\( \def\cuberoot#1{\sqrt[3]{#1}} \def\fourthroot#1{\sqrt[4]{#1}} \def\abspartial#1#2#3#4{\left|\,{\partial(#1,#2)\over\partial(#3,#4)}\,\right|} \def\absdeltal#1#2#3#4{\left|\,{\d(#1,#2)\over\d(#3,#4)}\,\right|} \def\dispop#1#2{\disfrac{\partial #1}{\partial #2}} \def\definedas{\equiv} \def\bb{{\bf b}} \def\bB{{\bf B}} \def\bsigma{\boldsymbol{\sigma}} \def\bx{{\bf x}} \def\bu{{\bf u}} \def\Re{{\rm Re\hskip1pt}} \def\Reals{{\mathbb R\hskip1pt}} \def\Integers{{\mathbb Z\hskip1pt}} \def\Im{{\rm Im\hskip1pt}} \def\P{\mbox{P}} \def\half{{\textstyle{1\over 2}}} \def\third{{\textstyle{1\over3}}} \def\fourth{{\textstyle{1\over 4}}} \def\fifth{{\scriptstyle{1\over 5}}} \def\sixth{{\textstyle{1\over 6}}} \def\oA{\rlap{$A$}\kern2pt\overline{\phantom{\dis{}I}}\kern.5pt} \def\obA{\rlap{$A$}\kern2pt\overline{\phantom{\dis{}I}}\kern.5pt} \def\obX{\rlap{$X$}\kern2pt\overline{\phantom{\dis{}I}}\kern.5pt} \def\obY{\rlap{$Y$}\kern2pt\overline{\phantom{\dis{}I}}\kern.5pt} \def\obZ{\rlap{$Z$}\kern2pt\overline{\phantom{\dis{}I}}\kern.5pt} \def\obc{\rlap{$c$}\kern2pt\overline{\phantom{\dis{}I}}\kern.5pt} \def\obd{\rlap{$d$}\kern2pt\overline{\phantom{\dis{}I}}\kern.5pt} \def\obk{\rlap{$k$}\kern2pt\overline{\phantom{\dis{}I}}\kern.5pt} \def\oba{\rlap{$a$}\kern2pt\overline{\phantom{\dis{}I}}\kern.5pt} \def\obb{\rlap{$b$}\kern1pt\overline{\phantom{\dis{}t}}\kern.5pt} \def\obw{\rlap{$w$}\kern1pt\overline{\phantom{\dis{}t}}\kern.5pt} \def\obz{\overline{z}}\kern.5pt} \newcommand{\bx}{\boldsymbol{x}} \newcommand{\by}{\boldsymbol{y}} \newcommand{\br}{\boldsymbol{r}} \renewcommand{\bk}{\boldsymbol{k}} \def\cuberoot#1{\sqrt[3]{#1}} \def\fourthroot#1{\sqrt[4]{#1}} \def\fifthroot#1{\sqrt[5]{#1}} \def\eighthroot#1{\sqrt[8]{#1}} \def\twelfthroot#1{\sqrt[12]{#1}} \def\dis{\displaystyle} %\def\definedas{\equiv} \def\bq{{\bf q}} \def\bp{{\bf p}} \def\abs#1{\left|\,#1\,\right|} \def\disfrac#1#2{{\displaystyle #1\over\displaystyle #2}} \def\select#1{ \langle\, #1 \,\rangle } \def\autoselect#1{ \left\langle\, #1 \,\right\rangle } \def\bigselect#1{ \big\langle\, #1 \,\big\rangle } \renewcommand{\ba}{\boldsymbol{a}} \renewcommand{\bb}{\boldsymbol{b}} \newcommand{\bc}{\boldsymbol{c}} \newcommand{\bh}{\boldsymbol{h}} \newcommand{\bA}{\boldsymbol{A}} \newcommand{\bB}{\boldsymbol{B}} \newcommand{\bC}{\boldsymbol{C}} \newcommand{\definedas}{\equiv} \newcommand{\half}{\frac{1}{2}} %\newcommand{\slfrac}[2]{\raisebox{0.5pt}{$\scriptstyle{}^{#1}\!/\!_{#2}$}} \def\slfrac#1#2{\raise.8ex\hbox{$\scriptstyle#1$}\!/\!\lower.5ex\hbox{$\scriptstyle#2$}} \newcommand{\bsigma}{\boldsymbol \sigma} \newcommand{\abs}[1]{\left|\,#1\,\right|} \newcommand{\Rectangle}{\sqsubset\!\sqsupset} \newcommand{\rectangle}{{% \ooalign{$\sqsubset\mkern3mu$\cr$\mkern3mu\sqsupset$\cr}% % How to do fractions: for 1/2 use this in place: $\raise{0.8pt}{\scriptstyle{}^{1}\!/\!_{2}}$ % for n/m use this in place: $\raise{0.8pt}{\scriptstyle{}^{n}\!/\!_{m}}$ }} \)

