Talk:Conservation of energy

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[edit] Formula

[edit] This doesn't make any sense!

The classical form of the energy conservation law (and in fact the notion of energy in the first place) is directly related (through the corresponding equation of motion) to the force- concept describing the interaction of particles. The latter can be shown to be necessarily instantaneous (i.e. Newtonian) as otherwise one would not be able to define a force objectively, i.e. independent of the state of motion of the observer. One can therefore say that the law of energy conservation does, by definition, only strictly hold for this case of a static interaction of particles, but is not more than an arbitrary ad hoc concept if applied to other situations, in particular those involving light: two light waves can be made to extinguish each other completely if superposed with the correct phase, which proves that a form of energy conservation does not apply here.

--- Roadrunner

This is not true. First of all, light cannot "extinguish". What you're talking about is destructive interference which doesn't destroy the light. For example, if you have one beam of light traveling right, and one traveling left, and they destrvtively interfere at a point, then an observer at that point won't see any light. However, the light will continue on after they "hit" eachother, in their original path - ie no energy is gained or lost, there is only a place in time and space where the light won't be observed.
The thing about conservation of energy is that it doesn't *need* to figure in any forces. The force can last decades, but after the force stops, the total energy will remain the same as it was before. I hope that helped. Fresheneesz 09:54, 20 April 2006 (UTC)
It is somewhat paradoxical when you are saying that destructive interference doesn't destroy light. Surely, for the particular example you mentioned it doesn't destroy it everywhere, but it violates already energy conservation when intermittently the energy disappears and then reappears. In principle, you can in fact arrange the situation such that the emission from two light sources vanishes completely (e.g. by putting two sources that are 180 deg out of phase sufficiently close together; you could in principle even make emissions of different frequencies disappear if you have a continuous emission spectrum and the emissions are somehow phase-locked; the radiation would then disappear with a time dependence as given by the Fourier-transform of the frequency spectrum). -Thomas-
I think you're going to have to simplify this problem and provide some math. So far as I can see, you're just wrong. Are you proposing that two sources of coherrent light 180 degrees out of phase will combine into darkness??
Well, the maths is actually the easiest part of it:
sin(k*x-ω*t) + sin(k*x-ω*t +π) =0. -Thomas-
More importantly and generally however, the concept of 'energy' in the first place requires that the principles of classical mechanics (and in particular that of a 'potential energy' ) can be applied. Noether's theorem purports to prove a general law of energy conservation, but it actually implicitly assumes that the physical system is a classical one as it uses the Lagrange function L which in turn is defined as the difference between the kinetic energy T and potential energy V (L=T-V). Now if a force field can be derived as the gradient of a potential energy function, it must be necessarily a conservative force. In other words, the use of Lagrangians (or Hamiltonians) *implies* already energy conservation, so it is no surprise if this is the result of Noether's theorem. However, it is obvious that this can not be applied to light as you can't define a conservative force field and hence a potential energy for it (in order for a force to be conservative, the curl of the force field must be zero; however, according to Maxwell's equations curl(E)=-dB/dt (Faraday's law)).(see my page http://www.physicsmyths.org.uk/conservation.htm for more). -Thomas-
There is nothing in the Lagrange function which demands a conservative force field per se. If the field isn't consevative, like a time varying B field, then the particle simply picks up kinetic energy continuously at the expense of energy being tapped from the field. That's how dB/dt (nonconservative) makes electrons circulate in the windings of a generator, or particles go faster and faster in a cyclotron. And light, which has a non-zero vector potential, does the same things to charged particles--- consider Compton scattering. But the photon which leaves in a Compton process does not have the same energy as the photon which goes in-- the difference is imparted to the electron, and that's the end of it. None of it violates conservation of energy. When you write down the Lagrangian of an EM interaction in field terms, you must do it for the WHOLE system, which means the kinetic energy is the energy of the accelerated particle, and the potential energy is the complete potential of the particle in the field, which is its charge multiplied by both scalar potential and vector potential terms. If the particle gains in kinetic energy, it produces a field which causes the vector potential to suffer. In a generator, those electrons getting their energy from dB/dt turn into a current which generates its own opposing B field and "back-emf" in the coils that supply it. The energy transferred comes out of the changing B field and the vector potential associated with it. Anyway, buy yourself a copy of Jackson, for Heavensake. Steve 18:41, 23 June 2006 (UTC)
First of all, the fact that in certain cases one observes experimentally some kind of 'energy conservation' in connection with light (or electromagnetic fields in general) is not the point of discussion here, but the assertion that a general principle in this sense follows theoretically from certain fundamental assumptions in physics.
It is in fact quite obvious that you are already implying energy conservation when you are using a Lagrangian, as the latter contains, as already mentioned, the potential energy. Using the notion of a 'potential energy' (in fact that of an 'energy' in the first place) would make no sense whatsoever unless you imply energy conservation i.e. assume that the system can be described like a conservative mechanical system. If one is not actually dealing with mechanical systems (e.g. in the case of light), one may be lucky in certain cases that this works out in reality, but there is no guarantee for it. -Thomas-
I have worked myself on the analysis of airglow observations where the intensity of the airglow exceeds that expected from energy conservation (i.e. assuming E=h*nu ) by more than one order of magnitude (see http://www.plasmaphysics.org.uk/papers/airglow2.htm#34 ; Chpt.3.4). The point is simply that the energy differences in the atom correspond to set frequencies of the radiative emissions but in general not to set intensities (i.e. amplitudes of the emitted electromagnetic wave). Furthermore, on detection, the apparent intensity also depends for instance on the coherency of the radiation. Completely incoherent radiation will simply not be detected anymore, i.e. for all practical purposes it is non-existent (see http://www.plasmaphysics.org.uk/photoionization.htm ).
By the way, the paragraph you commented on was literally taken from my website, but not by me. -Thomas-


