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In physics, the law conservation of energy states that the total energy of an isolated system cannot change—it is said to be conserved over time. (Source : wikipedia(conservation of energy)

And

Truly isolated systems cannot exist in nature, other than allegedly the universe itself, and they are thus hypothetical concepts only. (Source : wikipedia (isolated system)

Clearly depict a loophole in the law of conservation of energy as the law holds in case of isolated systems and apparently these do not exist.

I thought of various practical experiments to inspect the actuality of the law, but in reality I could not think of a single experiment which does not send off energy in form of heat/sound/light out of the system. Even the experiments performed in UCLA here states that some energy will be uncaccounted for in the experiment !

Even a simple experiment of a ball falling down creates heat from friction with air. Clearly the law must hold if we conduct the entire experiment in an isolated system, but these simply do not exist.

Magnetic levitation to experiment with conservation of energy experiment is not an option as the levitation requires energy and going back to source, we come up with the same heat release problem which makes this experiment only a complex version of the first one.

Note : I am not talking about approximations

Since we can not make any sort of isolated system without it leaking/absorbing energy into the surroundings. The discussion of the conservation of energy boils down to the conservation of energy of the entire universe.

Through various texts I came to the conclusion that the total energy of Universe is not a constant. Those texts being (1, 2, 3)

Even the ArxiV paper listed as 3 states only

Despite remaining hesitations about where additional mass could be coming from, on the overall balance of consistency, we conclude that the energy conservation law is better obeyed by means of increasing mass of the universe with its radius Conserves only a type of energy as it suggests increment in mass which is also a type of energy.

I believe this looks extremely like challenging the law of conservation of energy which is supported by neother's theorem among many others. But I just wish to determine whether practically this law is actually valid or not !

I do not expect to get answers of 99.99% conservation with the negligible heat being lost neglected.

I understand that GR does not say energy is conserved but the scales of day to day life and that of GR are different which makes energy conservation at earthly scales even if 99.99% a boon. But this just means that energy conservation depends on the working scale and experiment and ranges from nearly 100% in some to not conserved in various aspects of GR.

Finally the bottom line of question is, can we experimentally prove that energy, total energy is actually conserved ?
(a Yes answer requires a detailed experiment with complete conservation and no loopholes)

