Does a moving particle count as a wave?

[renormalize]

"Equilibrium is essentially the baseline we choose for a given physical system." If you disagree with this statement, I would appreciate it if you could provide a more rigorous alternative definition of equilibrium.

This is a more rigorous (https://www.britannica.com/science/equilibrium-physics):
equilibrium, in physics, the condition of a system when neither its state of motion nor its internal energy state tends to change with time. A simple mechanical body is said to be in equilibrium if it experiences neither linear acceleration nor angular acceleration; unless it is disturbed by an outside force, it will continue in that condition indefinitely. For a single particle, equilibrium arises if the vector sum of all forces acting upon the particle is zero. A rigid body (by definition distinguished from a particle in having the property of extension) is considered to be in equilibrium if, in addition to the states listed for the particle above, the vector sum of all torques acting on the body equals zero so that its state of rotational motion remains constant. An equilibrium is said to be stable if small, externally induced displacements from that state produce forces that tend to oppose the displacement and return the body or particle to the equilibrium state. Examples include a weight suspended by a spring or a brick lying on a level surface. An equilibrium is unstable if the least departure produces forces that tend to increase the displacement. An example is a ball bearing balanced on the edge of a razor blade.

 

[far far away]

This is a more rigorous (https://www.britannica.com/science/equilibrium-physics):
equilibrium, in physics, the condition of a system when neither its state of motion nor its internal energy state tends to change with time. A simple mechanical body is said to be in equilibrium if it experiences neither linear acceleration nor angular acceleration; unless it is disturbed by an outside force, it will continue in that condition indefinitely. For a single particle, equilibrium arises if the vector sum of all forces acting upon the particle is zero. A rigid body (by definition distinguished from a particle in having the property of extension) is considered to be in equilibrium if, in addition to the states listed for the particle above, the vector sum of all torques acting on the body equals zero so that its state of rotational motion remains constant. An equilibrium is said to be stable if small, externally induced displacements from that state produce forces that tend to oppose the displacement and return the body or particle to the equilibrium state. Examples include a weight suspended by a spring or a brick lying on a level surface. An equilibrium is unstable if the least departure produces forces that tend to increase the displacement. An example is a ball bearing balanced on the edge of a razor blade.

Thank you, but the resource you shared reads more like an extended introduction or overview of the concept of equilibrium rather than a single, compact definition.

 

[A.T.]

"Equilibrium is essentially the baseline we choose for a given physical system."

What is the source of that definition? Or did you just make it up yourself? It sounds like the definition of "reference value/state", which is a much broader concept than "equilibrium".

Thank you, but the resource you shared reads more like an extended introduction or overview of the concept of equilibrium

Which is exactly what you seem to need, given that your idea of what "equilibrium" means in physics is so far away from the common use of the word.

 

[far far away]

No. A theory is an attempt to describe the way Nature behaves. The words you use to describe that behavior have no effect on the theory itself.


Why? It's just an argument about semantics. Words can be defined to mean anything you want. Definitions are always true.

I definitely agree with you that "a theory is an attempt to describe the way Nature behaves".

However, the statement “the words you use to describe that behavior have no effect on the theory itself” is, in my view, imprecise. The meaning of words matters, because we rely on them to convey the theory. If the definition of a word is incorrect or inconsistent, then the theory cannot be communicated accurately.
For example, take the word force. In physics, force is rigorously defined as the vector quantity that causes acceleration, expressed mathematically as . If someone instead defines force loosely as “energy” or “effort,” they may confuse it with work or power. The mathematics of Newton’s laws remains unchanged, but the incorrect definition of the word leads to a distorted understanding of the theory.

 

[far far away]

What is the source of that definition? Or did you just make it up yourself? It sounds like the definition of "reference value/state", which is a much broader concept than "equilibrium".

I made that definition up myself, and I apologize — that was my mistake. Logically, I shouldn’t have done that. What I was really trying to do was to look across different fields of study, notice the patterns in how they treat “equilibrium,” and then summarize those patterns into a general idea of what equilibrium seems to represent.

The equilibrium situation is something we can define ourselves. It's the baseline or "rest state" against which disturbances are measured.
- In a string, equilibrium is the string lying straight with no displacement.
- In air, equilibrium is uniform pressure and density everywhere.
- In EM fields, equilibrium might be zero field or a constant background field.
- In this mass density example, I chose equilibrium as M(x,t)=0. That’s perfectly valid — it means "no mass density anywhere." Then the particle appears as a localized deviation (M=1 at its position).

Which is exactly what you seem to need, given that your idea of what "equilibrium" means in physics is so far away from the common use of the word.

I beg your pardon again. Perhaps I used the wrong word — I shouldn’t have chosen “equilibrium” here. What I really meant was a term to describe the baseline or reference state of a wave. My intention was to capture the idea of a rest state against which disturbances are measured, not to redefine equilibrium itself.

 

[A.T.]

I shouldn’t have chosen “equilibrium” here.

I thought you were quoting a Wikipedia definition of a "wave" that was using "equilibrium":

According to the definition of a wave from Wikipedia:
A wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities.

Is this an actual quote from Wikipedia? Can you provide a link to it?

 

[renormalize]

Thank you, but the resource you shared reads more like an extended introduction or overview of the concept of equilibrium rather than a single, compact definition.

A definition is whatever size it needs to be to achieve clarity. Why do you get to define the rules for the "size" of a definition?

 

[berkeman]

I beg your pardon, I think your reasoning is flawed.

- In this mass density example, I chose equilibrium as M(x,t)=0. That’s perfectly valid — it means "no mass density anywhere." Then the particle appears as a localized deviation (M=1 at its position).

Apologies if this has been asked already in this thread, but how do you apply the Wave Equation to your mass density discontinuity (your particle)?

https://en.wikipedia.org/wiki/Wave_equation

 

[gmax137]

@berkeman you beat me to it. An operational definition of "a wave" is, "a phenomenon consistent with the wave equation."