[edit] energy equivalence / conservation of energy?

I'm not a physicist or an engineer, but is conservation of energy really considered a special form of mass/energy equivalence? I would have expected it to be the other way around -- conservation of energy seems to apply in far more situations than mass/energy equivalence. Could somebody clarify this for me? --Fastfission 05:11, 6 Apr 2005 (UTC)

I see your confusion. That section was worded ambiguously. Check the way it is written now, and let me know if the matter is still unclear. — Cortonin | Talk 14:34, 6 Apr 2005 (UTC)

nguyenvantien

[edit] Separating Conservation of energy from First law

I have it in my mind to split this into two articles:

Any comments? Cutler 18:48, July 14, 2005 (UTC)

[edit] Removed paragraph

I removed the following paragraph:

I Loris Erik Kent Hemlof dissgree with the law of conservation of energy; that energy may never be created or destroyed only transformed. The repulsive force which keeps the universe expanding seems to be created in a vacume from nothing. Gravity seems to create from nothing the heat and pressure inside the sun to convert through fusion single atoms into higher atomic density elements. The strong and week atomic forces also seem to create energy from nothing. Perminant magnets attract and repel without any consumption of mass. All that is required to transform these forces into electricity or directed motive force is a method of turning off and on these forces. All energy is either free energy or an end product of free energy. For example fission is a product of uranium which is formed in a sun from gravity. Fusion is not a net producer but a consumer of energy. The effort to create energy from fusion should be directed into other new energy technologies. Coal is created from plants energy, from photosynthess, from sunlight, from gravity. The part which seems to be correct is that energy is not destroyed but transformed into elements or dissipated throughout the universe.

I encourage the author to find sources for this claim and cite them, without such citations it constitutes original research and cannot be included in wikipedia. Thanks for your interest. --best, kevin [kzollman][talk] 00:54, 12 December 2005 (UTC)

[edit] Antimatter

How does E = mc^2 relate to the energy created by the annhilation of matter and antimatter? 62.249.242.232 09:49, 21 December 2005 (UTC)

its the maximum amount of energy that can be emitted by such an annihilation (assuming the particles and antiparticles have no velocity - cause that would add more energy). In particle physics, matter and energy are the same thing, so in an annihilation like that you'd probably get a whole lot of light, but perhaps some other weird stuff like quarks or neutrinos or who knows what. Fresheneesz 10:00, 20 April 2006 (UTC)

[edit] Twin Towers claim

The events of September 11, 2001 appear to cast serious doubt on the scientific validity of conservation of energy. Calculations have shown the falling twin-towers expended far more energy than was originally available in the form of an elevated mass (gravitational potential energy). According to more modern theory, "conservation of energy" is subsumed and invalidated by "progressive collapse".

