Interesting bit of trivia: the S-matrix concept is also where the so-called S-parameters came from, which are used by RF engineers to describe amplitude and phase relationships at input and output ports [1].
There was some cross-pollination with the physics community in the 1960s that helped the RF people with circuit modeling problems they were facing due to the limitations of existing models. [2] Hewlett-Packard jumped on this with both feet [3], because S-parameters were a natural fit not only for modeling linear devices and circuits, but for measuring them using the vector network analyzers they were developing at the time.
Nice exposition on the physics side; the S-matrix formalism has also played a major role in the mathematical theory of quantum chaos and aspects of representation theory.
Maybe we don’t need a new model, but rather just accepting that the universe can be two seemingly opposite things at the same time
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)
The wave/particle duality has long-since been accepted, as have other dualities (e.g. the event horizon of a black hole is both a completely normal portion of spacetime, and a boundary region that emits Hawking radiation, depending on your trajectory), where it is impossible to make an experiment that could see both at the same time.
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.
If we hit an actual wall, then that could be the missing part of the unified theory, some boundary that needs to get applied to the equations of both that makes them explicitly inapplicable in the regimes where today we just observe they don't work.
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.
QFTs are effective field theories: they describe interactions at a particular energy scale, smoothing over whatever unknown physics is going on at lower (or sometimes higher) length scales. This makes the strengths of interactions scale-dependent. So in QED, for instance, the fine structure "constant" is actually a few percent larger at the GeV scale than it is at zero energy. Fortunately for us, we only need to measure the fine-structure constant at finitely many energies to calculate its value at any energy scale we like. But this is just because QED happens to be well-behaved. When we try to apply the same techniques to the gravitational constant, we end up with infinitely many free parameters for reasons which are too technical to explain here. Any intro QFT textbook will probably have a rough heuristic argument (I used Srednicki), but we don't actually know with certainty that there's no clever way to get all those higher order terms to cancel - we just haven't found one and have no reason to expect one.
This is one of the most eloquent explanations I’ve read. Thank you
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?
(Also not a physicist). GR works and has been tested experimentally on a large scale, but it doesn't always work on a small scale. QM works, has been tested experimentally on a small scale, but it doesn't always work on a large scale.
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".
I'm not a physicist, just a layman interested in this topic. So, if you're looking for very rigorous explanations, I can't help.
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.
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).
I pondered a little bit more to uncover why I felt this way about GR and QFT.
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.
>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
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
The main incompatibility is that QM predicts that all fields have a zero point energy associated with each mode. However, GR predicts zero point energy will cause spacetime to curve. However there are infinite modes in QM, so now using this in GR leads to all spacetime instantly collapsing. However we exist so this collapse hasn't happened. The solution is the elusive Quantum Gravity, something that physicists from Einstein, Feynman haven't been able to solve.
I propose the sharticle. Whereas particles and waves have energy and phase, the sharticle is always just in different states of shitting its pants. This makes it much more relatable to a human, who is already a type of sharticle.
There was some cross-pollination with the physics community in the 1960s that helped the RF people with circuit modeling problems they were facing due to the limitations of existing models. [2] Hewlett-Packard jumped on this with both feet [3], because S-parameters were a natural fit not only for modeling linear devices and circuits, but for measuring them using the vector network analyzers they were developing at the time.
[1] https://cds.cern.ch/record/1415639/files/p67.pdf
[2] https://typeset.io/papers/power-waves-and-the-scattering-mat...
[3] http://www.hparchive.com/Application_Notes/HP-AN-95-1.pdf