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Rijul Gupta
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    A theory can't be proved by experiment, it can only be shown to not contradict given experiment, or disproved. Moreover, the history of science suggests that physical theories are just approximations of laws of nature, and approximations break sooner or later. – Ruslan Feb 06 '14 at 14:53
  • @Ruslan : Do you mean to say that Conservation of Energy is ultimately just an approximation, and under various circunstances be circumvent to produce machines such as even a perpetual motion machine ! – Rijul Gupta Feb 06 '14 at 14:56
  • @rijulgupta I believe what he's trying to say is that the law fits everything we know today, but it might be possible that we find out that in some specific cases this interpretation might fail. For instance, we know that energy fluctuations do temporarly occur (see here https://en.wikipedia.org/wiki/Quantum_fluctuation) – cinico Feb 06 '14 at 15:03
  • I mean to say that it's currently known law, but no one can guarantee that it won't ever broken. In quantum mechanics you already have something which makes this law fuzzy: Heisenberg uncertainty principle. Something might be discovered which would indeed allow making perpetual motion machine, but according to current understanding of nature, it's impossible. – Ruslan Feb 06 '14 at 15:03
  • @cinico : I am trying to say it fits 99.99% the rest going out due to wasteful/resistive forces no one knows where in todays experiments ! – Rijul Gupta Feb 06 '14 at 15:07
  • Energy being conserved means it does not spawn out of nothing nor disappear into nothing. If it is going out due to wasteful/resistive forces, then while we may not know where it went, we know it still exists in the same quantity. Thus 100% conservation – Jim Feb 06 '14 at 15:09
  • @rijulgupta it is usually assumed that that the unmeasured energy is spread as vibrations of matter or radiation. But, if you want an answer to question, according to Heisenberg's uncertainty principle, NO we cannot make an experiment with infinite resolution that proves that 100% of energy is conserved. – cinico Feb 06 '14 at 15:10
  • @Ruslan : Which one are you saying is impossible ? The breaking of law or perpetual motion machine ? Both are related and if either is just an assumption and 100% true in todays understanding only then impossible. Since I am debating that the law goes 99.99% while pushing its boundaries and you agree that the law is just an approximation you can't deny the possibility of ppm even by todays understandings ! – Rijul Gupta Feb 06 '14 at 15:10
  • @rijulgupta PPM defies laws of thermodynamics. Those laws are more strict than conservation of energy. PPM will never exist because entropy – Jim Feb 06 '14 at 15:12
  • @Jim as well as others : You cannot say/assume that it spreads around but is still there, as soon as energy leaks out of your observable system you cannot apply energy conservation in your system and expanding your system to the universe is wasteful as energy is not conserved there ! – Rijul Gupta Feb 06 '14 at 15:14
  • @rijulgupta My sentence should read "according to current understanding of nature, perpetual motion machines are impossible". – Ruslan Feb 06 '14 at 15:16
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    This question and its answers might be useful. – Ruslan Feb 06 '14 at 15:17
  • @rijulgupta unless the energy from my experiment has found a new way of travelling faster than c, I can be reasonably sure that it is still contained within a static, locally flat spacetime. Classically (that is, on scales larger than what apply in Heisenberg's Uncertainty Principle), Noether's Theorem gives us a way to mathematically be certain that energy is conserved in that kind of spacetime. Therefore, I find no logical reason to conclude that the energy leaking out of my experiment has disappeared into nonexistence – Jim Feb 06 '14 at 15:19
  • @Jim : The question is not about ppm. But still ppm are of two types see here ppm of 1st kind is associated with law of conservation of energy while ppm of 2nd kind is assosiated with entropy ! – Rijul Gupta Feb 06 '14 at 15:22
  • @Jim : the debate of conservation of energy at scale of universe is not because energy is running out at speed of light, it is just simply not conserved. It has nothing to do with how fast your energy travels. As soon as energy leaves your system you have to account for a new system and the energy will keep leaking even when you make your system the entire universe ! And your comments are not really targeted towards answering the question but skimming by. – Rijul Gupta Feb 06 '14 at 15:27
  • @Ruslan : you just agreed the current understanding of nature is 99.99% conservation of energy which does not make ppm impossible but give it 0.01% chance ! If you do not agree and say 100% (total) energy is truly conserved you have to prove it, which is my question in first place. – Rijul Gupta Feb 06 '14 at 15:30
  • @rijulgupta I nowhere mentioned a single number. – Ruslan Feb 06 '14 at 15:31
  • I don't have to prove anything. It's current theory that all the energy is conserved. As I said in my first comment, a theory can't be proved, it can only be falsified, so your question is ill-posed. – Ruslan Feb 06 '14 at 15:34
  • @Ruslan : I wrote that you agreed to what I said, not that you said it yourself. And you are just asking me to ask "experiment to disprove conservation of energy" the entire question will be same with a little changes here and there. Even if you can't prove a theory you need to explain why I can't account for all energy in order to support the validity of current law. (It is just a complex way to say what I was saying in previous comments) – Rijul Gupta Feb 06 '14 at 15:48

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Finally the bottom line of question is, can we experimentally prove that energy, total energy is actually conserved ? (a Yes answer requires a detailed experiment with complete conservation and no loopholes)

Elementary particle physicists have been doing this for more than sixty years. Conservation of energy is one of the main constraints that built up the standard model of particle physics.

We have first to agree about "proof". In my above assertion I consider it a "proof" that the law has not been falsified by any of the data used to discover the great symmetries of nature in the standard model. And the number of experiments and events in the experiments are way over the five sigma deviation for statistical proof.

We also have to agree that for any measurement in the real world there will be errors, and all the values measured are accompanied by a +/- of the error of the measurement.