No, the events of September 11, 2001 do not appear to cast serious doubt on the scientific validity of conservation of energy. Which calculations are you talking about? According to WHICH more modern theory, "conservation of energy" is subsumed and invalidated by "progressive collapse"? Please, this is an encyclopedia, there is no room for speculations based on "I heard...", "somebody told me..", "they say..." —Preceding unsigned comment added by 76.26.73.179 (talk) 22:39, 4 September 2007 (UTC)

Such an extravagent claim demands some citation or authority.Cutler 09:49, 3 January 2006 (UTC)

I removed the paragraph. Jobh 11:37, 3 January 2006 (UTC)

I put the extravagent paragraph back, this time with the appropriate references. It is true ladies and gentlemen, the scientific community is almost unanimous in agreement that the twin towers crushed themselves, an obvious revocation of conservation of energy. There are "conspiracy theorists" who claim that energy was added to the twin towers via explosives (thus preserving conservation of energy), but such wild speculation has no place in a scientific article.

Thanks for providing the citations. A much better engineer than I once said something to the effect that engineering is the art of forming materials that we cannot accurately characterise into geometries that we cannot exactly specify while trying to convince the public that they will perform adequately in environments that we cannot truly assess. I think that the principle of conservation of energy survives these interesting calculations (published in some very "grey" non-peer-reviewed website). What is illustrated is just how difficult it is to establish an exact energy balance other than under experimental conditions. I have reframed the contribution. Please sign posts on talk pages by typing four tildes ~~~~. The date/ time and your username will then appear automatically. Cutler 23:34, 3 January 2006 (UTC)

Yes, Cutler, you've convinced me of my error. You are correct, conservation of energy DOES survive the Hoffman and Trumpman papers! Therefore, the 3 WTC "collapses" were controlled demolitions after all, and it is the official theory of 9-11 which must go. Clearly it has to be one or the other, no?

69.238.209.182 03:00, 4 January 2006 (UTC)

Discussion of 9-11 theories is interesting but doesn't belong here. May I suggest 9/11 conspiracy theories#World Trade Center towers where it's already covered? I don't mind a section on the practicality of large scale engineering energy budgeting, but it should be at the bottom, and preferrably use a less controversial example to avoid, well, controversy. Jobh 11:53, 4 January 2006 (UTC)

Wikipedia has strict guidelines about remaining NPOV. Avoidance of the most important scientific event in Amercian history would violate this, sorry. The discussion belongs here because the Wikipedia account of 9-11 hinges crucially on a violation of conservation of energy, and cannot be true. Or can it? Maybe Bazant and Zhou, Scientific American, FEMA, NIST, Poplular Mechanics are correct after all, and conservation of energy is doomed. We can't have a Wikipedia that is self-contradictory, we must resolve this. Does the official version of events violate conservation of energy, or doesn't it?

I've flip-flopped again. I think you guys are wrong, and the vast majority of mainstream scientists are correct. Each falling twin tower had about 100,000 kW/h of GPE, and manufactured >1,000,000 kW/h out of thin air. Conservation of energy is dead. I'm citing Bazant and Zhou.

69.238.209.182 16:14, 4 January 2006 (UTC)

WTC7.net is a nonscientific site which publishes minority theories about the 9/11 attacks. It is not a valid scientific reference and it has no business in this article. Neither Jim Hoffman nor Wayne Trumpman is a peer-reviewed scientist. Rhobite 18:45, 5 January 2006 (UTC)

Well, how about Steven Jones then ?

http://www.wtc7.net/articles/stevenjones_b7.html

Jones is a respected and published physics professor at BYU. In his paper, he points out that none of the official theories account for loss of momentum or angular momentum.

As to Hoffman, et al being "minority", this is an unsupported claim. As far as I can tell, a MAJORITY of the scientific papers which analyze the 911 collapses conclude that something is amiss with the gravity-driven theory. Please note that the FEMA, NIST and 911 commission reports do NOT analyze the collapses, merely the events leading up TO the collapses.

Please, if I have missed scientific literature on any of the 3 structural collapses that occured on 911, post links here.

208.57.142.128 19:22, 8 January 2006 (UTC)

I have removed an added sentence referencing the twin towers. [1] It was inappropriately added to a section describing the law, which as formalized never discusses skyscrapers. With respect to this later paper, it is not questioning conservation of energy, but rather concluding that there must have been explosives in the building. This is therefore, not an argument about conservation of energy, but rather one about the 9-11 attacks and should go to the appropriate pages. I hope that .128 can understand, while we strive to have a neutral point of view, this does not mean that every mildly relevant thing should be in every article. It is my opionion that this theory about the 9-11 attacks deserves mention, but not in an article about the conservation of engery. --best, kevin [kzollman][talk] 20:32, 8 January 2006 (UTC)

It is my opinion that it does deserve mention in an article on conservation of energy. The "law as formalized" is refuted. You have hundreds of photographs and dozens of videos of clear refutations of the conservation of energy, and they all involve skyscrapers. Scientific history is full of examples of discarded theories which failed to stand up to experiment and data. According to the rules, we must not allow speculation and conspiracy theories to clog up a scientific article. Since speculation and conspiracy theories are the only alternative to modifying conservation of energy, we must modify conservation of energy. You simply cannot have it both ways, it is unscientific to do so.

