What is the Quantum Theory? Enlighten Me!!!

[bluescience]

So I am more of a relativity guy, so I never ventured into the realm of quantum mechanics or the theory. I do know that it is an essential part in understanding the universe at the very small sized level. I also do know that it is related to research in time travel, teleportation and computers using a code more complex than the binary code. I also do now that is one of two theories that comes closest to the goal of science(in my eyes): to create a singular theory that describes everything in the universe.

 

But that is all a vague idea and I want to get started on understanding this theory, so I wanted to see if you guys could help me out on getting started. I am only looking for the basics of this theory or whatever it is.

[Eise]

I know this is dangerous in a room full of hard boiled physicists (I am only soft boiled...).

 

According to Quantum Theory (QT) everything physically existing must be described with wave and particle attributes. However, when we look at the corresponding wavelengths, we see that for everyday objects, this wavelength is many magnitudes smaller than the objects themselves, so we do not notice this. However, when the particles get smaller, their corresponding wavelength relatively increases, it can so to speak become even bigger than the particles themselves. This means that with very small particles we cannot neglect their wave character anymore, and physics must take this into account to describe their behaviour. As far as I know, the biggest particles with which the wave character was experimentally confirmed were 'bucky balls'. For the description of atoms, electrons, protons etc, we definitely need QT.

 

Small particles that are bound, e.g. in space or by electrical fields, form standing waves:

As you see, standing waves can only exist when they 'exactly fit in their limits'. So there is room for half a wave, for a whole wave, 1 and a half, etc: so you get discrete states: a wave with a wavelength of 4.2197465 'half-waves' just cannot exist: only states of 1, 2, 3, 4 ... etc 'half-waves' are possible. So you get the discrete, quantum character: a system can have state 3, or 4 but not 3.5.

 

The different states correspond to different energies: so in a system like e.g. a hydrogen atom, when the electron that is 'waving' around the nucleus can only get in certain states, and when it jumps from one state to the other, it can only emit its energy (in this case as a photon (=light)) in certain discrete values, being the difference in energy between the two states. From the other side, it can also only absorb light of the exact correct energy. This explains the discrete spectra of the elements.

 

Standing waves of electrons in atoms, called orbitals, are of course completely different then the simple standing waves above:

 

 

See also here.

 

As the first state is still a wave, the ground energy is never 0. So even the lowest state still has energy.

 

Another aspect of waves is that they are smeared out over space and time. You cannot measure the exact location of a wave, because it simply does not exist. This leads to the uncertainty principle: we cannot measure the frequency and the location of a wave in every detail. This is already true for simple classical wave mechanics, and it is true in QT too.

 

I know this is all simplified, but as a first understandable characterisation, it should do. Of course it is much more complicated.

 

From here on you can read Wikipedia...

 

https://simple.wikipedia.org/wiki/Quantum_mechanics

https://en.wikipedia.org/wiki/Quantum_mechanics

...

Edited April 14, 2016 by Eise

[studiot]

Nice overview +1

[Strange]

The other approach I would take is to look at the history of how quantum theory was developed.

 

One of the first things was that Max Planck found a way of solving a serious problem with the classical model for "blackbody radiation" by assuming that radiation could only be emitted in packets of a particular size.

https://en.wikipedia.org/wiki/Ultraviolet_catastrophe

 

I know some people like videos, so here is one on the subject (I have no idea if it is any good or not):

 

Then Einstein came up with a solution to the problem of the photoelectric effect where electrons are emitted from some materials when light shines on them. The classical theory said that if the intensity (brightness) of the light increased there should be more electrons emitted and if the intensity was low, then there should be a delay before the electrons gained enough energy to be emitted. Neither of these was true and Einstein showed that if you assume radiation comes in little packets (quanta or photons) as Planck had suggested then this explained the photoelectric effect.

https://en.wikipedia.org/wiki/Photoelectric_effect

 

They both got Nobel Prizes for their work.

 

Then it was just a matter of adding more detail to the theory....

 

Later, Einstein tried to show that quantum theory (or parts of it) were wrong because he didn't like the consequences. But he wasn't able to (and it was later proved that he was wrong).

