Physics

Non-conservation of Energy

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Physics

Science

In small blips of time, energy is not necessarily conserved. In the macroscopic world view, all energy is conserved for an isolated system and was <a href="https://en.wikipedia.org/wiki/Noether%27s_theorem">proven</a> to be true. But at the microscopic scale, there seems to be spontaneous energy generation and destruction, which seemingly goes against the "sacred" first law of thermodynamics. But in the macroscopic scale, energy always gets conserved. The reason for this anomaly is explained through the uncertainty principle. The uncertainty principle states that a particle's velocity and position can't be simultaneously measured with precision, which means, that increasing the accuracy of one parameter, decreases the accuracy of the other. A mathematical expression for this principle is <center><b><math display="block"><mrow>&Delta;x.&Delta;p</mrow> <mo>&ge;</mo><mfrac><mrow>&#x210F;</mrow><mrow>2</mrow></mfrac></math></b></center> The right side of the inequality is the reduced Planck constant divided by 2, which is basically a constant and the left side of the equation details the product of the error in position measurement and the error in momentum measurement. So, if you accurately measure the position, meaning error in position approaching 0, the error in momentum will have to increase as the left side has to be greater than a constant value. If we reinterpret the left side, we can also get this relation <center><b><math display="block"><mrow>&Delta;E.&Delta;t</mrow><mo>&ge;</mo><mfrac><mrow>&#x210F;</mrow><mrow>2</mrow></mfrac></math></b></center> If you see this expression, there can be some energy which might get generated(&Delta;E), but more the energy "generated", shorter the time it can stay present, so as to not violate the uncertainty principle. This basically means that some amount of energy can be generated but it also gets destroyed in a quick amount of time. A case where this has been seen is during a <i>barrier penetration</i>. This means that a particle can appear on the other side of a barrier, which has a specific energy requirement. This can also be explained by the wave property of a subatomic particle, which can have a particular probability of appearing at the other side of a barrier, even though it may be minuscule. Considering all of the above, the law of conservation of energy still holds, but it can be stated as, the law holds <i>on average</i>, but in some specific instances of time, there can be generation and destruction of energy.

- Shubham Anuraj, 12:14 AM, 10 Mar, 2022

Science