Like the particle/wave duality
Maybe the whole universe is both quantum and not, at the same time. And we just perceive it differently at different scales. Like with a stroboscopic light, we might perceive things differently depending on how we are sampling (and not necessarily because the thing is different)
But QM can't be reconciled with GR in the same way. One day we'll have precise enough instruments to measure the gravitational interactions of large particles. One day we'll have large enough particle accelerators to be able to measure quantum properties of huge molecules whose gravitational properties we already know. When those days come, we'll need a unified theory of how quantum fields cause gravitational effects.
And even if it turns out there is some fundamental limit of some type of measurement that does cause a QM/GR duality to exist, a theory that includes that specific limit would itself be a new, unified theory, that supersedes both QM/QFT and GR.
Would you care to explain?
Why are the models so fundamentally incongruent?
What exactly is the issue?
That said, my understanding is this: if you try to calculate the trajectory of small particles using the equations of GR, and then compare that to measurements, you'll find that GR is dead wrong. Conversely, if you try to calculate the motion of stellar objects in strong gravitational fields using the equations of QM or QFT, you'll again get results that don't match observations at all.
Further, for more complex mathematical reasons that I can't personally follow, if you just try to introduce the GR space-time deformation terms into QM equations, you can't compute anything because the equations diverge.
They just give different predictions in some very small or very large cases. Obviously they can't both be right: if one theory predicts A and the other theory predicts B then we can just do the experiment and one of them will turn out to be wrong. Unfortunately, they only differ in extreme circumstances that are hard to recreate, and we were not able to perform an experiment that will tell us which is right (or how to tweak them to make them compatible with each other).
Fun fact: There is a thing called a cosmological constant problem. It's the disagreement between the observed values of the cosmological constant (using GR) and a theoretical value suggested by QM. The observed value is... 10**120 times smaller than QM predicts it should be [1]. Now this is what I call a fundamental incongruence :).
[1] This is also called "probably the worst theoretical prediction in the history of physics".
Do you have any links to online resources that might go slightly more into the math and the free parameters issue? Without getting too technical with the math too quickly?
1. The first is philosophical. GR is classical, with smooth continuous fields, locality and determinism*. QM has superposition, entanglement, non-locality and indeterminism. GR seems more intuitive, but QM seems more of an irreversible revolution, so slight win.
2. The second is philosophical. GR provides equations for how spacetime is warped by matter and energy (background independent). QM assumes a static background 'stage' of spacetime (wavefunction is a function of spaces, Schrodinger Equation is a wave equation wrt time, so background dependent). GR seems deeper, QM seems superficial. GR wins this hands down, QM has to change or be extended to make it background-independent (perhaps see String Theory).
3. The third is philosophical. QM has a 'measurement problem'. Wave: the Schrodinger Equation is linear, unitary, time reversible and (hence) information preserving. Particle: measurement is discrete, discontinuous, non-linear and information destroying. So there is either a bizarre mismatch between the two parts of the theory, or you strike down measurement, and propose the Many Worlds interpretation, which punts all the measurement problems into other causally disjoint 'worlds', without a clear way to establish probabilities. This is purely a problem with incomplete/incoherent explanation by QM. The fact that physicists cannot agree on an interpretation is damning (is the wavefunction real? is Hilbert space real? what is measurement?)
4. The last is practical. QFT is just Fourier Analysis where it true, and a terrible hack everywhere else: double quantization, renormalization of infinities, energy cut-offs, virtual particles, incomplete Standard Model (neutrinos?), why 3 generations, what is the vacuum (dark energy).
My scorecard is 40:60 draw in QM's favor, GR total win, and two QM no-contest own-goal losses. So a clear GR win, in the sense that a new integrated theory of Quantum Gravity will have:
- a copy of GR, even if it is emergent from discrete substrate
- radically overhauled version of QM (philosophical, explanatory and model details), even as predictions don't change much, and some important philosophical revolutions are preserved
My own personal pure guess is that the next level substrate is discrete. The two signposts are: holography, dimensional reduction and AdS/CFT-ishness; and the huge clue that quantum entanglement seems to create relativistic spacetime (but perhaps not proper time).
What do you think would make a bigger impact in terms of our understanding of the universe?
I am sure there are no realized infinities, and I don't think nature can have an if statement.
It can have hysteresis curves, with some extreme exponent, but it cannot have a conditional. A square wave is an infinite Fourier Series, but infinite does not exist, so it is truncated, and there are no zero-step jumps. No Dirac Delta Function. Quantum jumps are layered over tunneling and decaying exponentials, but they do not need step changes or conditional laws.
So GR is pure in this sense (except singularities, but all bets are off, and I don't think they exist - no infinities, no infinitesimals that actually become zero). Singularities are not a prediction of GR (despite Penrose, whom I admire enormously), they are just a realm without solutions, a Terra Incognita, where we know we need a better theory.
One final thought... the Heisenberg Uncertainty Principle (HUP) is just Fourier Analysis. Every physicist and electrical engineer, just says, "yes ok", and moves on, even though there are various mystical properties ascribed in pop-sci woo-woo explanations. The one finding of the Wolfram Physics project that made me sit up and pay attention, is that they derived HUP as composed of two different structures of ambiguity (simplifying enormously: across and ancestrally within the branchial space). That sounds ~right to me, and indicates some profound insight they are generating from discrete combinatorial approaches.
At least right now, there's still a pretty big gap between the largest QM objects and the smallest objects with detectable gravitational effects.
Of course, we might also hit an "engineering" wall, where we don't have any explicit boundary, but it's just too hard to perform the experiments that would help us understand how these theories relate. That would mean that the current status quo will remain the best we can do - two separate theories which we know are wrong, but where for any experiment we can perform, one or the other predicts the results almost perfectly.
That's actually exactly what's going on with wave/particle duality. Everything's a wave, all the time, but in certain regimes, wave behavior very closely approximates particle behavior. The realization that particle behavior is therefore just a subset of wave behavior is part of the motivation for looking for an omnibus theory that accounts for everything.
Unification is not unprecedented, consider e.g. the unification of the weak nuclear force and electromagnetic forces into the electroweak force.
At a macro scale, anything that happens in time can be considered as a sort of wave that we perceive as an object because of the way we are sampling it
Even basic things, like when you measure your own weight, will vary throughout the day/time, but instead of considering them a wave, we usually just “collapse it” into some sort of average of observations
Conceptually at least, both models seem to represent the same
How are they not compatible? Is it a math issue?
What does it mean for “all spacetime instantly collapsing”?
It would be amazing to see a video of a simulation of that
Has anyone bothered to tell the universe this?