Quantum Mechanics.

Son Goku

I have to give a workshop to people in Maynooth on QM, so I just thought I'd make this thread to see can I actual explain it adequately.
Anybody with a question about the subject just ask and it'll be answered, hopefully in an easy to understand manner.

Panserborn

Cool.

The multi-universe theory, bull or real? How did the theory come about?

Son Goku

It was created by a man called Hugh Everett in 1957 in his PhD thesis.

As for whether it is bull or real is an interesting story.
Everett basically created it as a way of making it easier to calculate stuff in Quantum Mechanics by pretending that there was almost an infinity of separate worlds.

Its especially useful in some experiments today where using the regular way would be too difficult, although most of the time the many-worlds way is useless because its usually the more complicated method.

After Everett wrote the PhD, some people started wondering, if his many-worlds gave the same answer to problems as other ways of doing quantum mechanics maybe that meant that the many-worlds interpretation might be just as true as any other way of looking at quantum mechanics.

Eventually you got people who thought many-worlds was the only real one and the other ways of looking at QM were false and after more time there were a lot of these people saying that Quantum Mechanics said there was a multi-universe.

The truth is its a way of looking at the maths that is useful sometimes and not really useful most of the time. Its particularly useless when something happens to a lot of atoms together in a large object, like a cup.

So basically, its a useful tool when you're dealing with very few particles in certain situations and thats about it.

Civilian_Target

Son Goku wrote:

I have to give a workshop to people in Maynooth on QM, so I just thought I'd make this thread to see can I actual explain it adequately.
Anybody with a question about the subject just ask and it'll be answered, hopefully in an easy to understand manner.

Really? How heavy? Because I'd really like someone to explain to me exactly how the maths of Quantum Mechanics falls out of the 5 postulates, but thats beyond degree level stuff.

Failing that, are you sure you can explain Local Realism, Bells inequality and Quantum Entanglement?

Civilian_Target

Civilian_Target wrote:

Really? How heavy? Because I'd really like someone to explain to me exactly how the maths of Quantum Mechanics falls out of the 5 postulates, but thats beyond degree level stuff.

Failing that, are you sure you can explain Local Realism, Bells inequality and Quantum Entanglement?

If he can't I can try =D I did half a module on that crap. It's easy enough to pick up, even the maths is ok if you can use the notation. <x|y> stuff. And entanglement and stuff can be explained with coin analogies =D it was to us anyway.
I'd say goku can anyway, he r vry smrt.


Goku: You're giving a workshop? How in hell did that happen? I want to give a workshop =/

Panserborn

Crystal clear, the workshop will work well!

Son Goku

Civilian_Target wrote:

Really? How heavy? Because I'd really like someone to explain to me exactly how the maths of Quantum Mechanics falls out of the 5 postulates, but thats beyond degree level stuff.

Well I could explain it here.
I most familiar with the postulates been written in afrom where there is four of them.

1. The state of a particle is represented by a vector "|Ψ(t)>" in Hilbert Space.
2. Momentum, p, and position, x, from classical mechanics become operators X and P.
Dependant variables such as w(x,p) become Hermitian operators:
Ω(X,P)
3. A measurement of the Property associated with an operator Ω will give one of Ω's eigenvalues as a result. If we call one of these eigenvalues w the chance of w been the result is basically:
P(w) = |<w|Ψ>|^2. Where |w> is the state corresponding to w, |Ψ> is the state before measurement and |<w|Ψ>|^2 is the dot product of |w> and |Ψ> squared.
After the measurement |Ψ> will jump to |w>.
4. The state vector, when not being measured obeys the Schrodinger equation.

The four postulates basically set up Quantum Mechanics, they tell you how measurement works and how the particle acts when you aren't measuring them.

Tell me what you want to know about them and I'll attempt to answer.

Civilian_Target wrote:

Failing that, are you sure you can explain Local Realism, Bells inequality and Quantum Entanglement?

I'll give it a shot.

Lets say |up> is the state of a particle in spin up and |down> is the state of a particle in spin down.
Entanglement is when we make these two particles part of one super-state:
|up>|down>. So instead of a wavefunction for each particle we have a wavefunction for both.

I'm going to call one particle A and the other B, for the sake of this example.

Now we can entangle the particles in the state
|Ψ> = |A up>|B down>
or
|Ψ> = |A down>|B up>.

However because its quantum mechanics we can also make the following state:
|Ψ> = |A up>|B down> - |A down>|B up>.
This is the state I'll use.

So we put A and B in this state and we then shoot both the particles off, away from eachother. A goes to Earth, lets say, and B goes to Titan.

