Punches his opponent at the speed of light

[FizixFreak]

since i have always have been interested in combat sports i was just wondering what would happen if some one in the octagon or in the ring punches his opponent at the speed of light(i bet chuck norris has already done that) i mean will the fist time travel or something?

 

[Mentallic]

Well it's not possible for a mass to move at the speed of light (even chuck norris' fist, unless he also changed the laws of physics in his films to make him look better), but it can get arbitrarily close!

First of all, the acceleration you would need to get from 0 to near light speed in such a short distance would mean your arm would tear apart instantly - think about what happens when you try to quickly move a sponge cake really fast, it just falls apart.

But if you manage to hold yourself together (literally), you'll just make a hole in the guy. In fact, even a scrap of paper would go right through him.

 

[FizixFreak]

i think you misunderstood me here what i meant to ask was that whether the fist would slow down ,gain mass or contract in length i don't care what happens to the reciever of the punch (let chuck norris take care of that ) .
and yeah no one can reach the speed of light what if the punch is only close top that speed?

 

[dukeofsphere]

Hilarious.

I'll try to clarify a little; what I think you mean is what happens to the fist at relativistic speeds (not necessarily the speed of light, c). According to Wikipedia, anything above 0.1c is relativistic, so any fist flying at > 0.1c would require special relativity in order to describe its mechanics.

 

[dukeofsphere]

i think you misunderstood me here what i meant to ask was that whether the fist would slow down ,gain mass or contract in length i don't care what happens to the reciever of the punch (let chuck norris take care of that ) .
and yeah no one can reach the speed of light what if the punch is only close top that speed?

I'm not an expert on special relativity; all I know is that some really weird sh*t would happen. Also, what happens would depend on where the observer is - for example, if you were to be somehow riding the fist on its way to the opponent's face, things would look pretty normal (I think). Things would start changing and look different if you were the referee; they would change again and be different if you were a spectator outside the octagon; and again if you were watching from the moon, etc.

Also, I think that as v (the velocity of the fist) approached the speed of light, the fist would gain relativistic mass/energy. This would, in turn, increase the gravitational potential of the fist (again, I think, I'm not sure). Eventually (perhaps), the fist would have more gravitational pull than the Earth, and so then even weirder stuff would happen.

 

[Dr Lots-o'watts]

... what i meant to ask was that whether the fist would slow down ,gain mass or contract in length... only close to that speed?

Mass gain and contraction, but only while it's traveling. It would be back to its original specs when back to rest. I think the punching guy's body would have aged slightly less than the rest of the stadium. Or only the fist, I'm not sure.

 

[bp_psy]

Damn. This is the thousandth thread this week that asks what will happen if something that can't happen would happen.

 

[FizixFreak]

i have heard that the mechanical time slows down at close to the speed of light(am i right) if so than how would that effect the situation

 

[dxun]

i think you misunderstood me here what i meant to ask was that whether the fist would slow down ,gain mass or contract in length i don't care what happens to the reciever of the punch (let chuck norris take care of that ) .
and yeah no one can reach the speed of light what if the punch is only close top that speed?

The question appeares really simple, but if one would try to answer it in detail and precisely, it would become quite complex and would obscure the general points so let's instead of punching try to see what would happen should we try to hit a common tennis ball near the speed of light.

I think Mentallic already gave you a good answer to your question, but just so that we are clear on the subject, let me try to give you a few helpful tips.

What you are interested in is actually called Special Theory of Relativity (STR) - the theory that describes spacetime, or in other words, what we humans percieve as all our surroundings: three-dimensional space plus fourth dimension - time.

Einstein came up with 2 very important notions, so let's have a quick break down of these:
1) Principle of Relativity - which essentially says that laws of physics remain the same no matter what speed you are travelling,
2) Principle of Constant Speed of Light - which essentially says that nothing can travel faster than speed of light.

There are a number of consequences which we can derive from these 2 notions (we'll mention three, which are here most interesting):

A) Time dilation - the time lapse between two events is not constant but rather dependant on the speed the whole system (in which event occured) is travelling. So hitting a tennis ball on a static tennis court would look to you (observer in the audience) quite differently than hitting a tennis ball on tennis court which is itself moving close to speed of light (say, 0.99999c). In the first case, you would see nothing out of the ordinary, but in the second case, on slow motion you would see the players essentially frozen in time or moving very, very slowly.

B) Length contraction - the actual length of an object noticeably decreases as this object starts to move very closely to c. So if Roger Federer should serve the ball, you'd see it as you'd expect (a blurry greenish object moving fast), but if you were to launch a tennis ball parallel to the ground and very closely to c, then on a slow motion it would appear as if it is severely squished on the 3- and 9 o'clock position.

