Explaining Quantum Theory.

[SebastianOakes]

Obviously explaining quantum physics is in no way an easy thing to do, but I was hoping that if anyone has a deep understanding then they MAY be able to provide a basic explanation of the main principles. If you feel you can, then please do; I'm sure it would be considered useful to many on here.

I have a relatively strong understanding of physics in other areas, but quantum physics still blows my mind.

Edited January 21, 2013 by SebastianOakes

[Mike Smith Cosmos]

Obviously explaining quantum physics is in now way an easy thing to do, but I was hoping that if anyone has a deep understanding then they MAY be able to provide a basic explanation of the main principles. If you feel you can, then please do; I'm sure it would be considered useful to many on here.

I have a relatively strong understanding of physics in other areas, but quantum physics still blows my mind.

 

Keeping nice and simple to begin with, as it spans a lot of different famous scientists over 100 years and counting.:-

 

I will start the ball rolling by saying the word quanta probably started with :-

 

MAX PLANK.

 

Experimenting with the emission of light from hot metal , he solved the strange graph of emission against frequency of light ( red hot , yellow hot etc) by coming up with a formula with a fudge constant that he put in called h Planks constant . Later on in his research , and thinking he reasoned that the radiation, to do with vibrating electrons would come off in 'chunks' , he called them 'quanta.' .

He even worked out a value for the energy of a quanta as being Energy = h x f , in other words the energy coming away in chunks or 'quanta' is his Plank constant multiplied by the frequency of the light radiation coming off.

 

He did not get famous immediately , but when others including Einstein got hold of it , it made Max Plank and others famous.

 

So there is where the idea of Quanta or Quantum got its name and a bit of a boost . Many more scientists were to add to this .

 

Max Plank

Edited January 22, 2013 by Mike Smith Cosmos

[Arnaud Antoine ANDRIEU]

 

Obviously explaining quantum physics is in now way an easy thing to do

 

?

 

I have a relatively strong understanding of physics in other areas, but quantum physics still blows my mind.

 

I want to know more !

Edited January 21, 2013 by Arnaud Antoine ANDRIEU

[SebastianOakes]

Ahh thank you, I know of the Planck's constant, I just never made the connection!

 

And sorry, that was supposed to be 'in no way' not 'in now way', i have now changed it.

Edited January 21, 2013 by SebastianOakes

[Mike Smith Cosmos]

I was hoping that if anyone has a deep understanding then they MAY be able to provide a basic explanation of the main principles. If you feel you can, then please do; I'm sure it would be considered useful to many on here.

 

 

Part 2. Einstein

Einstein had been reasoning and researching the nature of atoms, and how they moved about. If anyone has ever done the smoke cell experiment , they will have seen how smoke particles are juggled around by bombarding air molecules ( atoms). Einstein made his break through with looking at pollen grains on water where the same buffeting occurs, in this case by water molecules. He became famous for this and his work trying to understand how light worked . ( He knew of Planks work with light) ( Chunks, Planks constant Very small, Frequency, Energy E=h x F)

 

Einstein played around with metals and the phot- electric effect . If you shine light of a certain frequency , getting up above red to Violet suddenly electrons are released by the light and a current ( individual or many electrons can flow. ) In chunks.Quanta ( quantum). A lot of Thinking , reasoning and experimenting with light being emitted when energy is supplied , he showed that the light came out in chunks, Quanta ( quantum). These became Known as Light Packets or PHOTONS By graphs of Energy plotted against frequency he produced a minimum frequency and a slope of a graph. The minimum frequency was as mentioned above. up toward Violet, and the Slope of the graph was exactly Planks Constant. Bingo. Einstein became famous for this and his work on motion , and relativity.