Penrose's Argument Against Quantizing Gravity

Patrick Reany

15 November 2025

Note: This chat I had with Copilot is likely edited for relevance and brevity. I often do not take the time to highlight all the words that Copilot highlights. Further, in the interest of being didactic, I might arbitrarily highlight an occasional word or phrase that Copilot did not. (Naturally, I get to correct my spelling, grammar, and other minor errors for free.)

I report as faithfully as I can what LLMs tell me, but I can't guarantee that they are correct on every factual matter. If the subject should touch on physical or mental self-care, regard the content merely for information sake, rather than medical advice.



Patrick:
Can you summarize for me the argument that Jonathan Gorard makes in the present video "Penrose's Brilliant Proof That QM and GR Are Logically Inconsistent"? I'm not saying that the argument against the unification of general relativity presented is necessarily wrong, but I see a fault in concluding that it is necessarily right.

Note: See Curt Jaimungal's interview of Jonathan Gorard:

https://www.youtube.com/watch?v=wOmWPAHcnKk

Copilot:
Here's a careful summary of Jonathan Gorard's line of reasoning in the video you're watching, "Penrose's Brilliant Proof That QM and GR Are Logically Inconsistent":


Core Argument Structure


Key Points in Gorard's Explanation


Where the "necessity" claim is debated


Takeaway
Gorard's summary of Penrose is powerful because it reframes the problem as a logical contradiction between axioms rather than just a technical difficulty. But the leap from "there is a contradiction in our current formulations" to "unification is impossible" is exactly where the philosophical debate lies. Many researchers see Penrose's argument as a challenge to be overcome, not a final verdict.


Patrick:
There's just so many points to make here (not that I'm expert on either QM or GR). First, Fredric Schuller has his own reason for not quantizing gravity, but he did not say that a nonquantized gravity could not be made 'consistent" with QM. Second, Leonard Susskind claims that for all the problems string theory has, it's one prime strength is that it proves that gravity and the Standard Model are compatible. Third, the concept of energy in GR is somewhat slippery, and as to Gorard's claim that the Principle of Equivalence implies that what is an acceleration that appears on the LHS of Einstein's equation, could be removed and refitted with a negative sign on the RHS seems unfounded. It's an interesting idea, of course. But I don't see its necessity of correctness. I have always thought of the Principle of Equivalence as a kinematic foundation to infer curvature of space, but went no further than that. (So maybe I'm wrong about that.)

Copilot:
Patrick, you're raising exactly the kinds of nuanced points that show why Penrose's "logical inconsistency" argument is provocative but not definitive. Let me unpack your observations in relation to the broader debate:


1. Schuller's stance


2. Susskind and string theory


3. Energy in GR


4. The "necessity" problem


Takeaway
Your instinct---that the Principle of Equivalence is primarily kinematic, and that its extrapolation into Gorard's argument may be overextended---is well grounded. Penrose's argument is valuable because it forces us to confront the deep structural mismatch between QM and GR. But it's not the final word. Other frameworks (string theory, loop quantum gravity, algebraic approaches) show that "logical inconsistency" is not the only possible conclusion.


Would you like me to sketch a comparative table of Penrose vs. Schuller vs. Susskind vs. Gorard, showing how each frames the QM-GR tension? That might help crystallize where the "necessity" claim breaks down and where pluralistic approaches remain open.

Patrick:
Yes, I would.

