Experimental proof for Conservation of Total Energy

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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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 6 '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 6 '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 en.wikipedia.org/wiki/Quantum_fluctuation) – cinico Feb 6 '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 6 '14 at 15:03
This question and its answers might be useful. – Ruslan Feb 6 '14 at 15:17

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:

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.

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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 9 '14 at 3:15
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 9 '14 at 4:34
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 9 '14 at 4:59
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 9 '14 at 5:12
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 9 '14 at 7:44

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.

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GR still has conservation of energy-momentum tensor – Jim Feb 6 '14 at 18:13