Testing the Limits of Special Relativity: Questions and Insights

In summary, our current understanding of special relativity is not violated by the integration over paths or the use of virtual particles and fields in loop integrations.
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1. Consider a correlation function between two points `A(x1,t1)` and `B(x2,t2)`, we need to integrate over paths which could be infinite long. But the time length `(t1-t2)` is finite, so if A and B are the coordinates of one single particle, then all of the paths from A to B should be time-like curves, the maximum length should be `c*(t1-t2)`, which is not infinitely long. It seems special relativity could be violated here.


2. Consider any loop integration of higher order correction to a Feynman digram calculation, we have infinitely many off-shell processes and "internal virtual particles", which could be created and annihilated without taking any time. Does this violate special relativity?

Is there any better reason than simply saying these are "internal virtual processes"? They do affect our final real physical observations!

for the second case, one might argue that no particles here but only fluctuating fields? But when, where, and how are those fields created? Do these fields exist even before our universe was born? This picture is not that physically clear to me.

Any better insight?
 
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  • #2


I would like to address these concerns and provide some insight into the concepts of correlation functions and loop integrations in the context of special relativity.

Firstly, in the case of correlation functions, it is important to note that the integration over paths is not actually infinite. In fact, it is only infinite in the mathematical sense, as it involves an infinite number of infinitesimal steps. In reality, the integration is limited by the maximum speed of light, which is `c`. This means that the maximum length of any path between two points `A` and `B` is `c*(t1-t2)`, as stated in the forum post. This does not violate special relativity, as it is still within the constraints of the theory.

Moreover, in the context of special relativity, time-like curves refer to paths that are consistent with the maximum speed of light. This means that any path between two points must follow the constraints of special relativity, and cannot violate its principles.

Moving on to the concept of loop integrations, it is important to understand that these are calculations in quantum field theory, which is a framework that combines the principles of quantum mechanics and special relativity. In this framework, particles are described as excitations of quantum fields, and the concept of "virtual particles" is used to represent the interactions between these fields.

It is important to note that these virtual particles are not actual particles, but rather mathematical constructs used to describe the interactions between quantum fields. They do not violate special relativity, as they are not actual physical particles that can travel faster than the speed of light.

Additionally, the concept of fields existing before the universe was born is a topic of ongoing research and is still not fully understood. However, it is important to note that these fields are not physical entities that exist in space-time, but rather mathematical constructs used to describe the interactions between particles.

In conclusion, the concepts of correlation functions and loop integrations do not violate special relativity, as they are consistent with the principles of the theory. The use of mathematical constructs, such as virtual particles and fields, is a necessary tool in understanding the interactions between particles in the quantum world. Further research and study in this area will continue to provide better insight into these concepts.
 

1) What is Special Relativity?

Special Relativity is a theory developed by Albert Einstein in 1905 that explains the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion, regardless of their relative velocities.

2) Why is it important to test the limits of Special Relativity?

Testing the limits of Special Relativity allows us to better understand the fundamental principles of the universe and potentially uncover new insights that could lead to advancements in science and technology. It also helps to validate the accuracy of the theory and confirm its applicability in different scenarios.

3) How can we test the limits of Special Relativity?

One way to test the limits of Special Relativity is through experiments that measure the effects of time dilation and length contraction at high speeds. Other methods include studying the behavior of particles at high energies and observing the behavior of objects in extreme gravitational fields.

4) What are some potential insights that could be gained from testing the limits of Special Relativity?

Testing the limits of Special Relativity could potentially lead to insights about the nature of space and time, the origins of the universe, and the possibility of faster-than-light travel. It could also help to refine our understanding of other theories, such as general relativity and quantum mechanics.

5) Are there any known limitations to Special Relativity?

While Special Relativity has been extensively tested and confirmed, there are still some unresolved questions and limitations, such as the inability to fully reconcile it with general relativity and the existence of paradoxes such as the twin paradox. Continual testing and refinement of the theory may help to address these limitations in the future.

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