Anonymous at Wed, 12 Feb 2025 12:14:26 UTC No. 16583557

>>16583554
Einstein Cartan*
goddamn it, fucking autocorrector

Anonymous at Wed, 12 Feb 2025 14:07:20 UTC No. 16583650

>>16583554
It “gets rid of it” by introducing torsion. The only fields with non-vanishing torsion are fermionic fields. Obviously this means that any empirical observations necessary to confirm EC theory are already in the realm of quantum gravity, but EC itself isn’t a quantum theory. So it sort of kills itself by the very nature of it. It can, however, be viewed as an effective field theory. See the Palatini formalism, which formulates GR in such a way that one can formulate it as an effective field theory in QFT.
>Why do we even need a quantum theory of gravity?
Because classical mechanics is fundamentally incomplete. For example, statistical mechanics breaks down. We get singularities at both low temperatures (third law of thermo) and high temperatures (the UV catastrophe). Quantum mechanics was historically introduced by Planck precisely to cure these divergences. In GR, these singularities lead to apparent paradoxes such as “information” loss with Hawking radiation and the Unruh effect.
>There isn't a single experiment showing that gravity is quantum
So? There wasn’t a single experiment showing photons are quantized when Planck introduced their quantization. I just described why classical mechanics is logically inconsistent regardless of experimental evidence. It’s just a garbage framework if you dig deep enough.

Anonymous at Wed, 12 Feb 2025 14:39:46 UTC No. 16583676

>>16583650
>There wasn’t a single experiment showing photons are quantized when Planck introduced their quantization
There was experimental data on the black body spectrum. Planck introduced the quantization to match the experimental data. The situation with the graviton is not analogous. There is no experimental data driving anything, it just seems natural for theorists to treat gravity as a quantized field.

Anonymous at Wed, 12 Feb 2025 14:47:16 UTC No. 16583679

>>16583676
>There was experimental data on the black body spectrum.
Yes, data purely within the classical range of validity.
>Planck introduced the quantization to match the experimental data
No. Planck introduced it because Rayleigh-Jeans was singular. Rayleigh-Jeans was derived using classical mechanics based on experimental data within the classical range, and it resulted in divergences when extrapolated outside of that range.

Your theory is garbage if it doesn’t work for the whole domain of values. Which is why GR is garbage, just like any other classical theory. You can cure divergences in single-body problems with these tricks like torsion, but statistical mechanics ALWAYS breaks down for any classical theory. The fundamental reason for this is that the configuration space in classical mechanics is ill-defined, whereas in quantum it’s always determined by the Hilbert space and unitarity ensures that the divergences are cured.

Anonymous at Wed, 12 Feb 2025 15:07:49 UTC No. 16583685

>Yes, data purely within the classical range of validity.
>No. Planck introduced it because Rayleigh-Jeans was singular.
No, there was already empirical evidence showing Rayleigh-Jeans was incorrect at all but the lowest frequencies. Moreover it is clear Planck was not influenced by Rayleigh-Jeans derivation at all, since he already had his own derivation in 1900 when Rayleigh first published. Planck was working on trying to fit the empirical data and understanding why the already existing Wien approximation worked so well.

This isn't just a bit of historical trivia, but you're getting it all wrong.

Anonymous at Wed, 12 Feb 2025 15:18:23 UTC No. 16583694

>>16583679
FWIW I had a typo in my post above that should say "this *is* just a bit of historical trivia, but you're getting it all wrong."

Regarding this:
>The fundamental reason for this is that the configuration space in classical mechanics is ill-defined, whereas in quantum it’s always determined by the Hilbert space and unitarity ensures that the divergences are cured.
This is too simplistic. There is a direct analogue in classical physics to the unitary time evolution in quantum mechanics, namely the evolution of probability distribution on phase space according to the Liouville equation. This all has nothing to do with why there is a ultraviolet catastrophe in many classical field theories.

Anonymous at Wed, 12 Feb 2025 16:53:36 UTC No. 16583780

>>16583694
The Liouville equation says nothing about the phase space structure. And classical mechanics says nothing about it. My main point was that the configuration space is well-defined in quantum, but there is no good definition in classical mechanics.

Consider a coin flip. It defines a configuration space {tails, heads}. There is no law in classical mechanics that says this isn’t a valid configuration space. You can speak of the “internal energy” or the “temperature” of n coin flips, even though our common sense tells us this is wrong.

On the other hand, it makes perfect sense to speak of the internal energy and temperature of a system of n spin-1/2 particles, even though mathematically it is the same thing. Why is that? Well, spin-1/2 is there because it’s a projective representation of SO(3) and Galilean (or Lorentz) invariance tells us Nature doesn’t care which angle you observe it from. And the configuration space of this system is simply the tensor algebra formed from the Hilbert space whose symmetry group (automorphism group) is SO(3). So we have a well-defined algorithm for constructing the configuration space of a physical system: determine the classical symmetries of that system, construct their unitary representations over a Hilbert space, and the configuration space is the tensor algebra on that space. Done.

