Planck times/second -- this is called being covariant to the 1st.
This 2nd differential has the astonishing value of:
(d²tP/s²) = 4.2709338x10^25 [(Planck times/second)/second]!
With this understanding comes the realization that Hubble's Constant is not (and never was) constant. When you simplify the units of [km/second/Megaparsec] this becomes [/second]. Hubble's parameter is simply the reciprocal of the age of the universe measured in seconds.
What makes this quantity so incredible is with this understanding comes the realization that this 2nd differential does all the work that the cosmological constant, Λ, hoped it could do.
I could go on for another 30-50 pages. Please see: (PDF) Foundations of Cosmological Relativity: Redefining Space~Time and Physical Constants (researchgate.net)
〖φ(±L^'〗_p)⇌|√((hG^')/(2πc^3 ))|; φ(±tp^') ⇌ |√((hG^')/(2πc^5 ))|
Ꞛ_Lo⇌ √(1-((nLp'/xtp')/(1Lp/1tp))^2 )
The ‘Recessional Velocity’ is what determines t’:
t^'=t_0/√(1-(v/c)^2 )
Quantized as:
c = 1Lp/1tp
v = nLp/xtp
〖tp〗^'=t_0/√(1-((nLp/xtp)/(1Lp/1tp))^2 )
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