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In a superhero setting, a thunder clap is where someone claps with superhuman strength, causing damage such as broken windows and burst eardrums. What I want to know is, taken to the extreme of the extreme what is the maximum possible damage a thunder clap can do?

Read https://what-if.xkcd.com/1/ for a good starting point but that's only 90% the speed of light. I'm allowing speeds much faster than that. Additionally, the collision of invincible fast objects should cause something at least slightly different.

I wonder if the waves could be strong enough to break the Earth into pieces which fly out near the speed of light smashing into stars and planets causing a chain reaction. Or maybe as time and space bends around the incoming hands (via special relativity?) the collision will punch a hole in the space-time continuum causing a sizable worm hole of disastrous effect.

The man doing the clap is strong, fast, and completely invincible. He is the size of an average adult male and is standing on Earth. His strength can be any finite number of newtons, his speed can be anything less than the speed of light, he is completely and utterly invincible even if the universe gets destroyed. Feel free to use speeds such as c - 10^(-(graham's number)) or even faster. He does not need to be standing at sea level but he does have to be standing and not in flight.

I'd like to see qualitative answers (such as the XKCD example) that I can understand. I am more interested in interesting answers than ones that strictly follow my rules.

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    $\begingroup$ Worldbuilding: when Physics just isn't enough. $\endgroup$ – SnoringFrog Aug 31 '15 at 16:31
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Short answer: as much damage as you want.

Long answer: it depends on how fast you can move your hands.

When your superhero claps, he converts all of the kinetic energy in his arms into other forms of energy. At low speeds, this is an acoustic pulse that ripples through the air, which we hear as a clap.

A single hand is about half a kilogram, so both hands together are about a kilogram of mass. (We'll ignore the energy in our superhero's arms.) We can plug this into Einstein's theory of special relativity to get the following equation for the energy of a single clap:

$e=c^2/\sqrt{1-v^2/c^2}-c^2$

$.0001c$

At 1/10000th the speed of light, we get around $9\times10^8$ Joules of energy. This is about the energy of a lightning bolt, but our energy will probably mostly be released in the form of a substantial pressure wave, rather than light and heat.

$0.01c$

At 1/100th the speed of light, our clap now has around $9\times10^{12}$ Joules of energy. Our clapper is now in possession of a small weapon of mass destruction, with each clap releasing about 100 times the energy of a MOAB bomb, the second most powerful non-nuclear device ever detonated.

$0.1c$

With his hands moving 1/10th the speed of light, our clapper releases $9\times10^{14}$ Joules of energy. This is about the same energy as ten of the bomb that was dropped on Hiroshima.

$.8c$

Now we're getting relativistic! At .8c, we get $1.6\times10^{17}$ Joules of energy. This is about the same amount of energy as what was released by the Tsar Bomba, the largest nuclear bomb ever detonated.

$.9999999c$

Now we've got an extinction event! This clap releases $10^{23}$ Joules of energy, or about as much as was released by the impact of the meteor that destroyed the dinosaurs.

$(1-10^{-16})c$

This clap would release around $10^{32}$ Joules of energy. At this energy, clapping will destroy the Earth.

$(1 - 10^{-65})c$

At this speed, the superhero's clap contains as much energy as there is in the observable universe. There will effectively be another big bang which occurs between the superhero's hands. The released energy will expand rapidly outward in a wave which will utterly annihilate everything it hits, with the wave expanding at close to the speed of light.

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    $\begingroup$ At first, there was darkness. And then God clapped his hands, and there was light. $\endgroup$ – DaaaahWhoosh May 27 '15 at 16:33
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    $\begingroup$ @DaaaahWhoosh God lives in a really fancy house, then $\endgroup$ – Desolationgame May 28 '15 at 10:42
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    $\begingroup$ @Josiah The number given for "loudest sound" is usually maximum undistorted sound, when the sound pressure is equal to atmospheric pressure: any higher and one side of the sound wave will be "clipped" at vacuum (since the total pressure can't go below zero). However, the positive-pressure side of a shock wave can have practically unlimited magnitude. $\endgroup$ – 2012rcampion May 30 '15 at 1:26
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    $\begingroup$ @Josiah At the upper limits of speed here, the energy won't be released as sound anymore. Instead, the superhero's hands will act as a particle accelerator, ramming particles in the air between them together at relativistic speeds and triggering nuclear fusion between the individual atoms. Energy will be released in the form of a pulse of gamma rays, followed shortly by a wave of high energy particles and finally by a blast of superheated plasma. The plasma blast will probably be quite loud, but the energy in the sound won't make up a significant part of the destruction. $\endgroup$ – ckersch May 31 '15 at 17:39
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    $\begingroup$ I applaud your answer. $\endgroup$ – Xandar The Zenon Feb 14 '16 at 3:49
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I think you might run into an issue here. Now with the word 'apocalyptic', that's pretty much guaranteed, but with the word 'clap'.