I appreciate your persistence. I suggest that your read wikipedia's guidlines on original research and verifiability. Unless there is a peer reviewed scientific publication supporting your claim that conservation of energy is refuted by the events of 9-11, it does not warrent inclusion in this article. The article you suplied above by Steven Jones does not assert that conservation of energy is refuted, but instead concludes that there were explosives in the towers. I understand that you wish to use the same argument to refute conservation of energy, but that is not the same as that argument appearing in a journal. --best, kevin [kzollman][talk] 00:05, 9 January 2006 (UTC)

I get all that, Kzolllman. Aware of all that, and aware that the article on "collpase of the WTC" has been singled out as being a "good article" and is considered for "article of the day", and noticing that that article is completely and utterly at odds with this one (as anyone with intellectual honesty will agree), I set out to resolve matters. Matters have not been resolved, but I will admit here in writing that the problem is with the other article. Conservation of energy is safe and sound, it is the theory of 9-11 that is unscientific hogwash. One cannot accept the "official" theory of 9-11 AND maintain a belief in conservation of energy. It is my sincere hope that you and others will help correct the scientific fallacies rampant in that article, as it is at odds with this one, which is great.

69.238.209.182 01:54, 9 January 2006 (UTC)

An event in which thousands of innocent people were burned, crushed, or died from falling from a great height should not be cavalierly or offhandedly used to discuss a crank theory in a Wikipedia article.Lestrade 03:35, 10 February 2006 (UTC)Lestrade
Shut up, using a tragedy as a front for trying to dismiss a valid claim is already done enough by our own government and has no place in Wikipedia. Thanks. --vex5 17:45, 14 March 2006 (UTC)
Unquestionably, this article is not the place for such speculation. -- SCZenz 23:45, 14 March 2006 (UTC)
Why do you so? Is it because this is is the first time in over a century that the laws of physics are seriously questioned? Or maybe it's because the pure fundamental structure of the conservation of energy has been rejected by many respectable minds after the 9/11 attacks? --vex5 05:51, 15 March 2006 (UTC)
The laws of physics are not seriously questioned by the event of 9/11 and they are far from that. Do you wonder why the real respectable minds in physics have not made a statement about it? Because it is a waste of time. I am a physicist with several years of training in this field and although I am not one of those respectable minds, even I find this 9/11 violation of the conservation of energy ridiculous. I urge you to rather research, but not only reading half-science articles, but instead try to understand the mathematical background of this phenomenon and you will find out how ridiculous this is. By the way, algebra and 1 year of calculus will not help at all, real physics takes more, much more than that, so please take some time to do your research because this is not a space to educate you or correct your indeficiencies in science, real and serious science. —Preceding unsigned comment added by 76.26.73.179 (talk) 22:54, 4 September 2007 (UTC)
Take it to the 9/11 pages. Noone is seriously questioning the laws of physics, its just a sarcastic attack on the US government. 137.138.46.155 12:45, 23 August 2006 (UTC)

[edit] theory?

I always thought that the Conservation of Energy was billed a theory, and not a 'fundamental law' in physics? Is this correct, since this 'law' cannot be proven with Newtonian physics? --vex5 20:00, 9 March 2006 (UTC)

Actually it follows from Neweton's laws. I just checked this on paper, and it works nicely. -- SCZenz 23:44, 14 March 2006 (UTC)
Please ellaborate. --vex5 05:50, 15 March 2006 (UTC)
In newtonian physics it does indeed follow from newton's laws. Equal and opposite reactions to forces embodies the conservation of energy, and object in motion stays in motion embodies conservation of momentum. If an object hits another, one forces the other, and vice versa - this is a transfer of energy - an equal transfer of energy. Since energy has no sign, the "opposite" part doesn't apply to it really, but it does apply to momentum. The conservation laws are all bundled up in newton's 3 laws.
These are considered fundemental laws nowadays. Of course, we've gone much farter than newtonian physics - and i'm pretty sure that there has not been a verifiable case of violation of this law. Sometimes you hear of physicists "creating" particles from "nowhere". I think that what the "media" means is that physicists transfer large kinetic energy of particles such as an electron, into larger particles with less kinetic energy. Mass goes up, kinetic energy must go down, or potential energy - either one. Fresheneesz 10:10, 20 April 2006 (UTC)

[edit] the conservation of energy-momentum???

