Recent content by far far away

That’s what I thought at first. But the issue is that the wave equation we usually deal with is the linear wave equation. In reality, there also exist nonlinear wave equations, which behave quite differently.

What do you mean? we can simply set $$u(x, t) = δ(x-ct)$$ This represents a delta pulse moving to the right at speed c. Isn’t this exactly an application of the wave equation?

Thanks. Indeed, the size doesn’t matter. However, if that is taken as the definition, then in my view it’s not a simple or elegant one. It feels more like a dictionary‑style explanation — a semantic description rather than a strictly physical definition — and it makes the discussion...

Yes, it's from Wikipedia https://en.wikipedia.org/wiki/Wave And it does use the word 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...

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...

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.

I beg your pardon, I think your reasoning is flawed. What I quoted is very simple: Notice that there is no strict, universal definition of "equilibrium." Different areas of physics define the equilibrium state differently, because “equilibrium” always depends on what quantity is being disturbed...

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...

If you define a mass density field M(x,t) with equilibrium M=0, then the particle corresponds to a localized disturbance (M=1 at its position). As the particle moves, this disturbance propagates through space and time. Each point in space experiences a temporary change from equilibrium as the...

But this also means a particle can be viewed as a wave if we take the statement from Wikipedia as the definition of waves.

OMG, thanks, that makes sense now. It means we have no rigorous definition here.

Okay, so now the problem becomes that a particle itself doesn’t necessarily have to propagate, right? Then what if I narrow the condition specifically to moving particles?

I understand that physics is grounded in empiricism, and I’m not denying that. But a physical theory, in addition to being based on experiments, must also rely on certain fundamental assumptions and prior conditions. My question here is this: if we assume that Wikipedia’s definition of a wave is...

You're trying to say that a wave must be periodic/oscillating? I don't think so.