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)
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.
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)