What are the dimensions of an integral in terms of energy and time?

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Homework Help Overview

The discussion revolves around dimensional analysis, specifically regarding the dimensions of an integral involving energy and time. Participants are examining the implications of integrating a function with respect to time and how the dummy variable affects the dimensional outcome.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning whether the dummy variable in the integral affects the overall dimensions, specifically in the context of the integral of energy with respect to time. There is a discussion about the significance of the resulting dimensions, with references to the concept of action in physics.

Discussion Status

Some participants have provided insights regarding the dimensions of the integral, suggesting that it results in energy times time, which is associated with the concept of action. There is an acknowledgment of different types of actions in physics, indicating a productive exploration of the topic.

Contextual Notes

Participants are navigating the nuances of dimensional analysis and the implications of different interpretations of action in physics. There is a reference to the potential for varying units of action in different contexts, highlighting the complexity of the discussion.

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Just a question on dimensional analysis here.

I believe that when an integral is taken with respect to time for instance, dt appears as a dummy variable yes? Imagine we had

\int E\ dt

Does this have dimensions of energy times time? Or doesn't the dummy variable count?
 
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energy times time isn't an insignificant dimension.
 
Woopydalan said:
energy times time isn't an insignificant dimension.

I beg to differ, energy times time is action.

edit (isn't an insignificant dimension) I thought you said it was.
 
Now can someone answer my question please?
 
help1please said:
Just a question on dimensional analysis here.

I believe that when an integral is taken with respect to time for instance, dt appears as a dummy variable yes? Imagine we had

\int E\ dt

Does this have dimensions of energy times time? Or doesn't the dummy variable count?

Yes, this have dimension of energy times time.
An obvious example is
v=\frac{dx}{dt} \Rightarrow x=\int v dt
Speed is m/s and space is m.

Woopydalan said:
energy times time isn't an insignificant dimension.

This is the dimension of an action!
 

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