 

Also, Light was seen to spread out across space as individual packets , chunks Quanta/Quatum or photons which remained intact, So the individual packet was as intense on the wave front , as it was when it started its journey. The number of photons were decreased as they spread out across an increasing wave front on a spherical surface. ( like a bubble growing in size, colours go a bit thin) but if you could get at an individual packet , although the density of photons per square meter would be going down as the sphere increased in size, individual photon packet would remain the same as it started its journey. ( this is all to do with the inverse square law and the area of the surface of a sphere having a ( pi r squared )term in it. The early extended history of the light Quanta/Quantum

 

So much for Einstein part 1 and Quantum Part 2

Edited January 21, 2013 by Mike Smith Cosmos

[Arnaud Antoine ANDRIEU]

We could also talk about Galilean !

[SamBridge]

I think the best way to explore quantum physics is with a metaphoric fishing rod. You jump to a really complex object, and work your way back using concepts you understand, gradually learning new ones that give you enough understanding to finally reel in the idea.

[Mike Smith Cosmos]

Well, you guys reel in your catch, from the wriggling, jumping quantum fishes. I will try to throw in the odd men/women of the giant quantum story and what they added to the subject.

[elfmotat]

I'm a bit tired so I'll try to do this with minimal effort (which is probably bad).

 

Essentially the fundamental equation of quantum mechanics is the Schrodinger equation:

 

[math]i\hbar \frac{\partial \Psi }{\partial t}=-\frac{\hbar^2}{2m}\nabla^2 \Psi +V\Psi [/math]

 

This equation gives you a relationship between the potential energy function in space, and the "wave function" for the particle in question. If you specify a potential V and solve the Schrodinger equation for [math]\Psi[/math], you essentially obtain the probability distribution for that particle. If we restrict our scenario to one dimension, then the probability that the particle can be found between the points x=a and x=b is given by:

 

[math]P(a\leq x\leq b)=\int_a^b|\Psi|^2dx[/math]

 

where [math]|\Psi|^2=\Psi^*\Psi [/math] and [math]\Psi^*[/math] is the complex conjugate of [math]\Psi[/math].

 

Using the wave function we can also determine the expectation values for various observables by "sandwiching" their corresponding operator between the wave function. For example, the expectation value of position (where we "expect" it to be - an average of its position) is given by:

 

[math]\langle x \rangle = \int_{-\infty}^\infty \Psi^*x\Psi dx [/math]

 

The momentum operator is determined by the fact that it should be the generator of spacial displacements (in accordance with Noether's Theorem):

 

[math]e^{-i\mathbf{a}\cdot \mathbf{P}/\hbar}|x \rangle=|x+a\rangle[/math]

 

[math]\Rightarrow ~~\mathbf{P}=-i\hbar \nabla[/math]

 

 

So the expectation value of momentum is given by:

 

[math]\langle p \rangle =\int_{-\infty}^\infty \Psi^*(-i\hbar \frac{\partial}{\partial x})\Psi dx[/math]

 

We can build up most other observables from the position and momentum observables. I have no idea whether or not this was helpful, but oh well.

Edited January 22, 2013 by elfmotat

[SebastianOakes]

You certainly sound extremely clued up on the subject! There was a lot of jargon there, but i suppose that is unavoidable. If i stare at it for long enough I'm sure it will make sense.

[SamBridge]

 

 

Using the wave function we can also determine the expectation values for various observables by "sandwiching" their corresponding operator between the wave function. For example, the expectation value of position (where we "expect" it to be - an average of its position) is given by:

 

I'm familiar with the sandwich method but I don't see how it is shown. The sandwich method involves the output of a function being equal to the limit of two other functions which are greater than and less than this 3rd function which are continuous, though particles can have nodal surfaces they are still continuous at the limits that are needed. However, I see only one limit equation. You can model a 1 dimensional probability density when solving it on Cartesian coordinates to an extent, however those coordinates cannot always be translated into 3 dimensions by spinning around an axis, the real Schrodinger equation is much more complex than that so that it can do that, especially when you have much more complex orbitals and higher energy levels like f orbitals around nuclei, and for things like uranium is complex as it goes beyond f orbitals into g orbitals, but these orbitals are not exact as there still remains repulsion between electrons and the nuclear charge is very strong in larger nuclei towards the right end of the periodic table which is another variable to consider because it will also effect the shape of the orbitals, however those equations lack the consideration or the shape change caused y nuclear charge. The original complex Schrodinger equation does not contain this, however advanced computer models can show these factors.