C) Mass increase - the mass noticeably increases as the object starts to move very closely to c. So if you were to somehow hook up a scale to a tennis ball and read it while Federer serves, the mass of the ball would appear unchanged. But if you were to launch the ball very closely to c, the ball would actually appear to have more mass.

Now, keep in mind A), B) and C) are not phenomena that appear only on speeds close to c, but are behaviours commonly present in everything that surrounds us - had that not been the case, we would violate Einstein's point 1). Instead, they are innate to all objects governed by laws of physics but it is only at relativistic speeds that they become humanly apparent.

With that said, let's crunch a few numbers that would give you a feel as to how much things change in common life as opposed to relativistic speeds.

Note that:
v - relative velocity between observer (you) and point of reference (referent system - in our case: tennis court/ball)
c - the speed of light (cca. 300 000 km/s)

A) Let's say you have a stopwatch and while standing right next to court, you've measured that it takes exactly 3.0 seconds on the nose for a player to contact with and hit a tennis ball, have the ball cross the net over to the other player and make contact with his racquet (but not him hitting the ball). We'll denote this time difference with [tex]\Delta t[/tex]. Our referent system is tennis court.

Since we are standing next to court, there is no difference in relative velocity between us, the observer, and the court, our point of reference - hence, [tex]v=0[/tex].

New time difference (should we accelerate the *whole* court) will be given with this formula:

[tex]\Delta t' = \frac{\Delta t}{\sqrt{1-v^2/c^2}}[/tex]

Now, let's say we somehow manage to get the whole court to spin around us at a speed an average car moves, say 100 km/h (60 mph). Our relative velocity has changed and now it's [tex]v=100 km/h = 0.02778 km/s[/tex]. Let's plug all this into formula above.

[tex]\Delta t' = \frac{\3 s}{\sqrt{1-(0.02778 km/s)^2/(300 000 km/s)^2}} = \frac{\3 s}{0.999999999999996} = 3.00000000000001 s[/tex]

So, instead of measuring 3 s, you'd measure that the time it took for ball to travel the field is 3.00000000000001 s. That's one hell of a stopwatch, measuring time to the precision of 10^-14 s. So, there you see the answer why don't we observe time dilation on daily bases - the change is to small to be humanly percieved, but it's there.

OK, let's try to accelerate our tennis court a bit more, say about the same as the fastest man-made object in history? That would be Helios 2 probe, which traveled towards the sun at about 253 000 km/h (cca. 172 000 mph or 240 Mach which is about 100 times faster than the top speed of F-16 fighter). That would make it travel at about 0.000234c, so plugging it in the formula gives us this:

[tex]\Delta t' (0.000234c) = \frac{\3 s}{\sqrt{1-(0.000234c)^2/(1c)^2}} = 3.00000008 s[/tex]

Well, not exactly spectacular difference, it would still take one heck of an equipment to record this time difference even when we've made the whole court spinning so fast that everything would be melting down in an instant due to enourmous air drag (not to mention other problems such as the wind, air pressure fluctuations, power requirements or electric bill which would pretty much destroy everything much sooner).

Barring these problems, let's get a bit more serious and accelerate the court to 0.5 c (about 540 000 000 km/h).

[tex]\Delta t' (0.5c) = 3.46 s[/tex]

That's hardly noticeable, so let's crank it up to 0.9 c (972 000 000 km/h).

[tex]\Delta t' (0.9c) = 6.88 s[/tex]

Ah, so, there is something! Now it would seem to us that the ball traverses the same distance taking more than twice the time. Let's spin it some more...

[tex]\Delta t' (0.99c) = 21.3 s[/tex]
[tex]\Delta t' (0.99999c) = 670.9 s = 11.2 min[/tex]
[tex]\Delta t' (1c) = \frac{\3 s}{\sqrt{1-(1c)^2/(1c)^2}} = \infty[/tex]

So the time increases exponentially as we approach 1 c asimptotically. Specially, for 1 c, it would take an infinity for ball to traverse from player A to player B - in essence, it would appear to us that they are frozen in time. But to them, exactly the opposite would appear - they would finish the point normally only to take notice that everything around them appears standing still!

B) OK, let's now see what would happen to a tennis ball as we launch it progressively faster. The formula for length contraction is eerily familiar:

L - length of tennis ball as we measure it resting in the palm of our hand (about 7 cm, or 0.00007 km)
L' - length of tennis ball as we measure it spinning around us at speed v

[tex]L' = L \, \sqrt{1-v^2/c^2}[/tex]

We'll start as before, serving a ball with 100 km/h up to 1 c, so let's see what happens.