This article says that its sometimes called the "conservation of energy-momentum". Is this right? Where does momentum fit in? I'm pretty sure this is a mistake. Fresheneesz 10:16, 20 April 2006 (UTC)

It's not a mistake. Translation invariance in Minkowski space entails both conservation of energy and conservation of momentum. The conservation law resulting from this symmetry is sometimes called "conservation of energy-momentum" (though I don't like that name). The larger law (energy-momentum) is more general than the particular law (energy), so it isn't quite right to say "the conservation of energy is sometimes called the conservation of energy-momentum". On the other hand, I don't think the article says that, so we might be OK. -lethe talk + 10:06, 27 April 2006 (UTC)

[edit] another nonsensical statement

This article (in the intro) has

"Law of conservation of energy is a mathematical consequence of continuous translational symmetry of time (no moment of time is different from any other)."

What does that mean? How does it help the article? Its very obscure. I'll actually remove it now, and we can discuss on how to change it so it makes sense. Fresheneesz 10:17, 20 April 2006 (UTC)

What it is trying to say is There are many physical phenomena that can best be understood in terms of a universal principle of conservation of energy. Further, the aesthetically appealing and empirically supported principle that the laws of physics are invariant under time translation (see Symmetry in physics#Spacetime symmetries can be shown mathematically to entail the conservation of energy. - but this is a subsection, not in the intro. Cutler 11:34, 20 April 2006 (UTC)
Maybe we should include a link to Noether's theorem if this is mentioned? As that should explain the derivation of conservation laws from invariance principles.137.138.46.155 12:47, 23 August 2006 (UTC)
Yes, such a link is a good idea. --Michael C. Price talk 12:54, 23 August 2006 (UTC)

[edit] Conditions on conservation?

I was wondering if conservation of momentum only holds in inertial reference frames. For example, given a stationary ball 1 a stationary star, and a moving ball 2 - if ball 2 hits ball one, then ball one jumps frames and now sees the star moving as well as ball 2. Since the star is now also moving, energy has been "created". 68.6.112.70 08:55, 27 April 2006 (UTC)

That's right, momentum (and energy) are not generally conserved in non-inertial frames. The general condition is this: momentum is conserved in systems that are translation invariant, and energy is conserved in systems that are invariant under shifts in time. An accelerating system is not invariant under translations in the direction of acceleration, so momentum is not conserved in that direction. It is invariant under translations in transverse directions, so momentum is conserved in those directions. -lethe talk + 09:57, 27 April 2006 (UTC)
Shall we add something to that effect about the conditions under which conservation holds? Becuase, I posed that ball one, ball two question to my physics teacher (teaching relativity and quantum mechanics) and he said that conservation always holds and that "theres something wrong in your assumptions but I can't see it". He is obviously wrong (which I find disturbing), but it shows that the assumptions people have of when conservation is relevant is not always the same. Fresheneesz 18:43, 27 April 2006 (UTC)
Currently the article states "Conversely, theories which do not have time translation symmetry result in lack of conservation of energy." Does that not meet your needs? (I sympathize with you for having a physics teacher who doesn't know physics. Probably you shouldn't take any more physics classes from that prof.) -lethe talk + 20:02, 27 April 2006 (UTC)
Well, ideally that sentence could be written in a more understandable way - translational symmetry is a term that I would think most people don't understand. Thanks for the sympathy. Fresheneesz 10:31, 28 April 2006 (UTC)
Hmmm... well, which bit is confusing you: translation, invariant, or theory? Or something else? Translation in space is the change of coordinates like x → x + a. Translation in time is a shift of the time parameter like t → t + t0. The term "invariant" refers to stuff that stays the same when you change the coordinates. Kinetic energy stays the same if you translate in space or time, but distance from the origin doesn't. The part of the theory which is supposed to be invariant varies, depending on the technical description you want to use, but one version is kinetic energy plus potential energy. Free particles have no potential energy, so there's just kinetic energy. That's invariant under both translation in space and in time, so free particles have constant energy and constant momentum. The Kepler problem has a potential energy like 1/r2, which doesn't change under shifts in time, so energy stays the same for a Kepler particle. It is not invariant under translations in space, so its momentum is not conserved. The general form of this idea is given by Noether's theorem, which says roughly that to every symmetry, there is a conserved quantity, and every conserved quantity (for some definition of quantity) gives rise to a symmetry. That's essentially what the statement says. I'm not sure of an easier way to convey the idea of "time translation invariance", but I agree that it is phrased awkwardly. I've reworded the sentence. How do you like it now? -lethe talk + 11:28, 28 April 2006 (UTC)
Its better, but I was under the impression that all theories or physical laws are invarient over time. Also, I don't see how that connects to ones frame of reference. Fresheneesz 20:37, 28 April 2006 (UTC)
Let me give you some situations which are not invariant over time: the equation of state of a star (stars are constantly losing energy), the temperature inside an over while it's preheating, the potential energy of an electron in an atom when the atom is in an external magnetic field which is oscillating, the motion of the planets around the sun (when you take into account friction), the entire universe (it's expanding). In summary, lots of systems are time dependent and your impression that all systems are time independent shows a disconnect of common sense with physical intuition: certainly you know that all kinds of things change. Now consider a physical model in the vicinity of any changing system, and you've got a time independent system. You can often get a time independent system from a time dependent one by incorporating the time dependent external bit into your system and using a more complex model. This never reaches an exactly time independent model, since the entire universe is expanding. There are no closed systems which are exactly time independent. Energy is never conserved exactly.
As far as what "reference frames" means. Well, my reference frame refers to those coordinates with which I make measurements. One of them is time. If I measure time since the birth of christ, that's one reference frame. If I measure time since the founding of the city, that's another reference frame. If density of Helium is the same whether I measure it in 2006 AD or 2006 AUC, then I say that's constant. If the name of Pope is different depending on which calendar I use, then I say that is not constant. Some stuff is constant, other stuff is not. -lethe talk + 21:41, 28 April 2006 (UTC)
Of course I understand that things change. However, laws of physics (as far as i know) only apply to closed systems. All the systems you described represent open systems (usually with implied boundries on the things outside the sysem which can act on the system of interest). In real life, there is only one closed system, the entire universe. Once you try to analyze an open system, you lose the ability to predict what will happen. This is why in all experiments, experimenters try to produce a situation that is approximately closed.
I also know what a reference frame is. My point was that - even considering a closed system - conservation of energy doesn't hold if the reference frame isn't inertial (if it changes speeds). 68.6.112.70 00:24, 29 April 2006 (UTC)

