# How do you explkain the difference of labels and dynamical variable?

• kof9595995
In summary, the conversation discusses the difference between Eulerian and Lagrangian coordinates in fluid theory and the use of labels and dynamical variables in different theories. The speaker is trying to understand the concept of labels and dynamical variables and how they relate to each other in different theories. They also bring up the idea of defining position as a dynamical variable and its relationship to coordinate labels.
kof9595995
I think I understand this, but when I tried to explain it to a friend I couldn't phrase it in a nice and clear way. How would you guys explain it to others?

I don't understand what you even mean. You need more context I think.

Like in fluid theory, Eulerian coordinate is (sort of?) labels and Lagrangian coordinate is dynamical variables?
Or in old quantum mechanics, when treating EM interation with particle, we write the field as $A(\hat {x})$, where $\hat {x}$ denote the position observable of the particle(so it's a dynamical varible), whereas in QFT we write the field as $\hat{A}(x)$ where x is just a spatial coordinate(a label),as said in http://press.princeton.edu/chapters/s7573.pdf : In quantum field theory, x is a label, not a dynamical variable. The x appearing in ϕ(t, x) corresponds to the label a in qa(t) in quantum mechanics. ...

Emm, it's a bit hard to even express my question clearly, but I'll give it a try: say position x, in order to specify a partcle's postion, which is a dynamical variable(DM for short), we must have a coordinate system, which has all possible values of x, and this coordinate system works like labels, so is it correct to say in order to define a position as a DM it's inevitable to define position labels first? Or is DM is a "subconcept" of coordinate labels?...
I realize my question is ambiguious, please bear with me...

## 1. What are labels and dynamical variables?

Labels and dynamical variables are two concepts used in physics and other sciences to describe and measure the properties of a system. Labels are used to identify and categorize objects or systems, while dynamical variables refer to the measurable quantities that can change over time.

## 2. How do labels and dynamical variables differ?

The main difference between labels and dynamical variables is that labels are fixed and do not change, while dynamical variables can change over time or in different situations. Labels are used to classify or group objects, while dynamical variables are used to measure specific properties or characteristics of a system.

## 3. Can you provide an example of labels and dynamical variables?

Sure! Let's take an example of a car. The label for this car could be its make and model, such as "Toyota Camry." The dynamical variables for the car could include its speed, acceleration, and fuel efficiency, as these are the properties that can change while the label remains the same.

## 4. How are labels and dynamical variables used in scientific research?

Labels and dynamical variables are essential in scientific research as they allow scientists to classify and measure the properties of a system accurately. By using labels, scientists can identify and group objects or systems, while dynamical variables help them understand how these systems behave and how they change over time.

## 5. Can labels and dynamical variables be interchanged?

No, labels and dynamical variables cannot be interchanged as they serve different purposes. Labels are used for identification and classification, while dynamical variables are used for measurement and analysis. However, they are both crucial for understanding and describing the properties of a system in scientific research.

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