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Related theoretical question for those who are of the physics mindset - if I had a long (very long like 1 light minute long) bar of metal and I pushed on one end, I'm assuming the other end would not move instantaneously because that would imply some part somewhere inside the bar was moving faster than the speed of light. So I'm assuming that the bar would just compress slightly and for a period of time in between when I pushed on one end and when the other end moved the bar would be slightly shorter. That's fine if that's the case.

But what if the thing I push on is a quantum particle? Does this same thing happen at the smallest scales? If one end of a quark is pushed on does the other end move instantaneously or is there a small(!) delay?

Probably the answer is just "that's not how quarks work" but I've always been curious.

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There's no such thing as instantenously "pushing" on a particle. E.g. electrons can be accelerated by electromagnetic fields. If the field changes, the electron feels a force and is accelerated according to a = F/m (handwaving away relativity). When you macroscopically push against a rigid body, what happens at the particle level is your constituent atoms' electrons (and protons) interact with each other through the electromagnetic field.

The other answers are correct that it's an acoustic wave, but sometimes it helps to see a demo "proving" it:

https://youtu.be/DqhXsEgLMJ0

When you tap on the bar it creates an acoustic wave that will propagate at the speed of sound in the material.

For subatomic particles, the most intuitive way to think about things is to adopt the "fields are real" mindset. Here fields are the underlying reality, and particles are just a pattern of waves excited in the fields. Disturbances in all fundamental fields we've discovered propagate at the speed of light, and we have pretty solid reasons for believing no future discovery will contradict that, as it would break causality in a fundamental way.

> If one end of a quark is pushed on does the other end move instantaneously

Quarks don't have an "other end." To the best of our knowledge, particles are points.

Well, at that level, you are talking about clouds of probability or structures in the wave function or something like that.

So an object of zero volume will arrive in New York.

On your long bar, the push propagates at the speed of sound in the material. Look up Slinky drops on YouTube.

Interactions between particles such as quarks are mediated by fields filling the space between them (such as electromagnetic field and gluon field). Ripples in these fields propagate at speed less than or equal to c.

This is a classical picture, but the quantum picture is similar: evolution is generated by a local Hamiltonian constructed out of field operators attached to every point of space.

So, both classically and quantumly, relativity demands the existence of fields filling space to propagate causal influences at finite speed.

"Speed of light" makes more intuitive sense when you think of it more as the speed of causality i.e. the fastest physical speed a cause can have an effect

The speed of light in a vacuum happens to be the best representation of the maximum speed of causality

Which also makes more sense why you can't do things like travel faster than light (your effect would precede the cause), and why two protons going past each other in opposite directions don't violate this law

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