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“Energy cannot be created.”
The conclusion
The statement accurately expresses the conservation-of-energy principle used throughout ordinary physics: energy changes form rather than being created. It is not strictly universal, because an expanding general-relativistic universe may lack a well-defined globally conserved energy total. That limitation does not establish a conventional process that physically creates energy.
Caveats
- The statement omits the conditions under which energy conservation is formally defined.
- Expanding spacetime may lack a meaningful globally conserved energy total.
- Global nonconservation or undefined energy does not automatically prove physical energy creation.
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Sources
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Instead, the law of conservation of energy says that energy is neither created nor destroyed.
Probably both of these groups are motivated by a view that the conservation of energy (and perhaps likewise the conservation of momentum) is a scientific fact of the form that energy can be neither created nor destroyed.
In the standard ΛCDM model, which relies on the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the energy conservation law for redshifted photons is violated. However, in a cosmological model based on the conformal cosmology (CC) metric, this law remains valid. … Since u = nE and u0 = n0E0, it follows that the energy of individual photons is conserved during cosmic expansion: E = E0 , (22) where E0 is the present-day energy of individual photons. This result holds for any cosmological metric used to describe the expansion of the universe, including both the FLRW and CC metrics [28].
Following Griffiths’ approach, we might say that so far we have merely defined some quantities (Griffiths 1999, p. 509 ff.). The physics really lies in the three corresponding conservation principles associated with these quantities: the principle of conservation of mass, the principle of conservation of energy, the principle of conservation of (linear) momentum.
Following Griffiths’ approach, we might say that so far we have merely defined some quantities (Griffiths 1999, p. 509 ff.). The physics really lies in the three corresponding conservation principles associated with these quantities: the principle of conservation of mass, the principle of conservation of energy, the principle of conservation of (linear) momentum. These principles contain the physics, because each one states that a certain quantity, mass, energy, or momentum, is conserved in all interactions.
At the macro-level, when a lump of soft clay strikes another lump of soft clay, their momentum is conserved but kinetic energy is lost. As noted above, rather than abandon the universality of his third law, Leibniz suggests instead that energy is conserved but redistributed to the minute parts of which the clay is composed.
As a result, it is widely accepted that energy is not locally conserved in general relativity 3, although claims are made that energy is globally conserved during expansion.
Given that, the current consensus among physicists is that the law of energy conservation in GR is not valid.
Within some problem domain, the amount of energy remains constant and energy is neither created nor destroyed.
One of the most important laws in all of physics is the conservation of energy: that energy can change forms, but can never be created nor destroyed. … Only, that’s not true in the expanding Universe: the Universe is different from one moment to the next. As a result, energy is not conserved, with truly cosmic implications. … As the Universe increases in volume, the total amount of “dark energy” increases as the volume increases: a Universe that’s eight times the volume has eight times the amount of energy in it, and as it continues to expand, the energy within the Universe increases without bound as well.
The First Law expresses the conservation of energy and is founded upon the impossibility of creating a machine that can create energy.
While energy conservation remains a robust and well-tested law within local and closed physical systems, its global applicability in an expanding cosmological framework is examined and challenged. … The absence of global time-translation symmetry, as required by Noether’s principle, undermines the theoretical foundation of universal energy conservation.
Energy cannot be created or destroyed, but it can be transformed from one form to another.
Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another.
Energy can neither be created nor destroyed. This principle, called conservation of energy, is one of our most cherished laws of physics. … The situation would be even more complicated if the accountants were to count dark energy, which is what is causing the universe’s expansion to accelerate. The nature and properties of dark energy are still a complete mystery, but it appears that dark energy does not dilute as the universe expands. Thus, as the volume in our membrane increases, the amount of energy in that volume increases as well, with the additional energy seemingly coming out of nowhere!
Energy can neither be created nor destroyed. This principle, called conservation of energy, is one of our most cherished laws of physics. … Thus, the universe does not violate the conservation of energy; rather it lies outside that law's jurisdiction.
The total energy is always conserved in these processes, although different forms of energy are converted into others.
It is 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.
The theorem proves a deep relationship between symmetries and conserved quantities.
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
The invariance of a Hamiltonian H ^ {\displaystyle {\hat {H}}} of an isolated system under time translation implies its energy does not change with the passage of time.
