You linked to some popular literature you don’t understand, but you provided nothing in the way of references that support some of your basic misconceptions. I can provide plenty of references, but it would be nice if you were more specific about which aspects of how I explained some of your many fundamental errors required references.
After all, if you want a reference to support the claim that quantum mechanics is based on continuous time and quantum systems evolve continuously in time and/or that “space” in QM (at least in so far as measurements are concerned) is 3D, then my suggestion would be “learn quantum mechanics” and my suggested reference would be “open any elementary QM textbook.”
It is likewise difficult to provide references that your bogus “quanta scale” approach amounts to speculation that has varying degrees of support depending upon which approach to emergent spacetimes and/or quantized spacetimes/quantization of the gravitational field one takes. It is even more difficult to specifically provide references to your claims about measurements at this scale since none exist, so I can’t provide you with references for measurements that can’t be done and never have been. That said, it’s essentially common knowledge:
“It is commonly accepted that, at the Planck scale, no experimentally verified theory provides a framework for measuring space or time.”
Perche, T. R., & Martín-Martínez, E. (2022). Geometry of spacetime from quantum measurements.
Physical Review D,
105(6), 066011.
Since I tend to regard QM as more fundamental than GR, I tend to side with approaches that attempt to see how the smooth manifolds required in QFT and GR may somehow be recovered at the appropriate limit or somehow emerge as a coarse-graining effect and scale transition.
That said, many disagree, going so far as to argue that GR is more fundamental and QM is the approximation to a more fundamental (continuous) theory. On this, see e.g.,
Sachs, M. (1986).
Quantum Mechanics from General Relativity. An Approximation for a Theory of Inertia (
Fundamental Theories of Physics). Springer.
And for an elementary treatment of the general problems with a theory of quantum spacetime that is can incorporate (or is even consistent with) gravitation, see e.g.,
Woodard, R. P. (2009). How far are we from the quantum theory of gravity?.
Reports on Progress in Physics,
72(12), 126002. (see attached)
Also, just for kicks, concerning your claims ahout discrete time and space in quantum mechanics:
“Textbook quantum mechanics cannot describe measurements of time, since time is a parameter and not a quantum observable”
Maccone, L., & Sacha, K. (2020). Quantum measurements of time.
Physical Review Letters,
124(11), 110402.
“Newtonian Absolute Time is what ordinary QM is based upon.”
Anderson, E. (2012). Problem of time in quantum gravity.
Annalen der Physik,
524(12), 757-786.
On the difficulties associates with doing quantum theory on curved spacetimes that go beyond the standard unsolved difficulties of doing quantum theory on flat (Minkowski) spacetimes, see e.g.,
Sorkin, R. D. (1993, July).
Impossible measurements on quantum fields. In
Directions in general relativity: Proceedings of the 1993 International Symposium, Maryland (Vol. 2, pp. 293-305).
And on the difficulties with formulating relativistic quantum theory that doesn’t rely on mathematical nonsense:
“Can we dispense with continuous models and their analytical problems?...There is a fundamental reason why we stubbornly keep infinite models. Probably the most important guiding principle in finding good models is that a proper theory should be Lorentz invariant, reflecting the fact that physics should be the same for all inertial observers (who undergo no acceleration). There is no way this can be implemented in a finite model, say one which replaces the continuous model of physical space by a finite grid. ...considering finite models does not really solve anything. The infinities reappear in the guise of quantities that blow up as the grid becomes finer, and it is very hard to make sense of this behavior.
For these reasons we uncomfortably but realistically consider continuous models, even though they are not really well defined. Since nobody really knows how to solve the analytical difficulties related to these models, there is little point in working toward a partial solution to these difficulties, and our efforts in this direction will be minimal.” (pp. 30-31)
Talagrand, M. (2022).
What Is a Quantum Field Theory? A First Introduction for Mathematicians. Cambridge University Press.
The issues of the impossibility of measuring any continuous parameter, process, property, etc. of any physical system are more subtle and too seldom addressed. However:
"even in a hypothetical laboratory furnished with test-particles and perfect rulers, infinitely precise measurements cannot be carried out unless the following additional conditions are fulfilled:
(i) The ruler is calibrated with infinite precision.
(ii) Irrational numbers are recorded precisely.
The impossibility of meeting these conditions does not spring either from quantum-mechanical roots, or from the atomistic structure of inanimate nature. It springs from the nature of the real number system. Quantum mechanics cannot improve upon this situation; it can only make it worse." (p. 106)
Sen, R. N. (2010).
Causality, Measurement Theory and the Differentiable Structure of Space-Time (
Cambridge Monographs in Mathematical Physics). Cambridge University Press.
And, for an elementary treatment, see also
Hargar, A. (2014).
Discrete or Continous?
The Quest for Fundamental Length in Modern Physics. Cambridge University Press.
Finally, among the physicists since Max Born through Wheeler and Feynman and beyond, Nicolas has probably produced the most accessible and relevant work on the problems associated with the problems associated with the non-measurability of any continous processes, properties, etc., in both classical and quantum physics. See e.g.:
Gisin, N. (2020).
Real numbers are the hidden variables of classical mechanics.
Quantum Studies: Mathematics and Foundations,
7(2), 197-201.
Gisin, N. (2021).
Indeterminism in physics, classical chaos and Bohmian mechanics: Are real numbers really real?. Erkenntnis,
86(6), 1469-1481.
And just to drive the point about continuous space, time, and properties in QM, when you do go out and get that elementary textbook in quantum mechanics, you’ll see symbols like d/dx or ∫ (integral). Recall from basic calculus that differentiation requires continuity and that non-zero integrals over discontinuous intervals/regions/etc. must have at most finitely many discontinuities (actually, to even integrate widely oscillating functions one must dispense with Riemann integrals and extensions such as improper integrals and use measure theoretic integrals like the Lebesgue-Stieltjes, a useful integral in QM in particular as even the Riemann-Stieltjes integral expands greatly the range of integrable functions and the Lebesgue version more so, plus we have that the Stieltjes integral is with respect to another function or integrand obeying certain conditions that lend themselves to the kind of measures (spectral, probability, etc.) one requires often enough in QM).
For more references, you’ll have to go beyond just a demand in general, as I made multiple points and your grasp of QM is negligible, so it is difficult to provide references to support common knowledge, and I suspect your lack of familiarity with the basics of quantum theory is the problem, as it prevents you from distinguishing claims that remain highly theoretical from those that we have at least some empirical evidence for.