Quantum Theory...help!

[i blame blame]

I just picked up a book dealing with this subject. I couldn't get past the first several pages before I was as lost as lost could be. Can anyone give me some pointers on how to begin to understand this subject? Maybe an outline of the very basics?

OK a couple of tings:
It was discovered in the early 20th century that some metal charged up (emitted electrons) when exposed to light whose frequency (which is proportional to energy) was superior to some cutoff value. According to the traditional light-is-a-wave model, it should have been possible to create this effect by using a lower-frequency light source with higher energy, because to give an electron enough energy for escaping the metal, one would simply need to illuminate it twice as long with a wave with half the frequency. However, this was not the case. This led to the postulate that light is made up by particles, light-quanta or photons, that each have an energy proportional to the frequency of the light. The theroy goes that an electron hit by a photon of slightly insufficient energy cannot cannot be excited to a higher energy level and remain there long enough for it to be hit by a second photon of equal energy.

Now to "quantum-uncertainty":
To observe something, one must illuminate it with something that can "bounce off it" and into the observer's observational mechanism. Everything that can be used for this (light, sound, pebbles, electrons, neutrons) has some energy and will inevitably transfer some of its energy to the observee. The lighter the object of interest is, the more energy transferred to it will be noticeable, and therefore the more the process of illuminating it will influence it. Now the trouble is, to observe smaller and smaller things, one needs illumination of higher and higher energies. Wave optics tells us that the wavelength needs to be shorter than the object of interesest. Waveelength is inversely proportional to frequency, which in turn is proportional to energy. Therefore, the smaller something is, the more energy we need to see it. But the more energy we use, the more we alter it's energy, and therefore momentum.

So the rule goes that to know an object's momentum we need to sacrifice knowledge of its position (i.e. inspect it with low-energy light/electrons) and if we want to know its position precisely (i.e. employ high-energy illumination) we alter it's momentum in an unknown way.

[i blame blame]

Bet I have more.
p.s.
Yah wanna go page by page or some combination thereof?

Sounds like a plan. I'm on page 18 where Clausius describes entropy (S). We know that the 2nd law states a hot to cold flow of heat. Why would entropy max out at thermal equilibrium? Wouldn't the higher-entropy cold object and lower-entropy hot object average out at any point before equilibrium?

Thermal equilibrium indicates high homogeneity, and disorder and entropy is some sort of quantization of those.

[i blame blame]

Hi John,
I'm still unclear about what exactly Entropy is?
I think I understand the ideas on pages 16 & 17 about Thermal equlibrium and how Energy can be described(formalised?) as the exchange of Work and Heat and that there is a Law called The Conservation of Energy, i.e. Energy is a constant that can be equal or unequal amounts of Work and Heat. If I understand right, Clausius's idea is that some heat is 'wasted' or non-useful in the process of a hot object effecting a cold one until they are both at the same temperature. This means that the total energy of the combined objects when at the same temperature will be slightly less
than the sum of energy of the two objects measured seperately. I think this is what he means by Entropy, the 'missing' energy.

Close but no cigar. Entropy and energy are not measured in the same units. Entropy is measured in Joules per Kelvin. Entropy kind of measures the quantity of energy's ability to be "useful" or "missing" but it is not itself the "missing" energy.

With respect to your questions. The way I'm trying to understand it is that we have two containers of the same liquid. Joined but with a gate between them one is coloured, the other clear. We heat the coloured one and then open the gate. Apparently the coloured one will rush into the clear one. It is the process that 'creates' the Entropy by losing Heat out of the system thereby reducing the level of Energy at the end. So it will at its maximum(?) when the process is complete, i.e. when Thermal Equlibrium(TE) is reached.
Sorry if this misses the point of your questions but if you could explain more about this idea of the hot and the cold objects averaging out before TE it might help me.
(If any Physicists out there want to drop in to correct our ideas I think JWK and I would be delighted)
a_uk

The entropy of the universe cannot decrease. If it does, time is running backwards. If you drop a superball, it will bounce to a lower height each time, because some of its energy is lost as heat to the ground each time. Heat will not magically come from the surroundings into a resting superball and make it bounce.

[John W. Kelly]

It'll take me a bit of time to sift though your info. Thanks ibb.

[Arising_uk]

Hi blame,

...Close but no cigar. Entropy and energy are not measured in the same units. Entropy is measured in Joules per Kelvin. Entropy kind of measures the quantity of energy's ability to be "useful" or "missing" but it is not itself the "missing" energy.