[ajb]

Let us just restrict attention to nonrelativistic stuff for now.

 

I hope you know a little classical mechanics, if not then you should do if you want to have some idea of quantum mechanics. Anyway, in classical mechanics we have the Poisson bracket on phase space, that is the space where the points are position and time- (x,p). We have the fundamental Poisson bracket

 

[math]\{x,p\}=0[/math]

 

In standard nonrelativistic quantum theory this gets replaced with a commutation relation and we have to think even more algebraically here.

 

[math][x,p] = i \hbar[/math]

 

where just because of the dimensions we need to include a new constant in nature known as Planck's constant. It has units of action and sets the scale of quantum mechanics. This constant is set by observations.

 

So, nonrelativistic quantum mechanics with a finite number of degrees of freedom (so not field theory) is 'nothing' but looking at representations of the above communation relations!

 

One such representation, and the one commonly used to introduce quantum mechanics is the Schrödinger picture, which is where we describe particles as waves which are solutions of a kind of wave equation. This is the link with what Eise has said.

 

I hope that is enough for you to start 'googleing' more terms to fill in the gaps.

 

 

[Eise]

Just in addition to what I said about buckyballs, from here:

 

In 1999, the diffraction of C₆₀fullerenes by researchers from the University of Vienna was reported. Fullerenes are comparatively large and massive objects, having an atomic mass of about 720 u. The de Broglie wavelength is 2.5 pm, whereas the diameter of the molecule is about 1 nm, about 400 times larger. In 2012, these far-field diffraction experiments could be extended to phthalocyanine molecules and their heavier derivatives, which are composed of 58 and 114 atoms respectively. In these experiments the build-up of such interference patterns could be recorded in real time and with single molecule sensitivity.

In 2003, the Vienna group also demonstrated the wave nature of tetraphenylporphyrin—a flat biodye with an extension of about 2 nm and a mass of 614 u. For this demonstration they employed a near-field Talbot Lau interferometer. In the same interferometer they also found interference fringes for C₆₀F_48., a fluorinated buckyball with a mass of about 1600 u, composed of 108 atoms. Large molecules are already so complex that they give experimental access to some aspects of the quantum-classical interface, i.e., to certain decoherence mechanisms. In 2011, the interference of molecules as heavy as 6910 u could be demonstrated in a Kapitza–Dirac–Talbot–Lau interferometer. In 2013, the interference of molecules beyond 10,000 u has been demonstrated.

 

 

Is there a theoretical or practical limit to the mass that wave phenomena can be measured?

[ajb]

Is there a theoretical or practical limit to the mass that wave phenomena can be measured?

 

I am not sure... what I do know is that large molecules can show wave behaviour when sent through a double slit. I know that molecules with 114 atoms have been shown to give the expected interference pattens.

 

http://www.nature.com/nnano/journal/v7/n5/abs/nnano.2012.34.html

[RobC673]

To solve the mysteries of the quantum world I reckon we will have to wait for the emergence of another Newton/Einstein.

 

Normally I would have said it’s going to be a century or so but looking at the population explosion, it could be a lot sooner. I have the feeling that their nationality will be Chinese and their sex is going to be male.

 

Just hope I am here to see it happen.

Edited April 29, 2016 by RobC673

[ajb]

To solve the mysteries of the quantum world I reckon we will have to wait for the emergence of another Newton/Einstein.

I would say that this is off topic. we have a reasonable notion of what we mean by 'quantum theory' and anyone can get to grips with the basic ideas including the mathematics, well for non-relativistic particles anyway.

[Eise]

To solve the mysteries of the quantum world I reckon we will have to wait for the emergence of another Newton/Einstein.

 

What mysteries?

[RobC673]

One of the mysteries for me is why when electrons are fired one at a time through a single slit they form a diffraction pattern.

Edited May 3, 2016 by RobC673

[swansont]

One of the mysteries for me is why when electrons are fired one at a time through a single slit they form a diffraction pattern.

 

 

They are waves, and going through the slits means they interfere. With themselves.