FizixFreak said:
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 \Delta t. 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, v=0.
New time difference (should we accelerate the *whole* court) will be given with this formula:
\Delta t' = \frac{\Delta t}{\sqrt{1-v^2/c^2}}
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 v=100 km/h = 0.02778 km/s. Let's plug all this into formula above.
\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
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:
\Delta t' (0.000234c) = \frac{\3 s}{\sqrt{1-(0.000234c)^2/(1c)^2}} = 3.00000008 s
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).
\Delta t' (0.5c) = 3.46 s
That's hardly noticeable, so let's crank it up to 0.9 c (972 000 000 km/h).
\Delta t' (0.9c) = 6.88 s
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...
\Delta t' (0.99c) = 21.3 s
\Delta t' (0.99999c) = 670.9 s = 11.2 min
\Delta t' (1c) = \frac{\3 s}{\sqrt{1-(1c)^2/(1c)^2}} = \infty
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
L' = L \, \sqrt{1-v^2/c^2}
We'll start as before, serving a ball with 100 km/h up to 1 c, so let's see what happens.
L' (100 km/h) = 0.00007 \, \sqrt{0.999999999999996} = 6.999999999999985 cm
L' (0.000234c) = 0.00007 \, \sqrt{1-(0.000234)^2/(1)^2} = 6.99999981 cm
L' (0.5c) = 0.00007 \, \sqrt{1-(0.5)^2/(1)^2} = 6.062 cm
L' (0.9c) = 3.051 cm
L' (0.99c) = 0.99 cm
L' (0.9999999c) = 0.0031 cm
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
m_{\mathrm{rel}} = \frac{m}{\sqrt{1-{v^2/c^2}}}
m_{\mathrm{rel}} (100 km/h) = \frac{0.06}{\sqrt{0.999999999999996}} = 60.00000000000012 g
m_{\mathrm{rel}} (0.000234c) = \frac{0.06}{\sqrt{1-(0.000234)^2/(1)^2}} = 60.00000016 g
m_{\mathrm{rel}} (0.5c) = 69.2 g
m_{\mathrm{rel}} (0.9c) = 137.6 g
m_{\mathrm{rel}} (0.99c) = 425.3 g
m_{\mathrm{rel}} (0.9999c) = 4242.75 g = 4.24 kg
m_{\mathrm{rel}} (0.9999999c) = 134.16 kg
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.
