Undergrad What does coupling mean in physics?

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SUMMARY

The term "coupling" in physics refers to the interaction between particles or fields, as discussed in Carroll’s "Spacetime and Geometry." Coupling can manifest in various contexts, such as the relationship between matter fields and the curvature of spacetime, as well as in coupling constants and entanglement. Two fields are considered coupled when they appear multiplied in the action, indicating that the equations of motion for one field involve the other. Conversely, decoupled fields exist independently without interaction.

PREREQUISITES
  • Understanding of Einstein's equations and their implications.
  • Familiarity with action principles in physics.
  • Knowledge of equations of motion (EOM) for fields.
  • Basic concepts of quantum entanglement and coupling constants.
NEXT STEPS
  • Research "Einstein's equations and curvature of spacetime" for deeper insights.
  • Study "action principles in field theory" to understand coupling in detail.
  • Explore "coupled harmonic oscillators" to grasp practical examples of coupling.
  • Investigate "quantum entanglement and its implications" for a broader perspective on coupling.
USEFUL FOR

Physicists, students of theoretical physics, and anyone interested in the interactions between particles and fields in the context of modern physics.

luke m
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I am reading Carroll’s Spacetime and Geometry, and I have seen the word “coupled” used multiple times in seemingly different ways. I have gotten the sense that it means some sort of interaction between particles, but Carroll refers to coupling between matter fields and the curvature of spacetime. Furthermore, these are said to to not be directly coupled, even though they are related by Einstein’s equation. I have also seen “coupled” used in the context of coupling constants, entanglement, and forces in the early universe. Is there a rigorous definition for this word?
 
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Two fields are coupled when, in the action, they appear multiplied to each-other in some way. The equations of motion then indicate that the EOM of field A also involves field B.

The other way around: if fields are decoupled, they live "along each other without noticing each-other".
 
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luke m said:
I am reading Carroll’s Spacetime and Geometry, and I have seen the word “coupled” used multiple times in seemingly different ways. I have gotten the sense that it means some sort of interaction between particles, but Carroll refers to coupling between matter fields and the curvature of spacetime. Furthermore, these are said to to not be directly coupled, even though they are related by Einstein’s equation. I have also seen “coupled” used in the context of coupling constants, entanglement, and forces in the early universe. Is there a rigorous definition for this word?

haushofer said:
Two fields are coupled when, in the action, they appear multiplied to each-other in some way. The equations of motion then indicate that the EOM of field A also involves field B.

The other way around: if fields are decoupled, they live "along each other without noticing each-other".
I thought the "common denominator" was lightlike or closer stuff. But apparently "coupled" was used in the context of "entanglement". I think "coupled" much like entanglement, is used poetically in said contexts.
 
As i understand it two or more variables are considered to be coupled whenever they are described by simultaneous equations.
 
luke m said:
Is there a rigorous definition for this word?

Say any two objects (particles, fields, quantum states, etc.) of the same caterory or other, have a correlation, they are coupled. Please take care it is just my interpretation, not the definition of the term.
 
In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...

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