If we could not see, would we think that nothing can go faster than sound?

Question

And if so, then why does everybody keep asserting nothing can go faster than light speed (I'm implicitly assuming there could be something which we do not observe, which goes faster than light)?

Answer 1

No. We can experimentally confirm that for a particle with rest mass $m$ and velocity $v$, its total energy is given by $E = mc^2/\sqrt{1 - v^2/c^2}$, and this equation goes to infinity as $v$ approaches the speed of light $c$; if anyone tried to put forward a similar equation with the speed of sound in place of the speed of light, this equation could easily be shown to give incorrect predictions for particles moving slower than the speed of sound. Likewise with various other equations that work for slower-than-light particles and approach 0 or infinity as $v$ approaches $c$, like the time dilation equation (which can predict how the decay rate of a given particle type changes as a function of its velocity).

For example, if you used a subsonic bullet with mass 0.0095 kg and speed 300 m/s or 0.8816 times the speed of sound s=340.29, then if you used an equation like the one above with s in place of c, and calculated kinetic energy as (total energy) - (rest-mass energy) = $(ms^2/\sqrt{1 - v^2/s^2}) - (ms^2)$ you'd predict a kinetic energy of $[(1/\sqrt{1 - v^2/s^2}) - 1]ms^2$ = $1.119ms^2$ = 1.119*0.0095*(340.29)^2 = 1231 Joules. Whereas in reality its speed is so low compared to the speed of light that you can just use the classical formula $E = (1/2) mv^2$ to calculate its kinetic energy, giving 0.5*0.0095*(300)^2 = 427.5 Joules, which is substantially smaller. You could easily determine which was correct by firing this bullet into a block of known mass M mounted on wheels and seeing how much velocity V it gained after stopping the bullet and absorbing its kinetic energy (making sure it was massive enough so that its change in velocity would be very small compared to the speed of sound, so that the formula $E=(1/2)MV^2$ could be used regardless of your assumptions about whether the limiting speed was the speed of sound or the speed of light). If the block plus wheels had a mass of 50 kg, the velocity gain upon absorbing kinetic energy E should be $V = \sqrt{2E/(50)}$, so if you predicted the bullet to have kinetic energy 1231 Joules you'd predict a velocity gain of 7.02 m/s, whereas if you predicted the bullet to have a kinetic energy of 427.5 Joules you'd predict a velocity gain of 4.14 m/s.

For experiments that show the corresponding energy formula does work with c in place of s, I think you'd want to look at particle collider experiments where the particles can attain a significant fraction of light speed, and the total energy of the particles produced by the collision must equal the energy of the particles before the collision, but since the rest mass of the particles coming out can differ from the rest masses of the particles going in, kinetic energy before the collision can transform into rest-mass energy after the collision or vice versa. Various experimental confirmations or relativistic predictions about how energy conservation should work can be found on this page.