[tex]L' (100 km/h) = 0.00007 \, \sqrt{0.999999999999996} = 6.999999999999985 cm[/tex]
[tex]L' (0.000234c) = 0.00007 \, \sqrt{1-(0.000234)^2/(1)^2} = 6.99999981 cm[/tex]
[tex]L' (0.5c) = 0.00007 \, \sqrt{1-(0.5)^2/(1)^2} = 6.062 cm[/tex]
[tex]L' (0.9c) = 3.051 cm[/tex]
[tex]L' (0.99c) = 0.99 cm[/tex]
[tex]L' (0.9999999c) = 0.0031 cm[/tex]

Again, if tennis ball would travel at 1 c, it would appear to have vanished from our sights. Of course, such a tennis ball would have infinite mass (as we'll soon see), so that would create a few interesting things.

C) Finally, let's see how the mass changes as we accelerate the ball to 1 c. I guess you can already expect the results since formula is again very similar to the ones before:

m - mass of the object as we measure it resting (tennis ball has a mass of about 60 g or 0.06 kg)
m(rel) - "relativistic" mass, mass of the object as we measure it spinning around us at speed v

[tex]m_{\mathrm{rel}} = \frac{m}{\sqrt{1-{v^2/c^2}}}[/tex]

[tex]m_{\mathrm{rel}} (100 km/h) = \frac{0.06}{\sqrt{0.999999999999996}} = 60.00000000000012 g [/tex]
[tex]m_{\mathrm{rel}} (0.000234c) = \frac{0.06}{\sqrt{1-(0.000234)^2/(1)^2}} = 60.00000016 g [/tex]
[tex]m_{\mathrm{rel}} (0.5c) = 69.2 g [/tex]
[tex]m_{\mathrm{rel}} (0.9c) = 137.6 g [/tex]
[tex]m_{\mathrm{rel}} (0.99c) = 425.3 g [/tex]
[tex]m_{\mathrm{rel}} (0.9999c) = 4242.75 g = 4.24 kg[/tex]
[tex]m_{\mathrm{rel}} (0.9999999c) = 134.16 kg [/tex]

So there you have it, I hope that cleared a few things.

Bear in mind that these behaviours are not separated from each other - a body experiences all these phenomena at the same time, so if we were to have infinite energy reserves, an infinite track of total vacuum and infinite time, it would be possible to reach the speed of light only to have our target object degenerate to something extremely massive and extremely small (i.e. a black hole).

Realistically, at our current technology level we experience problems with accelerating things far sooner (due to a host of different engineering problems). The only place that we actually do come near relativistic speeds are particle accelerators such as LHC or Fermilab.

 

[FizixFreak]

that was one hell of a post you described STR in great detail but the tennis ball situation is quite different from some one punching his opponent at the speed of light in the tennis ball case the object moves away from the person and experiences the consequences of STR but in the other case the ''object'' is the part of the person which makes this situation interesting to me .
it seems to mee that the both puncher and the reciever would see the fist to be slowing down will the fist ''time travel'' as well?

 

[dxun]

that was one hell of a post you described STR in great detail but the tennis ball situation is quite different from some one punching his opponent at the speed of light in the tennis ball case the object moves away from the person and experiences the consequences of STR but in the other case the ''object'' is the part of the person which makes this situation interesting to me .
it seems to mee that the both puncher and the reciever would see the fist to be slowing down will the fist ''time travel'' as well?

The laws apply to tennis ball and fist equally, so it doesn't matter whether you accelerate the ball or the fist, except that the fist example is much more complex and thusly obfuscates the ideas and concepts.

To punch an opponent it is not enough for the fist to move; rather the whole system (i.e. the body) has to move in a series of complex coordination (branch of science that studies these movements is kinesiology or more precisely, biomechanics). It takes a few weeks just to study the motions of human hand and arm on a graduate level (the whole biomechanics takes 2 semesters), so it's rather tricky to incorporate relativistic mechanics into all that (not to mention entirely pointless). The ball example contained all the phenomena the hand+arm might experience, except it was much simpler.

But let's give it try, this time without math (my biomechanics is a bit rusty these days :) ). Let us suppose that we're trying to hit a stationary target. If the fist is to move at the relativistic speed, so must the lower and probably upper arm. The shoulder should remain sub-relativistic and so would the torso.

Remember, since the hand is not massless, it really cannot reach c. Barring drag and barring the fact it would be instantly ripped off from the shoulder socket and would fall to the ground, if it were to somehow reach near relativistic speeds it would simply liquefy into a smorgasbord of bones, liquids and tissue, crashed due to its sheer mass and falling to the floor as an unrecognizable biomass.