OK, I think I see better what your concern is now. There are two ways to look at this. Imagine a free particle which is not accelerating in an inertial frame. Its energy is 1/2mv2. The basic principles of physics say that its laws of motion are the same in any inertial frame. Therefore you expect the energy to be conserved under any change of coordinates to another inertial frame, where the energy will be 1/2mv2 again. In this view, you can either agree not to try to do physics in non-inertial frames (or just say that the laws don't hold in that frame). You can also recognize that even noninertial frames are just another choice of coordinates, and the equivalence principle says that any frame is valid, except that the transformation rules will be more complicated. If you're willing to put up with that, then you can still say that energy is conserved. So like if you boost to reference frame accelerating at a, the energy gets changed to 1/2m(v–at)2, and this quantity is still conserved. This is the point of view you have to use in relativity theory, where any reference frame (inertial or not) is allowed, and energy is conserved in all frames (if it is conserved in any of them).

If you don't want to deal with the machinery of transformations into noninertial frames, then you have another option. You can view the noninertial frame as your new inertial frame. This introduces pseudoforces (like the centrifugal force in a rotating frame). In this frame, the pseudoforces are some how external, and they destroy the symmetries of the old inertial frame. In this frame, energy need not be conserved. This is the process by which gravity in relativity theory (which is simply the motion of free particles along geodesics) is turned into a force in Newtonian gravity. Thus, if you move to the accelerating frame, the particle is accelerating with rate a, so its energy is constantly increasing due to the pseudoforce.

To sum up: conservation of energy is a mathematical property of the theory, it doesn't depend on what coordinates you use (even noninertial). This is done in relativity. Nevertheless, we often like to view noninertial systems as inertial systems attached to noninertial frames. This is done in transitioning from relativity to Newton. In that view, pseudoforces are introduced, symmetry is gone, conservation fails. -lethe talk + 09:25, 29 April 2006 (UTC)