Not only that but using Cartesian probability distribution is a problem, you can't always find solutions to Cartesian equations to create models, and it's much more efficient to use polar coordinates.

Edited January 23, 2013 by SamBridge

[elfmotat]

I'm familiar with the sandwich method but I don't see how it is shown. The sandwich method involves the output of a function being equal to the limit of two other functions which are greater than and less than this 3rd function which are continuous, though particles can have nodal surfaces they are still continuous at the limits that are needed. However, I see only one limit equation.You can model a 1 dimensional probability density when solving it on Cartesian coordinates to an extent, however those coordinates cannot always be translated into 3 dimensions by spinning around an axis, the real Schrodinger equation is much more complex than that so that it can do that, especially when you have much more complex orbitals and higher energy levels like f orbitals around nuclei, and for things like uranium is complex as it goes beyond f orbitals into g orbitals, but these orbitals are not exact as there still remains repulsion between electrons and the nuclear charge is very strong in larger nuclei towards the right end of the periodic table which is another variable to consider because it will also effect the shape of the orbitals, however those equations lack the consideration or the shape change caused y nuclear charge. The original complex Schrodinger equation does not contain this, however advanced computer models can show these factors.

 

I have literally no idea what you're talking about. That looks like nonsensical word-salad to me.

 

 

 

Not only that but using Cartesian probability distribution is a problem, you can't always find solutions to Cartesian equations to create models, and it's much more efficient to use polar coordinates.

 

First of all, if you can find a solution in polar coordinates then you automatically have a solution in Cartesian coordinates since they only differ by a coordinate transformation. I'm also not sure what this has to do with my post, or how it's relevant to the conversation in any way.

[SamBridge]

 

I have literally no idea what you're talking about. That looks like nonsensical word-salad to me.

Perhaps you should simply what you mean then. You said you could "sandwich" it. I guess its possible you did not mean that as a mathematical term in any fashion but I was thinking you were referring to the sandwich formula relating limits.

 

 

First of all, if you can find a solution in polar coordinates then you automatically have a solution in Cartesian coordinates since they only differ by a coordinate transformation. I'm also not sure what this has to do with my post, or how it's relevant to the conversation in any way.

you can, but not vice versa. You can't always find the Cartesian solution, but you can certainly find the polar solution and then also have the Cartesian solution if you want. I guess I'm just not really seeing what the point of your post is or what you are trying to say with it. The probability distribution of it models simple 1 dimensional Cartesian distribution, but in reality it is much more complex than that, and what you're saying won't be of much help to the layman, you need to work you're way up to big concepts gradually, you can't just throw Schrodinger's equation at someone and expect them to understand it. I would also be more careful about the term "word-salad". If it means what I think it means, the post definitive wasn't "word salad", it's just that it apparently was not in he same context as the point of your post.

Edited January 23, 2013 by SamBridge

[elfmotat]

Perhaps you should simply what you mean then. You said you could "sandwich" it. I guess its possible you did not mean that as a mathematical term in any fashion but I was thinking you were referring to the sandwich formula relating limits.

