Verify any claim · lenz.io
“Energy can neither be created nor destroyed.”
The conclusion
The statement accurately expresses the standard conservation law: total energy in a closed system remains constant while changing form. Its unqualified wording is not fully universal, however, because general relativity may provide no well-defined globally conserved energy in dynamic curved spacetimes. Local energy-momentum conservation still applies.
Caveats
- The law concerns total energy in a closed or isolated system, not energy within an open subsystem.
- Dynamic curved spacetimes may lack a well-defined globally conserved energy.
- Energy may change form, including through mass-energy conversion, without violating conservation.
Fact-check inside the tools you already use
Connect Lenz to ChatGPT, Claude, or WhatsApp and check a claim mid-conversation.
Or create a free account to bookmark this verification and run your own checks.
Sources
Ranked by source quality and relevance
We argue that the matter energy is not necessarily conserved in a curved space time due to a lack of time translational invariance, and adding energy of gravitational fields to recover the conservation law of energies fails due to Noether’s 2nd theorem.
Instead, the law of conservation of energy says that energy is neither created nor destroyed.
There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no exception to this law — it is exact as far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy that does not change in the manifold changes which nature undergoes.
The total energy is always conserved in these processes, although different forms of energy are converted into others.
Energy and its conservation are a pivotal part of almost all of physics. … But the quest for a fully satisfactory account of gravitational energy continues. … Locally, the energy-momentum of matter is indeed conserved, with no need for gravitational energy contributions to restore an energy balance.
Within some problem domain, the amount of energy remains constant and energy is neither created nor destroyed.
We argue that the matter energy is not necessarily conserved in a curved space time due to a lack of time translational invariance, and adding energy of gravitational fields to recover the conservation law of energies fails due to Noether’s 2nd theorem.
In general — it depends on what you mean by "energy", and what you mean by "conserved". … Those who harbor no qualms about pseudo-tensors will say that radiant energy becomes gravitational energy. Others will say that the energy is simply lost.
This may seem a strange question to be asking in 1997 considering that conservation of energy in general relativity was established by Einstein himself in 1916, the year after the theory was published [1] . Yet there remains a sour taste to Einstein's pseudotensor formulation because of its lack of covariance. … Sometimes the null total energy is taken as an indication that energy conservation in general relativity is an empty statement. This is not true because the energy is only zero dynamically, not kinematically.
Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another.
The law of conservation of energy, also known as the first law of thermodynamics, states that the energy of a closed system must remain constant—it can neither increase nor decrease without interference from outside.
The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes.
Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another.
In general, it depends on what you mean by "energy", and what you mean by "conserved".
Time-translation symmetry is closely connected, via Noether's theorem, to conservation of energy. … Many general relativity systems are not static in any frame of reference so no conserved energy can be defined.
Invariance of an isolated system with respect to time translation (i.e. that the laws of physics are the same at all points in time) gives the law of conservation of energy(which states that the total energy of an isolated system is constant)
In physics, the principle of conservation of energy states that within a closed system of interacting bodies or particles, the total energy remains constant. … The first law of thermodynamics expresses this principle, asserting energy is neither create
Total energy is constant in any process. It may change in form or be transferred from one system to another, but the total remains the same.
For instance the time-translation invariance of a physical system equivalently means that the quantity of energy is conserved, and the space- translation invariant of a physical system means that momentum is preserved.
The first law asserts that if heat is recognized as a form of energy, then the total energy of a system plus its surroundings is conserved; in other words, the total energy of the universe remains constant.
While the energy in our covariant definition is not conserved, we show that our definition allows a conserved charge as the generalization of the energy, which we identify the entropy.
The global aspect is that an invariant integral of any symmetrical 2-tensor in non-Euclidian space does not exist (the noninvariant integration generally used in GR is not valid despite the fact that it gives correct results in a few special cases) i.e., the global conservation laws depend on spatial symmetry (because one can define invariant integration only in symmetrical spaces).
Equation 7.1 expresses a basic statement of the Law of Conservation of Energy: “Energy can neither be created nor destroyed, it can only be changed from one form to another.”
Total energy is constant in any process. It may change in form or be transferred from one system to another, but the total remains the same.
A conserved quantity, in the scientific sense, can be transformed, but not strictly created or destroyed.
It’s clear that cosmologists have not done a very good job of spreading the word about something that’s been well-understood since at least the 1920’s: energy is not conserved in general relativity.
The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy to another.
Time translation symmetry gives conservation of energy; space translation symmetry gives conservation of momentum; rotation symmetry gives conservation of angular momentum, and so on.
The first law is a statement of energy conservation.
Most famously, energy is conserved by time translations.
It’s sometimes said Noether showed symmetries give conservation laws. But this is only true under some assumptions: for example, that the equations of motion come from a Lagrangian.
time-translation symmetry (the laws of physics don't change over time) implies conservation of energy … You are correct that time invariance of laws does not require energy conservation. … Noether's theorem does not say "physics concept of energy is conserved", it says "there is a corresponding conserved quantity based on the action expression and the transformation that leaves $S$ invariant, its interpretation is on you, it may be energy, or not".