Ahh, that is very interesting. \frac{1}{2} m(v - \bar{a} t)^2 seems to fix everything. But I think that implies one special initial-rest frame from which all others are judged. I'll have to think about that. Fresheneesz 01:19, 30 April 2006 (UTC)
You should think of it this way: there is a physical number, called energy, which is conserved. You can do anything you want to the coordinates, and all that does is make the formula for the coordinates change. The value that the formula takes is still the same. You're absolutely correct that the formula I gave you ties me to a particular reference frame. Energy is not invariant, it depends on your reference frame. Change frame, change formula. Energy is covariant, not invariant. Whether or not energy is conserved is a consequence of the symmetry of the theory, not of the symmetry of the coordinates you chose to describe the theory. Still, there is a point of view in which you like to pick a privileged inertial frame and form for the theory, and if you violate that choice, you can violate the form (and conservation can fail). Depends on where you stand on the issue of active versus passive transformations, which is something of a philosophical question. -lethe talk + 03:36, 30 April 2006 (UTC)

[edit] Intermediate Gauge Bosons

If energy cannot be created or destroyed then where do the carries for the four fundamental forces come from ? The gluons that exert the strong force upon quarks and hold nuclei together can't jsut appear if this law holds true. Naming them virtual particles and then creating an uncertainty principle seems to me to show that the law is wrong and an attempt is being made to hide this fact. Should it jsut not be ammended that energy can be created and destroyed but only by gauge bosons? I don't have a very good physics background but my teacher can't really help with my queries so any feedback would be appreciated

The conservation laws are true statistically, and only within the uncertainty principle. So a given particle of energy E can appear out of vacuum for a period of approximately t = E/h, so long as it all goes back before the time is over. It's sort of like a rule that an employee can embezzle all they want from petty cash, so long as it's back in the box to be counted the next morning. This rule holds not just for guage bosons, but any kind of bosons, and for fermions also. Electrons and positrons pop in and out of the vacuum and disappear again, for short times. This has real physical effects-- it slightly changes the spectra of elements, and it actually causes some of the "spontaneous" emission effects. By the way, remember that massless guage particles can last a longer time because they have less energy. This is one of the things that makes electrical fields so long-range compared with nuclear fields. "Virtual" particles can have real and big and lasting amounts of energy-- there's energy in static charges like the charge on a big capacitor, and also a lot of energy in the magnetic field of your MRI machine, and both both cases all that energy is "made" of virtual photons. The missing energy in atomic nuclei is basically virtual pions in hydrogen that have been destroyed in fusion. Virtual photons transfer all the energy between the windings of a transformer, too. In that sense, these things are as real as "real" particles, and have all the same energy, in many circumstances. It's just that a virtual particle is sort of like a check rather than a coin, and if the energy it contains is used (check is cashed), then there's a time limit on how long it takes to show up as a draft on nature's books. But energy conservation and Planck's constant set that time-- it's not arbitrary. 22:26, 18 May 2006 (UTC)

[edit] I don't believe the law!

If the law is true that energy cannot be created or destroyed - I have a theory that proves the theory wrong. This theory takes place in an airless room. If a book is dropped in an airless room, the kinetic energy won't be transferred into any type of energy than a minute amount of heat energy due to some friction. If you say that heat will be transferred into the air...well that's not possible is it?-since it is an airless room. At the moment, the book which had potential energy before it was dropped now has no potential because it is on the ground. The book has also lost kinetic energy.

My question is where has the energy gone...has it been transferred as some unknown type of energy?

--Dhanish007 09:16, 29 June 2006 (UTC)

As I understand it, the gravitational potential energy was converted to work when it was dropped. After all, couldn't you attach the book to a pulley system and have it do work? Splintercellguy 10:51, 29 June 2006 (UTC)
All of the energy of the book has been converted to heat. When the book hits the ground, its kinetic energy is converted to sound waves which propagate inside the book and the ground, since there is no air. These sound waves are then absorbed by the book and the ground and converted to heat. PAR 13:57, 29 June 2006 (UTC)

Err, have you guys forgotten about the object the book hits? It will absorb all the book's energy and start moving Bipedia 01:19, 26 October 2006 (UTC)

Well, not exactly, but it is a fact that the motion of the earth has not been taken into account. There is the book and the earth separated by some distance. Neither are moving, so their total momentum is zero. Then the book is "let go" and the book goes most of the distance until it hits the earth. The earth moves an extremely small amount upwards to meet the book. When they collide, both stop moving relative to each other, and all of what was once potential energy of the book-earth system now becomes sound waves inside the book and the earth, which dissipate to become heat energy. But in their final position, neither are moving. (conservation of momentum) (forget orbital and rotational motions). PAR 03:03, 26 October 2006 (UTC)

[edit] Creating energy

I think that the fact that energy can be created by destroying matter was included in his law, but he put that "energy cannot be created or destroyed". They both seem to contradict! It just doesn't make sense to me at all!

