What is possible in Star Trek scientifically.

[ProtoAvatar]

YellowSubmarine, “precisely measured” means that you "just read the exact momentum of the particle".
Once you do that, the particle's momentum will become determined, precise on its own (wave function collapse).

Well then, what you say is that a “precisely measured momentum” is a function that maps all possible values for the momentum to a certain probability amplitude? Since that's what an exact reading of the momentum would be.

First - What do the wave function's solutions represent?

As I said, a quantum particle is, simultaneously, in more places at once/has more momentum values at once.
But which places/which momenta does the particle have?
Quantum particles are 'jumpy', the values for position/momentum can be probable (no large 'jumps') or improbable (the tunneling effect; a non-zero, but really small chance for the particle to 'jump' on the other side of the universe).
The wave function will give you both the probable values and the improbable ones.


Now - All non-measured particle's possible momenta will be given by its wave function.
Among those, the particle will have, simultaneously, only a small subset of momenta. Which subset? The probabilities are given by the wave function.

When you measure the particle's momentum, its wave function will collapse - it will name far fewer possible momenta for the particle.
How few? Depends on the precision of the measurement.

All you need to do to in order to restrict/determine a particle's momentum is to measure the particle.

 

[KJbushway]

Well, i have actually done a lot of research on what is possible and what is impossible.
First just because someone with a degree says its impossible don't just give up(there has been occasions when they been proven wrong)
As long as you can dream off it don't give up on it.
Warp Speed is Possible, the mechanics are simple but yes they do require a lot of energy, but if a fusion generator were to be created then you could very well see a anti-matter/matter energy core.
Phasers are possible just not as you see in trek, you wont be able to see the phaser hit but the damage could very well be the same.
Torpedoes would be like the ones you see in ENT, missile like, could even have a anti-matter warhead.
Shields maybe possible, but more than likely, we will look for tougher/harder metals than can handle micro-meters and damage from weapons.
Impulse drives are possible we have those technologies today.
Hand held CT/X-RAY scanners are a bump scientists are trying to tackle right now for ambulances, etc.
Star trek technology is quite possible, though you will probably never see a transporter in your time or mine. But you might see technology like the rings from Stargate. Sorry i mentioned it.