[-ELM]

Due to some other posts I’ve seen around these forums it’s come to my attention that there are a substantial number of you with an interest in ideas surrounding the world of all things quantum. I thought I’d make this little thread to try and explain some of these phenomena to you as coherently as I can without getting bogged down in the mathematics surrounding the respective theories.

Whence came the quantum theory?

In the late nineteenth century the German Bureau of Standards, in an effort to save money, wanted to improve the already established light bulb in order to produce a maximum amount of light per minimal energy input. Max Planck was one such scientist commissioned to work on this project. This work related to a problem proposed nearly half a century by Kirchoff: black-body radiation. So what is a black-body? And why was this problem unsolved? An object is considered to be a black-body if and only if any radiation it emits comes solely from the temperature of the body. It sometimes also defined as a physical body which absorbs electromagnetic waves perfectly; I however believe this definition leaves some ambiguity. What is slightly misleading is that a black-body does not necessarily have to be black, it can be baby pink for all intensive purposes, what is important is that for all black-bodies at a given temperature there must be a single radiation curve regardless of the size of the black-bodies. A common example to show the significance of this result is that the curve produced by a metal behaving as a black-body in a furnace let’s say at 2500k would be identical to the curve produced by a star at 2500k which is light years from Earth.

The black-body problem remained unsolved as the theoretical predictions at the time did not pair up with experimentally data nicely at all. For smaller wavelengths of radiation the classical theory broke down, suggesting that the radiation produced was of infinite intensity and therefore of infinite energy. While investigating the work he was commissioned to, that is the light bulb, Max Planck found that by suggesting that if energy was released in small packets rather than continuous emission this problem would not arise. And thence with a bit of mathematical jiggery-pokery Planck helped to solve the black-body problem matching theory with experimental data.

So there we have it, quantum theory was born out of trying to improve the efficiency of light bulbs.
Before I move on, I’ll try and clarify what should’ve been taken from this. Energy comes in little packets called quanta, which means that energy is discrete and therefore only takes certain values. For those of you that may be wondering, just because energy is considered quantized this does not necessarily infer that every other physical property is quantized.

Ideas behind quantum theory

As hinted at earlier the rules that govern our macroscopic world are not the same as those for a system on the atomic scale. When systems on this atomic scale are investigated things become highly unintuitive; here is where things get interesting.
The first step in understanding quantum lies in a complete dismantlement of things you were probably taught when you were younger. Light is no longer just a wave, it can also be a particle; light particles are referred to as photons. This is referred to as wave-particle duality, an idea which was extended by a French physicist named De Broglie (Pronounced Deh-broy). De Broglie concluded that just as light exhibited wave-particle duality so did all matter. For example, electrons are not simply particles but also have an associated matter-wave. A property of electrons which is exploited in modern microscopes to produce images of objects that would not simply be possible with optical microscopes. For example, an electron traveling at a velocity of the order 10^6 m/s would be able to produce an image of something or the order of the size on an atom, somewhere around the order of 10^-10 m. You too also have an associated matter wave, let’s suggest you weigh 75kg and walk to the kitchen to get a drink at 1 m/s, your associated matter wave would be of the order 10^-36 which is obviously too small for even the most modern scientific equipment to come close to detecting. You may be wondering at this stage how an electron would know when it should act as a wave or act as a particle. Well, simply by observing the electron and taking a measurement you collapse the wave function. This leads nicely to the next topic of discussion: What the hell is a wave function?

The wave function is a mathematical formality which contains all measurable information regarding a given particle. However, the wave function is not magical – it can’t tell us everything with absolute certainty about the particle but it can tell us about the probabilities of particular features of the particle. An example of this could be whether the particle is located within a given region of space, and while because of the uncertainty involved in quantum measurements we can’t say the particle will definitely be in a given region of space unless that region is infinite, we can say that there is a given probability of finding it there. I know that isn’t the clearest explanation of what a wave function is and does but without introducing integrals and complex conjugates I can’t really elaborate much further. It should however provide enough information to understand future parts of this thread.

Now let’s consider some quantum phenomena, beginning with quantum tunneling: Imagine you put a marble inside a bowl, the marble happily rolls around inside the bowl but will never be able to escape the bowl unless you give it enough energy to do so. As you may have guessed things do not work like this on the quantum scale. To help explain this quantum tunneling imagine a process called alpha-decay, this is where heavy nuclei randomly “spit out” particles composed of two protons and two neutrons, these particles are helium nuclei and are also called alpha particles. Classically, similar to our marble stuck in the bowl, forces holding the original heavy nuclei together should prevent this alpha-decay occurring altogether. So, how does this process happen? Let’s bring in our example about the wave function being able to represent the probability of finding a particle in a given region of space: for a given region of space, ignoring the notion of anything being infinite, there will be a probability that the alpha particle is found. It does not matter how far away this location is from the original nuclei there will still exist a small, but finite probability of finding the alpha particle. So, by this process the alpha particle is able to “tunnel” through the potential energy that should classically confine it to the heavy nuclei and finds itself detached from its parent nuclei.