Perhaps the only question is whether time dilation would be sufficient for the observers to actually see the whole gruesome event, but I leave that to you as an excercise - the equations are right above so give it a go. That way you can also answer another question - whether the punch would actually damage the target.

So, to cut a long story short - no time travelling, no black hole opening, just a whole lotta pain and a huge mess to clean up after.

 

[FizixFreak]

yes you bring up a good point any guy who knows about punching knows that the real strength of the punch comes from the hip so most parts of the body will also move with great speed(not as fast as the fist though) possibly experiencing relativistic effects right?

correct me if i am wrong but does not the drag force acts on a body moving in a fluid up to a specific speed and beyond that speed there is no further drag?

this is the trickiest part i think time dilation would occur right before the arm is ripped it is a bizarre thought but if the arm is still travels at close to speed of light after being ripped it will experience time dilation just like the tennis ball

 

[dxun]

correct me if i am wrong but does not the drag force acts on a body moving in a fluid up to a specific speed and beyond that speed there is no further drag?

You probably refer to terminal velocity during free fall. Since the fist is not in free fall, I don't see how that applies here. Drag will generally vary with square of velocity.

this is the trickiest part i think time dilation would occur right before the arm is ripped it is a bizarre thought but if the arm is still travels at close to speed of light after being ripped it will experience time dilation just like the tennis ball.

I don't think that you fully appreciate the forces in play here :)

Just for the fun of it (since this example is beyond ridiculous anyway), here's a really cursory run-down of the mechanics here (I am not completely sure of the calculation, so if I made any blatant errors, please correct me) - the more precise calculation would be more complex due to biomechanics.

Let's be modest by reusing the example above and saying that we want to make a fist-sized object move at 253 000 km/h, beating the record speed of any man made object. Also, let's try to do it on a warm day (20 degrees C), on a sea-level altitude on Earth. The fist-sized object is approximately the same mass as an average human hand (say, 5 kg). Since we're simulating a punch, it must reach its top speed very quickly, for example in 0.5 s.

OK, let us now set the stage:
[tex]m_{hand}=5 kg[/tex]
[tex]t_{acceleration}=0.5 s[/tex]
[tex]v_{target}=70220 m/s[/tex]
[tex]A_{fist}=67.5 cm^2=0.00675 m^2[/tex]
[tex]\rho_{air 20C}=1.204[/tex]
[tex]C_d_{(hand)}=1.0 [/tex] (approximate drag coefficient)

Acceleration needed is:
[tex]a=\frac{dv}{dt}=\frac{70220 m/s}{0.5 s} = 140 400 m[/tex]

To accelerate target object to desired speed, we would need:
[tex]F= ma = 5 kg*140 400 m = 702 kN[/tex]

To give you an idea of this force, it is about half the thrust of the Space Shuttle main engine.

Now, the "fist" drag is another story in entirety. Drag at such speeds becomes a dominant force (which is one of the reasons you don't see aircraft flying around at Mach 240).

Drag force in our case is given by:

[tex]F_D\, =\, \tfrac12\, \rho\, v^2\, C_d\, A=0.5*1.204*(70220)^2*1*0.00675= 20 036 502 N \approx 2*10^7 N[/tex]

That is 20 MN, about equal thrust of 10 (ten) Space Shuttle engines. To overcome such unbelievable drag, you'd need astronomical amounts of power.

[tex]P_d = \mathbf{F}_d \cdot \mathbf{v} = {1 \over 2} \rho v^3 A C_d = ... = 1.4*10^{12} W[/tex]

That's about the same power about 60 Hoover dams yield just to overcome drag alone. And we haven't even tackled the problems of heat and air pressure, huge shockwave, etc.

Basically, you'd probably need some kind of equivalent of tactical nuke to propel this fist at this speed (which is somewhat natural - this speed is about 10 times the speed of expansion of high-grade detonation cords).

Now, here are the numbers for accelerating a fist to 0.000234c. What do you think would be energy expense and consequences of propelling an object to 0.5 c?

Won't you agree it's nonsensical to even continue discussing something that will never, never, ever happen?

 

[Mentallic]

dxun I don't think you're capable of appreciating the forces in play here either

Firstly because you made a very quick assumption at the start that the top speed must be reached in 0.5 seconds approx. That might be the time it takes for an average human to extend their arm in a punching motion, but we are talking about accelerating the arm to relativistic speeds. In 0.5 seconds this fist would reach a lot further than an arm's length, so what we are really looking for is the acceleration of the fist so that it goes from zero to nearly the speed of light in a distance of about 1m.

