I will try to make this easier for u, by making this organized.



[Heisenberg Uncertainty Principle]
uncertainty principle states that the product of position and momentum of let say, a particle, is constant. so, if you were to measure the position, you will never be able to measure its momentum accurately; and vice versa.
this is deduced from the following fact:
if you wish to measure the, position of, let's say, a particle,
the most direct way is by observing it, which means we will have to shine photons (light particles) on it, the photons were bounced back to our observing tool, and we get the image.
however, true for you get the accurate position and motion of that particle at that instance, because you see it,
however the photons that you introduced earlier, causes changes in the momentum in the particle, for it contain momentum too and causes change that can't be neglected.
to minimize this effect you would use less photon, so the overall momentum change is small, but now you can't observe the particle that accurate anymore.
now you get the idea of uncertainty principle? this principle will the the basic for quantum mechanics, and it revolutionize the physical world.



[Schrodinger's cat]
this case is somewhat related to electron too.
imagine a particle, which can spin, (electron is the most popular example)
a dot like electron is Spin=0, that is it looks the same from every point.
Ace in poker card is Spin=1, you will have to turn it 360 degree to get the same picture as you've started.
a Queen in poker card is of Spin=2, you will just have to turn in 180 degree to get the same image.
spin=3 is 360/3 degree to get back the same picture and etc.
and the spin property is not to be confused with the spin direction below (0 or 1)
(not quite relevant actually)

now, an electron can be imagined as a Top or planet spinning on its own axis.
with only one axis, wat is the possible direction of spin? to the left and to the right?
let's represent each different direction with digits.
to the left=0, to the right =1.
so the direction of spin of an electron can be used to represent data using binary codes. 10101000101010 .... bla bla those things?
that is quantum computing. or spintronics.
and researches are being made in constructing the future quantum computer, data will be processed and stored by spins of electrons, rather than the numerous transistors.
now imagine, what is the electron don't spin to the left or right, instead it spin upwards or downwards?
so is it 0 or 1?
can we assume that it's spinning in both left and right? this is not wrong after all right?
so it is both 0 and 1 at the same time, this is called superposition.

now we're gonna put this into a real situation.
we will link the binary output of the electron spin to the trigger of a gun, and the gun is aimed at a cat.
if the output is 0, the gun will not fire; if it is 1, the gun will fire, and the cat dies.
now, the electron is in superposition state, and the output is both 0 and 1,
so the cat is both alive and dead at the same time.
this was the idea of schrodinger, so that is the name.



[location of electron cannot be pinpoint]
well this is rather an extension from uncertainty principle.
from classical mechanics' point of view,
yep we can imagine every day's matter are made from discrete and tiny particles.
a block of, gold, can be divided and divided again, until we get a single gold atom.
a gold atom is a particle, and then as science advanced forward,
someone called Rutherford bombarded gold foil (sheets made from gold particles) with alpha particles (helium)
and he discovered there's inner structure within an atom, i.e. the nucleus and electrons.
so we imagine them as planets orbiting around a star, electrons orbiting around a central nucleus,
where electron is a tiny billiard ball, and proton and neutron are balls which are way larger.
this became the basis of what we learn, in chemistry as well as in physics other than quantum mechanics,
here we learn them as 'tiny balls', which means we are suppose to be able to see them or, pinpoint them or etc.

in quantum mechanics things are way more different.
the founder of quantum mechanics James Clerk Maxwell said: the true logic of this world is in the calculus of probabilities.
this is the basic idea, and it is true.
things at this scale can't be measured using conventional method anymore.
because we can't measure a single particle accurately.
but the use of probability can measure a whole bunch of particles,
for example 100000000 coins to be tossed.
if one coin is tossed you can only predict the probability of it getting head, that is 0.5. but you won't know the outcome.
with 100000000 coins, you know there will be half of the coins showing head and the other half showing tails.
the case is same with measuring particles.
we use probability to calculate everything.

how do we, for example, know the position of the shells of electrons?
1st shell 2nd shell 3rd shell?
do we measure the electrons' exact position?
no, the real method is, we take numerous photographs, and we see the position of the electrons in the atom.
then we plot the position where electrons appear and join them together, we get an area in which electrons pass by them.
so in fact it is 'cloud of electrons' that we are measuring,
more accurately saying, it is a wave function.
same as you plot many points on a graph paper, then you join the points and you get a graph, and then you calculate the wave function.

the same principle applies for many other things in quantum physics.
maths and probability plays a key role in quantum physics, and in string theory too.
on these, we don't rely on conventional method of deriving conclusion and physical laws anymore.
from this point onward, everything is based on mathematical calculations and equations.
and then we interpret the math into sentences, physics laws, and even predict new things.
and then only we testify them with experiments.

this is the other way round as in the conventional method,
in which we carry out experiment first, and observe, make inference, interpret data and make conclusions, generalizing the laws.





and one thing that most people might not realize.
let me ask you a question,
why mass possess gravitational force?
why charged particle (like electron) possess electrical charges?
why mass has inertia? preserves its original state of motion?
and, why is 1+1=2?

can't be explained right?

the point is, there's a limit in physics in which we are allowed to explain things.





alright i hope you enjoy reading although it is quite long.
the books i've read are even longer.
hope I helped. feel free to seek further help from me,
btw do correct me if I'm wrong on anything,
I'm just a 17 years old kid anyway.
still learning.

aren't we here to answer d cute pikachu's problem and, well, discuss on quantum physics? ghahhaaha

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Added on September 10, 2010, 1:24 amwell cute lil pikachu, an addition to my previous second post
this was what i wrote on the different thread 'energy'

in fact, the truth,
as stated by physicist like stephen hawking,
is as follow:
though we can define some quantities or explain things or define them in terms of more fundamental quantities (e.g. speed in terms of distance and time),
some concepts are so fundamental that any such attempt leads to a circulation definition like that just stated.
to escape from this, we will have to define such quantities 'operationally', which means we describe what they do,rather than what they are. i.e. we can explain how do they operate.
such as mass, we can explain it through the force an object experiences when exposed to gravity, that is, objects of same mass will experience the same force when placed at the same point or in the same strength of gravitational field.

why physics involves maths so much that one can't really understand it without maths?
because the physical world appears to be largely governed by the laws of cause and effect, and maths is used to explain such casual relationship,
and it is used to make prediction and measurement.
every single row of correct maths equation or formula that can be written is a valid representation of certain event in this physical world.

This post has been edited by KeNGZ: Sep 10 2010, 01:24 AM

I think he is referring to Participatory Anthropic Principle,
this has been used by physicists for quite a long time