Vacuum Fluctuation Dimensional Constraints

[Chalky]

I understand that vacuum fluctuations can spring into and out of
existence within a sufficiently short period of time, under the
uncertainty constraint.
However, I am currently a little confused over how this constraint is
applied.

1) Does one use del E.del t = h bar (the commutation relationship) or
h bar /2 (the uncertainty relationship)?
2) Does the temporal duration of this vacuum fluctuation thus extend
from - del t to + del t ?
3) Consequently, to the extent that it is potentially meaningful, does
this mean that the maximum spatial extension of the vacuum fluctuation
is 2c del t?
4) Therefore, if this vacuum fluctuation comprises a virtual particle
- antiparticle pair, does this mean they can be treated as having a
typical separation of c del t?
5) Finally, would del E in the above formula be the massenergy of
either particle if real, or the massenergy of the pair if real?

Any advice on this would be appreciated, as these various factor of
two possible differences in interpretation could become vitally
important in determining what types of particles and antiparticles
could potentially be released by a given strength of tidal
gravitational field.

 

[AndyW]

Thank you for your questions regarding vacuum fluctuations and the uncertainty constraint. Let me try to address each of your questions in turn:

1) The uncertainty constraint is typically applied using the uncertainty relationship, which states that the uncertainty in energy (del E) and the uncertainty in time (del t) are related by the constant h bar/2. This is different from the commutation relationship, which is used to describe the behavior of quantum particles.

2) The temporal duration of a vacuum fluctuation can be described as extending from -del t to +del t, as this is the time interval over which the uncertainty in energy is present.

3) Yes, to the extent that it is meaningful, the maximum spatial extension of a vacuum fluctuation can be described as 2c del t. However, it is important to note that the concept of spatial extension may not be applicable to vacuum fluctuations in the same way it is for physical particles.

4) It is important to note that vacuum fluctuations do not necessarily manifest as virtual particle-antiparticle pairs. This is a common analogy used to explain the concept, but it is not a completely accurate representation. The relationship between energy and time in vacuum fluctuations is more complex and cannot be reduced to a simple particle-antiparticle picture.

5) In the formula del E.del t = h bar/2, del E represents the uncertainty in energy, which can include the massenergy of particles. However, as mentioned before, this is a complex relationship and cannot be reduced to a simple interpretation of particles and antiparticles.

I hope this helps to clarify some of your questions about vacuum fluctuations and the uncertainty constraint. It is important to keep in mind that these concepts are complex and can be difficult to fully grasp, even for scientists. If you have further questions or would like to discuss this topic in more detail, please do not hesitate to reach out.

 

[sir-pinski]

1) The uncertainty principle, which states that there is a fundamental limit to how precisely we can measure certain pairs of physical properties, is what leads to the concept of vacuum fluctuations. This means that the uncertainty relationship (h bar/2) is used to describe the time-energy uncertainty of these fluctuations, rather than the commutation relationship (h bar).

2) Yes, the temporal duration of a vacuum fluctuation would extend from - del t to + del t. This means that the fluctuation can exist for a very short period of time before disappearing again.

3) The maximum spatial extension of a vacuum fluctuation would indeed be 2c del t, as this is the distance that light can travel in the time del t.

4) If the vacuum fluctuation comprises a virtual particle-antiparticle pair, they can be treated as having a typical separation of c del t. However, it's important to note that these particles are not real and do not have a physical separation.

5) The del E in the formula would represent the total energy of the virtual particle-antiparticle pair, not just the energy of one particle or the other. This is because the energy of the pair is constantly fluctuating and is not attributed to one specific particle.

In terms of gravitational fields, the strength of the field would not affect the type of particles that can be released. The concept of vacuum fluctuations applies to all types of particles and antiparticles, regardless of the strength of the field.