Well, it can be if you consider mass to be a sort of frozen energy. It's mass+energy which is conserved. This is total energy (if you count any mass as energy also) OR it's also total mass (if you don't let any energy or mass out of the system, the mass doesn't change, even if some energy is liberated inside).
This is confusing, yes. See the main article mass in special relativity.Steve 02:33, 7 July 2006 (UTC)
The thing is that matter is energy. So when you speak of energy being able to be created by destroying matter, that's only because you didn't consider the matter as being energy. But in reality it is, and you're just looking at energy in different forms. The statement "energy can't be created/destroyed" refers to energy in the strictest sense, i.e. including matter. So that's why things don't contradict. -- Northgrove 13:37, 19 August 2006 (UTC)


[edit] Conservation of kinetic energy

This article doesn't give the formula of the change of kinetic energy in relation to the potential energy. -Iopq 08:50, 9 October 2006 (UTC)

Mentioned now in the intro sentence.--Michael C. Price talk 10:04, 9 October 2006 (UTC)

[edit] Section ordering

Would anyone object to the current order of the sections Modern physics (which appears first) and Thermodynamics be reversed to follow chronological order? --Michael C. Price talk 10:04, 9 October 2006 (UTC)

[edit] Wait a sec...

If energy cannot be created or destroyed, then why does anything exist in the first place? JONJONAUG 13:47, 15 November 2006 (UTC)

Because the universe has zero total energy -- probably. See cosmic inflation and note that gravitational energy is usually negative.--Michael C. Price talk 16:23, 15 November 2006 (UTC)
Quantum fluctuation universe as the ultimate free lunch. A joke that never palls. Beats hell out of universe as God's screensaver program, waiting for him to get back from lunch and hit the space bar. SBHarris 16:58, 9 December 2006 (UTC)

[edit] How does this apply in real life?

You have all done outstanding work with the level of detail and intricacy in this article, however, after reading the piece in its entirety, I am still very curious as to how the law of conservation of energy appears out in the world. That is, if I were to go about my normal routine, where would I see this law in practice? Thank you all. 66.10.167.1 20:47, 10 December 2006 (UTC)

You see it everytime you apply a force through a distance. That either stores up energy (like lifting a bucket of water) which can be released later, or it puts something into motion (like a auto which must then be stopped). Stored energy and energy of motion are interconvertable into each other. But either can also be turned into heat (as in your brakepads). When this happens, the heat has an equivalent in terms of mass and motion, or force and distance. And some of the heat can be turned back into these, but not all. In any case, all this stuff is the same thing in different forms. It connects to mass itself, so it's apparently some kind of "stuff" like mass is. Ultimately, it's hard to say what. SBHarris 22:04, 10 December 2006 (UTC)
Thank you. Another quick one: how would you see this law applied in something like, say, a roller coaster? Would the energy be converted into "stuff" like the noise that the coaster makes? 66.10.167.1 22:45, 10 December 2006 (UTC)
Some would. Both the kinetic energy (velocity-related) and the potential energy (height related) of the roller coaster are available to make any other kind of stuff that has energy. This includes heat and noise. The more heat and noise made, the faster the thing loses height or comes to a stop to sap this energy to do the job.SBHarris 22:49, 10 December 2006 (UTC)

[edit] inertial reference frame

This is my first wikipedia edit. Yay! Anyway, the main reason for my edit was that the statement that "Each of the four components... of [the energy-momentum 4-vector] is separately conserved" jumped out at me because, by itself, it makes it sound like there is something special/invariant about the components. However, the components vary depending on the observer's inertial reference frame. The vector itself is conserved, but it's components vary with your coordinate system. So I thought it required that qualification. I was also wondering whether it needs an explicit mention that energy depends on your reference frame.

The sentence after, I tweaked a little because I felt that it wasn't immediately clear what "The latter" refered to. Also I changed "associated with rest mass" to "is the rest mass" because the 4-momentum is equal to the rest mass times the 4-velocity, which has unit length.

Finally, the sentence, "The relativistic energy of a single massive particle contains a term related to its rest mass in addition to its kinetic energy of motion," is a little hand-wavy. It seems like it would be better to just give the formula. The formula is found half-way down the page on mass in special relativity. Is it possible to link to that spot on that page? —The preceding unsigned comment was added by Jgompert (talk • contribs) 07:13, 12 December 2006 (UTC).

[edit] Overlap between this article and the vis viva article

It seems that some of the text in this article overlaps text in the vis viva article. Are there any guidlines regarding duplication of material/internal plagiarism within Wikipedia? Robert K S 16:00, 11 April 2007 (UTC)