Secondly, F=ma isn't a suitable formula to use at such speeds, we would need to use the relativistic force formula!

So I believe it's going to be much more than what you've shown

 

[FizixFreak]

Now, here are the numbers for accelerating a fist to 0.000234c. What do you think would be energy expense and consequences of propelling an object to 0.5 c?

Won't you agree it's nonsensical to even continue discussing something that will never, never, ever happen?

yes it will never happen but the situation seemed quite interesting to me thanks for telling me about the drag force i totally did not realized that

 

[Mentallic]

I'm also curious if drag will act the same at low speeds as it would with accelerations and velocities as high as these?

 

[FizixFreak]

I'm also curious if drag will act the same at low speeds as it would with accelerations and velocities as high as these?

i am not an expert on that topic but i think it is reasonable to believe that there might be a different set of rules for drag force at such high speeds and one more thing if the drag is limited in free fall case(confined to a specific velocity) than why is it not limited in this type of situation?

 

[dxun]

Firstly because you made a very quick assumption at the start that the top speed must be reached in 0.5 seconds approx. That might be the time it takes for an average human to extend their arm in a punching motion, but we are talking about accelerating the arm to relativistic speeds. In 0.5 seconds this fist would reach a lot further than an arm's length, so what we are really looking for is the acceleration of the fist so that it goes from zero to nearly the speed of light in a distance of about 1m.

Duh! You're right, of course, but note that we're not accelerating the fist to truly relativistic speeds, but rather "just" to Mach 240, which still doesn't exhibit noticeable relativistic phenomena.

Let's assume punching distance is 1 m.

[tex]v=\frac{ds}{dt}\Rightarrow t=\frac{ds}{dv}\Rightarrow t=\frac{1m}{70220 m/s} \Rightarrow t=1.4241*10^{-5}s [/tex]

Now, acceleration needed is

[tex]a=\frac{dv}{dt}=\frac{7.0220*10^4 m/s}{1.4241*10^{-5} s} = 4.931*10^9 m[/tex]

Since Mach 240 is really not a relativistic speed (at least not for our purposes), I think it's appropriate to use classical Newton's second law here.

[tex]F= ma = 5 kg*(4.931*10^9 m) = 2.466 * 10^{10}N[/tex]

Let's see how much power do we need to accelerate this fist:

[tex]W = \Delta E_k = E_{k_2} - E_{k_1} = \tfrac12 m (v_2^2 - v_1^2) = 2.5 kg * ((70220m/s)^2 - 0 ) = 12 327 121 000 J = 12.33 GJ[/tex]

[tex]P = \frac{dW}{dt}. = \frac{1.232*10^{11} J}{1.4241*10^{-5} s}= 1.755*10^{16} W = 17.5 PW[/tex]

That's immense, I would say only nuclear devices produce such amounts of power over timeframe we're talking about here.

Drag at this speed is now:

[tex]F_D\, =\, \tfrac12\, \rho\, v^2\, C_d\, A=1.4241*10^{-5}*1.204*(70220)^2*1*0.00675= 570.67 N [/tex]

Power needed to overcome this drag basically becomes miniscule compared to power needed to propel the fist to Mach 240.

[tex]P_d = \mathbf{F}_d \cdot \mathbf{v} = {1 \over 2} \rho v^3 A C_d = ... = 40 073 061.8 W \approx 40.1 MW [/tex]

I think this is more realistic, what do you think? Personally, I find these number much more plausible, do you have anything else to add? Are there any other mistakes in calculation?

Secondly, F=ma isn't a suitable formula to use at such speeds, we would need to use the relativistic force formula!

So I believe it's going to be much more than what you've shown

I agree, if we were to go relativistic, these figures here would literally go through the roof, but I fail to see the point of it (except as a small math exercise, for which I am too tired now), since we've shown that should we accelerate fist to only a small portion of desired speed would totally annihilate everything in a vast radius around experiment.

 

[Mentallic]

That's a hell of a lot of power! The power consumption of humans worldwide last year was only 0.1% of that.

Oh yes sorry I just quickly glanced over the speed thinking it was a significant fraction of c.

The time required for the punch to reach its target should be twice that, but it doesn't really change the numbers as we're only really interested in the magnitude of the scale.

Let 70,220=v

[tex]v^2=u^2+2as[/tex]
u=0
s=1

[tex]a=\frac{v^2}{2}[/tex]

[tex]s=ut+\frac{1}{2}at^2[/tex]

[tex]t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2}{\frac{v^2}{2}}}=\frac{2}{v}[/tex]