Can Quantum Mechanics Enlighten My Philosophical Ideas?

[Cuban Lincoln]

I have just recently become interested in quantum mechanics after having a series of conversations with my friend who is a chemistry buff. My background is mostly in philosophy, so my initial interest in quantum mechanics stems from its philosophical implications which are staggering to say the least. Unfortunately I haven't had much of a propensity for science in the past so I'm having to familiarize myself with very basic concepts. A part of me thinks it is rather futile to pursue a study of something so opaque considering I have very little foundational knowledge to begin with, but I'd really like to understand quantum mechanics enough to interrogate and strengthen my own ideas about philosophy. That being said, would anyone condescend to answer some questions I have?

1) What exactly is the correlation between line spectra and electron orbitals?

2) What is the simplest way to depict the wave function?

3) What exactly is Planck's constant?

4) What does it mean for something to be quantized? How is electromagnetic energy quantized?

Thank you.

 

[Feldoh]

I'm going to go a bit out of order because it makes more sense:

4.) Something is quantized it it comes in discrete multiples. For example we say charge is quantized by n*e, where n = 1,2,3,... and e is the charge of an electron (1.602*10^-19 Coulomb). In this sense you can think of it like this: in elementary physics electrons are the smallest particles to have electric charge.

The idea that charge is quantized came out about initially because electrons orbit a nucleus and from earlier developments accelerating charges emit electro-magnetic waves. So the big question was how can an electron stay in it's orbit if it's constantly losing energy by emitting electromagnetic waves. This isn't quite right but the fact that charge is quantized still holds.

1.) As previously stated charged particles can emit electromagnetic waves -- Light itself is just an electromagnetic wave with wavelength ~ 400nanometer - 700 nanometer (Violet - Red, and everything in between). Now when an electron makes the jump to a lower energy state (lower orbital) it gives off energy (since lower orbitals correspond to lower energy states, essentially) in the form of electromagnetic radiation, or light.

This brings about the question of why are there bands versus a continuous distribution? It all goes back to quantization. Electrons can only have certain energy levels, which means they can only release discrete energy in the form of light. This is why we see bands. The bands correspond to the discrete amounts of energy given when an electron makes a transition.

2.)The wave function essentially has a spatial, and spin part. The wave function is a bit of a funny thing. It's interpreted that the solution to the wave function gives us the probability that a particle is at a particular place at any given time. The implications of this assumption are that we don't actually know where a particle is, all we know is the probability of a particle being there -- Which brings about another interesting philosophical point in the uncertainty principle.

3.) Planck studied something called the blackbody problem. Essentially it goes like this: A blackbody is an object that absorbs approximately all radiation. However as the blackbody heats up it changes color by emitting thermal radiation.

I think it might help to show this: http://en.wikipedia.org/wiki/File:Blackbody-lg.png

If you notice the classical line it shoots up to infinity, which didn't fit experimental data. Planck purposed a different model, which fit the data. However he needed to scale his model by a factor of (6.626*10^-34 Js) which came to be known as Planck's constant.

 

[sylas]

1) What exactly is the correlation between line spectra and electron orbitals?

Electrons in an atom are always in one of a number of distinct possible energy states, corresponding to "orbitals". They are a bit like standing waves, and the crucial point is that (unlike conventional orbits) there is no continuum of possibilities between orbitals. You are either at orbital number 1, or number 2, or number 3, etc, with nothing in between.

An atom absorbs or gives off energy when electrons jump from one orbital to another. There are very precisely defined changes in the energy between orbitals, and hence there are very precisely defined increments in the energy given off, or absorbed.

The line spectra are from photons that have those energy increments.

2) What is the simplest way to depict the wave function?

There is no simple way to depict the wave function.

That's a bit blunt. There are of course various attempts to make it comprehensible or intuitive, ultimately, my favourite is expressed on this T-shirt:

(image link)

3) What exactly is Planck's constant?

6.626069 * 10^-34 joule-seconds.

(That's not really "exact", but it's getting there.)

It's the ratio between the frequency of a photon, and its energy. Since photons are the basic quantum of electromagnetic energy, this constant shows up lots of contexts associated with energy.

4) What does it mean for something to be quantized? How is electromagnetic energy quantized?

Something is "quantized" if it comes in discrete packets you can count, as opposed to a continuous stream you can measure. In our normal experience, water is continuous and apples are quantized.

It turns out that deep down, just about everything is quantized. The "quantum" of water would be a single molecule of H₂O. Any amount of water is a number of such molecules, and you can't have less than one molecule of water. Hence, the molecule is how water is quantized.

It turns out that light (ie, electromagnetic energy) is quantized as well. It comes in discrete countable packets, called photons.

Cheers -- Sylas

 

[granpa]

one can associate a specific frequency with each orbital. (the frequency associated with the ground state of hydrogen is R. the Rydberg constant). the frequency of the emmitted or absorbed light is equal to the difference between the frequencies associated with the 2 orbitals that the electron transitions between. the transition between orbitals is not an instantaneous thing. there is a finite time during which the electron is in a superposition of both states.

http://modelingnts.la.asu.edu/html/GAinQM.html

 

[Naty1]

A part of me thinks it is rather futile to pursue a study of something so opaque considering I have very little foundational knowledge to begin with,

Don't even think THAT way! Of course it is NOT futile...