I like! close when I'm don't know what I'm talking about (And smoking is bad for you after all).
If Entropy is measured as Joules per Kelvin and these Joules(page 17) are the measure of Work from Heat, and this Kelvin is a measure of Heat. Is this saying that Entropy is the amount of possible Work lost for each graduation of this Kelvin Heat scale? So Entropy is an abstract idea? As all that is 'lost', i.e. relative to the system, is Heat? And Energy is an abstract idea as its really Heat and Work, i.e. mechanical motion?

The entropy of the universe cannot decrease. If it does, time is running backwards. If you drop a superball, it will bounce to a lower height each time, because some of its energy is lost as heat to the ground each time. Heat will not magically come from the surroundings into a resting superball and make it bounce.

The universe? I was thinking about two containers? What I don't understand is that if the containers were perfect insulators why the combined system would lose Heat not turned into Work, i.e. Entropy?
With respect to the superball. Does this mean if you bounce two superballs together they would bounce forever?
a_uk

[Psychonaut]

I hate physicists with a passion, because I have the creeping suspicion that they have the ability to out-bullshit me

[i blame blame]

It'll take me a bit of time to sift though your info. Thanks ibb.

Hope it helps.

Hi blame,

I like! close when I'm don't know what I'm talking about (And smoking is bad for you after all).

But you're not supposed to inhale cigars, so they'll only give you mouth-cancer.

If Entropy is measured as Joules per Kelvin and these Joules(page 17) are the measure of Work from Heat, and this Kelvin is a measure of Heat.

Nearly. Both work and heat are forms of energy and have units of Joules. Temperature is measured in Kelvin. Temperature is how we measure the internal energy of a system (the kinetic energy of the particles making it up).

Is this saying that Entropy is the amount of possible Work lost for each graduation of this Kelvin Heat scale? So Entropy is an abstract idea? As all that is 'lost', i.e. relative to the system, is Heat?

Kelvin temperature scale, but yes.

And Energy is an abstract idea as its really Heat and Work, i.e. mechanical motion?

Yes. Energy, entropy are abstract ideas that we use to relate measured "concrete ideas" like temperature, length, time, mass, quantity, charge, spin to one another.

The universe? I was thinking about two containers? What I don't understand is that if the containers were perfect insulators why the combined system would lose Heat not turned into Work, i.e. Entropy?

If the two containers are perfectly insulated from the surroundings, then those two containers are your universe. The set of the two containers would not lose heat and no work would be done if the gate were removed. However, entropy would increase because the system has become more homogeneous and some information is lost. When the gate was in place we knew that all clear particles were in container 1, while all coloured ones were in container A. We also knew that the average kinetic energy of clear particles was inferior to that of the colored ones (because they were warmer). With removal of the gate, colored and clear particles could be anywhere and their kinetic energies would be distributed along the same average.
Let's consider this: The two containers have equal volume and an equal number of equal particles. If container A is warmer then container 1, it will exert a greater pressure on its walls. If the gate is movable, then it will move into container 1 to equalize the pressure. This movement is work done because it could be used to lift a weight along a series of pulleys or something. If however, we open the gate before it can move along the walls entropy is increased, because if we were to close the gate again, there would be no more difference of heat between the two containers, which means that their pressure would be equal, leading to the conclusion that no more work can be done.

With respect to the superball. Does this mean if you bounce two superballs together they would bounce forever?
a_uk

Why don't you try it out.

[John W. Kelly]

[quote="i blame blame"]
It was discovered in the early 20th century that some metal charged up (emitted electrons) when exposed to light whose frequency (which is proportional to energy) was superior to some cutoff value. According to the traditional light-is-a-wave model, it should have been possible to create this effect by using a lower-frequency light source with higher energy, because to give an electron enough energy for escaping the metal, one would simply need to illuminate it twice as long with a wave with half the frequency. However, this was not the case. This led to the postulate that light is made up by particles, light-quanta or photons, that each have an energy proportional to the frequency of the light. The theroy goes that an electron hit by a photon of slightly insufficient energy cannot cannot be excited to a higher energy level and remain there long enough for it to be hit by a second photon of equal energy.[quote]

Is this what is refered to as the ultraviolet catastrophy ?

[i blame blame]

Is this what is refered to as the ultraviolet catastrophy ?