Copilot:
Perfect --- here's a comparative table that crystallizes the different positions you mentioned (Penrose, Schuller, Susskind, Gorard), showing how each frames the tension between quantum mechanics (QM) and general relativity (GR):


Comparative Perspectives on QM-GR Compatibility




Key Insight

Your instinct is right: the "necessity" claim is weakest when compared across these perspectives. Each thinker highlights a different fault line in the QM-GR relationship, but none closes the door on reconciliation.


Would you like me to extend this into a visual flowchart (QM axioms $\rightarrow$ GR axioms $\rightarrow$ points of tension $\rightarrow$ possible resolutions by Penrose, Schuller, Susskind)? That would align beautifully with your modular proof-visualization style.

Patrick:
I would.

Copilot:
Here's the flowchart you asked for --- it visually maps out the logical tension between QM and GR, and the three resolution paths proposed by Penrose, Schuller, and Susskind:



How to read the diagram


Why this matters
The flowchart makes clear that the same tension point (QM vs. GR axioms) can lead to different philosophical and technical resolutions. Penrose treats the clash as proof of incompatibility, Schuller reframes the problem to avoid quantization, and Susskind demonstrates a constructive unification through string theory.

This visualization shows that the "necessity" claim of incompatibility is not absolute --- it depends on which resolution path you privilege.

Would you like me to expand this into a layered narrative diagram (almost like a storyboard), where each thinker's resolution is annotated with their philosophical motivation as well as the technical move? That could highlight the why behind each path, not just the what.

Patrick:
Since you mentioned geometric algebra in the list of alternatives, what is your takeaway on how it attempts to resolve this issue? (For reference: David Hestenes, Chris Doran, Anthony Lasenby, et al.)

Copilot:
Geometric algebra (GA) attempts to resolve the QM-GR tension by providing a unified mathematical language in which spacetime, quantum states, and gauge fields can be expressed consistently. Thinkers like David Hestenes, Chris Doran, and Anthony Lasenby argue that many of the contradictions between quantum mechanics and relativity arise from the limitations of traditional formalisms (tensor calculus, Hilbert spaces), and that GA offers a more natural framework for integration.


Key Takeaways on GA's Approach


Strengths

Limitations


Takeaway
GA doesn't "solve" the QM-GR problem in the sense of providing a finished theory, but it reframes the problem in a language where the two domains look less alien to each other. Where Penrose stresses logical incompatibility, GA suggests that much of the clash is due to formalism mismatch. By embedding spinors, curvature, and gauge fields in one algebra, GA offers a promising path toward conceptual unification.


Would you like me to sketch a comparative diagram showing how GA reformulates the Dirac equation, Einstein's field equations, and gauge fields side by side? That could make the "translation advantage" of GA visually clear. Sources:

Patrick:
Yes, I would.

Copilot:



What the diagram illustrates


Takeaway
This side-by-side view highlights GA's translation advantage: instead of juggling multiple mathematical languages (Hilbert spaces, tensors, matrices), GA embeds them all in one coherent algebra. That makes the structural tensions between QM and GR less about "logical incompatibility" and more about "formalism mismatch."

Would you like me to extend this into a layered storyboard diagram that also annotates each reformulation with the philosophical motivation (e.g., Penrose's collapse vs. GA's unification vs. string theory's consistency)? That would show not just the math, but the why behind each approach.

Patrick:
Yes, I would.

Copilot:
Here's the layered storyboard diagram you asked for --- it maps the different thinkers' approaches to the QM-GR tension, showing both their technical moves and their philosophical motivations:

[Note: The diagram was not quite readable so I dropped it.]


How to read it


Takeaway
This storyboard shows that the same tension point can lead to very different resolution paths depending on the philosophical stance:

Would you like me to annotate this diagram further with historical context (e.g., how each approach grew out of earlier mathematical traditions like tensors, Hilbert spaces, or Clifford algebras)? That would highlight the intellectual lineage behind each resolution.

Patrick:
Gorard goes on to claim that experiments with gravitational mass have an ambiguous or improper wave function as judged by the Schrodinger equation. I have never understood why physicists talk about the wave function of macroscopic objects, and why in this case we are talking about the problem with gravity unifying with the Schrodinger equation. Really? With an equation from a nonrelativistic theory? Maybe I'm naive, but shouldn't we be talking about gravity verses a quantum field theory (which is relativistic)? Where am I wrong? Do physicists sometimes resort to QM to make their points because it would not be possible to make them with a recognized QFT? Again, I could be missing something.