Contrary to popular belief, when you clap you aren't simply throwing your hands together. Your hands, arm muscles, brain and even eyes are engaged in complex interplay to make sure your hands collide just so (if you want proof your eyes are involved try placing just the tips of your index fingers together with your eyes closed). Your hero has infinite speed, which removes the need to worry about nerve signal transmission time (except it doesn't, but I'll get to that later), but what he doesn't have is a nervous system designed to deal with relativistic lag.

It's well known that when you reach relativistic speeds weird things start happening with time, notably you have to start worrying about how old your twin is. Our hero has the problem of his brain having to worry about how old his hands are. For a bit of reference: we have to correct for relativistic lag in satellite communications.

The amount of time it takes a signal to reach a satellite at the top of the Low Earth Orbit boundary is about 5ms. The amount of time it takes a normal human nerve signal to get to the end of the arm is about 5ms (thank you, XKCD). The satellite is moving at a speed considerably lower than c. Unless our hero can perform relativistic reference frame substitution in his head while tied to a centrifuge then he's going to run into issues with nerve signal interpretation.

Now, I don't claim to know what happens when a brain is sending messages to muscles that are sending feedback at a completely different rate, and I wouldn't even want to try modelling a neurochemical reaction on a changing temporal boundary. If you speed up the signal transmission you just end up with more confusion, as the problem isn't with speed of signal but differences in the rates with which the signals are being sent and intercepted. If you say that the nerve signals are instantaneous then you end up with a causal violation. From the point of view of the brain the clap happens before it's sent the signal for the clap to begin.

With this amount of bodily confusion I reckon that our hero isn't going to have the level of fine motor control required for a good, solid 'CLAP'. In fact, I'd wager that there would be something more like a localised seizure in their biceps, followed by the most apocalyptic derp in history.

Even if their hands don't collide at all (like missing your own high-five), our indestructible hero's hands will stop in some way, most likely a highly uncoordinated pirouette. Assuming that by 'indestructible' you mean they are in no way affected by external forces and that nothing can enter their body their arms will leave a trail of vacuum where they've pushed all of the air ahead of them. The leading edges of their hands and forearms will be a thin incandescent layer of plasma where adiabatic compression has taken place, and the sudden shock of their asymmetrical epic flail will briefly transmit an ungodly amount of energy into the ground below their feet (This wouldn't happen if their actions were perfectly symmetrical, but as they aren't their feet will be exerting a nontrivial torque on the floor, much like if you swing one arm while on a swivel chair)

The exact amount of energy transmitted to the floor will be somewhat under ckersch's excellently calculated energies, but as you can see from the ungodly exponents that he produced, even if our hero's indestructible shoulder sockets re-absorb 99% of the energy involved we're still talking continent-crackingly huge numbers. Oh, and the air around our hero is now a combination of on fire and propagating a huge shockwave from the vacuum implosion. And that's before we figure out if our hero's shoes and shirt have vaporised from the friction.

All in all, maybe not an apocalyptic clap, but it's certainly apocalyptic. And you can guarantee his immortal buddy will somehow get a photo of it and put it on whatever's left of instagram with a caption like:

'Hurr-Durr, Imma destroyin' the wurld!'.

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    $\begingroup$ "the most apocalyptic derp in history". +1 just for that, but the science was good too. $\endgroup$ – DaaaahWhoosh May 29 '15 at 14:28
  • $\begingroup$ Re "try placing just the tips of your index fingers together with your eyes closed": Ok, I tried. No problem. So am I a superhero? $\endgroup$ – jamesqf May 29 '15 at 17:32
  • $\begingroup$ @jamesqf: the finger thing is a test of Proprioception (the sense of where your body is). Most people can touch the fingertips together but very few can get it as bang on as they can with their eyes open. $\endgroup$ – Ballisticsfood May 30 '15 at 14:58
  • $\begingroup$ Nice try. This answer was fun to read but superpower baggage (tv tropes calls it Required Secondary Powers) covers this problem. The small things that make the superpower work as intended. For example using super strength to punch through a wall and having your arm survive. $\endgroup$ – SkySpiral7 May 31 '15 at 21:35
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You need to check out the Alpheidae, it is underwater but the principles of water is almost the same as air.

Sorry about the hunk of quote but it is pretty interesting in your case.

Alpheidae - Pistol shrimp

The snapping shrimp competes with much larger animals such as the sperm whale and beluga whale for the title of loudest animal in the sea. The animal snaps a specialized claw shut to create a cavitation bubble that generates acoustic pressures of up to 80 kPa at a distance of 4 cm from the claw. As it extends out from the claw, the bubble reaches speeds of 60 miles per hour (97 km/h) and releases a sound reaching 218 decibels.[11] The pressure is strong enough to kill small fish.[12] It corresponds to a zero to peak pressure level of 218 decibels relative to one micropascal (dB re 1 μPa), equivalent to a zero to peak source level of 190 dB re 1 μPa at the standard reference distance of 1 m. Au and Banks measured peak to peak source levels between 185 and 190 dB re 1 μPa at 1 m, depending on the size of the claw.[13] Similar values are reported by Ferguson and Cleary.[14] The duration of the click is less than 1 millisecond.

