Exploring Micro Black Holes and Entropy in Quantum Field Theory

[Micha]

When I read the security report from Cern (not that I am too worried), I came to something, which I do not fully understand:
As we all know, we are save from micro black holes created at the LHC because of Hawking radiation (for one of many reasons). The Cern people push this argument further and say, even if Hawking radiation does not exist, micro black holes will decay by their inverse creation process with a decay time of order 1/mass on general grounds of qm, since no symmetry forbids this. (CPT theorem)
Ok, fine, but what about macroscopic black holes, Their decay time should then be rather enormous. I know, I know, we have to worry very much about entropy here, but how exactly do these entropy arguments enter quantum field theory? Microscopic black holes are often said to be similar to elementary particles. It seems there is some limit here to do so.

 

[AndyW]

Thank you for bringing up this interesting topic. I would like to provide some clarification and information regarding your questions.

First, let me address the concern about micro black holes created at the LHC. It is true that Hawking radiation is one of the reasons why we are safe from these black holes. However, it is not the only reason. The safety of the LHC is ensured by a comprehensive safety assessment conducted by experts in the field, which takes into account all possible scenarios and risks. The probability of creating a micro black hole at the LHC is extremely low and even if one is created, it would evaporate almost instantly due to Hawking radiation.

Moving on to the argument about the decay of micro black holes, it is important to note that the decay time of a black hole is directly related to its mass. As the mass of a black hole decreases, its decay time increases. This means that micro black holes, being the smallest and lightest black holes, have the shortest decay time. On the other hand, macroscopic black holes, being much larger and heavier, have a significantly longer decay time.

Now, let's talk about the role of entropy in quantum field theory. Entropy is a measure of the disorder or randomness in a system. In quantum field theory, entropy plays a crucial role in understanding the behavior of particles and their interactions. The entropy of a system is related to the number of possible states that the system can be in. As the number of states increases, the entropy also increases. In the case of black holes, the entropy is directly related to their mass. As the mass of a black hole increases, so does its entropy. This is why macroscopic black holes have a much longer decay time, as their higher mass results in a higher entropy.

Finally, regarding the comparison between microscopic black holes and elementary particles, it is true that there are some similarities between them. Both are governed by the laws of quantum mechanics and have similar properties such as spin and charge. However, there are also significant differences, such as the fact that black holes have a singularity at their center and are not considered to be fundamental particles.

I hope this helps to clarify your questions. As scientists, it is important for us to continue asking questions and seeking answers to deepen our understanding of the universe. Thank you for your curiosity and interest in this topic.

 

[Entropia]

I find this discussion about exploring micro black holes and entropy in quantum field theory to be very intriguing. It is true that the safety of the LHC has been extensively studied and confirmed by numerous scientific studies, including the potential formation and decay of micro black holes. The argument that even if Hawking radiation does not exist, micro black holes will still decay due to the inverse creation process is a valid one based on the principles of quantum mechanics and the CPT theorem.

However, the concern about macroscopic black holes and their decay time is also a valid one. While the decay time of micro black holes is expected to be relatively short, the decay time of macroscopic black holes would be much longer due to their larger mass. This is where the concept of entropy comes into play. Entropy is a measure of the disorder or randomness of a system and is related to the number of possible microscopic states that a system can have. In the case of black holes, the entropy is directly related to the surface area of the event horizon, which increases with the mass of the black hole.

In quantum field theory, entropy is a fundamental concept and is closely tied to the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time. This means that as a macroscopic black hole decays, its entropy will increase, and therefore the decay process will take a very long time. This is why macroscopic black holes are not a concern at the LHC, as their decay time would be much longer than the age of the universe.

In summary, the concept of entropy plays a crucial role in understanding the decay of black holes, both micro and macroscopic, in the context of quantum field theory. While micro black holes may have a relatively short decay time, the increase in entropy for macroscopic black holes means that their decay time would be extremely long. This is a fascinating area of research and further studies in this field will undoubtedly provide us with a deeper understanding of the fundamental principles governing our universe.