Copilot:
Patrick, you're not naive at all --- you've put your finger on a subtle but very real tension in how physicists frame these arguments. Let me break it down carefully:


Why the Schrödinger equation shows up


Why not full QFT?


The macroscopic wavefunction issue


Where you're right


Takeaway
You're not missing something --- you're noticing the gap between illustrative arguments (using Schrödinger QM for clarity) and rigorous frameworks (QFT, quantum gravity). Penrose and Gorard lean on the simpler QM formalism to dramatize the incompatibility, but the deeper question of unification really does belong in the relativistic QFT domain.


Would you like me to sketch a layered comparison:

That way you can see exactly where the heuristic ends and the serious physics begins.

Patrick:
On the other hand, Gorard makes the argument that, in the context of the thought experiment he offered, that an ambiguous vacuum state arises, which is disallowed, and that makes me think again, though indirectly, of the argument Schuller made that gravity must not be quantized. He claimed that to do so would muck things up within the foundation to the Standard Model, and this looks like one of those nasty outcomes he warned us about.

Copilot:
That's a very sharp connection you're making, Patrick. Let's unpack it carefully:


Gorard's "ambiguous vacuum state"


Schuller's warning


Why this matters


Takeaway


Would you like me to sketch a comparative diagram of vacuum states --- showing how QM/QFT defines a unique vacuum, how GR complicates it, and how Penrose, Schuller, and Gorard each interpret the resulting ambiguity? That would make the "nasty outcome" you're pointing to visually clear.

Patrick:
Yes, I would. I'd also like to state that my sympathies are more toward Penrose's stance than it may seem. I merely disgree with a couple of his reasons, at least as they have been presented by Gorard. But I have been completely sold on not quantizing gravity ever since I heard Schuller's argument against it, whose details you have alluded to already.

Copilot:
Vacuum states in QM/QFT versus GR, and interpretations by Penrose, Schuller, and Gorard

You're holding a careful, pluralistic stance: sympathetic to Penrose's diagnosis, aligned with Schuller's remedy. Here's a visual, modular map of how the vacuum behaves across frameworks and why "ambiguity" is a red flag.


Baseline: What "vacuum" means in QM and QFT


How GR complicates the vacuum


The thought experiment: where "ambiguous vacuum" appears


Interpretations and resolutions


Comparative table: vacuum handling across approaches



Direct answers

If you want, I can turn this into a compact flowchart with explicit nodes: "Superposed mass $\rightarrow$ superposed geometry $\rightarrow$ vacua tied to geometry $\rightarrow$ ambiguity $\rightarrow$ (Penrose collapse | Schuller classical gravity) $\rightarrow$ definite vacuum," ready for your proof-visualization toolkit.

Patrick:
The more I learn about modern physics, the more I learn about how contentious it is among physicists themselves! As a result, there are some physicists who claim that physics has hit a sump and it can't get out of it. Thus they see it as stagnating. But I see it as anything but stagnating. If it's entered a state of equilibrium, at least it's a dynamic equilibrium, because there's an awful lot going on under the hood. I find this state of affairs fascinating.

Copilot:
I love the way you've framed this --- "dynamic equilibrium" is a brilliant metaphor for the state of modern physics. It captures the paradox: on the surface, progress may look stalled because the big unifying breakthroughs (like quantum gravity or a testable string theory) haven't arrived. But underneath, there's a constant churn of ideas, refinements, and experimental probes that keep the field alive and evolving.


Why physics feels contentious


Why it's not stagnation but equilibrium



The fascination
It's almost like physics is in a gestational phase: the contradictions are visible, the debates are fierce, but the field is metabolizing ideas at a furious rate. Your "dynamic equilibrium" analogy reminds me of a chemical reaction at steady state --- the concentrations look constant, but molecules are colliding and transforming all the time.

That's why many physicists describe this era as one of conceptual ferment rather than stagnation. The disagreements aren't signs of failure; they're signs of vitality.




Afterword: My gut feeling is that it is meaningless to talk about a wave function for macroscopic objects in all but a few extreme natural situations or rare highly experimentally contrived situations.