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Suppose that there's a button at the other end of the universe, and a 'stick' that goes all the way there.

If I push the stick, will the button get pushed instantly, or there is some latency that I am missing?

(Suppose that the stick is made from whatever strong enough material that can stand whatever physical or practical constraints over there.)

I want to use this mechanism to build a real-time communication system that spans multi-light-years areas. So is this a good idea?

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    $\begingroup$ This has been asked and answered many times on physics.stackcxchange.com. The short answer is no, it won't work. The latency that you're missing is that when you push on one end of a stick, you're pushing on a bunch of atoms. Those atoms push against other atoms, which push against other atoms, and so on - but they don't move instantaneously, and the influence of your push travels as a wave, somewhat slower than light. This will be true no matter what the stick is made of, for fundamental reasons having to do with relativity. $\endgroup$ – Nathaniel Feb 28 '16 at 11:39
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The pressure allowing the stick to move when pushed at one end will move at the speed of sound in that material.

Imagine the rod is a slinky. Understand springs (Hooke's Law, etc.) and you understand solids in general: they are just orders of magnitude stiffer. It might be more philosophically correct to note that a spring is just like any solid rod, just wimpier. A wall resists pushing because it compresses by some invisible amount. When you apply a compression stress to a solid sample cylinder it gets shorter and the force pushing back at you is proportional to the change in length. When that force balances the load the column is in equilibrium. Picture a concrete piller as being exactly like a bedspring except for the size of the constant: the concrete compresses by micrometers.

concrete tester

I’ve seen video like the concrete strength tester above, but with a micrometer (pictured below) in parallel with the rock sample. You could clearly see that stress (force squeezing the column) and strain (the change in length) were in sync until something broke.

dial

It’s all a matter of the scale of the compression relative to the size of the member, and the human perception scale.

Imagine a short rod of steel the size of a pencil. On this scale you find it hard and unbending. But, it's really a sample of a product sold as rope! It comes in spools 10 feet in diameter. For a length of a bridge span, it wobbles and is obviously ropelike.

Conversly, if you have a steel I-beam a mile long, and you push one end hard enough to shove it, you will note a delay before the far end moves, and the length shortens like a piece of rubber, compressing first, and then the wave of compression moving to the other end where that wave eventually causes the far end to move. The compression moves as a logitudinal wave in the solid, since the sample is long enough to make the speed of sound (the speed at which the atoms react to their neighbors) slow in proportion to the total time involved.

Radio would be far faster than mechanical linkages.

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    $\begingroup$ Excellent explanation, just one thing to add. The speed of sound is not constant. In Room Temperature air it's around 340m/s, in steel 6 100m/s. Around 20 times faster, although still nothing like as fast as light at 299 792 458m/s. engineeringtoolbox.com/sound-speed-solids-d_713.html $\endgroup$ – Tim B Feb 28 '16 at 10:36
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    $\begingroup$ "If you have a steel I-beam a mile long, and you push one end hard enough to shove it, you will note a delay before the far end moves" - OK, I want to see that in a video. $\endgroup$ – John Dvorak Feb 28 '16 at 12:13
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    $\begingroup$ That's going to take a lot of energy. And steel. And a huge warehouse. I'd watch that too. $\endgroup$ – Polyducks Feb 28 '16 at 13:14
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    $\begingroup$ @JörgWMittag can we adopt the term "speed of causality" already? :-) $\endgroup$ – John Dvorak Feb 28 '16 at 19:36
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    $\begingroup$ @LightnessRacesinOrbit The causality is opposite of your phrasing. As you push on a wall, it begins compressing. As it compresses, it pushes back against your force which grows as it compresses (at least until a breaking point). The wall stops compressing at the point where that force exactly matches whatever force you are applying to it. $\endgroup$ – Cort Ammon - Reinstate Monica Sep 7 '16 at 21:55

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