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)
The First Law of Thermodynamics applied to stationary closed systems as a conservation of energy principle.
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.
in all cases we find no satisfactory way to define a (useful) notion of energy that is generically conserved … the conservation of energy were not a fundamental principle of physics … the violation of the conservation law would be wrong
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.
law of conservation of energy: The law stating that the total amount of energy in any isolated system remains constant, and cannot be created or destroyed, although it may change forms.
Although energy cannot be created or destroyed, it can be converted from one form to another.
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.”
The law of conservation of energy states that energy can neither be created nor destroyed; it can only change form.
The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy 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.
The first law of thermodynamics is a statement of the principle of energy conservation tailored to systems where energy enters or exits as heat or work. … The first law of thermodynamics is the familiar conservation of energy principle adapted to thermal systems.
The two Friedmann-equations, however, are not independent of each other because General Relativity presumes that the various forms of energy-densities are locally conserved. … And if you don’t, you don’t get back general relativity, but a modification of general relativity in which energy conservation is violated – in a mathematically consistent way.
The invariance of the Lagrange function of distinct physical fields under parallel translations and Lorentz transformations (which is a consequence of the homogeneity and isotropy of Minkowski space-time) leads, by Noether's theorem, to the energy-momentum tensor and the angular momentum tensor of the field and to corresponding conservations laws for the energy, momentum and angular momentum of the motion. … In classical mechanics, $ n = 1 $ and the coordinate $ x ^ {1} $ is interpreted as time. If the Lagrange function does not depend explicitly on $ x ^ {1} $, then the vector field $ \partial / \partial x ^ {1} $ is a symmetry, and Noether's theorem leads to the law of conservation of energy.
### Plain English paraphrase of the 1st law The universe’s total energy never changes.
►Energy is conserved. This is the first law of thermodynamics.
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 first law of thermodynamics is essentially an energy conservation law.
The first law is a statement of energy conservation.
The first law of thermodynamics is actually the law of conservation of energy stated in a form most useful in thermodynamics.
Time translation symmetry gives conservation of energy; space translation symmetry gives conservation of momentum; rotation symmetry gives conservation of angular momentum, and so on.
We consider the First Law of Thermodynamics applied to stationary closed systems as a conservation of energy principle.
If we have a physical system set up on a table and we notice that we can move the table by any amount in any of the three spatial directions without a↵ecting the dynamics of the system, we can conclude that there is a quantity — called momentum by definition — that remains constant in time. … Hence, if we note that the results of an experiment do not change with the time schedule of the observation, we would expect that there is a quantity — called energy by definition — that remains constant in time.
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. … When the space through which particles move is changing, the total energy of those particles is not conserved.
The Hamiltonian is usually taken to be the energy E of the system, so we see that Noether’s theorem applied to a symmetry under time translation results in energy being the corresponding conserved quantity.
The recommended starting point for any application of the conservation of energy is the rate form of the conservation of energy equation:
It’s the 100th anniversary of the paper in which Noether proved two theorems relating symmetries and conserved quantities: the first is commonly called “Noether’s theorem", while the second concerns what we now call gauge symmetries.
First Law of Thermodynamics Review the broader energy conservation principle used for closed systems, open systems, and thermodynamic cycles.
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Debate
Two AI advocates debated this claim using the research gathered.
Argument for
The claim is the core content of the conservation-of-energy law: the U.S. Energy Information Administration states that energy is “neither created nor destroyed,” and NASA likewise states that, within its applicable physical domain, energy is neither created nor destroyed (Sources 1 and 9). This is independently embedded in the first law of thermodynamics and standard physics instruction, with MIT stating total energy is conserved as forms convert and Stanford's Encyclopedia identifying conservation of energy as a governing physical principle (Sources 17 and 5).
The Proponent's argument commits a hasty generalization fallacy, treating textbook restatements (Sources 1, 9, 17) as if they apply universally, when those very sources implicitly assume closed, local, non-expanding systems and never address cosmological scales. Source 47 (Carroll), Source 7, Source 8, and Source 12 directly rebut this by showing that in general relativity—our best description of the actual universe—energy conservation fails because global time-translation symmetry is absent, meaning the Proponent's cited authorities are simply silent on, not victorious over, the domain where the claim demonstrably breaks down.
