Very interesting, John. Thanks for that.
Brent
On 5/26/2025 4:56 AM, John Clark wrote:
On Sun, May 25, 2025 at 3:33 PM Alan Grayson <[email protected]>
wrote:
/> I'm disagreeing with anyone, including you, who thinks the EP
is an absolute, when in fact it's a relative, an approximation./
The Equivalence Principle, which is the foundation of General
Relativity, states that at sufficiently small scales there is no way
to tell the difference between a gravitational field and a simple
acceleration. And it is not an approximation. But is it always
correct? That is not certain because General Relativity does not take
Quantum Mechanics into account, nevertheless so far at least the
Equivalence Principle has easily passed every experimental test put to
it.
For fun I asked GPT to do "Deep Research" on the following questions:
"Have there been any proposed experimental tests to see if Einstein's
Equivalence Principle remains true even when quantum mechanics is
taken into account? In other words tests to determine if gravity can
change the quantum entanglement of two particles, and if not are any
such tests planned?"
_SPOILER ALERT_: GPT's ultimate conclusion was "So far, all completed
tests have found *no anomalous effect* – entangled states remain
intact in different gravitational or accelerated frames, consistent
with EEP and standard quantum theory"
GPT put those words in boldface type, not me. Below is GPT's full
response:
========
Tests of the Equivalence Principle with Quantum Entanglement
Einstein’s equivalence principle (EEP) – that all objects fall
identically in a gravitational field – is classically tested to
extreme precision. Extending EEP to quantum systems, especially
entangled ones, poses conceptual challenges (the EEP is classically
formulated and its quantum generalization “requires careful
considerations”ar5iv.org
<https://ar5iv.org/pdf/2203.11628#:~:text=The%20EEP%20is%20however%20formulated,the%20notion%20of%20test%20particles>).
Recent proposals and experiments therefore ask: *Can gravity alter
quantum entanglement?* Would any change signal a breakdown of EEP?
Below we summarize key efforts, completed or proposed, that probe this
question using entangled photons or atoms in varying gravitational or
inertial conditions.
Space- and Satellite-Based Experiments
*
*Micius satellite test (Xu /et al./ 2019)* – An experiment by Pan,
Ren, Ralph /et al./ (China/U.S.) sent one photon of a
time-energy–entangled pair to orbit aboard the Micius satellite
while keeping the other photon on the groundpub.math.leidenuniv.nl
<https://pub.math.leidenuniv.nl/~gillrd/Peking/Files/Xu-2019-Satellite-testing-of-a-gravitationa.pdf#:~:text=containing%20closed%20timelike%20curves%20and,the%20prediction%20of%20event%20formalism>.
This setup exposed the two photons to different gravitational
potentials. The goal was to test predictions of a speculative
“event formalism” model that entanglement would *probabilistically
decohere* when particles traverse different gravity gradients. The
result (published in /Science/) was that no abnormal decoherence
was seen: the entanglement correlations matched standard quantum
theory, *not* the model’s decohering
predictionpub.math.leidenuniv.nl
<https://pub.math.leidenuniv.nl/~gillrd/Peking/Files/Xu-2019-Satellite-testing-of-a-gravitationa.pdf#:~:text=containing%20closed%20timelike%20curves%20and,the%20prediction%20of%20event%20formalism>.
In other words, despite the large gravitational potential
difference, the quantum entanglement survived intact. /(Team:
Jian-Wei Pan et al., USTC and collaborators; status: completed
2017/19.)/
*
*Space-QUEST mission concept (Joshi /et al./ 2017)* – A European
“Quantum Entanglement Space Test” proposal (ESA/Topical Team) led
by Ursin, Ralph, Cacciapuoti /et al./. This feasibility study
outlined sending entangled photon pairs between ground and the
International Space Station (ISS)ar5iv.labs.arxiv.org
<https://ar5iv.labs.arxiv.org/html/1703.08036v1#:~:text=Models%20of%20quantum%20systems%20on,theoretical%20predictions%20of%20Ralph%20and>.
One photon would be sent upward while its partner remained on
Earth, testing theories (e.g. by Ralph and co-workers) that such a
setup could *induce decoherence of entanglement* if each photon
samples a different gravitational field
gradientar5iv.labs.arxiv.org
<https://ar5iv.labs.arxiv.org/html/1703.08036v1#:~:text=Models%20of%20quantum%20systems%20on,theoretical%20predictions%20of%20Ralph%20and>.
