Quantum mechanics predicts Hawking radiation. Einstein's relativity doesn't.

Einstein identified that there was a second conceivable route to relativity theory, that involved full light-dragging (Hertz). Interestingly, Hertzian relativity does seem to predict Hawking radiation, as its redder Newtonian equations generate softer "relative" horizons rather than the "hard", "absolute" event horizons of Schwarzschild and Wheeler.

Preprint Two Routes to General Relativity

So maybe Einstein's is simply the wrong theory of relativity.

Both, in the sense that global Lorentz invariance-in the absence of gravity-and local Lorentz invariance-in the presence of gravity-are exact symmetries and quantum mechanics, in the sense that the probability distribution of a system, subject to quantum fluctuations, can be obtained in a well-defined way, once the space of states has been identified.

Quantum mechanics doesn't predict Hawking radiation-because the space of states of a gravitational system, in general, isn't known, due to the appearance of spacetime singularities, which the semi-classical approximation, that implies Hawking radiation, doesn't resolve. What exactly is Hwking radiation, beyond the semi-classical approximation, remains to be understood. A more robust prediction of quantum mechanics, in the presence of gravity, is that black holes, when probed by quantum matter, have finite entropy (the Bekenstein-Hawking entropy), for which the degrees of freedom that can account for it have been identified, in certain cases, where the space of states can be found, cf. Article Microscopic and Macroscopic Entropy of Extremal Black Holes ...

There are many issues, nonetheless, that remain to be understood, pertaining to quantum gravity.

If its about GR, then i understand QM much better.

There is a tradeoff. If 95% of all the energy in the universe is due to stochastic fluctuations of spacetime, caused by "a fundamental breakdown in predictability", then gravity is classical general relativity, quantum gravity does not exist, dark matter effects are entropic, and emergent classical gravity is asymptotically free because stochastic white noise vanishes at short distances.

Jonathan Oppenheim and Andrea Russo, “Anomalous contribution to galactic rotation curves due to stochastic spacetime” 1 May 2024, https://arxiv.org/abs/2402.19459v2

Einstein's special relativity is a cornerstone for quantum mechanics to be an exact and successful physical theory,and without it,quantum mechanics becomes non-relativistic and fails to explain a lot of major real aspects such as spin ,pair production,high energy physics, and even the spectrum of the hydrogen's atom, and the list goes on. Following Günther, there is no way to prove that special relativity is wrong,and thus quantum mechanics without Einstein's relativity is a failure.

Both are inexact.

Special Relativity theory because the community chose to ignore the experimentally confirmed electromagnetic behavior of electrons as measured with the Kaufmann experiments and confirmed by all leading physicist of the time:

"Herr Kaufmann has determined the relation between [electric and magnetic deflection] of 𝛽-rays with admirable care. ... Using an independent method, Herr Planck obtained results which fully agree with Kaufmann. ... It is further to be noted that the theories of Abraham and Bucherer yield curves which fit the observed curve considerably better than the curve obtained from relativity theory. However, in my opinion, these theories should be ascribed a rather small probability because their basic postulates concerning the mass of the moving electron are not made plausible by theoretical systems which encompass wider complexes and phenomena."Albert Einstein (1907)

"Special Relativity killed the classical dream of using the energy-momentum-velocity relations of a particle as a means of probing the dynamic origin of its mass. The relations are purely kinematic. The classical picture of a particle as a finite little sphere is also gone for good. Quantum field theory has taught us that particles nevertheless have structure, arising from quantum fluctuations. Recently, unified field theories have taught us that the mass of the electron is certainly not purely electromagnetic in nature. But we still do not know what causes the electron to weigh." Abraham Pais (1982)

In Pais, Abraham (2008) Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press. 2008. p. 159.

Quantum mechanics because it was historically grounded on a wrong frequency of the energy induced at the Bohr radius of the hydrogen atom as calculated by de Broglie, due to the neglect by the community of referencing in textbooks the Kaufmann discovery made 20 years earlier:

Article Critical Analysis of the Origins of Heisenberg's Uncertainty Principle

The thread question and the introduction in

“…Which is more exact, quantum mechanics or relativity?... Quantum mechanics because the statistics. Relativity is more theoretical…”.

- look as are rather vague wordings. The real criteria for a theory to be really scientific one are, first of all [more see SS post page 29 in https://www.researchgate.net/post/What-criteria-do-you-have-in-mind-while-characterizing-a-scientific-theory#view=66676972acb8f78a2601bd55/37/36/35/34/35/34/33/32/31/30/29], is – with what extent of adequacy to the objective reality the theory describes and predicts what exists and happens in studied objects/systems; physical theories describes and predicts what exists and happen in fundamental for humans system “Matter”. Including in Matter objectively everything exists and happens only completely “exactly” – with what precision a physical theory works.

That doesn’t depend on – theory describes some random or rigorously determined objects/events/effects/processes. Say, the mathematical probability theory is completely “exact” science, despite that it relates to some principally random things/ “statistics”.

The same is in QM. All what is necessary in this theory is to describe/predict maximally exactly the probabilistic dependences/equations and the parameters of the dependences, that describe behavior of QM objects, etc.; really till now – equations for Ψ-functions the objects, etc., of particles, atoms, etc., when they are free and when compose some coupled by some fundamental Nature forces systems.

So, since really adequate to the reality theories are, nonetheless, principally based on experimental data about key universal parameters, say, about strengths/charges of fundamental Forces , the precision – and sometimes adequacy, though, of a theory is principally limited by experimental errors of the parameter’s values.

That is another thing, that all theories are based also on postulates, that are interpretations of experimental data, and when some interpretations are wrong, the theories logically inevitably really are wrong as well.

Physics yet in last 1800s was developed up to level, when for further development it was necessary to define really scientifically what are really fundamental phenomena/notions, first of all in this case “Matter”, “Consciousness”, “Space”, “Time”, “Energy”, “Information”, which were, and are till now, in the mainstream philosophy and sciences, including physics, fundamentally completely transcendent/uncertain/irrational,

- including so really everything in Matter, i.e. “particles”, “fundamental Nature forces” – and so “fields”, etc., is/are fundamentally completely transcendent/uncertain/irrational as well.

That above in Matter so are introduced in physical theories as defined in their postulates, which so in most cases really are completely transcendent assertions, which have to the reality rather strange relation. In Relativity that are, say, postulates that there is no absolute Matter’s spacetime and that all inertial reference frames are absolutely equivalent; that so exist mystic “space contraction” and “time dilation”, both of which, and not only in Relativity though, really fundamentally cannot exist; in QFTs some mystic virtual particles by some mystic way quite non-virtually act on real particles, etc. In Relativity there is no antiparticles – which really exist, in QETs it is postulated that antiparticles move back in time, what is fundamentally impossible. Etc., in the mainstream physics there are numerous other examples when really complete mystic is claimed as something scientific – and even postulated fundamental - facts.

The post is rather long, so now

Cheers