On Gravity and the Uncertainty Principle

David I. Santiago; Ronald J. Adler

RECORD

On Gravity and the Uncertainty Principle

Ronald J. Adler, David I. Santiago

General Relativity and Quantum Cosmology · Submitted 12 Apr 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,632 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.16 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.77 · compares with prior results 0.94 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length. A modified uncertainty relation of this form is a standard result of superstring theory, but the derivation given here is based on simpler and rather general considerations with either Newtonian gravitational theory or general relativity theory.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons.	background 1.00	0.02	0.03	asserted 1.00
s1	As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term.	result 0.50	0.92	0.43	asserted 1.00
s2	From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length.	result 0.88	0.80	0.74	asserted 1.00
s3	A modified uncertainty relation of this form is a standard result of superstring theory, but the derivation given here is based on simpler and rather general considerations with either Newtonian gravitational theory or general relativity theory.	contribution 0.62	0.79	0.09	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length. A modified uncertainty relation of this form is a standard result of superstring theory, but the derivation given here is based on simpler and rather general considerations with either Newtonian gravitational theory or general relativity theory.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Macroscopic Black-Hole Remnants in a Nonlocal Field Theory: Towards Hawking Radiation in SFT
hep-th 2026-06 unverdicted novelty 6.0 of 10

In a smeared massless scalar on dynamical black hole, outgoing particle number drops to zero after scrambling time due to SFT nonlocality, implying macroscopic remnant.
Doubly Quantum Mechanics
quant-ph 2024-12 conditional novelty 6.0 of 10

Replacing SU(2) with SU_q(2) turns measurement probabilities into operators and makes reference-frame alignment between two observers fundamentally imprecise even in the limit of infinitely many exchanged spins.
UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox
hep-th 2024-11 unverdicted novelty 5.0 of 10

Hawking radiation terminates around the scrambling time due to trans-Planckian stringy effects in GUP and string-field-theory-inspired toy models, yielding negligible evaporation and a mostly classical black hole.
HWF Analysis of TRN Black Holes
gr-qc 2026-10 conditional novelty 4.0 of 10

For charged, higher-dimensional (Tangherlini-Reissner-Nordström) black holes, the authors compute horizon wave functions and formation probabilities, finding strong suppression with dimension and a sharp rise of the i...
Statistical Entropy Based on the Generalized-Uncertainty-Principle-Induced Effective Metric
gr-qc 2025-08 reject novelty 4.0 of 10

With GUP-modified effective metrics and tuned cutoffs (or tuned GUP parameter), the brick-wall entropy is made to reproduce the Bekenstein-Hawking area law.

Show 4 more citing papers

Black Hole Remnants and the Information Loss Paradox
gr-qc 2014-12 conditional novelty 4.0 of 10

Remnants remain a viable end state of Hawking evaporation, but they only ease the information paradox and firewall if a black hole's interior stores far more information than its horizon area counts.
Minimal Length Scale Scenarios for Quantum Gravity
gr-qc 2012-03 accept novelty 3.0 of 10

Every major approach to quantum gravity points to a finite resolution of structure, though the 'minimal length' takes different forms, so the review argues for the broader term 'minimal length scale'.
The Quantum and Statistical Theory of Early Universe and Its Possible Applications to Cosmology
gr-qc 2006-04 reject novelty 3.0 of 10

A deformed density matrix with trace less than one is proposed for early-universe physics, yielding claimed recoveries of the Bekenstein-Hawking entropy and a solution to the information paradox.
Deformed Density Matrix and Quantum Entropy of the Black Hole
gr-qc 2006-03 reject novelty 3.0 of 10

The paper qualitatively claims that deformed density matrices at Planck scale resolve the black hole information paradox, but the central entropy-correction claim is not supported by its own equations.

How later papers used it

69 later papers cite it

Evidence: substantial. 69 of the citing papers share no author with it, and 5 of those carry a confident label from Pith's citation classifier.

Pith read 18 of the 94 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 compared its own results with it.

Compares with it 1 of 3 papers with this label

Stated that its own expression of the generalized uncertainty principle differs from this paper's by a factor of 1/2.

Generalized Uncertainty Principle: Implications for Black Hole Complementarity (2014) · 0.80 · paraphrased: the licence does not allow quoting

How the literature uses it

48 arXiv papers cite this in 66 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 39 sentences without a confident label

Uses its data or values 1 paper

This was done in [ref] with the result that the additional uncertainty in electron's position due to gravitational attraction of the photon is [equation] The second step follows from the fact that the electron momentum uncertainty $Δp$ must be of order of the photon momentum $p$.

On deformations of classical mechanics due to Planck-scale physics · Generalized Uncertainty Principle · 0.85

Compares with it 3 papers

In order to be consistent with Eq.([ref]), our expression of GUP differs from [ref] by a factor of 1/2.

Generalized Uncertainty Principle: Implications for Black Hole Complementarity · Section · 0.80
It corresponds to a different scenario that has been proposed by other GUP approaches, where the final stage of a black hole corresponds to a remnant [ref] .

The Compton/Schwarzschild duality, black hole entropy and quantum information · Introduction · 0.98
Adler and Santiago [ref] offer pretty much the same argument, but add that the particle's momentum uncertainty $Δp$ should be on the order of the photon's momentum $ω$.

Minimal Length Scale Scenarios for Quantum Gravity · The Heisenberg microscope with Newtonian gravity · 0.91

Cites it as background 22 papers

Yet another modification to quantum mechanics is the so-called “Generalized Uncertainty Principle” [GUP], which generalizes the usual Heisenberg's Uncertainty Principle [ref] .

Generalized Uncertainty Principle: Implications for Black Hole Complementarity · Section · 0.98
The notion of a minimal length also emerges from the Generalized Uncertainty Principle (GUP) [ref] , which can be thought of as an extension of the standard Heisenberg Uncertainty Principle (HUP) with a gravitational uncertainty, ΔxΔp≥ħ/2 +αΔp^2/c^3 ⇒Δx ≥ħ/2[ 1/Δp + 2 α Δp/^2 c^2] .

Reconciling microscopic and macroscopic tests of the Compton-Schwarzschild correspondence · Review of `M+1/M' model · 0.85
Such modifications have been obtained via various general considerations of gravity and quantum mechanics [ref] , as well as from string theoretical considerations [ref] .

Generalized Uncertainty Principle, Black Holes, and White Dwarfs: A Tale of Two Infinities · Introduction: Generalized Uncertainty Principle · 0.98

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.