Using early 21st century technology how do I design a katana that can only be wielded by its owner and also to execute a special attack? In my story the surviving samurai still practice bushido (code of conduct) and they will be trained on how to swing the special katana. This katana is customised according to each individual and the razor sharp blade will turn into rubber if either not wielded by owner or switched to training mode. The user can also execute a special attack using the special katana called "vacuum slicer" by moving the blade quickly enough to generate a sonic boom that can cause significant damage to the opponent/enemy. My question is how can I produce a sonic boom using this special katana?
A sonic 'boom' depends on the velocity of a projectile through the air - it needs to travel faster than sound.
A whip crack is an example of a small sonic boom and there lies your problem. A sonic boom that causes damage has to be produced by displacing a very large volume of air. Your blade isn't going to do that - no matter how fast it is wielded.
Maybe you could cause temporary damage to someone's hearing by producing the sound near to their ear, but if you do that with a sharp blade then you've probably followed through and sliced through their shoulder to a considerable depth. This would sever a number of vital blood vessels thus causing death within moments.
The cracking sound a bullwhip makes when properly wielded is, in fact, a small sonic boom. The end of the whip, known as the "cracker", moves faster than the speed of sound, thus creating a sonic boom. The whip is probably the first human invention to break the sound barrier.
Sonic boom - Wikipedia, the free encyclopedia
As chasly mentioned, a sonic boom is caused when something breaks the sound barrier. The speed of sound on Earth is approximately
340 m/s, so your katana will have to be going that fast in order to 'boom'. You could strap it to a fighter jet to achieve those speeds, but I assume you want to do this the old-fashioned way, and accelerate it with pure human strength.
Let's assume the samurai winds all the way up for this strike, and thrusts the katana straight forward as far as it'll go. At the absolute maximum, assuming he doesn't jump, I'd say we can get the length of two legs, two bodies, and two arms(reaching all the way back to reaching all the way forward). I found the average height of a human to be 175cm, so cut off the head (like the samurai do) and you've got about 145cm. The average arm length is 65. So
$145 \; cm \times 2 + 65 \; cm \times 2 = 420 \; cm = 4.20 \; m$
That is the distance the katana will be travelling. Using the equation
v=at (v is change in velocity, a is acceleration, t is time), and knowing we want to get to the speed of sound, we get
$v = a \times t\\ 340m/s = a \times t$
Plugging this and our distance into the equation $x=1/2\,a\, t^2$, we get
$4.2\;m = 1/2 \times a \times t \times t \\ 4.2\;m = 1/2 \times 340 \;m/s \times t \\ 4.2\;m = 170\;m/s \times t\\ 4.2\;m = 170 \;m/s = t\\ t = 0.0247s$
That means your samurai has about 2 and a half milliseconds to begin and end their strike in order to achieve the desired velocity in the given distance. They could do it faster, but this is the absolute longest it can take. Plugging this value of t back into the first equation, we get
$340\;m/s = a * 0.0247s\\ 340\;m/s \; / \; 0.0247 \;s = a\\ a = 13765\;m/s^2$
And I have no idea how to get that much acceleration. Since this is the maximum distance you have to accelerate, and probably the fastest way you can move a katana (not to mention a thrust is going to have less air resistance, which was not factored into this answer), I'm going to say it's effectively impossible using anything close to a katana and samurai.
You could probably just fire it out of a really big gun though.
You would need a fake katana - something more than a real katana.
"Only the owner can wield it" is relatively easy, even if much depends on who you're going to fool and what exactly is meant by "wield".
Recognizing the owner is the easy part: fingerprint (or palmprint) we already have, and we are not very far from fast and reliable DNA checks.
Deactivating the sonic effect is also easy, since it cannot be obtained through blade motion imparted from the outside - no swordsman can move the blade at the required ~333 m/s. So you need to get it through some trick, i.e. technology and a energy source hidden in the blade, or more likely in the handle. Therefore, simply turn off the energy source, and no sonic boom.
Making it impossible to wield the weapon as a katana is difficult, though.
The two options I see are:
fake blade. It's actually two blade slices with a middle dull third slice running lengthwise. This has two purposes: until the real owner strikes, the middle blade is extracted, and the blade edge is dull. At the right moment an electromagnet brings the third blade in, and the two outer blades together, resulting in a single, sharp blade. The cutting edge will not be as tough as a real katana, but the air displacement will be enough to get you the sonic bang - actually a very loud "thwack". Also, the momentum of the middle blade being pushed backwards will force the rest of the katana forward; for a very brief moment, the blade can strike with many times the force of a human blow. As soon as the middle blade arrives in its rest position, its momentum expended, the blade will "brake", so we can pierce an armor, but can't cleave it in two.
blade used as sound convector. It's a single blade, but again electromagnetically, a powerful transversal wave is sent along the metal, effectively producing a whip crack at the far end. Of course, the blade is still a blade, so anyone can wield it.
Against low technology or unprepared witnesses, other options are available. A low-voltage pulse at the right moment will be enough to make any unworthy wielder release the grip on the weapon (I'd be more comfortable if some contact on the back of the hand, or better yet the lower arm, was available. Otherwise I'd need large capacitors and the wielder would feel that the sword "bit" him).
Several weak nerve agents can also be released with similar effects, but the wielder would have a numb hand and arm for up to several hours afterwards.
In both cases, the witness report can be prevented by increasing the effect past the lethal threshold - dead men tell no tales.
And in both cases, a gloved wielder would be a problem.
Another possibility would be to have the handle (which is cylindrical) made up of several joined sections. To render the katana inoperable, we quickly spin whatever section pressure is applied on. The katana would "twist" in the wielder's grip, spoiling the strike. At worst, it would be like trying to hold a drill by the bit. Or the handle could subtly rotate a few degrees, making the wielder doubt his own senses and fruitlessly try to straighten his grip :-)