Instead, consider that IF you are interested it IS worth your time and effort to invesitigate because that's how everyone approaches their potential...and if you get bored, move on to something else you do find interesting.

I have absolutely NO reason to be here except that I find many of the subjects and questions interesting...that's all it takes to make progress in your understanding of the world around you...

 

[Cuban Lincoln]

Thank you everybody for your helpful responses. I've been reading more and beginning to grasp some of the basic rudiments of quantum physics. I predict it will consume a lot of my free time.

It's the ratio between the frequency of a photon, and its energy. Since photons are the basic quantum of electromagnetic energy, this constant shows up lots of contexts associated with energy.

Could somebody elaborate on the idea of a photon's frequency? I understand frequency as an oscillation, but what would it be in the context of of a photon?

1.) As previously stated charged particles can emit electromagnetic waves -- Light itself is just an electromagnetic wave with wavelength ~ 400nanometer - 700 nanometer (Violet - Red, and everything in between). Now when an electron makes the jump to a lower energy state (lower orbital) it gives off energy (since lower orbitals correspond to lower energy states, essentially) in the form of electromagnetic radiation, or light.

This brings about the question of why are there bands versus a continuous distribution? It all goes back to quantization. Electrons can only have certain energy levels, which means they can only release discrete energy in the form of light. This is why we see bands. The bands correspond to the discrete amounts of energy given when an electron makes a transition.

So if the basic quantum of light is a photon then what relationship do electrons have to photons? Can it be said that electrons are equally as instrumental in the uncertainty principle?

3.) Planck studied something called the blackbody problem. Essentially it goes like this: A blackbody is an object that absorbs approximately all radiation. However as the blackbody heats up it changes color by emitting thermal radiation.

I think it might help to show this: http://en.wikipedia.org/wiki/File:Blackbody-lg.png

If you notice the classical line it shoots up to infinity, which didn't fit experimental data. Planck purposed a different model, which fit the data. However he needed to scale his model by a factor of (6.626*10^-34 Js) which came to be known as Planck's constant.

The introductory work I've read on quantum physics hasn't so far delved to deeply into the concept of black bodies. According to Wikipedia it's an idealized object. How is it integral to quantum theory?

Don't even think THAT way! Of course it is NOT futile...

Instead, consider that IF you are interested it IS worth your time and effort to invesitigate because that's how everyone approaches their potential...and if you get bored, move on to something else you do find interesting.

I have absolutely NO reason to be here except that I find many of the subjects and questions interesting...that's all it takes to make progress in your understanding of the world around you...

I think you're absolutely right. The most essential thing in studying anything is an invested interest. I'm pretty dedicated to gaining at least a basic knowledge of the fundamentals of quantum mechanics. I definitely think it is worth my time and a great backdrop to understand the supposed knowledge I do possess.

 

[sylas]

Could somebody elaborate on the idea of a photon's frequency? I understand frequency as an oscillation, but what would it be in the context of of a photon?

It's exactly the same thing. Electromagnetic radiation is a wave, with wavelength and frequency in the usual sense.

What may be tough to grasp is that it is also quantized. It comes it discrete packets, called photons. A photon is an indivisible wave packet of electromagnetic radiation.

So if the basic quantum of light is a photon then what relationship do electrons have to photons? Can it be said that electrons are equally as instrumental in the uncertainty principle?

Both the photon and the electron are fundamental particles. Electrons have charge. If you accelerate a charged particle, it will emit a packet of electromagnetic energy -- a photon.

The uncertainty principles is fully general; it applies for all particles. It's consequences are negligible for a big particle, like a baseball, but it still applies for them all.

The introductory work I've read on quantum physics hasn't so far delved to deeply into the concept of black bodies. According to Wikipedia it's an idealized object. How is it integral to quantum theory?

Simple cases are a good way to isolate certain phenomena ... in this case, the emission of radiation by virtue of an objects heat. A blackbody is one that where the internal oscillations of the material are able to match strongly with light of any frequency. Such a body is simpler to describe and analyze.

The spectrum of radiation from a blackbody depends only on temperature. The quantum nature of light was the key to explaining certain characteristics of this spectrum; in particular the fall off of the spectrum at higher frequencies.

Cheers -- sylas

 

[granpa]

from wikipedia:

In the laboratory, black-body radiation is approximated by the radiation from a small hole entrance to a large cavity, a hohlraum. (this technique leads to the alternative term cavity radiation) Any light entering the hole would have to reflect off the walls of the cavity multiple times before it escaped, in which process it is nearly certain to be absorbed. This occurs regardless of the wavelength of the radiation entering (as long as it is small compared to the hole). The hole, then, is a close approximation of a theoretical black body and, if the cavity is heated, the spectrum of the hole's radiation (i.e., the amount of light emitted from the hole at each wavelength) will be continuous, and will not depend on the material in the cavity (compare with emission spectrum).