Quantum fluctuations and Inflation

In summary, quantum fluctuations are temporary changes in the amount of energy in a point in space, arising from the uncertainty principle. These fluctuations allow for the creation of particle-antiparticle pairs of virtual particles, which can have measurable effects. In the modern view, energy is always conserved but the eigenstates of the Hamiltonian (energy observable) are not the same as the particle number operators. These fluctuations may have played a role in the origin of the structure of the universe, as suggested by the model of inflation. The success of this model in predicting the form of microwave background fluctuations has led to its widespread acceptance. The interpretation of virtual particles as mathematical artifacts versus physical entities is still a topic of debate, but the difference can be seen
  • #1
rodsika
279
2
Wikipedia defines quantum fluctuations as:

"In quantum physics, a quantum fluctuation is the temporary change in the amount of energy in a point in space,[1] arising from Werner Heisenberg's uncertainty principle.

According to one formulation of the principle, energy and time can be related by the relation

delta E delta t ~ h/2pi

That means that conservation of energy can appear to be violated, but only for small times. This allows the creation of particle-antiparticle pairs of virtual particles. The effects of these particles are measurable, for example, in the effective charge of the electron, different from its "naked" charge.

In the modern view, energy is always conserved, but the eigenstates of the Hamiltonian (energy observable) are not the same as (i.e. the Hamiltonian doesn't commute with) the particle number operators.

Quantum fluctuations may have been very important in the origin of the structure of the universe: according to the model of inflation the ones that existed when inflation began were amplified and formed the seed of all current observed structure."Also I read elsewhere"It is primarily the successful prediction of the form of the microwave background fluctuations that has caused inflation to be generally accepted today by most early universe physicists. Since these small inhomogeneities are what later gave rise to galaxies, stars, and us, all of the structure we see in the universe arose because of quantum fluctuations."

Now question:Virtual particles are supposed to be mathematic artifact of perturbation theory as many emphasized here. But how could virtual particles fluctuations got amplifed and and formed the seed of all current observed structure if they were supposed to be just mathematical artifacts without physical contents??!

Hope someone can settle this once and for all.
 
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  • #2
As the Wikipedia article says, the Hamiltonian does not commute with the number operator. The difference arises in which boundary conditons you choose to impose. You can solve for a steady state in which the solution is a superposition of states with different particle numbers. You may wish to interpret this by saying that virtual particles are continually being created and destroyed.

Or you can start with an initial state with a definite number of particles present and solve for its time evolution. In this case, since the initial state is not an eigenstate of H, real particles will be created.
 

FAQ: Quantum fluctuations and Inflation

What are quantum fluctuations?

Quantum fluctuations refer to the tiny, random changes in the energy levels of particles at the subatomic level. These fluctuations are a fundamental aspect of quantum mechanics and can affect the behavior of particles and systems on a microscopic scale.

How are quantum fluctuations related to inflation?

During the inflationary period of the early universe, quantum fluctuations were amplified and stretched out to a much larger scale, leading to the formation of the large-scale structures we see in the universe today. These fluctuations are thought to be the seeds of the cosmic microwave background radiation and the distribution of galaxies in the universe.

What is the role of quantum fluctuations in the Big Bang theory?

In the Big Bang theory, quantum fluctuations are believed to have played a crucial role in the rapid expansion of the universe. They are thought to have caused small irregularities in the density of matter, which eventually grew into the large-scale structures we see today.

Can quantum fluctuations be observed?

Due to their small scale, quantum fluctuations cannot be directly observed. However, their effects can be detected through indirect measurements, such as the cosmic microwave background radiation and the distribution of galaxies in the universe.

How do quantum fluctuations affect our understanding of the universe?

Quantum fluctuations play a significant role in our understanding of the universe, as they are a fundamental aspect of quantum mechanics and are believed to have played a crucial role in the formation of the universe. The study of these fluctuations can provide insights into the early stages of the universe and help us better understand the laws of physics at the subatomic level.

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