The basic implication of this is that energy is not conserved in any spacetime with a time-varying gravitational field. … The most important example of a problem which is not asymptotically stationary is the FLRW expanding Universe. There is no timelike Killing vector anywhere and thus no conserved energy, even globally.
The laws of thermodynamics describe how the energy in a system changes and whether the system can perform useful work on its surroundings.
Continue your research
Verify a related claim next.
Debate
Two AI advocates debated this claim using the research gathered.
Argument for
The claim is the established law of conservation of energy: the U.S. Energy Information Administration states verbatim that energy is “neither created nor destroyed” (Source 2), while NASA likewise states that within the relevant problem domain energy remains constant (Source 6). MIT's physics materials describe this as an exact law with no known exception and explain that apparent changes are conversions among forms, not creation or destruction (Sources 3 and 4).
The Proponent relies exclusively on classical mechanics frameworks while conveniently ignoring the explicit caveat in Source 6 that energy conservation only applies within a specific problem domain. By failing to account for general relativity, the Proponent ignores that in non-static, curved spacetimes like our expanding universe, time-translational invariance is lost and energy is demonstrably not conserved (Sources 1, 15, 26).
Argument against
Although classical thermodynamics treats energy conservation as an absolute rule, modern physics demonstrates that energy is not conserved in general relativity due to a lack of time-translational invariance in curved spacetimes (Sources 1, 15, 26). Consequently, in time-varying gravitational fields such as our expanding universe, no conserved energy can be defined, proving that the rigid assertion that energy can never be created or destroyed is fundamentally false on a cosmic scale (Sources 7, 34).
The Opponent equivocates between the absence of a globally definable conserved energy in some general-relativistic spacetimes and physical creation or destruction of energy; Source 5 explicitly states that matter energy-momentum is locally conserved, while Sources 1 and 7 address the difficulty of global conservation in curved spacetime. The Opponent's leap from that definitional and global limitation to a proof of energy creation or destruction is a non sequitur, whereas the claim states the established conservation principle documented directly by EIA and NASA (Sources 2 and 6).
Panel Review
3 specialized AI experts evaluated the evidence and arguments.
Reviewer 1 — The Logic Examiner
Sources 2, 3, 4, 6, 10, 11, 12, 17, 18 and 23 directly state the conservation principle that energy is neither created nor destroyed (only transformed), while Sources 1, 5, 7, 8, 15, 26 and 34 show that global conservation can fail to be definable in non-stationary GR spacetimes lacking time-translation symmetry even though local matter energy-momentum remains conserved. The claim therefore holds as the established physical law under the conditions where it is ordinarily applied, with only scope-limited exceptions that do not equate to literal creation or destruction, so the inference supports mostly true.
Reviewer 2 — The Source Auditor
Authoritative educational sources from EIA, NASA, and MIT (Sources 2, 3, 4, and 6) affirm conservation of energy within closed systems or defined domains, while the peer-reviewed discussion indexed by DOI and ScienceDirect (Sources 1 and 5) shows that a global conserved energy is not generally available in curved, nonstationary general-relativistic spacetimes, even though local matter energy-momentum is conserved. Therefore, the unqualified claim is only conditionally true: it accurately states the standard conservation law in its proper domain but overstates it as a universal rule without the general-relativistic qualification.
Reviewer 3 — The Precision Analyst
The claim as worded is the unqualified, universal statement 'Energy can neither be created nor destroyed,' which is precisely how it appears verbatim in Sources 2, 10, 13, 23, and 27, and matches the standard formulation in classical mechanics and thermodynamics as taught by MIT, NASA, OpenStax, and Britannica (Sources 3, 4, 6, 12, 17-20, 24-25); however, the evidence pool also shows a significant scope caveat: in general relativity, particularly non-static spacetimes like the expanding universe, no globally conserved energy quantity can even be defined due to lack of time-translation symmetry (Sources 1, 7, 15, 26, 34), and Source 5 clarifies that only local, not always global, conservation holds. The claim's phrasing omits any domain qualifier ('within an isolated/closed system' or 'in flat spacetime'), so while it is true and precisely worded as the standard classical/thermodynamic law that virtually all textbooks state without qualification, it overstates universality when GR contexts are considered, making it accurate as the commonly understood physical law but imprecise as an unbounded, exceptionless claim about all of physics.
Panel summary
Authoritative government, university, and textbook sources support the statement as the standard conservation law for closed systems. Logic analysis shows that difficulties defining global energy in general relativity do not automatically demonstrate literal energy creation or destruction. Precision analysis nevertheless identifies a real scope limitation: dynamic curved spacetimes may lack time-translation symmetry and therefore a well-defined globally conserved energy. This caveat does not materially overturn the statement's ordinary classical and thermodynamic meaning, but it prevents treating the wording as an exceptionless rule across every physical framework.