 

Ah, I see what you were saying there. I was referring to the fact that you literally stick the operator between the wave function and its conjugate to calculate the corresponding observable:

 

[math]\langle x \rangle = \int_{-\infty}^{\infty}\Psi^*(\hat{X})\Psi dx=\int_{-\infty}^{\infty}x | \Psi |^2 dx[/math]

 

[math]\langle p \rangle = \int_{-\infty}^{\infty}\Psi^*(\hat{P})\Psi dx=-i \hbar \int_{-\infty}^{\infty}\Psi^*\frac{\partial \Psi}{\partial x} dx[/math]

 

[math]\langle E \rangle = \int_{-\infty}^{\infty}\Psi^*(\hat{H})\Psi dx=i \hbar \int_{-\infty}^{\infty}\Psi^*\frac{\partial \Psi}{\partial t} dx[/math]

 

 

you can, but not vice versa. You can't always find the Cartesian solution, but you can certainly find the polar solution and then also have the Cartesian solution if you want.

 

I don't know what you're trying to say here. If you can find a solution in polar coordinates then you can automatically find a solution in Cartesian coordinates. This is a mathematical fact - there's no arguing it. One coordinate system may be more useful than another when solving the Schrodinger equation, but that's physically meaningless. Nature doesn't care how you decide to label points.

 

 

I guess I'm just not really seeing what the point of your post is or what you are trying to say with it.

 

The OP wanted a basic explanation of QM, so I gave him one.

 

 

The probability distribution of it models simple 1 dimensional Cartesian distribution, but in reality it is much more complex than that,

 

What is "it?" What are you talking about?

 

 

 

and what you're saying won't be of much help to the layman, you need to work you're way up to big concepts gradually, you can't just throw Schrodinger's equation at someone and expect them to understand it.

 

I explained it the only way I understand it: mathematically. If it were possible to paint an intuitive picture of what's going on in the OP's head, I might be inclined to try that approach. But as things stand there is no intuitive explanation of QM, nor is there even a consensus on what its standard interpretation should be. As far as anyone's concerned, the math is the theory.

 

The OP said he had a strong knowledge of physics in other topics, so I figured my post shouldn't be too far of a stretch for him.

 

 

I would also be more careful about the term "word-salad". If it means what I think it means, the post definitive wasn't "word salad", it's just that it apparently was not in he same context as the point of your post.

 

You started rattling off random stuff about electron orbitals and how Cartesian coordinates aren't good. It looks like word salad to me.

[SebastianOakes]

So there is no non mathematical explanation?

Perhaps if someone could explain what occurs during the single photon double slit diffraction experiment?

Most explanations seem to just give 'The photon goes through both slits and interferes with itself', which makes no sense at all, It is OVERLY simplified. On top of this is the whole concept of the photon only acting in this manner when unobserved; again however most explanations just appear to personify the photon in question for dramatic effect - 'The photon almost seems to KNOW it is being watched'. What is the definition of being 'observed' in this sense, and how does it affect the outcome?

[SamBridge]

 

Ah, I see what you were saying there. I was referring to the fact that you literally stick the operator between the wave function and its conjugate to calculate the corresponding observable:

 

[math]\langle x \rangle = \int_{-\infty}^{\infty}\Psi^*(\hat{X})\Psi dx=\int_{-\infty}^{\infty}x | \Psi |^2 dx[/math]

 

[math]\langle p \rangle = \int_{-\infty}^{\infty}\Psi^*(\hat{P})\Psi dx=-i \hbar \int_{-\infty}^{\infty}\Psi^*\frac{\partial \Psi}{\partial x} dx[/math]

 

[math]\langle E \rangle = \int_{-\infty}^{\infty}\Psi^*(\hat{H})\Psi dx=i \hbar \int_{-\infty}^{\infty}\Psi^*\frac{\partial \Psi}{\partial t} dx[/math]

Ok that's easier to see now

 

 

I don't know what you're trying to say here. If you can find a solution in polar coordinates then you can automatically find a solution in Cartesian coordinates. This is a mathematical fact -

 

Just slow down and actually read what I said, because I never said you couldn't.

The OP wanted a basic explanation of QM, so I gave him one.

And now of course he's asking for a non mathematical explanation. Classical physics as you know is different than quantum physics. If he knows much classical physics it isn't going to help much.