The experimenter on Earth measures Particle A to find out what its spin is.
He finds that it is spin up, which gets rid of the |A down> part of the state |Ψ> above.
However because |A down> is attached to |B up> it is also destoryed and we can only have |B down>.
So an experimenter on Titan has to measure B to have spin down, which he does.

Now if you notice, nothing happened faster than light here. The particles both moved to Titan and Earth slower than light. However once A is up, B has to be down. Lets say A is measured one second before B. How does A tell B to be spin down in less than a second, if it takes light a few minutes to get from Earth to Titan.
Or more accuratly how does
|Ψ> = |A up>|B down> - |A down>|B up>
collapse to
|Ψ> = |A up>|B down>
everywhere instantly.

The law of Local Realism isn't broken but its spirit is. It would appear that wavefunctions live outside spacetime, collapsing faster than light to make everything consistent.

I anything is unclear or you want more info, just ask.

Son Goku

bluewolf wrote:

Goku: You're giving a workshop? How in hell did that happen? I want to give a workshop =/

Four people are giving different workshops on Astronomy, Quantum Mechanics, Cosmology and Einstein's work.
I said I'd do the QM one and everybody was like "Yuh!, lets get laid".

Spear

Son Goku wrote:

The law of Local Realism isn't broken but its spirit is. It would appear that wavefunctions live outside spacetime, collapsing faster than light to make everything consistent.

I anything is unclear or you want more info, just ask.

Last I heard decoherence did take a measurable and finite time period to occur (though this doesn't rule a faster than light process). Have you got a link or other resource about decoherence speeds and timeframes?

Son Goku

Decoherence isn't the same thing as wavefunction collapse, even though it is often stated in such a way as to make the two appear the same.

Decoherence is quite rapid and has a measurable speed. Any search on an experiment called the "parametric down-converter". I'll get you better links shortly.

Decoherence is basically multiple wavefunction collapses causing a quantum system to go classical. How quickly the system turns classical has a measurable rate, but individual wavefunction collapse does not.

Civilian_Target

Son Goku wrote:

I anything is unclear or you want more info, just ask.

Well, I'm studying QM at the moment, so I'm reasonably OK, but your definition of the postuates is quite different from mine, and I'd always say that the Time Dependant Schrodinger Equation is the 5th postulate

Son Goku

Civilian_Target wrote:

Well, I'm studying QM at the moment, so I'm reasonably OK, but your definition of the postuates is quite different from mine, and I'd always say that the Time Dependant Schrodinger Equation is the 5th postulate

These are Dirac's postulates, slightly modified by Shankar.
Although there are a few ways of writing QM's basic postulates.
What are the jist of yours?

(The Schrödinger equation referred to in the 4th is the time-dependant Schrödinger equation, in case it came across as the time-independent one)

Civilian_Target

Son Goku wrote:

What are the jist of yours?

5 Postulates

I - Quantum Mechanics is a complete theory in which any particle in a field can be completely described by a normalised wavefunction Ψ which contains discrete quantized variables, and is usually complex.

II - When a variable A of a system is measured, what is measured will be an eigenvalue λ which is derived from an eigenvector Φ which is an operand of wavefunction Ψ. ie A Φ = λ Φ

III - When the state of a system is measured, at that given time, the wavefucntion Ψ will collapse onto the eigenvector Φ related to the eigenvalue which was measured (because as in postulate 2, each eigenvector has an associated set of eigenvalues).

IV - The probability of measuring a given eigenvalue from a system is given by P, which is the integral of the normalised square of the wavefunction.
If one attempt to measure 2 incompatible variables of a system, such as momentum & position (on the same set of axes), there will be an uncertaintly related to that eigenvalue, and therefore the measurement. Otherwise, the measurement may commute and there will be no uncertainty.
(I've treated the probablility of measurement and the collapse of the wavefunction as seperate postulates).

V - When a system is not being measured or perturbed, the wave function will evolve as given by the time dependant Schrodinger equation.

[EDIT]That'll be the time dependant, not indepenant Schrodinger equation...[/EDIT]

juddd

Where do atoms get their energy from, all that spinning needs energy does it not?
Could it be that "string theory" is creating that energy, the vibrations of the closed or open string would create the energy?
Or is it gravity creating that energy, where the nucleus is bigger than the spinning object around it, like the moon and the earth?

they say there are 4 dimensions and more, x,y,z+time, they also say that the other dimensions are too compact and that is why we cannot interact with them, I know this is just theory but what are your opinions of this theory?

