What is Zero Action? What is zero action?

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In summary, "zero action" refers to the minimum change in energy between a system's potential and kinetic energy. In unconstrained motion, the action is always zero, while in constrained motion it is never zero but minimized. The actual value of the action is not important, only that it is minimized, and can be made arbitrarily large or small by adding a constant offset to the potential. It is possible for a system's potential and kinetic energy to have the same function, resulting in a constant action, but this is not commonly seen.
  • #1
Sunfire
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What is "zero action"

Hello All,

I have been reading this thread, trying to understand the concept of action. There is one very intriguing (to me) statement in that thread:
"So your action is the difference between your capability of motion and your actual motion.
The principle of least action says that there is no difference without some sort of constraint - in which case the motion will be such that this difference is as small as possible." /by Simon Bridge/

Do I understand this correctly - the action is always zero for unconstrained motion; and never zero (but minimal) for constrained motion. Is this reasoning true?

Is free fall a constrained motion? Because the action is zero only at y = y_initial / 2, y is the vertical position.

Perhaps someone has an idea...
 
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  • #3
Thank you, UltrafastPED; I read the chapter you suggested. Quite a few good points there. I am still having trouble to understand something, though. What is "zero action"? Does it have any significance?

In the chapter by Feinman, the free falling body moves downwards and its lagrangian changes from negative to positive. At some point (half the initial height), it becomes zero. Does this zero lagrangian have any physical significance?
 
  • #4
The actual value of the action is not important, only that it is minimized. The value of the action can be made arbitrarily large or small simply by adding a constant offset to the potential.
 
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  • #5
DaleSpam said:
The actual value of the action is not important, only that it is minimized. The value of the action can be made arbitrarily large or small simply by adding a constant offset to the potential.

This makes perfect sense.
What if, in a system,
Ep = f(x) - C, C is arbitrary constant
Ek = f(x)
for all x.

Then L = Ek - Ep = C for all x, thus the action remains constant. Does this ever happen?
 
  • #6
In principle, it is possible, but I have never seen such a system. Usually the potential energy is a function of the generalized positions and the kinetic energy is a function of the generalized velocities, so I haven't seen a case where they are the same functions like that.
 

What is Zero Action?

Zero action refers to the absence of any action or activity. It can also be described as a state of inactivity or lack of movement.

Why is Zero Action important in science?

In science, zero action is important because it serves as a baseline or reference point for measuring changes or effects. It allows scientists to compare different states or conditions and observe any differences or effects that may occur.

How is Zero Action measured in scientific experiments?

Zero action can be measured in various ways depending on the specific experiment or study. For example, in physics, zero action may be measured through the use of a motion detector or by tracking the position of an object over time. In biology, it may be measured by observing the absence of a response in an organism.

Can Zero Action ever truly be achieved?

In theory, yes, zero action can be achieved if all factors that could potentially cause movement or activity are eliminated. However, in reality, it is nearly impossible to achieve complete zero action as there are always external forces or factors that may influence a system.

How does Zero Action relate to the laws of motion?

According to Newton's first law of motion, an object at rest will remain at rest unless acted upon by an external force. This means that in order for an object to achieve zero action, there must be an absence of any external forces acting upon it.

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