Argument against
The claim that 'energy cannot be created' is presented as an absolute universal law, but the physics literature explicitly contradicts this in cosmological contexts: Sean Carroll's analysis (Source 47) states plainly that 'energy is not conserved in general relativity,' Sources 7, 8, and 12 confirm that 'the current consensus among physicists is that the law of energy conservation in GR is not valid' and that global time-translation symmetry breaks down in an expanding universe, and Sources 10 and 15 describe dark energy's total quantity literally increasing without bound as the universe expands—energy seemingly 'coming out of nowhere.' Since the textbook conservation statements (Sources 1, 9, 13, 14, etc.) only hold within closed, local, non-expanding systems and explicitly fail at the cosmological scale where Noether's theorem's required symmetry is absent, the blanket claim 'energy cannot be created' is an oversimplified and, in the most fundamental description of the universe we have, actually false.
The Opponent commits an equivocation fallacy by treating the absence of a well-defined globally conserved energy in an expanding spacetime as evidence that energy is physically created; Sources 7, 8, and 12 address limits on global conservation in general relativity, not an observed creation mechanism. The cited cosmological discussion therefore does not overturn the conservation principle applicable within its stated domains, which EIA and NASA explicitly affirm and which MIT and Stanford describe as governing physical conservation (Sources 1, 9, 17, and 5).
Panel Review
3 specialized AI experts evaluated the evidence and arguments.
Reviewer 1 — The Logic Examiner
Sources 1, 5, 9, and 17 directly support conservation of energy in their applicable systems, while Sources 7, 8, 10, 12, and 15 show that global energy conservation is not generally available in expanding general-relativistic cosmology, but do not directly establish a physical mechanism by which energy is created. Thus the claim is mostly true as the standard conservation principle but is too unqualified to be a universally valid statement across all cosmological settings, and the opponent does not logically convert nonconservation or an undefined global total into demonstrated creation.
Reviewer 2 — The Source Auditor
The overwhelming majority of high-quality, independent sources—EIA (1), NASA (9), Wikipedia physics articles (13,14), Stanford Encyclopedia entries (4,5,6), MIT OCW (17,24), Britannica (20), and dozens of university physics textbooks—affirm that energy cannot be created or destroyed, which is the standard formulation of the first law of thermodynamics as taught and applied in essentially all physical contexts. However, a smaller but credible cluster of physics-literature sources (Sean Carroll's expert commentary in Source 47, the peer-reviewed cosmology paper Source 8, arXiv paper Source 7, and Big Think/Scientific American explainers 10, 15, 16) reliably establish that in general relativity, particularly in the expanding universe, strict global energy conservation via Noether's theorem breaks down due to the absence of time-translation symmetry, meaning the claim as an unqualified universal law is not strictly true at cosmological scales, though this is more a matter of energy conservation being ill-defined/not applicable in GR's most general context than energy literally being observed to be 'created' in a mechanistic sense—as the Proponent's rebuttal correctly notes. Weighing all this, the claim is essentially true within the vast majority of physical contexts (all standard closed and local systems, which is virtually the entirety of applied and everyday physics) but requires qualification at the cosmological/GR scale, so it merits a Mostly True verdict rather than fully True.
Reviewer 3 — The Precision Analyst
The claim asserts as an absolute rule that 'energy cannot be created,' which reflects the standard textbook definition of the conservation of energy (Sources 1, 9, 13, 14). However, the evidence demonstrates that this principle is not universally true; in the context of general relativity and an expanding universe, energy is not conserved and dark energy increases as the universe expands (Sources 7, 8, 10, 12, 15, 47).
Panel summary
Authoritative government, academic, and textbook sources support the statement as the standard conservation-of-energy principle. Logical analysis also shows that the absence of a well-defined globally conserved energy total in expanding spacetime does not itself demonstrate physical energy creation. Precision concerns arise because the wording is universal: global conservation may be undefined or inapplicable in general-relativistic cosmology without time-translation symmetry. That specialized limitation does not materially overturn the statement's meaning in ordinary physics, so the evidence supports Mostly True rather than Mixed.