Do you like a challenge?

[bindeweede]

Just part-watched a prog on BBC4 on "Atoms". (I was visiting another forum at the time.) It mentioned "quantum mechanics".

There are lots of really brainy peeps on this forum, so here's a challenge....

as someone who doesn't really understand electricity, can you explain the principles of quantum mechanics, but in a simple way.......?

[Admin]

Now that IS a challenge Bindeweede. ;D

It's the explanation for all things unknown: psychic powers, homeopathy... ;D

Seriously though, it's quite a topic (and I'm certainly no expert in this area) but there are some books that are quite a good introduction - John Gribbin. Hang on... found it. :cheesy:

Found it - page 1 on our Amazon bookstore: http://www.ukskeptics.com/bookstore.php

In Search of Schrodinger's Cat


http://ec1.images-amazon.com/images/I/21F8V55DX1L._SL210_.jpg

I've read this book and as long as you have a rudimentary understanding of science, it's an excellent introduction. O0

It gives you a good basic knowledge of what it's all about. I think it begins with the double-split experiments and the dual nature of the wave/particle duality of the nature of light and goes on from there IIRC.

Added:

I've just read the review and it says that you require some mathematical knowledge too.


Does this book claim to explain quantum physics without maths? No. Maths is too central to physics to be bypassed. But if you can do basic algebra, you can understand the equations in In Search of Schrödinger's Cat.

[Cuddles]

I haven't read the book, so I can't really comment on it, although I have heard of it being decent before. As the quote from John says, it really isn't possible to explain quantum physics without the maths, however, I disagree with it a bit. While algebra may allow you to understand how the equations follow given some starting equations, a much deeper understanding of the maths is required to really understand what it actually means. Anyway, I'll try to explain the basics.

Firstly, all "quantum" actually means is that a system is quantised. That is, it has a set of discrete states instead of a continuous distribution. For example, a blank sheet of paper is continuous since you can draw on it absolutely anywhere, while graph paper covered with a pattern of dots is quantised, you are only allowed to conect the existing points.

A common misconception is that the idea of a quantised system is an assumption which then leads to the rest of quantum physics as a model that fits the universe. The exact opposite is actually true, the quantisation of a system is an inevitable consequence of the maths describing it. This is probably misunderstoof because of the history of quantum physics. The quantisation of light was first suggested around the turn of the century by Planck, although he maintained that it was simply a useful description and not actual reality. A few years later Eistein proposed his solution of the photoelectric effect, based on Planck's ideas. However, while these early theories did assume quantisation, later derivations have quantisation as a conclusion rather than an assumption.

Most of quantum physics is based on the idea of wave-particle duality. This is not actually a new idea, it has been argued about since well before Newton's time. Light has always been confusing for physicists because it doesn't behave itself. If you play with mirrors and lenses it behaves as if it is a wave, but if you play with it in other ways it behaves as a particle. Possibly the most important idea for quantum physics was the realisation that it doesn't have to be either a particle or a wave, it could be both. Following fairly shortly after this was the realisation that if waves could act as particles, why shouldn't particles act as waves.

Working the maths, it turns out that everything can be described by an equation with exactly the same form as a classical wave equation (such as that for describing the vibrations in a string). The general form of this is the Schrodinger equation, which is the fundamental foundation for the rest of quantum physics. The important thing to realise here is that there is actually no such thing as wave-particle duality. There are not waves that act like particles and particles that act like waves. These are both just aspects of some underlying thing that can act in a similar way to the waves and particles we are familiar with. I like the word "wavicle" to describe these, although I'm not sure who first coined it.

Here I should point out that because of this, common questions like "How can particles have a wavelength?" do not actually make sense. Particles don't have wavelengths, but on a fundamental level there is no such thing as a particle. A wavicle has the properties of both waves and particles, so if you try to measure particle properties like momentum you can do so, but if you try to measure wave properties like wavelength you can also do so. As a (rather bad) analogy, think of a flying boat (yes they do exist). If you think it is a boat and measure it's bouyancy you can do so and will conclude it is a boat. If you treat it as a plane and measure it's airspeed you can also do so and will conclude it is a plane. In reality it is both and neither, it can act as both and be treated as both, but it isn't exactly either one.

A lot of the basic ideas can be explained by looking at an electron orbiting an atom (although it is actually a wavefunction probablility distribution, the orbit analogy is close enough for most purposes). The lowest energy orbit would be a circle, and higher energy ones can be approximated by sine waves of different frequencies. The sine wave must have a whole number of wavelengths and must meet up with itself once it has gone all the way around. If this is not the case then the difference in phase of subsequent orbits will result in deconstructive interference, which would be effectivly the same as the electron not existing. This means that the energy levels must be quantised.

This simple idea explains many observations. For example, absorption and emssion spectra exist because since only certain energy levels are possible, the electron can only emit or absorb exactly the right amount of energy to change from one level to another. It also explains the fact that the electrons don't gradually lose energy and collide with nucleus, which is predicted by classical mechanics, because the electron simply can't lose energy in a gradual way. Finally, it also explains the idea of zero point energy. The lowest energy orbit possible would just be a circle, and there simply isn't a lower one that exists. However, the electron clearly has non-zero energy in this lowest state, so the lowest state possible is not actually zero. Hence, zero-point means that this lowest level acts as zero for this system, even though it is not actually zero (as an analogy, the ground acts as our zero point for gravity even though true zero would be the centre of the Earth).