Quantum entanglement is becoming more and more real as scientists are discovering new ways to trap entangled particles on microchips, which will herald a new age of computing as the particle can be in both states at the same time 0+1, how is it that a set of entangled particles can know the state of it's counter part even if they are seperated by light years, say one on earth and another on the far side of the universe, if you interact with the one on earth then the one on the far side of the universe knows this and acts accordingly, can atoms actually communicate?

Son Goku

if you interact with the one on earth then the one on the far side of the universe knows this and acts accordingly, can atoms actually communicate?

A better way to think about it, instead of communication, is that the particles form one system, which has to stay self consistent. So if one is spin up, the other must be spin down because of how the system was set up. The system is actually more elementary than the particles.

The real question is "How does the system ensure it is consistent faster than light?".

More on your other questions later.

Gone West

Son Goku wrote:

Four people are giving different workshops on Astronomy, Quantum Mechanics, Cosmology and Einstein's work.
I said I'd do the QM one and everybody was like "Yuh!, lets get laid".

can randomers show up or is it specifically for certain classes?

Son Goku

FuzzyLogic wrote:

can randomers show up or is it specifically for certain classes?

Anybody, it's a society thing. So as long as you're part of the college.

Gone West

Son Goku wrote:

Anybody, it's a society thing. So as long as you're part of the college.

cheers.
I'm assuming this is astro2. I'll make sure to be at at least one of these workshops. cheers for the quick answer.

munky

Tuesdays at...7ish...6:30ish? in JHT2=)

misty floyd

Hi,
I'm not being smart but why do we have to learn QM? When will I ever use it after college? What the hell is it for?

David19

Well, its one of the most important theorys in physics. Just read the introduction on Wikipedia:

Quantum mechanics is a fundamental physical theory that replaces Newtonian mechanics and classical electromagnetism at the atomic and subatomic levels and is the underlying framework of many fields of physics and chemistry, including condensed matter physics, quantum chemistry, and particle physics. Along with general relativity, it is one of the pillars of modern physics.

On its applications:

Quantum mechanics has had enormous success in explaining many of the features of our world. The individual behavior of the subatomic particles that make up all forms of matter - electrons, protons, neutrons, and so forth - can often only be satisfactorily described using quantum mechanics.

Quantum mechanics is important for understanding how individual atoms combine to form chemicals. The application of quantum mechanics to chemistry is known as quantum chemistry. Quantum mechanics can provide quantitative insight into chemical bonding processes by explicitly showing which molecules are energetically favorable to which others, and by approximately how much. Most of the calculations performed in computational chemistry rely on quantum mechanics.

Much of modern technology operates at a scale where quantum effects are significant. Examples include the laser, the transistor, the electron microscope, and magnetic resonance imaging. The study of semiconductors led to the invention of the diode and the transistor, which are indispensable for modern electronics.

Researchers are currently seeking robust methods of directly manipulating quantum states. Efforts are being made to develop quantum cryptography, which will allow guaranteed secure transmission of information. A more distant goal is the development of quantum computers, which are expected to perform certain computational tasks exponentially faster than classical computers. Another active research topic is quantum teleportation, which deals with techniques to transmit quantum states over arbitrary distances. There is also a book called Quantum Finance

Civilian_Target

misty floyd wrote:

Hi,
I'm not being smart but why do we have to learn QM? When will I ever use it after college? What the hell is it for?

Why learn Physics? How much of University Physics do you think most people use after their Physics degree? Its to expand your knowledge of the world. If you're not interested in it, you shouldn't be studying it.

munky

misty floyd wrote:

Hi,
I'm not being smart but why do we have to learn QM? When will I ever use it after college? What the hell is it for?

Depends on what Burger King you end up in:rolleyes:

apostata

munky wrote:

Depends on what Burger King you end up in:rolleyes:

Guys - the original poster was asking specifically (if not a little rhetorically) about QM, not physics in general.

Son Goku

misty floyd wrote:

Hi,
I'm not being smart but why do we have to learn QM? When will I ever use it after college? What the hell is it for?

Due to the fact that it is an important aspect of physics.
As David19 has shown above it is used in creating significant amounts of modern technology, so it is needed.
If you don't do physics, certain areas of mathematics or microscopic engineering after your degree you won't use it.
There is also the fact that, as Civilian_Target said, for the general understanding about nature.

A physics degree is there to train physicists primarily. If you don't decide to do physics after college then you have a degree for your CV. It would be inconceivable for every college course to have an application to the future career of everyone of its graduates.

misty floyd

Cheers for the replies. I did only have a question about QM and not Physics in general. Its just that sitting in class trying to get to grips with QM sometimes feels like learning Japanese and if you put a lot of work into something, you want to see some uses for it. I see that now.

In relation to the comment about working in Burger King. Thats just stupid.