No. This is the photo electric effect. The ultraviolet catastrophe is another thought experiment that's important to quantum mechanics however:

Inside an oven there are electromagnetic standing waves. The boundary condition is that at the walls of the oven their amplitude must be zero. Therefore, not all thinkable wavelengths are allowed but only wavelenghts equal to twice the oven's length divided by an integer. In other words, the oven's length is half an integer multiple of the wavelength

λ=2L/n

Therefore, the shorter a wavelength, the more likely it is to fit in the oven's boundary conditions.
Now in classical physics there's this thing called the equipartition theorem, which states that all vibrational modes have an average energy proportional to the temperature of the oven. So there should be an infinite number of modes at lower and lower wavelengths, resulting in infinite energy. This has never been observed in real life.
This is where the quantum postulate comes in and states that the electromagnetic energy could only come in quanta proportional to the mode's frequency. So the high-frequency (low-wavelength) modes will be supressed because their energy (derived by the frequency) is superior to the energy it "should" have (as derived by the oven's temperature)

[Arising_uk]

hi Blame,

...If the two containers are perfectly insulated from the surroundings, then those two containers are your universe. The set of the two containers would not lose heat and no work would be done if the gate were removed. However, entropy would increase because the system has become more homogeneous and some information is lost.

I think I'm getting this thanks. So if the gate was removed no Work would be done due to no mechanical harness(by the definition of Work I suppose) but the Heat would still flow from Hot to Cold. Is a flow some kind of Work? In fact whats a "flow" in this sense?
"homogeneous" and "information " are new and I get the homogeneous.
The way I'm thinking about it is, say the hot side is twice as hot as the cold side. When the gate is removed the hot side gives the cold half its heat, this means that the resulting fluid is hotter than the cold was but cooler than the hot, TE I assume. But why would Entropy increase in this situation? As Entropy is the possible Work lost through Heat to the outside but we are in a perfect insulator so all Heat is retained? I think I understand why no Energy would be lost in this example as the volume of the two fluids should make up for the lower Heat available for Work.(Shit sorry, this is beginning to sound like I'm blagging an intro to basic Physics )

When the gate was in place we knew that all clear particles were in container 1, while all coloured ones were in container A. We also knew that the average kinetic energy of clear particles was inferior to that of the colored ones (because they were warmer). With removal of the gate, colored and clear particles could be anywhere and their kinetic energies would be distributed along the same average.

Could they be anywhere? Only at TE I'd have thought. The removal of the gate is the start of the process to reach TE. Is TE instantaneous? If not there must be an interface of some kind between the two fluids that mediates(?) the process. I'd originally thought of the exchange of Heat as having to be a two-way flow but know think that I need to think about what a transfer of Heat is.

Let's consider this: The two containers have equal volume and an equal number of equal particles.

"particles"(page 20) are yours the same as Maxwells Molecules?

If container A is warmer then container 1, it will exert a greater pressure on its walls.

Because Heat is causing the particles to move faster, yes?

If the gate is movable, then it will move into container 1 to equalize the pressure. This movement is work done because it could be used to lift a weight along a series of pulleys or something.

Ah! So could Work be described as the difference in pressure between two fluids?

If however, we open the gate before it can move along the walls entropy is increased, because if we were to close the gate again, there would be no more difference of heat between the two containers, which means that their pressure would be equal, leading to the conclusion that no more work can be done.

So Flow is instantaneous? How can that be? As it must take time for Heat to flow from hot to cold. Are you saying that when the gate is closed the same process continues within each container? And when settled to TE because they were the same fluids they will be at the same temperature therefore no Work possible as no Heat difference?

Why don't you try it out.

Okay I might have deserved the razz(if this is a raspberry? Or is razz some Yank slang?)
You said it was absorbed by the ground. Do you mean that the 'waste' Heat is radiated out somewhere? Some to the ground, some to the 'air', some back into the superball. Does this explain why a superball is a super ball? As it retrieves more Heat than the other bouncey substances?
a_uk

[John W. Kelly]

Inside an oven...

This is the so-called "Black Box?"

[Arising_uk]

Inside an oven...

This is the so-called "Black Box?"

Page 27/8 a Cavity.

[i blame blame]

Inside an oven...

This is the so-called "Black Box?"

Page 27/8 a Cavity.

Yes, cavity or blackbody. The known universe is the closest thing to a "perfect black body" we know of. I may reply to the rest tomorrow.

[John W. Kelly]

If the two containers are perfectly insulated from the surroundings, then those two containers are your universe. The set of the two containers would not lose heat and no work would be done if the gate were removed. However, entropy would increase because the system has become more homogeneous and some information is lost.

It is becoming clear to me that alot of QT is how one thinks of these concepts. The black-body as our universe makes perfect sense once thought of in these terms. Same with entropy as a loss of information, as well as an increase of disorder.

[Arising_uk]

...Yes, cavity or blackbody. The known universe is the closest thing to a "perfect black body" we know of. I may reply to the rest tomorrow.

How is the known universe a cavity? Whats heating it? Sorry if I miss the point.
a_uk