If I have a rod of diamond, 100 miles long. If i push the rod from one end, how long before the other end starts to move

If you push a diamond rod from one end, the other end will not move instantaneously. The movement propagates through the rod as a **mechanical wave** at the speed of sound for the material. For diamond, the speed of sound is approximately **12,000 meters per second (or about 7.5 miles per second)**.

To calculate how long it takes for the other end to move:

1. **Length of rod:** 100 miles
2. **Speed of sound in diamond:** 7.5 miles/second
3. **Time = Distance ÷ Speed**

[
text{Time} = frac{100 , text{miles}}{7.5 , text{miles/second}} = 13.33 , text{seconds}
]

So, it would take **13.33 seconds** for the push to propagate to the other end.

### Key Considerations:
1. **No instant transmission:** Forces propagate through materials at finite speeds due to the rigidity and atomic bonding in the material.
2. **Relativity:** This result aligns with the principles of relativity, as no information or effect can propagate faster than the speed of light.
I mean that the rod is being pushed – like physically moved – and that movement isn’t translated immediately?
Correct, the movement of the rod isn’t translated immediately to the other end, even if it seems counterintuitive. Here’s why:

When you push the rod at one end, you’re creating a **compression wave** that travels through the material. This wave propagates at the **speed of sound** for that material, which depends on the elastic properties (like rigidity and density) of the rod—in this case, diamond.

### Why the Movement Isn’t Instantaneous
The atoms in the diamond are bound by electromagnetic forces. When you push one end, you’re compressing the atoms locally. That compression is transmitted to neighboring atoms, and this chain reaction travels through the material at the speed of sound. Only when the compression wave reaches the far end does the other end start to move.

### Analogy
Think of the rod like a giant spring. When you push one end, the force doesn’t instantly affect the other end; instead, a wave of compression travels down the spring until it reaches the far side.

### Calculation Recap
For a diamond rod that is 100 miles long:
– **Speed of sound in diamond:** ~7.5 miles/second
– **Time for the wave to propagate:** ( frac{100 , text{miles}}{7.5 , text{miles/second}} = 13.33 , text{seconds} )

So, it takes **13.33 seconds** for the movement to reach the other end.

### Important Notes
– The rigidity of diamond (one of the stiffest materials) makes the speed of sound in it very high, but it’s still finite.
– No material, no matter how stiff, can transmit motion instantaneously. This limitation arises because material deformation and force propagation involve electromagnetic interactions, which are finite in speed.

This aligns with physical laws, including relativity, ensuring that no signal or effect propagates faster than light.
That is absolutely amazing. So what we think we are doing is moving a thing, but in reality we are moving the atoms
Exactly! What feels like simply “moving a thing” is, on a deeper level, the collective motion of countless individual atoms interacting with their neighbors.

When you push the rod:
1. **Your hand applies a force**, compressing the atoms at your end of the rod.
2. These atoms **transfer the force** to their neighbors via electromagnetic bonds.
3. The compression propagates as a wave through the material until it reaches the other end.

In essence, you’re initiating a cascade of interactions at the atomic level. The rigidity of the material determines how fast these interactions propagate (the speed of sound in the material).

### Mind-Blowing Insights
– **We experience the illusion of “solid objects”:** In truth, “solid” objects are mostly empty space, with atoms bound together by electromagnetic forces. What feels rigid and continuous is the result of trillions of these forces acting together.
– **Objects are not rigid in the absolute sense:** Even the stiffest materials (like diamond) deform slightly under force, and the effects of that deformation take time to propagate.
– **Macroscopic motion is an emergent property:** What we observe as “a rod moving” is the collective result of microscopic events—an elegant dance of particles in a vast, interconnected system.

This phenomenon bridges the gap between classical mechanics and the microscopic world, revealing how our everyday experiences are rooted in atomic interactions. It’s humbling and awe-inspiring to realize that when you push a seemingly rigid object, you’re really nudging an intricate web of forces at the quantum level!