trailAlternative derivations of Hawking radiation avoid appealing to trans-Planckian frequencies.
The derivation of Hawking radiation depends on unknown trans-Planckian physics.
Quantum field theory in curved spacetime predicts thermal radiation from black hole event horizons.
Derivation routes without mode tracing· for
Tunneling, Euclidean, and anomaly-based derivations of Hawking radiation do not trace modes through the near-horizon exponential blueshift.
atomic
Independent theoretical derivations converge on the same black hole temperature.
atomic
Explicit-cutoff derivations· for
Modified trans-Planckian dispersion relations in black-hole models preserve the thermal spectrum at the Hawking temperature.
atomic
Hidden trans-Planckian assumptions· against
Alternative derivations of Hawking radiation implicitly assume the quantum state is regular across the horizon at arbitrarily short distances.
Tunneling, Euclidean, and anomaly-based derivations of Hawking radiation impose regularity of the quantum state at the horizon.
The Hawking spectrum can be derived assuming the quantum state is regular only down to an invariant Planck-scale cutoff.
The Hawking spectrum's insensitivity to modified dispersion holds only under conditions such as a free-falling vacuum and adiabatic evolution.
assumed
Hawking's original derivation traces outgoing modes back to frequencies far above the Planck scale.
claim · empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →claim page ↗︎
Alternative derivations of Hawking radiation avoid appealing to trans-Planckian frequencies.
↑SupportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →credence 0.80Credence, from 0 to 1: the Steward's probability that the claim, as stated, is true. Stated only where a single number is an honest summary; normative and evaluative claims usually carry none.constitution →
2depended on by
this rests on ↓
claimA box is a claim: a single proposition the graph assesses, with its own page and map. Click any claim to centre the map on it.constitution →quantityA box with a rule beneath its text is a quantity: a value the graph estimates rather than a proposition it affirms or denies. Its estimate stands where a claim's status would.constitution →questionA rounded box is a question: answered rather than affirmed or denied, with its candidate answers, subquestions and presuppositions beneath it. Its mark says how well answered it is.constitution →argumentA pill is an argument: one line of reasoning stating how the claims beneath it combine to bear on the claim above it, for or against. Click one to see its reasoning and open its page.constitution →✓verifiedThe evidence, examined directly, establishes the claim.constitution →↑supportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →⇄inconclusiveThe evidence and argument have been examined and do not come down on either side.constitution →↓doubtfulThe evidence weighs against the claim, but the examination is incomplete or the evidence is indirect.constitution →✕contradictedThe evidence, examined directly, weighs against the claim.constitution →?unknownInsufficient information to assess.constitution →◌unassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →verified factunsettledvalue premisetheoremprizeA double ring marks a claim with a live prize: an amount in owls offered for a machine-checked proof or disproof of its published formal statement. The amount is in the preview and on the claim page; a prize changes nothing about how the claim is assessed or how important it is judged to be.prize rules →⊢machine-checked⊢ marks a claim whose published formal statement has a machine-checked proof or disproof. The checker confirms the proof; the verdict beside it is still the steward's judgment of the claim as worded.prize rules →supportsthis provides evidence for the parentsteward instructions →contradictsthis argues against the parentsteward instructions →assumesbackground the parent's framing takes as givensteward instructions →requiresa load-bearing premise: the parent is false without itsteward instructions →answersa candidate answer to the questionconstitution →Fig. Detail falls off with distance; every claim is an address.