## On Conservation

Conservation of different properties in nature immensely simplifies calculations to the point where some are impossible without the consideration of them. In some cases, it seems completely intuitive and impossible not to consider. However, not only are there many conservations laws unknown to many but there are also, in some sense, “violations” to these laws.

To start with the most known conservation laws, there is momentum, angular momentum, energy, mass (although this is not true in reality), and charge. However, in particle physics, there is also conservation of properties like lepton number and baryon number which help calculate particle collisions or decay products. These are usually just grouped and called the conservation of flavor in quantum chromodynamics. As an extension of this for solely strong and electromagnetic interactions, there is also the conservation of strangeness, charm, topness, bottomness, and isospin. Most of these are intrinsic properties of particles. They are usually defined by discrete quantum numbers. All of these help in the consideration of particle interactions. It is interesting to see that there exists such unique conservation properties in nature.

There is however sometimes a “violation” as mentioned before of conservation in space. The Heisenberg uncertainty principle relating the deviation of position and momentum is defined by the equation $\inline&space;\sigma&space;_x&space;\sigma_p&space;\geq&space;\frac{h}{4\pi}$. However, this principle can be restated to describe the uncertainty between energy and time as $\inline&space;\sigma&space;_E&space;\sigma_t&space;\geq&space;\frac{h}{4\pi}$. If one knows the exact energy of a particle, the time of arrival is unknown and the same visa versa. In the vacuum of space, photons or particle and antiparticle pairs pop in and out of existence for brief periods of time temporarily breaking the conservation of energy. Photons merely disappear while particles and antiparticles annihilate. These are called quantum vacuum fluctuations. The time period in which this occurs is so small that the uncertainty principle prevents the detection of this break in the conservation. Even detecting the particle would require adding energy so this would not show that the conservation was broken. In any case, the universe can break these laws if it does it quick enough.

Although the concept may seem useless, it is actually a very important concept when looking into concepts like the Casimir effect and the evaporation of black holes. The Casimir effect describes imaginary forces that form in very small vacuums and the evaporation of black holes occurs when these particles pairs form on the boundary of the event horizon causing one of the particles to shoot in and the other to leave. This process however is not completely confirmed and has complications which will not be acknowledged in this article.

Altogether, property conservation over time is not as simple as it seems and should be studied more closely in certain system to have a more holistic idea of the state of the system.

If you want to learn more or see where I got it from, watch this Sixty Symbols video or read the book “Fundamentals of Physics” by Halliday & Resnick. It should be in the “Books” category of the site.