You started rattling off random stuff about electron orbitals and how Cartesian coordinates aren't good. It looks like word salad to me.

Just because you don't understand how it pertains to what you're saying doesn't make it word salad. What makes it word salad if it's literally just randomly seeming illogical statements strung together.

Edited January 23, 2013 by SamBridge

[beefpatty]

So there is no non mathematical explanation?

Perhaps if someone could explain what occurs during the single photon double slit diffraction experiment?

Most explanations seem to just give 'The photon goes through both slits and interferes with itself', which makes no sense at all, It is OVERLY simplified. On top of this is the whole concept of the photon only acting in this manner when unobserved; again however most explanations just appear to personify the photon in question for dramatic effect - 'The photon almost seems to KNOW it is being watched'. What is the definition of being 'observed' in this sense, and how does it affect the outcome?

 

Hello Sebastian,

 

The reason we say the photon "interferes with itself" is because a photon can be expressed as a wavefunction instead of a discrete particle. When a wave (i.e. a water wave) passes through two slits it simultaneously goes through both slits and then interferes with itself on the other side.

 

What constitutes an observation is often not defined and hence can be a source of mysticism as you alluded to. By observation we really mean measurement. When you "look" at a photon, for example, you're really using some test particle (i.e. another photon) to measure some observable such as position or momentum. But this inherently disturbs the measured particle. Before the measurement the particle is in a superposition, or combination, of possible states. It isn't until we measure the particle that we force it to be in one state, which "collapses" the wavefunction and destroys the interference pattern.

 

None of this is intuitive since we do not experience these effects in our daily lives so it is natural to feel uncomfortable with all of this. In that sense, to get a true understanding you have to delve into the math as there really is no intuitive connection to our experiences.

[SamBridge]

So there is no non mathematical explanation?

Perhaps if someone could explain what occurs during the single photon double slit diffraction experiment?

Most explanations seem to just give 'The photon goes through both slits and interferes with itself', which makes no sense at all, It is OVERLY simplified. On top of this is the whole concept of the photon only acting in this manner when unobserved; again however most explanations just appear to personify the photon in question for dramatic effect - 'The photon almost seems to KNOW it is being watched'. What is the definition of being 'observed' in this sense, and how does it affect the outcome?

Excellent question, what happens is it interferes with itself because it has diffraction like a wave. The simplest illustration of like a ripple in a pond. If you ran a wave of water through the two slits you'd see the same pattern, as well as the fact that you can model different orbital structures using polar coordinates, it's only natural that it would be assumed that certain properties of a particle act like a wave just as light does.

Edited January 23, 2013 by SamBridge

[john5746]

So there is no non mathematical explanation?

Perhaps if someone could explain what occurs during the single photon double slit diffraction experiment?

Most explanations seem to just give 'The photon goes through both slits and interferes with itself', which makes no sense at all, It is OVERLY simplified. On top of this is the whole concept of the photon only acting in this manner when unobserved; again however most explanations just appear to personify the photon in question for dramatic effect - 'The photon almost seems to KNOW it is being watched'. What is the definition of being 'observed' in this sense, and how does it affect the outcome?

The universe owes us no explanation. Smart people have to determine it and they have been trying.

 

Some links: Interestingly, the blog references this site's physics brain Swansont.

 

 

http://www.preposterousuniverse.com/blog/2013/01/17/the-most-embarrassing-graph-in-modern-physics/

 

 

 

 

I get the feeling we are missing something fundamental, like an extra dimension or the lack of a time dimension, but thats coming from extreme ignorance on my part. These things need to be tackled by those who can apply the math and rigor. Or, someone like Swansont needs to trip on some acid

[Mike Smith Cosmos]

 

Hello Sebastian,

 

The reason we say the photon "interferes with itself" is because a photon can be expressed as a wavefunction instead of a discrete particle.