Now let’s consider the principle of superposition in quantum physics. From Wikipedia: Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system exists partly in all its particular, theoretically possible states simultaneously; but, when measured or observed, it gives a result corresponding to only one of the possible configurations. So, let’s apply this to something that’s easily visualised and can help explain what the hell it all means. Let’s imagine that we have a cat placed in a box and inside this box is a vial of poison. There is a probability that this vial will break and the poison will be released killing the cat. However, without making any measurements such as opening the box at a later time we can’t know whether the cat is alive or dead. Intuitively, without prior knowledge of quantum superposition, you would suggest that the cat is either alive or it dead. Let’s classify the cat’s life similar to how bits operate: if the cat is alive then it is in the 0 state, however if it is dead then it’s in the 1 state. However, as the definition above states that if a system has not occurred any measurements then it must exist in all possible states simultaneously. So, without looking into our box it must be true that the cat is simultaneously alive and dead. This famous thought experiment was proposed by a pioneer of quantum theory and is known more commonly as Schrodinger’s cat paradox. Now, let’s review our analogy to states representing bits. For the cat to be alive and dead at the same time there can’t simply be a 1 and 0 state but rather a combination of both of these states. This relates closely to the upcoming field of quantum computers where this combination of bits is referred to as a quantum bit or a qubit for short. For some calculations, this would make quantum computers much faster than the traditional counterparts of whom we are so familiar and dependent upon.

Despite this thread being somewhat irrelevant on these forums I thought I’d help clear up any misconceptions some of you were having even if I haven’t done the greatest job explaining things. I welcome any criticism or questions any of you may have. Please note that I did most of this from memory so there are more than likely going to be mistakes; skimming through myself I can already see areas where if I was to be pedantic I would eliminate for not being “strictly true”, but without introducing needless mathematics to over complicate an already ramble filled thread I will conclude things here. Thanks for your time reading.

[-ELM]

Due to some other posts I’ve seen around these forums it’s come to my attention that there are a substantial number of you with an interest in ideas surrounding the world of all things quantum. I thought I’d make this little thread to try and explain some of these phenomena to you as coherently as I can without getting bogged down in the mathematics surrounding the respective theories.

Whence came the quantum theory?

In the late nineteenth century the German Bureau of Standards, in an effort to save money, wanted to improve the already established light bulb in order to produce a maximum amount of light per minimal energy input. Max Planck was one such scientist commissioned to work on this project. This work related to a problem proposed nearly half a century by Kirchoff: black-body radiation. So what is a black-body? And why was this problem unsolved? An object is considered to be a black-body if and only if any radiation it emits comes solely from the temperature of the body. It sometimes also defined as a physical body which absorbs electromagnetic waves perfectly; I however believe this definition leaves some ambiguity. What is slightly misleading is that a black-body does not necessarily have to be black, it can be baby pink for all intensive purposes, what is important is that for all black-bodies at a given temperature there must be a single radiation curve regardless of the size of the black-bodies. A common example to show the significance of this result is that the curve produced by a metal behaving as a black-body in a furnace let’s say at 2500k would be identical to the curve produced by a star at 2500k which is light years from Earth.

The black-body problem remained unsolved as the theoretical predictions at the time did not pair up with experimentally data nicely at all. For smaller wavelengths of radiation the classical theory broke down, suggesting that the radiation produced was of infinite intensity and therefore of infinite energy. While investigating the work he was commissioned to, that is the light bulb, Max Planck found that by suggesting that if energy was released in small packets rather than continuous emission this problem would not arise. And thence with a bit of mathematical jiggery-pokery Planck helped to solve the black-body problem matching theory with experimental data.

So there we have it, quantum theory was born out of trying to improve the efficiency of light bulbs.
Before I move on, I’ll try and clarify what should’ve been taken from this. Energy comes in little packets called quanta, which means that energy is discrete and therefore only takes certain values. For those of you that may be wondering, just because energy is considered quantized this does not necessarily infer that every other physical property is quantized.

Ideas behind quantum theory

As hinted at earlier the rules that govern our macroscopic world are not the same as those for a system on the atomic scale. When systems on this atomic scale are investigated things become highly unintuitive; here is where things get interesting.
The first step in understanding quantum lies in a complete dismantlement of things you were probably taught when you were younger. Light is no longer just a wave, it can also be a particle; light particles are referred to as photons. This is referred to as wave-particle duality, an idea which was extended by a French physicist named De Broglie (Pronounced Deh-broy). De Broglie concluded that just as light exhibited wave-particle duality so did all matter. For example, electrons are not simply particles but also have an associated matter-wave. A property of electrons which is exploited in modern microscopes to produce images of objects that would not simply be possible with optical microscopes. For example, an electron traveling at a velocity of the order 10^6 m/s would be able to produce an image of something or the order of the size on an atom, somewhere around the order of 10^-10 m. You too also have an associated matter wave, let’s suggest you weigh 75kg and walk to the kitchen to get a drink at 1 m/s, your associated matter wave would be of the order 10^-36 which is obviously too small for even the most modern scientific equipment to come close to detecting. You may be wondering at this stage how an electron would know when it should act as a wave or act as a particle. Well, simply by observing the electron and taking a measurement you collapse the wave function. This leads nicely to the next topic of discussion: What the hell is a wave function?