The paper presents a detailed mission design (Space-QUEST) and
notes that under standard quantum field theory no decoherence is
expected, but some exotic models (the same “event operator”
models) predict irrecoverable loss of
entanglementar5iv.labs.arxiv.org
<https://ar5iv.labs.arxiv.org/html/1703.08036v1#:~:text=Models%20of%20quantum%20systems%20on,theoretical%20predictions%20of%20Ralph%20and>.
(Team: international quantum optics collaboration including
Austrian Academy of Sciences, University of Vienna, ESA, etc.;
status: proposed/concept study.)
Laboratory/Accelerated-Frame Experiments
*
*Acceleration (free-fall/centrifuge) test (Fink /et al./ 2017)* –
In Vienna, Fink, Ursin, Scheidl /et al./ placed a
polarization-entangled photon source and detectors on a platform
that was /dropped/ 12 m (microgravity) and separately spun in a
centrifuge up to 30 g. They measured an entanglement witness for
accelerations spanning 0.03 g (near-free-fall) up to
30 gnature.com
<https://www.nature.com/articles/ncomms15304?error=cookies_not_supported&code=0de1ebbf-a81e-4d7e-a5a1-d5e23484627f#:~:text=at%20rest%20in%20gravitational%20fields%2C,uniform%20acceleration%20on%20photonic%20entanglement>.
The result (Nature Communications) was that entanglement quality
showed *no significant loss* beyond noise limits at any
acceleration testednature.com
<https://www.nature.com/articles/ncomms15304?error=cookies_not_supported&code=0de1ebbf-a81e-4d7e-a5a1-d5e23484627f#:~:text=at%20rest%20in%20gravitational%20fields%2C,uniform%20acceleration%20on%20photonic%20entanglement>.
In effect, even extreme inertial forces (equivalent to
gravitational fields by the EP) did not degrade the photon
entanglement. The experiment set an upper bound on any
acceleration-induced decoherence of the entangled statenature.com
<https://www.nature.com/articles/ncomms15304?error=cookies_not_supported&code=0de1ebbf-a81e-4d7e-a5a1-d5e23484627f#:~:text=at%20rest%20in%20gravitational%20fields%2C,uniform%20acceleration%20on%20photonic%20entanglement>.
/(Affiliation: Vienna Institute of Quantum Optics (IQOQI) and
University of Vienna; status: completed 2017.)/
*
*Rotational (Sagnac interferometer) test (Cromb /et al./ 2023)* –
At the University of Glasgow, Cromb, Padgett, Faccio /et al./
placed a Hong–Ou–Mandel interferometer (entangled photons) on a
rotating platform (fiber Sagnac loop). They observed that as
rotation rate increased, the two-photon interference pattern
*flipped* from the usual HOM dip to a peakjournals.aps.org
<https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.L022005#:~:text=a%20Hong,curved%20space%20on%20quantum%20entanglement>.
This indicates that noninertial (rotating) motion fundamentally
altered the symmetry of the entangled state. While not directly a
gravity test, this table-top demonstration (Phys. Rev. Research
2023) shows that entangled photons are sensitive to rotational
(relativistic) effects and “paves the way” to test entanglement in
curved spacetimejournals.aps.org
<https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.L022005#:~:text=a%20Hong,curved%20space%20on%20quantum%20entanglement>.
/(Affiliation: University of Glasgow; status: completed 2023.)/
Proposed and Future Tests
*
*Entangled-atom interferometer (Geiger & Trupke 2018)* – A
theoretical proposal (Phys. Rev. Lett.) by Geiger (Paris
Observatory) and Trupke (Vienna) suggests using *two entangled
atoms of different species* in a differential free-fall
interferometer. Each atom (e.g. ^85Rb and ^87Rb) forms its own
atom interferometer; the two are prepared in an entangled
superposition via a heralded photon detection at the input beam
splitterhal.science
<https://hal.science/hal-01707541/document#:~:text=We%20propose%20an%20experiment%20to,the%20detection%20of%20a%20single>.
The interferometers then measure the differential acceleration of
the two species. Crucially, because the atoms start entangled,
this probes WEP in a regime where “the two particles involved …
are not classically independent, but entangled”hal.science
<https://hal.science/hal-01707541/document#:~:text=We%20propose%20an%20experiment%20to,the%20detection%20of%20a%20single>.
Their proposed setup (high-finesse cavity, Raman processes)
predicts sensitivity to Eötvös parameter η below 10^−7hal.science
<https://hal.science/hal-01707541/document#:~:text=two%20particles%20involved%20in%20the,E%C3%B6tv%C3%B6s%20parameter%20can%20be%20achieved>.
