What exactly does a degree of freedom mean?

In summary, degrees of freedom refer to independent variables that describe a system. They are used to distinguish between otherwise identical particles and the number of degrees of freedom can be reduced by constraints. Spin is one example of a degree of freedom, and it is also used in quantum mechanics to describe the state of a particle. Linear algebra and general relativity also use degrees of freedom to describe properties of a system.
  • #1
HomogenousCow
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I have seen this word used in every context, is there a solid definition??
 
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  • #2
Dimension I believe.

3 degrees of freedom = 3 dimensions.

Edit: Opps. I didn't realize this was the quantum physics section. I learned about degrees of freedom from a linear algebra textbook.
 
  • #3
Yeah well Shankar refers to spin as a degree of freedom, I believe I read somehwere that Born did thr same
 
  • #4
Also, although not related to QM, my GR text refers to the free indices of the metric tensor as "degrees of freedom" in that section about what we can make zero with arbitrary coordinates.
 
  • #5
HomogenousCow said:
Yeah well Shankar refers to spin as a degree of freedom, I believe I read somehwere that Born did thr same

My understanding of degree of freedom is that any dynamic variable that can distinguish two otherwise identical particles can be thought of as a degree of freedom. For example, two electrons at the same orbital state could be further distinguished by their spin, so spin is another degree of freedom.
 
  • #6
A degree of freedom is an independent variable that describes some property of a system. The number of the collection of these independent variables that are required to completely describe a system, are called “the degrees of freedom of the system”. For each constraint that you impose the degrees of freedom reduce by one. For example, for an ideal gas in a closed container, there are the variables of “volume”, “pressure” and “temperature”, which can take any positive value. But, the three of them are not independent, because they are related by the state equation, so one variable can be expressed as a function of the other two. So the ideal gas has two degrees of freedom.
 

1. What is the definition of a degree of freedom?

A degree of freedom is a measure of the number of independent variables or parameters that are needed to fully describe a system. In other words, it represents the number of ways a system can move or change without violating any constraints.

2. How is a degree of freedom different from dimensions?

Dimensions refer to physical measurements such as length, width, and height, while a degree of freedom is a mathematical concept that represents the number of variables needed to describe a system. In some cases, a degree of freedom may correspond to a physical dimension, but they are not always the same.

3. How does the number of degrees of freedom affect a system?

The number of degrees of freedom can affect the behavior and stability of a system. For example, a system with fewer degrees of freedom may be more rigid and less able to change or adapt, while a system with more degrees of freedom may be more flexible and have a wider range of possible states.

4. Can a system have an infinite number of degrees of freedom?

No, a system cannot have an infinite number of degrees of freedom. This is because there are always constraints and limitations that restrict the number of possible variables that can describe a system. However, in some cases, the number of degrees of freedom may be so large that it is considered practically infinite.

5. How is the concept of degrees of freedom used in science and engineering?

The concept of degrees of freedom is used in various fields of science and engineering to analyze and understand the behavior of complex systems. It is particularly useful in systems with multiple variables and constraints, such as in thermodynamics, mechanics, and statistics. By determining the number of degrees of freedom, scientists and engineers can better understand and predict the behavior of a system.

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