No such algorithm exists in classical mechanics. It’s always ad hoc “sum n copies of a particular Hamiltonian” or “take an integral over all copies (whatever that means) of a particular Hamiltonian”. This always results in a contradictory mess. In particular, the third law of thermo never holds in classmech.

Anonymous at Wed, 12 Feb 2025 17:09:02 UTC No. 16583798

>>16583780
There is no magic in quantum mechanics here. In quantum mechanics you can define a Hilbert space and choose a Hamiltonian (and possibly a symmetry algebra too if you want). Once you have a Hamiltonian you can define what thermal equilibrium means. There is no algorithm to pick a unique Hamiltonian.

In classical mechanics exactly the same situation holds. You pick some Hamiltonian on a phase space and that defines thermal equilibrium. Although if you want an analogue to unitary evolution, you need a continuous phase space, you can easily define statistical mechanics for your case of a tensor product of {tails, heads} too by the way. A physically relevant example is the Ising model.

None of this has anything to do with the ultraviolet catastrophe.

Anonymous at Wed, 12 Feb 2025 20:33:55 UTC No. 16583967

>>16583798
I didn’t say there was any magic. Quite the opposite. Quantum mechanics has a clear definition of configuration space, whereas classical mechanics always conjures up some explanation.
>There is no algorithm to pick a unique Hamiltonian.
There is. Your action has to respect the symmetries of whatever system you’re looking at. If it’s relativistic, then it has to be Lorentz-invariant. If it’s non-relativistic, it has to be invariant under the Galilean group (Schrödinger equation’s symmetry group btw). If there’s EM involved, it has to be invariant under the U(1) gauge group. You then obtain the Hamiltonian from the Lagrangian. The only arbitrary piece is which representations (quantum numbers) to choose, but that’s obvious from the physical situation. If you’re looking at an electron, you pick spin 1/2, electron mass and electron charge. Other than these degrees of freedom, the symmetries restrict the Hamiltonian to an essentially unique form for that system.

Anonymous at Wed, 12 Feb 2025 20:37:34 UTC No. 16583971

>>16583967
>There is
No there isn't. You have a very limited understanding of this.

Anonymous at Wed, 12 Feb 2025 20:41:16 UTC No. 16583975

>>16583971
Use arguments like a grown up instead of acting like a nigger and going
>nuh uh u stoopid

Anonymous at Wed, 12 Feb 2025 20:54:28 UTC No. 16583981

>>16583975
I did already. Right now I'm in a situation where you are saying many obviously wrong things, and it takes more effort to respond to you point by point than it is worth.

But here's a hint. Can you write more than one Lagrangian obeying symmetry principles? (Yes) Can you write Lagrangians obeying symmetry principles in classical mechanics too? (Yes) You are completely on the wrong track with this.

Anonymous at Wed, 12 Feb 2025 21:07:37 UTC No. 16583989

>>16583981
Your argument was irrelevant. And then you said that there is no unique Hamiltonian for a given system and I provided a retort. Your “counterargument” was “I know better than you”. Not an argument.
>many obviously wrong
So explain why they’re wrong.
>Can you write more than one Lagrangian obeying symmetry principles?
I already mentioned that it depends on the choice of representations. And there’s a natural way we can “ignore” higher order terms in a perturbative sense. Nice reading comprehension.
>Can you write Lagrangians obeying symmetry principles in classical mechanics too?
The restriction of unitarity is not enforced in classmech, which is why things break down. There are more possibilities and the non-quantum ones produce inconsistencies. Unitarity is yet another severe restriction on the form of the Lagrangian, but class mech ignores it.

🗑️ Anonymous at Wed, 12 Feb 2025 21:56:24 UTC No. 16584019

>>16583989
>The restriction of unitarity is not enforced in classmech, which is why things break down
Probability is conserved under Hamiltonian evolution in classical mechanics. That is the same thing as unitary time evolution in quantum mechanics. You can further pretty much translate everything you said about Lagrangians and symmetry principles word to word in classical field theories too. Classical EM (which has an UV "catastrophe") is the only parity invariant Lagrangian involving a singe U(1) gauge field and two time derivatives.

What happens if we have 'irrelevant' (in the sense of renormalizability) terms in the classical Lagrangian obeying U(1) gauge symmetry but having more time derivatives (like higher order powers of F^2)? Then for a Hamiltonian framework we would need to enlarge our phase space to include time derivatives of the field. Oh no unitarity in the original phase space is broken!

Or we can close our eyes to this and just look at the analogue of the formal argument leading to Rayleigh-Jeans but including the irrelevant terms. We'll see that the higher order terms only contribute in the UV, and they can be "ignored" in the same sense as in QFT.

So don't reply to me until you think about this more.

Anonymous at Fri, 14 Feb 2025 15:28:02 UTC No. 16585778

>>16583554
>Why is nobody shilling for this theory
Look up Nikodem Poplawski and his work.