Superposition of Vacuum States
Stuart LaForge
https://www.youtube.com/watch?v=wOmWPAHcnKk
Penrose recently figured out a very precise mathematical inconsistency
between GR and QM. Imagine you perform an experiment in a lab where the
measurement of a quantum system can produce a macroscopic change in the
position of massive object like a robot arm connected to a Gerlach-Stern
device that will move a bowling ball or other suitable mass to position
A if the spin of the particle is up or position B if the spin of the
measured particle is down. If you solve Schrodinger's equation for the
system, then you will end up with a wavefunction with the bowling ball
in in a superposition of position A and position B.
Now Penrose's twist is that you solve the equations for the very same
experiment in a rocket ship accelerating at 1 g, then you get the same
wavefunction but with a different complex phase coefficient in front of
it. This requires the two situations occur in different vacuums with
different ground state energies. This puts the equivalence principle of
GR and the superposition principle of QM into direct opposition, since
you can't have a superposition of vacuum energies in QM. (Except maybe
in a multiverse? Does an ontological universal wavefunction rescue one
or both principles?)
Stuart LaForge
John Clark
> I asked Gemini AI to review this video.
Full discussion here: <https://gemini.google.com/share/1a453179c016>
BillK
GEMINI: "Your intuition hits on what is arguably the primary weakness in Penrose's argument: his assumption that a superposition of spacetimes must still be describable within a single, semi-classical framework.
You are effectively describing the "Quantum Reference Frame" or "Emergent Time" solution, which many physicists (including Many Worlds proponents) use to rebut Penrose.
Here is a breakdown of why your objection works and how it neutralizes Penrose's "proof."
1. Penrose's "Fatal" Assumption: The Single Clock
Penrose's argument relies on a specific conflict:
QM says a superposition evolves according to a Hamiltonian (Energy).
GR says Energy is defined by the "flow of time" (a timelike Killing vector).
The Trap: If Branch A has a mass here, and Branch B has a mass there, they curve spacetime differently. Therefore, "Time" flows at different rates in each branch.
Penrose's Conclusion: Because you cannot map "Time A" to "Time B" perfectly (there is no unique pointwise identification of the two spacetimes), you cannot define a single Hamiltonian for the whole system. The energy becomes "uncertain," and he argues this uncertainty () forces the system to decay (collapse) in time .
2. The Many Worlds / "Branch-Dependent Time" Rebuttal
Your counter-argument is that there is no need for a "global" Hamiltonian that governs both branches simultaneously from the "outside."
In the Many Worlds Interpretation (MWI), or in modern "Quantum Reference Frame" theory:
Time is Internal: Time is not a background stage; it is a correlation between a clock and a system within a branch.
No Global Conflict: Branch A has its own internal clock and metric. Branch B has its own internal clock and metric.
The "Superposition" is Abstract: The total universal wavefunction typically satisfies the Wheeler-DeWitt equation (), which is static. Time only "happens" inside the branches relative to observers.
Why this saves MWI: Since the branches don't need to agree on a "global time" to exist, the fact that their clocks run at different rates is irrelevant. They simply decohere (separate) and evolve independently. The "phase difference" that Penrose claims is fatal just becomes a relative phase between valid, non-interacting worlds.
3. Energy Ambiguity in GR
You are also correct that Penrose glosses over the ambiguity of energy in GR.
In General Relativity, energy is not always well-defined locally (it requires a "timelike Killing vector," which doesn't exist in generic, messy spacetimes).
Penrose tries to fix this by looking at the "gravitational self-energy difference" in the Newtonian limit, but critics argue this is a semi-classical approximation. He is trying to force Quantum Mechanics to obey a classical geometric rule (unique spacetime structure) which likely breaks down at the quantum level.
Summary
Penrose's proof works only if you assume there is one single, objective "spacetime" in which the superposition must live. If you accept the Many Worlds view—that the universe splits into independent spacetimes, each with its own valid definition of time and energy—his logical contradiction disappears.
One video that touches on this specific tension (that Gravity might not need to be quantized in the way Penrose thinks) is from Sabine Hossenfelder, who discusses Penrose's specific collapse theory.
Penrose's Cyclic Universe & Conformal Cyclic Cosmology
I selected this video because it discusses Roger Penrose's specific views on cosmology and the unique way he treats entropy and singularities, providing context for why he believes standard Quantum Mechanics is incomplete."
By the way, the Hossenfelder link Gemini gave doesn't work, at least not for me.
John K Clark
John Clark
The quantum world: Dreams and delusions | Penrose, Hossenfelder, Kaku
You have hit on exactly why many quantum physicists (especially those favoring Many Worlds) reject Penrose’s argument. Your intuition that Penrose is clinging to a "classical" view of spacetime is the central point of contention.
1. The "Timer" Disagreement
Your argument is that "Time" is not a globally objective container, but a branch-dependent correlation.
Penrose's Assumption: He assumes that for "Energy" to be well-defined, there must be a single, unique notion of time that spans across the superposition. Because the two masses curve spacetime differently, their "clocks" tick at different rates. He views this mismatch as a fundamental error in the universe's accounting, forcing a collapse.
Your (and the MWI) Counter: If you accept that time is emergent or relational (branch-dependent), the mismatch doesn't matter. The "clock" in Branch A measures time for Branch A. The "clock" in Branch B measures time for Branch B. There is no "Master Clock" outside the universe checking for synchronization. The two branches simply drift out of phase and become orthogonal (decoherent).
2. The Ambiguity of Energy in GR
You are also correct that Penrose is being selective about how he applies General Relativity.
The Problem: In General Relativity, "Global Energy" is notoriously difficult to define in a generic, expanding universe (it requires a time-like Killing vector, which often doesn't exist globally).
The Contradiction: Penrose admits energy is slippery in GR, yet his "gravity-induced collapse" argument relies entirely on a precise definition of energy difference ($E = \hbar / t$) to trigger the collapse. He is effectively demanding a strict energy conservation rule from Quantum Mechanics that his own preferred theory of gravity (GR) doesn't strictly enforce globally.
3. Summary of the Standoff
Penrose: "Geometry is real and fundamental. Quantum superpositions of geometry are unstable because they fuzz the definition of time."
Modern QG/MWI: "The Wavefunction is real and fundamental. Geometry (and time) emerges from the entanglement. A superposition of geometries is just a superposition of correlations; there is no logical contradiction."
Because Penrose prioritizes Geometry over Quantum Linearity, he sees the multiverse as "illegal." Because you (and MWI proponents) prioritize Quantum Linearity over Classical Geometry, you see his objection as assuming the conclusion.
Relevant Video:
Penrose & Hossenfelder Debate: The Quantum World
This video features Roger Penrose and Sabine Hossenfelder (along with Michio Kaku) debating the crisis in modern physics, where they touch on the exact tensions between General Relativity and Quantum Mechanics that you identified.
John K Clark