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# Planck Units: Physics Beyond The Standard Model?

Updated: Oct 8, 2023

Author: Arpan Dey

There are five fundamental constants in physics.

Manipulating the units of the above constants, we can find the Planck natural units. These are the most fundamental units, and provide a rough idea about the value of the units during (or just after) the Big Bang. The Planck natural units are essentially the limits of our physics today. For instance, the Planck length is significant because at shorter distances, quantum fluctuations allowed by the uncertainty principle disrupt the smooth geometry of space which is central to general relativity. On larger scales, quantum mechanics and general relativity independently describe different aspects of the physical reality. But at smaller scales, we don’t have the physics required to describe the physical reality, yet. Similarly, we need a theory that unifies quantum mechanics and general relativity to deal with time intervals smaller than the Planck time.

Planck units arise when effects of quantum field theory and general relativity, both, become considerable, i.e., get to the same order of magnitude.

For massive-enough quantum objects, general relativistic effects can’t be ignored. The particular mass at which this is achieved is the Planck mass. The expression of the Planck mass can be determined by setting the Compton wavelength equal to the Schwarzschild radius. The Compton wavelength is integral to quantum field theory here. If a quantum particle of mass m travels through distances smaller than the Compton wavelength, then the energies get high enough to produce particle-antiparticle pairs out of vacuum. This is when quantum field theory enters the scene.

If a particle with momentum (linear) p moves through distances smaller than the de Broglie wavelength, the particle must be described by quantum mechanics. To find out at what length scale both quantum mechanics and special relativity (which form integral parts of quantum field theory) becomes considerable, we set (m^2)(c^4) equal to (p^2)(c^2). [(E^2) = (m^2)(c^4) + (p^2)(c^2).]

All Planck quantities are expressions in terms of fundamental physical constants. The full explanation of these phenomena and true experimentation on such conditions require physics beyond the Standard Model, which has not yet been entirely achieved.

## References

Pretty Much Physics - YouTube. "Planck Scale | Where QFT and General Relativity Meet | Beyond the Standard Model". 2020. https://youtu.be/la8v2nUSZ6M.