Does a moving particle count as a wave?

[far far away]

TL;DR

I am not talking about quantum mechanics

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


Now, imagine a particle as a disturbance in mass density that propagates through space and time. From this perspective, I cannot think of a single reason why this could not be interpreted as a wave.

 

[Ibix]

A classical particle won't diffract when passing through a slit. In particular, it will not pass through a slit that is narrower than the particle, whereas a wave would pass something through.

 

[A.T.]

Now, imagine a particle as a disturbance in mass density that propagates through space and time.

What equilibrium is being disturbed here? Non-uniform mass distributions can be in equilibrium, so changing the mass distribution is not necessarily disturbing an equilibrium.

 

[martinbn]

TL;DR: I am not talking about quantum mechanics

From this perspective, I cannot think of a single reason why this could not be interpreted as a wave.

This way any change can be interpreted as a wave. It would be so general that it would be a useless terminology.

 

[kuruman]

TL;DR: I am not talking about quantum mechanics

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

So I googled "What is a wave?" and this is what I got. If you go by this more complete AI overview and not by what Wikipedia says, your question is answered.

 

[jingcai]

A moving particle is not a wave; a particle is just a particle. A wave is a state exhibited by a particle when it loses the structure that sustains its condensed form. Scattered photons with depleted energy give rise to energy waves.

 

[kuruman]

A wave is a state exhibited by a particle when it loses the structure that sustains its condensed form.

I don't know what that means.

For example, an ice cube is a collection of water molecules in "condensed form." If I add enough heat to un-sustain the condensed form by converting the ice cube into steam, do the free H₂O molecules constitute a wave?

I am sure you will say no, so let's take this further. I can un-sustain the "condensed form" of a water molecule further by zapping it with an electrical discharge to get a H⁺ ion and a OH^- ion. Is that a wave? Do I need to un-sustain the condensed form of the proton (H⁺) into quarks to get a wave?

You see where this is going.

 

[russ_watters]

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

The first word of the next sentence of the article is "periodic". I guess what you are implying/asking is whether a wave can be non-periodic/oscillating. I don't think so.

 

[far far away]

A classical particle won't diffract when passing through a slit. In particular, it will not pass through a slit that is narrower than the particle, whereas a wave would pass something through.

Thanks and that's a good point. It's true that in the case you mentioned, the particle can not pass through the slit, but that conclusion is empirical rather than something that follows directly from the definition. According to the definition of wave, there's no restriction that would prevent a particle from passing through the slit. So your argument is indeed correct, but not valid in this context.

What I am asking here is not about the phenomenon or experimental results but the nature of how we fundamentally recognize a classical wave. The definition speaks nothing about whether a wave should pass through a slit or not.

 

[far far away]

What equilibrium is being disturbed here? Non-uniform mass distributions can be in equilibrium, so changing the mass distribution is not necessarily disturbing an equilibrium.

The disturbed equilibrium here is the lump of mass‑density moving through space. In this picture, the mass itself is the wave quantity, just as the electric field is the wave quantity in an electromagnetic wave. Do you see what I mean? Or I misunderstand what you are trying to point out?

 

[far far away]

This way any change can be interpreted as a wave. It would be so general that it would be a useless terminology.

That’s exactly why my question arises. According to that definition, everything could be considered a wave, and I’m trying to determine whether that’s actually true. If it is true, then great — the theory becomes simpler. If it’s not true, then I want to understand what breaks the argument.

 

[far far away]

So I googled "What is a wave?" and this is what I got. If you go by this more complete AI overview and not by what Wikipedia says, your question is answered.

View attachment 370758

I’ve already asked several AIs before coming here—probably more than you did—and none of their answers were satisfying. The AI responses usually distinguish between two types of waves: linear waves and nonlinear waves. For linear waves, it’s true that they transfer energy without transporting matter. However, for nonlinear waves, such as those described by the Korteweg–de Vries (KdV) equation, matter can indeed be transported.

So matter transport should not be the key issue here, unless the AI explanation is simply incorrect. And this actually matches the idea in the Wikipedia definition.