The snap can also produce sonoluminescence from the collapsing cavitation bubble. As it collapses, the cavitation bubble reaches temperatures of over 5,000 K (4,700 °C).[15] In comparison, the surface temperature of the sun is estimated to be around 5,800 K (5,500 °C). The light is of lower intensity than the light produced by typical sonoluminescence and is not visible to the naked eye. It is most likely a by-product of the shock wave with no biological significance. However, it was the first known instance of an animal producing light by this effect. It has subsequently been discovered that another group of crustaceans, the mantis shrimp, contains species whose club-like forelimbs can strike so quickly and with such force as to induce sonoluminescent cavitation bubbles upon impact.[16]

As you can read the heat and pressure is pretty impressive, you just need to increase the size of the shrimp - make it human and give it super powers, combine it with the XKCD - WHAT IF, and then you would have a pretty good idea. The math i will leave to someone more capable.

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  • $\begingroup$ Pistol shrimp is cool but the mantis shrimp is probably a closer analogy. $\endgroup$ – SkySpiral7 May 31 '15 at 22:19
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The clap actually can't do all that much. Consider that the damage done by a thunderclap/clap is not actually done by the person, but by the shockwave through the air. This shockwave is not made of the same material as the man, it has limits.

You're going to run into interesting issues such as the fact that your hand is not actually solid. Most of the space in your hand is basically empty, and you rely on electrostatic forces to make it appear as though things cannot go through the hand. If you start moving at relativistic speeds, most likely the air molecules will just pass right through the hand, unaffected. A few nuclear collisions will occur and generate fusion type energies, but not much.

However, consider, if instead of trying to clap, he simple begins moving at nearly the speed of light (perhaps a raving motion), the mass of his arms could approach infinity, with nearly infinite gravitational effects. Who needs a thunderclap when you can literally just turn your arms into black holes and suck the planet up.

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  • $\begingroup$ Are you saying that at relativistic speeds, you can cause nuclear fusion just by moving through the air? That sounds pretty powerful to me (even if it's not as powerful as black holes). $\endgroup$ – DaaaahWhoosh May 27 '15 at 15:41
  • $\begingroup$ @DaaaahWhoosh Yes, though the quantity of fusion may not be very large. Every now and then an air atom nucleus will collide with the nucleus of an atom in your hand. If you think about it, the way the sun fuses two hydrogen atoms is literally by banging them together at high speeds. $\endgroup$ – Cort Ammon - Reinstate Monica May 27 '15 at 18:08
  • $\begingroup$ @DaaaahWhoosh: Yes, that's essentially what particle accelerators do, accelerate some matter to nearly the speed of light, and smash it into a stationary target, or another beam moving in the opposite direction. Would think you'd get more smashed-up atoms (and all sorts of subatomic particles) than fusion, though, because you need to keep the protons confined for fusion to take place. $\endgroup$ – jamesqf May 28 '15 at 4:40
  • $\begingroup$ I would think the hands being invincible ensures their electrostatic forces which means that they would also be completely tangible resulting in an answer more like ckersch's. Also the black hole arms are interesting... $\endgroup$ – SkySpiral7 May 31 '15 at 20:59
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In your scenario, the superhero can clap his hands at speeds arbitrarily close to the speed of light. This would suggest that each hand clap could produce arbitrarily large amounts of energy - like a particle accelerator, but using much more mass than a single proton. I may be wrong, but I believe this would have fatal consequences for our entire observable universe. I'll try to explain why, but I can't guarantee it is going to be coherent because I'm not a physicist.

Physics suggests that our universe should seek to be in its lowest energy state. If it is not, it could tunnel into a lower energy state. For example it could decay from our present false vacuum state into a true vacuum state. If this where to happen, then space would undergo some sort of phase transition, similar to water turning from liquid to solid when it freezes.

I seem to recall reading one scenario (I think it was Max Tegmark) describing a sufficiently advanced race performing a physics experiment similar to our particles accelerators, where a sufficient amount of matter is smashed together to create enough energy that the local false vacuum would be propelled through whatever barrier is currently holding it in its false vacuum state, ultimately into a lower (or zero) energy state. The resulting phase transition of space would then spread out at near the speed of light in a metastability event often referred to as a Death Bubble.

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  • $\begingroup$ Then by virtue the universe would prevent superpowers in the first place. Superpowers have always had indefinite energy from absolutely nowhere. Conservation of mass and energy need not apply (and also the lowest energy state thing). $\endgroup$ – SkySpiral7 May 31 '15 at 21:39
  • $\begingroup$ @SkySpiral7 I don't think it would prevent superpowers, but it would certainly limit them. I guess I misread your use of the science-based tag. $\endgroup$ – Nick Jun 1 '15 at 16:51
  • $\begingroup$ Yeah good point. My question is vague about what is and isn't going to have science applied to it (complete invincibility for example can't really be explained). In any case thanks for your interesting answer. $\endgroup$ – SkySpiral7 Jun 7 '15 at 23:46

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