Energy conservation is, within errors, always true in decays. Look at these decays in the bubble chamber of a lambda and an antilambda:

lmdaantilamda

Caption: Bubble chamber photo of the production & decay of a lambda particle & its antimatter equivalent, an antilambda. The particles are produced from the annihilation of an antiproton which enters the picture at bottom. Being neutral, these lambda & antilambda leave no tracks, but they reveal their presence by decaying into charged particles which form V-shaped pairs of tracks. The two "vees" near the bottom of the picture are produced by the antilambda (left) & the lambda. The antilambda decays into an antiproton (left) & a positive pion, the lambda into a proton (left) & a negative pion.

We can measure the momenta of the decay products, with the experimental errors, we can identify the proton(anti) and the pi-(+) by the ionization they leave in the bubble chamber . We have done this in a huge number of experiments and measured the mass of the lamda as

1115.683±0.006 MeV/c**2

It all comes because in elementary particle interactions four momentum is conserved . Fitting interactions with the constraint of four momenta conservation has built up for us the particles and resonances that fit so beautifully into the group representations of the standard model.

anna v
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  • My apologies if my comment is based on wrong understanding of your answer, but haven't energy conservation most doubtful in the realm of sub atomic particles ? I have read many times that due to the necessity of energy conservation we keep on finding new particles to balance the equations, I suppose their might be many particles still not discovered that might be in use to satisfy equations of energy conservation at the scale. If what I am saying is in fact true then woudnt it be wrong to chose these experiments to prove energy conservation ? – Rijul Gupta Mar 09 '14 at 03:15
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    Well, you can stop using your eyes too if you see too many new sights. I have shown the lamdas above because they cannot fall into your argument of "keep finding new particles" . We see them, they are there, we can measure their four vectors, and a bubble chamber is a hands on instrument even for non physicists. Experimental physicists believe the evidence of the highly enginneered detectors at the LHC ( for example) as much as their eyes looking and measuring the bubble chamber pictures by ruler and angular meter. You are free to believe in angels on the tip of a pin, but that is not physics – anna v Mar 09 '14 at 04:34
  • I see that the above experiments is very very loosely like a collision of two balls and then measuring their moments before and after to check energy conservation or other things. Is there in no way anything we are not accounting ? Like in macroscopic balls we leave the heat changes. Since these particles must not be releasing heat, are we accounting for everything ? Maybe some loose photons ? – Rijul Gupta Mar 09 '14 at 04:59
  • Yes we are leaving out little angels which force what we call the decay products of the lambda to always have the mass of the lambda with great accuracy. – anna v Mar 09 '14 at 05:12
  • Then I assert that we accomplish determining mass of lambda but same cannot be said for energy conservation. Bear with me for a moment, at the macroscale in very much elastic collision we leave out very little amounts of heat energy in checking energy conservation or other experiments, this is what I have based my question on that we never actually account for total energy so how can there be any proof for it..... [Continued] – Rijul Gupta Mar 09 '14 at 07:44
  • [Continued]....Now if we reduce the scales millions of times and reach microscopic scales and conduct said experiment with say molecular balls, we would be leaving even smaller heat unnoticed. And finally in sub nuclear matters we are leaving out some photons and some decay products which leave my question as it is. – Rijul Gupta Mar 09 '14 at 07:44
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    You are wrong. The scales of this lamda detection are of the order of weak interactions http://hyperphysics.phy-astr.gsu.edu/hbase/forces/funfor.html look at that 10^-18m . Heat has no meaning in elementary interactions. Heat is an emergent quantity in large numbers of statistics. If there were photons missing the mass would not come accurate. I am no longer going to respond because it is evident that your mind is made up, and not by physics arguments. – anna v Mar 09 '14 at 09:31
  • Its okay if you do not respond, but I did not refer to heat at the scale I just talked of photons and decay products. I did add photons on my own, but you did say in a previous comment that the experiment does not account for some decay products which you referred to as little angels I suppose. If it was a sarcastic comement and we do account for truly everything then I take back what I previously said. Btw my mind is not made up in anything, I have just begun my long journey in the field and I am keeping a very skeptical view so that I do not accept anything very fast. – Rijul Gupta Mar 09 '14 at 10:52
  • the liitle angels was sarcastic, it is the medieval idea that what one does not understand is controlled by angels. Here you find the Feynman diagram of the decay of the lamda http://teachers.web.cern.ch/teachers/archiv/HST2002/feynman/examples.htm#Example%205 Feynman diagrams are the prescription describe the integrals for calculating elementary particle interactions pictorially. lets stop this here then – anna v Mar 09 '14 at 11:40
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No, we cannot prove that energy is perfectly conserved experimentally.

