My question is, if it is possible at all to reach the nearest Stars without referring to unproven hypothesis and technologies which probably will never be developed.
(Like FTL, "free Energy").

no , its not possible.

without using free energy theres no space travel to other stars.

using what we have now all at one shot might accelerate a ship carrying everything we now have on the earth such as oil , coal , natural gas , atomic fussion materials etc...

towards another star , but how big would that ship be?

remember the bigger it is the more energy will be needed for acceleration.

186 million miles per second.
thats travelling from the earth to our sun and then back to the earth in 1 second.
do that for 1 year and you have traveled 1 light year.

our closest neiboring star Proxima Centauri is 4.3 light years away.

the ship would eventually reach the star , if anybody survived the initial acceleration and nothing got in the way.

then you will need at least 1/4 the amount to slow the ship down.

unless you eject from the main ship and slow down a smaller landing ship.

not trying to burst the bubble just being realistic here.

thats why we should start going to our planets using our energy sources first.

then later maybe a better form of propulsion could be found made available.

3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.