 

None of this is intuitive since we do not experience these effects in our daily lives so it is natural to feel uncomfortable with all of this. In that sense, to get a true understanding you have to delve into the math as there really is no intuitive connection to our experiences.

 

I think that all that you say is correct, except the last sentence, as quoted above.

 

I am probably in a silent science minority, as I have and hear this and similar statements said very often. I really wonder if most people are saying " the king has beautiful robes on " when he is naked , but because everybody else can see he has no clothes on but dare not disagree with the majority, they repeat " the king has beautiful clothes on ".

 

This is not meant as personal criticism , as I hear this repeated over and over.

 

I am just throwing this comment in here as I wonder if we are not trapping ourselves into a massive mathematical swamp, only to be occupied by mathematicians who are trying to calculate themselves out of the swamp. When what is really needed is an old Door and a Rope

 

I know quantum physics is amazingly different from everyday life. Its taken about 50 Great Renouned Scientists to take it from 1890, if not before

to the present day and they were not all mathematicians.

 

All I ask is , give the Ideas, concepts, exploratory models , discussions, reasoning , thinking out of the box, plenty of headroom .

[beefpatty]

 

I think that all that you say is correct, except the last sentence, as quoted above.

 

I am probably in a silent science minority, as I have and hear this and similar statements said very often. I really wonder if most people are saying " the king has beautiful robes on " when he is naked , but because everybody else can see he has no clothes on but dare not disagree with the majority, they repeat " the king has beautiful clothes on ".

 

 

Hello Mike Smith,

 

I think you make a fair point, no personal offense taken. But I also can't, for example, give an every day analogy to the fact that the photon can act like a wave in some cases and a particle in other cases. Observing a water wave does not give this effect, and neither does leaving a tennis ball to its own devices. In this sense it directly counters our intuition and I cannot give someone a satisfactory reason for why it acts that way. The non-mathematical explanation would be it just does, as far as we can tell. Mathematically, however, you can see how it acts the way it does, and that is what I meant.

[MigL]

The double slit experiment has a mathematical explanation but certainly not a verbal explanation. When you guys say it is because a photon can act as a particle or a wave you are just confusing the OP. In some experimental situations it can be both and in some, neither.

If you set up an experiment to detect wave-like behaviour, then you will find the photon to act wave-like.

If you set up an experiment to detect particle-like behaviour, you will find the photon to act particle like.

 

The math does not describe quantum particles as waves of anything, but as quasi-probability waves. It is these waves which interfere with each other, even for a single photon, and which make the situation so hard to verbalize and the emperor's clothes so hard to see.

[PainwithoutLove]

I will make a clear answer to the question, what is quantum theory? The answer is that the quantum theory is based upon an observation that causes many interpretation or theory if you like. The observation of the double slit experiment is one that can bring someone to the notion of quantum world, or world of the very small if you want. Now, the experiment consist of making a matter thrown at two slits on a flat surface. The results of throwing lets say an atom or an electron at the the surface will be that the wall behind that flat surface will get a pattern of atoms or electrons or whatever you feel comfortable with, on that wall. Now, the reason why scientist put an emphasis on taking small objects is ridicule, because with larger objects the results would be the same, but they prefer sticking on to atoms and electrons to be more precise. Now, the conclusion of that experiment is simply that when capture as a picture, the atom acts like a wave, but when motion captured like a film, they act like an matter. So the interpretation of scientist made up all complicated consequences of that interpretation, called quantum mechanics.

By having an interpretation of what happened to the matter or light in the double slit experiment makes you a quantum scientist. Just remember one thing, reality contains only one true interpretation, wich means that 1 over all the possible interpretation is right, so don t get cocky at playing the game of hypothesis, since yours stands a very low chance of being The One.

[ACG52]

 

I will make a clear answer to the question, what is quantum theory?

 

But you didn't. You've just shown that you don't know.

[hypervalent_iodine]

!

Moderator Note

Please keep this on topic and PainwithoutLove, please do not hijack other threads with your own speculations.