Tolman–Ehrenfest effect
E145217
The Tolman–Ehrenfest effect is a relativistic thermodynamic phenomenon stating that, in a system at thermal equilibrium within a gravitational field, temperature varies with gravitational potential so that hotter regions occur deeper in the gravitational well.
All labels observed (7)
How this entity was disambiguated
This entity first appeared as the object of triple T1263727 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
Target entity: Tolman–Ehrenfest effect Context triple: [Richard C. Tolman, notableConcept, Tolman–Ehrenfest effect]
-
A.
Unruh effect
The Unruh effect is a predicted phenomenon in quantum field theory where an accelerating observer perceives what inertial observers consider vacuum as a warm bath of particles with a characteristic temperature.
-
B.
Mach principle
Mach principle is a philosophical and physical concept proposing that local inertial properties of matter are determined by the large-scale distribution of mass and energy in the universe.
-
C.
Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
-
D.
Lorentz
Lorentz is a Dutch surname most famously associated with physicist Hendrik Lorentz, a pioneer of electromagnetic theory and relativity.
-
E.
Does the Inertia of a Body Depend Upon Its Energy Content?
"Does the Inertia of a Body Depend Upon Its Energy Content?" is Albert Einstein’s 1905 paper that first articulated the mass–energy equivalence principle, commonly expressed as E = mc².
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Tolman–Ehrenfest effect Target entity description: The Tolman–Ehrenfest effect is a relativistic thermodynamic phenomenon stating that, in a system at thermal equilibrium within a gravitational field, temperature varies with gravitational potential so that hotter regions occur deeper in the gravitational well.
-
A.
Unruh effect
The Unruh effect is a predicted phenomenon in quantum field theory where an accelerating observer perceives what inertial observers consider vacuum as a warm bath of particles with a characteristic temperature.
-
B.
Mach principle
Mach principle is a philosophical and physical concept proposing that local inertial properties of matter are determined by the large-scale distribution of mass and energy in the universe.
-
C.
Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
-
D.
Lorentz
Lorentz is a Dutch surname most famously associated with physicist Hendrik Lorentz, a pioneer of electromagnetic theory and relativity.
-
E.
Does the Inertia of a Body Depend Upon Its Energy Content?
"Does the Inertia of a Body Depend Upon Its Energy Content?" is Albert Einstein’s 1905 paper that first articulated the mass–energy equivalence principle, commonly expressed as E = mc².
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
physical phenomenon
ⓘ
relativistic thermodynamic effect ⓘ |
| appliesTo |
systems in static gravitational fields
ⓘ
systems in thermal equilibrium in curved spacetime ⓘ |
| assumes |
general relativistic description of gravity
ⓘ
global thermal equilibrium ⓘ static spacetime metric ⓘ |
| clarifies | relationship between temperature and time dilation ⓘ |
| compatibleWith |
gravitational time dilation
ⓘ
local validity of special relativity ⓘ |
| context |
curved spacetime thermodynamics
ⓘ
equilibrium of self-gravitating systems ⓘ |
| contrastsWith | naive Newtonian expectation of uniform temperature at equilibrium in a gravitational field ⓘ |
| describes | temperature distribution in a gravitational field at thermal equilibrium ⓘ |
| explains | how local temperature must vary to maintain equilibrium in gravity ⓘ |
| field |
general relativity
ⓘ
statistical mechanics ⓘ thermodynamics ⓘ |
| formulatedBy |
Paul Ehrenfest
ⓘ
Richard C. Tolman ⓘ |
| hasAlternativeName |
Tolman–Ehrenfest effect
ⓘ
surface form:
Tolman law of temperature in a gravitational field
Tolman–Ehrenfest effect ⓘ
surface form:
Tolman temperature relation
|
| hasConsequence |
thermodynamic equilibrium is frame and metric dependent
ⓘ
uniform temperature in a gravitational field is incompatible with full relativistic equilibrium ⓘ |
| holdsWhen | no heat flow occurs in the system ⓘ |
| implies | hotter regions occur deeper in a gravitational well at equilibrium ⓘ |
| involvesQuantity |
gravitational potential
ⓘ
local temperature ⓘ metric component g00 ⓘ proper time ⓘ |
| mathematicalForm | T(r)·sqrt(g00(r)) = constant in static spacetime ⓘ |
| predicts | temperature increases with depth in a gravitational potential well at equilibrium ⓘ |
| relatedTo |
Einstein field equations
ⓘ
Tolman–Ehrenfest effect self-linksurface differs ⓘ
surface form:
Tolman law
Tolman–Ehrenfest effect self-linksurface differs ⓘ
surface form:
Tolman temperature gradient
equivalence principle ⓘ gravitational redshift ⓘ relativistic thermodynamic equilibrium ⓘ |
| statesThat | temperature varies with gravitational potential in thermal equilibrium ⓘ |
| usedIn |
analysis of thermal radiation in gravitational fields
ⓘ
black hole thermodynamics ⓘ cosmological thermodynamics ⓘ relativistic stellar structure models ⓘ |
| yearProposed | 1930 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Subject: Tolman–Ehrenfest effect Description of subject: The Tolman–Ehrenfest effect is a relativistic thermodynamic phenomenon stating that, in a system at thermal equilibrium within a gravitational field, temperature varies with gravitational potential so that hotter regions occur deeper in the gravitational well.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.