failexam said:Why do quantum fluctuations of fields arise at high energies and temperatures?
failexam said:Why are the sizes of these quantum fluctuations approximately the Planck size?
It's actually the reverse.failexam said:Why do quantum fluctuations of fields arise at high energies and temperatures?
The particular fluctuations you seem to be talking about are zero-point fluctuations of the inflaton field. If you want a really in-depth look, here's one source:failexam said:What is the mathematical formulation of these quantum fluctuations?
I think that's more of an assumption than anything. How big they were depends more upon the properties of inflation: the fluctuations would have been close to the size of the horizon at the time of inflation. But we don't know what that horizon size was yet because we don't know for sure what the energy scale of inflation was.failexam said:Why are the sizes of these quantum fluctuations approximately the Planck size?
If by "size" you mean wavelength, then there is no assumption that they must be Planck size, though that is generally how they are treated (i.e. you can have a quantum fluctuation of any wavelength). The thing is that larger wavelength fluctuations spend less time within the horizon during inflation and so are amplified much less than Planck sized fluctuations. How to evolve the fluctuation from sub-Planckian to super-Planckian scales is known as the "trans-Planckian problem", since, lacking a UV-complete theory of gravity, we don't actually know how sub-Planckian fluctuations evolve.failexam said:Why are the sizes of these quantum fluctuations approximately the Planck size?
Quantum fluctuations refer to the spontaneous and temporary changes in the energy levels of particles at a subatomic scale. In the early universe, these fluctuations played a crucial role in the formation of the universe's structure, including the formation of galaxies and clusters of galaxies.
Quantum fluctuations are a necessary component of the Big Bang theory. According to the theory, the universe began as a singularity, a point of infinite density and temperature. As the universe rapidly expanded, it also underwent quantum fluctuations, which eventually led to the formation of matter and energy in the universe.
Yes, quantum fluctuations have been observed through various experiments and observations. For example, the cosmic microwave background radiation, which is considered the remnant of the Big Bang, shows slight variations in temperature that are a result of quantum fluctuations in the early universe.
No, quantum fluctuations do not violate the laws of physics. They are a natural occurrence at a subatomic scale and are governed by the principles of quantum mechanics. These fluctuations are essential for understanding the behavior of particles and the formation of the universe.
Studying quantum fluctuations in the early universe allows scientists to gain insights into the fundamental processes that led to the formation of the universe. It also helps in refining and improving our understanding of the laws of physics, particularly in the realm of quantum mechanics.