Lorentz Invarience and Spontaneous Symmetry Breaking

In summary, spontaneous symmetry breaking is a phenomenon where small factors can affect the outcome of a system, illustrated by the example of a marble rolling down a Mexican hat. This concept relates to Lorentz invariance and particle invariance, and has been studied in relation to the properties of the Higgs boson in experiments at CERN. There is ongoing research and discussion about the validity and usefulness of spontaneous symmetry breaking in understanding systems and models such as the Standard Model Extension.
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Spontaneous symmetry breakingI’m not sure if I understand spontaneous symmetry breaking.In the context of the Mexican hat (and marble) example, wouldn’t the actual path of the marble down the Mexican hat from the top be determined by several small factors that one would normally not consider (I.e. deformations in the hat due to manufacturing imperfections, temperature in the hat’s material differences causing or caused by the same, an imperceptible breeze from the room’s ventilation, time divots in the marble)?Could someone please explain to me why I’m horribly wrong here?How does this relate to Lorentz invariance in the context of particle invariance?

The idea of a particle altering a magnetic field doesn’t really alter the traditional understanding of Lorentz invariance does it (observational invariance)? Therefore, is this idea of particle invariance generally accepted or even useful? How is it useful?I understand there seem to be properties relating to CERN experiements worth the Higgs boson that may prove and explain spontaneous symmetry breaking?
 
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In other words, can someone explain to me how exactly Spontaneous Symmetry Breaking (as related to Lorentz Invariance and even possibly the Standard Model Extension) has validity?
 

1. What is Lorentz Invariance?

Lorentz Invariance is a fundamental principle in physics that states that the laws of physics remain the same for all observers in uniform motion. This means that the laws of physics are independent of the observer's frame of reference or their relative velocity.

2. What is Spontaneous Symmetry Breaking?

Spontaneous Symmetry Breaking is a phenomenon in physics where a system that is symmetric at a fundamental level is observed to have a lower symmetry in its actual state. This can occur when the system is in a low energy state, causing the symmetry to be broken and leading to new properties and behaviors.

3. How are Lorentz Invariance and Spontaneous Symmetry Breaking related?

Lorentz Invariance and Spontaneous Symmetry Breaking are both fundamental principles in physics that play important roles in understanding the behavior of physical systems. In some cases, Spontaneous Symmetry Breaking can lead to violations of Lorentz Invariance, as the broken symmetry can cause certain physical quantities to vary with direction or time.

4. What are some examples of systems that exhibit Spontaneous Symmetry Breaking?

Some examples of systems that exhibit Spontaneous Symmetry Breaking include magnets, where the symmetry of spin orientations is broken at low temperatures, and superconductors, where the symmetry of electric charge is broken at low temperatures. The Higgs field in particle physics is also thought to undergo Spontaneous Symmetry Breaking, giving rise to the masses of particles.

5. How does Spontaneous Symmetry Breaking contribute to our understanding of the universe?

Spontaneous Symmetry Breaking is a crucial concept in modern physics and has helped us understand many phenomena in the universe, such as the origins of mass, the behavior of phase transitions, and the structure of the early universe. It is also an important tool in the development of theories such as the Standard Model in particle physics and the theory of cosmic inflation in cosmology.

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