 

[far far away]

A moving particle is not a wave; a particle is just a particle. A wave is a state exhibited by a particle when it loses the structure that sustains its condensed form. Scattered photons with depleted energy give rise to energy waves.

Your argument fails because you ignored the definition I provided.

 

[far far away]

The first word of the next sentence of the article is "periodic". I guess what you are implying/asking is whether a wave can be non-periodic/oscillating. I don't think so.

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

 

[Ibix]

that conclusion is empirical rather than something that follows directly from the definition.

Particles don't necessarily propagate.

Physics is an empirical science. A pool ball won't pass through a gap smaller than its size, a sound or water wave will, usually in an altered state. You can stop a particle and pick it up in your hands. Wave vs particle is a useful classification rooted in our experience of the world.

 

[far far away]

Particles don't necessarily propagate.

Physics is an empirical science. A pool ball won't pass through a gap smaller than its size, a sound or water wave will, usually in an altered state. You can stop a particle and pick it up in your hands. Wave vs particle is a useful classification rooted in our experience of the world.

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 valid, then is the statement “a particle can also be understood as a wave” internally consistent, or does it contain a flaw? Our intuitive classification of waves and particles is not part of what I’m discussing since it isn’t strict enough for this discussion.

 

[Ibix]

if we assume that Wikipedia’s definition of a wave is valid, then is the statement “a particle can also be understood as a wave” internally consistent, or does it contain a flaw?

Particles don't necessarily propagate, as I said in the post you quoted.

 

[Gavran]

"While waves are ubiquitous features of physical systems, no single definition adequately describes the topic."
(from Wikipedia)

 

[far far away]

Particles don't necessarily propagate, as I said in the post you quoted.

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?

 

[far far away]

View attachment 370784
"While waves are ubiquitous features of physical systems, no single definition adequately describes the topic."
(from Wikipedia)

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

 

[far far away]

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

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

 

[A.T.]

The disturbed equilibrium here is the lump of mass‑density moving through space.

How do you define 'equilibrium' here, precisely and quantitatively?

 

[far far away]

How do you define 'equilibrium' here, precisely and quantitatively?

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 particle passes.

But the particle has to be moving or it would violate the definition which claims that a wave is propagating.

 

[A.T.]

If you define a mass density field M(x,t) with equilibrium M=0

Why would that be the requirement for an equilibrium? As already said:

Non-uniform mass distributions can be in equilibrium

 

[far far away]

Why would that be the requirement for an equilibrium? As already said:

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).

 

[Gavran]

A wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities.

In my opinion, your definition is correct, but it is incomplete. I agree with @kuruman (post #5) that a wave in classical physics does not include a matter transfer.

 

[A.T.]

The equilibrium situation is something we can define ourselves.

That is obviously not the meaning of "equilibrium" used in the definition of a wave you quoted. Mostly because if "equilibrium" is whatever you want it to be, then it is a meaningless term.

 

[kuruman]

The equilibrium situation is something we can define ourselves. It's the baseline or "rest state" against which disturbances are measured.
$\dots$
- 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).

From a utilitarian point of view, how useful is your approach to formulate a mathematical description of physical events occurring around us?

Take the simple case of two point masses $m_1$ and $m_2$ travelling in opposite directions and colliding elastically. You could use Dirac delta functions to describe each mass and write the density function $M(x,t)=m_1\delta(x-v_{1i} t)+m_2\delta(x+v_{2i} t)$. You can also say that collision time $t_c$ you have a collision at point $x=x_c$ so that at that point at that time $M(x_c,t_c)=m_1\delta(x_c-v_{1i} t_c)+m_2\delta(x_c+v_{2i} t_c)$.

Now what? You need a model to describe how the waves transfer momentum and energy m ]\so that you can write $M(x_c,t+\Delta t)$ in the limit $\Delta t \rightarrow 0.$ My point is that you can always write down $M(x,t)$ but to what end?

 

[Herman Trivilino]

According to that definition, everything could be considered a wave, and I’m trying to determine whether that’s actually true. If it is true, then great — the theory becomes simpler.

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.

If it’s not true, then I want to understand what breaks the argument.

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