The first problem is that you would have to run an uncountably infinite number of experiments to "prove" that conservation of energy is true. In some hypothetical universe, you might run one trillion experiments where you calculate the energy of, say, a falling ball as well as the energy it imparts to the air on its fall. In this wonderful universe, these two things add up to exactly 100% with no decimals. What if when you hold your tongue out 45 degrees to the left, the ball falls faster or some other ridiculous thing? So, from a philosophical stance, it's not possible to prove any scientific hypothesis/theory/law perfectly. You can "prove" it beyond reasonable doubt, but not perfectly.

A second problem is that of accuracy and precision. Where should we get a machine that measures energy (or some value from which energy can be calculated) to an infinite number of decimal places? You're saying that accounting for 99.99% of the energy is insufficient. I assume that accounting for 99.99999999999% of the energy would also be insufficient? In that case we would need some kind of perfect instrument that could never exist in our universe (so far as we know).

A third problem: ∆E∆t >= hbar/2. Our current understanding of the universe indicates that even if we somehow had perfect equipment, energy can never be measured perfectly. Essentially, the uncertainty in energy multiplied by the uncertainty in time can never be less than hbar/2.

So, what does that all mean? Ultimately, all of science (and therefore physics) is our current best guess. To say that something is absolutely proven beyond any possible doubt is to say that we are no longer open to new information. This goes against everything that science stands for. But does this mean that we're shooting in the dark? Did some crazy person just guess that energy is conserved and we all went with it?

Not quite.

There have been probably hundreds of thousands or millions of measurements of the conservation of energy. Of those many measurements, no set of measurements that disagrees with conservation of energy has ever stood up to serious scrutiny. In science, when we make a measurement we need to also look at the uncertainty in the measurement. Perhaps we have a system where we can measure both the before and after energy of an object, as well as the heat and sound generated by it. We add up all the before energies and all the after energies to find the before is 10 J, and the after is 9.9 J. There. Conservation disproven? The experiment, and any instruments used in it will have some uncertainty. What we should really write is before = 10.0 ± 0.2 J and after = 9.9 ± 0.1 J. Since they agree to within experimental error, all we can say is that conservation does not appear to be violated.

Unfortunately, that's the reality. No measurement can ever be exact. If you think that only accounting for 99.99999% of the energy in a system means that energy isn't actually conserved... there's a small (so small as to be virtually indistinguishable from zero) chance you could be right! In science though, we have to eventually accept certain things as true in order to move on. In a perfect world, every scientist would verify every principle for themselves from first principles. But if that were the case, we would all still be tossing rocks in the air and timing how long it takes them to fall. Perhaps the best argument that conservation of energy works is that planes stay in the air, phones connect to the internet, and the sun rises every morning. It would be amazing if one of the core tenets of physics was found to be extremely incorrect and yet all these things that we've based our physics on actually work.

No physicist can ever impart absolute truth to you. We leave that up to the mathematicians.

MassDefect
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1) Homogeneity of time throughout the universe (electronic transitions of atoms and molecules, then telescopes and spectroscopy).
2) Noether's theorems.
3) Mass-energy is conserved.

However, (1) is not exactly true locally. We live at the bottom of a gravitational potential well. GPS demonstrates that time passes faster when residing higher in that well. General Relativity lacks conservation laws. Magnitude matters! Given the uncontested loophole in Noether, exploit it.

Uncle Al
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