/(Institutions: LNE-SYRTE/Observatoire de Paris, University of
Vienna; status: proposed in PRL 2018.)/
*
*Entanglement-witness protocols (Bose /et al./ 2023)* – Sougato
Bose and collaborators (UCL, Groningen, Glasgow) have introduced
the idea of a “quantum equivalence principle” test using
entanglement. They propose creating massive particles in large
spatial superposition and using an entanglement entropy witness to
detect any WEP violationar5iv.org
<https://ar5iv.org/pdf/2203.11628#:~:text=quantum%20entities,principle%20via%20witnessing%20quantum%20entanglement>.
In essence, both matter and the gravitational source are treated
as quantum; any difference between inertial and gravitational
masses in this fully quantum regime would reveal itself through
lack of entanglement. Their 2022/23 paper provides a protocol for
such experiments and argues it is “unique” for testing the weak
equivalence principle in the quantum domainar5iv.org
<https://ar5iv.org/pdf/2203.11628#:~:text=quantum%20entities,principle%20via%20witnessing%20quantum%20entanglement>.
/(This work is theoretical/preprint (Entropy 2023) but outlines
concrete tabletop schemes.)/
*
*SUPREME-QG space mission (Shahriar /et al./ 2023–25)* – A
NASA-funded concept (NIAC Phase I, 2025) led by Selim Shahriar
(Northwestern U.) envisions a spaceborne WEP test using
*macroscopic entangled atomic states*nasa.gov
<https://www.nasa.gov/directorates/stmd/niac/niac-studies/supreme-qg-space-borne-ultra-precise-measurement-of-the-equivalence-principle-signature-of-quantum-gravity/#:~:text=entanglement%20to%20test%20the%20EP,N%20SC%20states%20are%20difficult>.
The idea is two simultaneous atom interferometers with ^85Rb and
^87Rb, each using a Schrödinger-cat–like state of N≈10^6 entangled
atoms generated by cavity spin-squeezingnasa.gov
<https://www.nasa.gov/directorates/stmd/niac/niac-studies/supreme-qg-space-borne-ultra-precise-measurement-of-the-equivalence-principle-signature-of-quantum-gravity/#:~:text=entanglement%20to%20test%20the%20EP,N%20SC%20states%20are%20difficult>.
Such a many-particle entangled state behaves as one massive
superposition, boosting sensitivity by √N∼10^3. The goal is to
measure differential free-fall with precision η∼10^−20nasa.gov
<https://www.nasa.gov/directorates/stmd/niac/niac-studies/supreme-qg-space-borne-ultra-precise-measurement-of-the-equivalence-principle-signature-of-quantum-gravity/#:~:text=entanglement%20to%20test%20the%20EP,N%20SC%20states%20are%20difficult>
– orders of magnitude beyond current tests. (The proposal outlines
technology development for these giant entangled statesnasa.gov
<https://www.nasa.gov/directorates/stmd/niac/niac-studies/supreme-qg-space-borne-ultra-precise-measurement-of-the-equivalence-principle-signature-of-quantum-gravity/#:~:text=entanglement%20to%20test%20the%20EP,N%20SC%20states%20are%20difficult>.
Status: concept study, NIAC-awarded 2025.)
Each of these efforts is explicitly aimed at the *intersection of
gravity and entanglement*. So far, all completed tests have *found no
anomalous effect* – entangled states remain intact in different
gravitational or accelerated frames, consistent with EEP and standard
quantum theorypub.math.leidenuniv.nl
<https://pub.math.leidenuniv.nl/~gillrd/Peking/Files/Xu-2019-Satellite-testing-of-a-gravitationa.pdf#:~:text=containing%20closed%20timelike%20curves%20and,the%20prediction%20of%20event%20formalism>nature.com
<https://www.nature.com/articles/ncomms15304?error=cookies_not_supported&code=0de1ebbf-a81e-4d7e-a5a1-d5e23484627f#:~:text=at%20rest%20in%20gravitational%20fields%2C,uniform%20acceleration%20on%20photonic%20entanglement>.
Future and proposed experiments (e.g. entangled atoms in free-fall)
aim to push these tests into new regimes; any observed entanglement
degradation tied to gravity would signal new physics.
*Sources:* Peer-reviewed articles and official reports as cited
abovepub.math.leidenuniv.nl
<https://pub.math.leidenuniv.nl/~gillrd/Peking/Files/Xu-2019-Satellite-testing-of-a-gravitationa.pdf#:~:text=containing%20closed%20timelike%20curves%20and,the%20prediction%20of%20event%20formalism>
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