Undergrad Understanding the 'vacuum fluctuations'

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Vacuum fluctuations refer to temporary changes in energy levels in empty space, leading to the creation of particle-antiparticle pairs. These fluctuations are often misunderstood, with some claiming they are not valid due to misconceptions about quantum mechanics. To explain this concept to an 11th grader, it's essential to simplify the idea that even "empty" space is dynamic and can produce brief bursts of energy. Clarifying the scientific basis behind vacuum fluctuations can help dispel myths and enhance understanding. Overall, accurately conveying these principles is crucial for effective communication in scientific discussions.
raracon
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Hello!
As you might know or not know I am wroting a paper about the vacuum etc.
Now I am having trouble understanding the fluctuations in the vacuum.

I've seen many tell me that the fluctuations are not correct etc., but why? And how can I phrase it so that someone in 11h grade would understand?
 
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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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