The wave function is a mathematical formality which contains all measurable information regarding a given particle. However, the wave function is not magical – it can’t tell us everything with absolute certainty about the particle but it can tell us about the probabilities of particular features of the particle. An example of this could be whether the particle is located within a given region of space, and while because of the uncertainty involved in quantum measurements we can’t say the particle will definitely be in a given region of space unless that region is infinite, we can say that there is a given probability of finding it there. I know that isn’t the clearest explanation of what a wave function is and does but without introducing integrals and complex conjugates I can’t really elaborate much further. It should however provide enough information to understand future parts of this thread.

Now let’s consider some quantum phenomena, beginning with quantum tunneling: Imagine you put a marble inside a bowl, the marble happily rolls around inside the bowl but will never be able to escape the bowl unless you give it enough energy to do so. As you may have guessed things do not work like this on the quantum scale. To help explain this quantum tunneling imagine a process called alpha-decay, this is where heavy nuclei randomly “spit out” particles composed of two protons and two neutrons, these particles are helium nuclei and are also called alpha particles. Classically, similar to our marble stuck in the bowl, forces holding the original heavy nuclei together should prevent this alpha-decay occurring altogether. So, how does this process happen? Let’s bring in our example about the wave function being able to represent the probability of finding a particle in a given region of space: for a given region of space, ignoring the notion of anything being infinite, there will be a probability that the alpha particle is found. It does not matter how far away this location is from the original nuclei there will still exist a small, but finite probability of finding the alpha particle. So, by this process the alpha particle is able to “tunnel” through the potential energy that should classically confine it to the heavy nuclei and finds itself detached from its parent nuclei.

Now let’s consider the principle of superposition in quantum physics. From Wikipedia: Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system exists partly in all its particular, theoretically possible states simultaneously; but, when measured or observed, it gives a result corresponding to only one of the possible configurations. So, let’s apply this to something that’s easily visualised and can help explain what the hell it all means. Let’s imagine that we have a cat placed in a box and inside this box is a vial of poison. There is a probability that this vial will break and the poison will be released killing the cat. However, without making any measurements such as opening the box at a later time we can’t know whether the cat is alive or dead. Intuitively, without prior knowledge of quantum superposition, you would suggest that the cat is either alive or it dead. Let’s classify the cat’s life similar to how bits operate: if the cat is alive then it is in the 0 state, however if it is dead then it’s in the 1 state. However, as the definition above states that if a system has not occurred any measurements then it must exist in all possible states simultaneously. So, without looking into our box it must be true that the cat is simultaneously alive and dead. This famous thought experiment was proposed by a pioneer of quantum theory and is known more commonly as Schrodinger’s cat paradox. Now, let’s review our analogy to states representing bits. For the cat to be alive and dead at the same time there can’t simply be a 1 and 0 state but rather a combination of both of these states. This relates closely to the upcoming field of quantum computers where this combination of bits is referred to as a quantum bit or a qubit for short. For some calculations, this would make quantum computers much faster than the traditional counterparts of whom we are so familiar and dependent upon.

Despite this thread being somewhat irrelevant on these forums I thought I’d help clear up any misconceptions some of you were having even if I haven’t done the greatest job explaining things. I welcome any criticism or questions any of you may have. Please note that I did most of this from memory so there are more than likely going to be mistakes; skimming through myself I can already see areas where if I was to be pedantic I would eliminate for not being “strictly true”, but without introducing needless mathematics to over complicate an already ramble filled thread I will conclude things here. Thanks for your time reading.

[Coder-san]

Great thread, we rarely get something intelligent (non-programming) these days.
Perhaps some little pictures here and there would be helpful for the readers.
But seriously leave the poor kitteh alone!

[Coder-san]

Great thread, we rarely get something intelligent (non-programming) these days.
Perhaps some little pictures here and there would be helpful for the readers.
But seriously leave the poor kitteh alone!

[Ex094]

Agreed with @"Coder-san", Thank you for this thread

[Ex094]

Agreed with @"Coder-san", Thank you for this thread

[Linuxephus™]

Yes sir indeed, a very well written and thought out tutorial.
As a matter of fact, I'm going to slap that Tutorial tag on here right now.:thumbs:

Footnote: Never mind, it's a Poll.:lol:

[Linuxephus™]

Yes sir indeed, a very well written and thought out tutorial.
As a matter of fact, I'm going to slap that Tutorial tag on here right now.:thumbs:

Footnote: Never mind, it's a Poll.:lol:

[-ELM]

I am glad you have all enjoyed it. I will certainly look into your suggestion and try and find some images to help support the text.

[-ELM]

I am glad you have all enjoyed it. I will certainly look into your suggestion and try and find some images to help support the text.