I Are vacuum energy and vacuum fluctuations the same thing?

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Vacuum energy and vacuum fluctuations are closely related concepts in quantum physics, but they are not the same. Vacuum energy refers to the energy present in empty space due to quantum fluctuations, while vacuum fluctuations are the temporary changes in energy that occur in a vacuum, leading to the creation and annihilation of virtual particles. The relationship between the two suggests that vacuum fluctuations can be seen as a manifestation of vacuum energy. Understanding this connection is crucial for grasping concepts in quantum field theory and cosmology. Further exploration of these topics can be found in the linked Insights article.
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what is the relationship between vacuum energy and vacuum fluctuation
are vacuum energy and vacuum fluctuations the same thing or is one the the consequence of the other, I understand they are related in some way but I don't know how.
 
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For the quantum state ##|l,m\rangle= |2,0\rangle## the z-component of angular momentum is zero and ##|L^2|=6 \hbar^2##. According to uncertainty it is impossible to determine the values of ##L_x, L_y, L_z## simultaneously. However, we know that ##L_x## and ## L_y##, like ##L_z##, get the values ##(-2,-1,0,1,2) \hbar##. In other words, for the state ##|2,0\rangle## we have ##\vec{L}=(L_x, L_y,0)## with ##L_x## and ## L_y## one of the values ##(-2,-1,0,1,2) \hbar##. But none of these...
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