The other important part of quantum physics is uncertainty. Again, this is often misunderstood as an assumption or a result of imperfet measurements, but this is not the case. Uncertainty between certain pairs of parameters are a consequence of the existence of a wavefunction. It is impossible to really describe why without the maths, but the result is that what are known as "conjugate pairs" of coordinates can never multiply to zero. Depending on the exact notation and derivatino used the minimum uncertainty is defined as either h or h/(2pi) (h is Planck's constant).

The best known pairs are position-momentum and energy-time. These are actually equivalent since one can be derived from the other, but they intuitively lead to different ideas. Firstly, position-momentum. As I said earlier, this is nothing to do with the accuracy of measurements, it is inherent to the particle itself. Even if only interacting with another particle with no measurements involved, the result of the interaction will be based on a probability distribution.

Many people, including Eistein himself, argued against the idea of uncertainty because it flise in the face of the apparently deterministic observed world (hence the "God does not play dice" quote). However, this is actually a very pleasing result philosophically, because it effectively eliminates the Newtonian idea of absolute determinacy. Since it is impossible to know exactly how any particles will interact it is not possible to predict the future and allows the possibility of free will.

The position-momentum uncertainty is very well known but, while it is fundamental to our understanding of quantum mechanics, it has less obvious consequences than the energy-time uncertainty. What this essentially says is that it is impossible to know both the energy of something and the length of time it exists for to absolute accuracy. This puts a fundamental limit on the accuracy of things like lasers, since there will always be a spread of energy (and therefore wavelengths). This then has consequences for the limits of how well we can look at very small things, since the purity of light used is very important. This also gives proof that the uncertainty principles are really properties of matter and energy and not just observational phenomena, since if this was not true lasers should be much more monochromatic than they actually are.

The other important consequence of energy-time uncertainty is pair production. What the uncertainty effectively says is that although energy can't be created on a macroscopic scale, it can be created and destroyed as long as it doesn't violate the uncertainty. This means that particles can appear out of nowhere as long as they disappear within a short time. Again, this provides proof that uncertainty is fundamental and not observational, since the effects of these particles can be seen.

One effect is the Casimir effect. Since the particles have an associated wavelength it is possible to restrict which particles can appear by making only certain wavelengths possible (in a similar way to waveguides for light). This has been demonstrated by placing two almost perfectly flat metal plates very close together in an almost perfect vacuum. Since only certain types of particle can be produced betwen the plates, less particles appear here than outside them and so there is a pressure pushing them together. This is often known as "vacuum energy". Although it was initially thought this could be a supply of free energy it is subject to the same conservation laws as everything else. While you can get energy from the plates being pushed together, it takes exactly the same amount of energy to pull them apart again, just as dropping a weight does not give free energy since you have to lift it up again.

Vacuum energy and zero point energy are often equated with each other, but this is not strictly true. Some quantum theories, notably quantum field theory, treat space as filled with some kind of field, and then the vacuum energy appears as the zero point of this field. However, even in these theories the two are not equivalent because although vacuum energy is a type of zero point energy, there are many other types, the zero point energy of electrons around atoms for example. In standard quantum theory the two are not the same at all. It is therefore important not to use the terms interchangeably, which is a common mistake of perpetual motion believers.

And that's it really. Ignoring the maths, there are really only two important principles to know. Wave-particle duality and uncertainty. Everything else follows from these. In fact, although quantum physics is often called illogical and counter-intuitive, if you accept these two principles then pretty much everything follows as a logical consequence.

So. Any questions?:tongue:

[Admin]

I was just about to say that. 8) ;D

Excellent post Cuddles. We'll have to keep that one for posterity somewhere. O0

[bindeweede]

Cuddles,
Well, I'll go to the bottom of our stairs.
"Thank you" seems a rather inadequate reply to your post. You must have spent ages putting that down, unless you have all of this on your mind all of the time. [And don't you have a job to do?;)]

I am going to print it out, and read it slowly and carefully, probably several times. This week's edition of "Hello" magazine has me challenged enough, at the moment.:cheesy:

I'm no expert (!), but summing up quantum mechanics in 2 and a half pages of A4 must be a great achievement. Thank you.

[bindeweede]

I was just about to say that. 8) ;D

Excellent post Cuddles. We'll have to keep that one for posterity somewhere. O0
So, John, were you a R.G.S. boy, or was it D.A's?

[Cuddles]

No problem. It was only supposed to be a quick couple of paragraphs, but apparently summarising the whole of quantum physics in less than a book is harder than it first seems. Bear in mind this was written off the top of my head, so it probably won't be 100% accurate. Also, I didn't really get into different interpretation here, but many theories, and people, see various parts in different ways. If you see things that disagree with other things you are told, it is not necessarily that one is right and the other isn't, it's just that the maths can be done in several different ways which all give the same answers, but with different assumption about what is actually "real".

[Dr B]

does all this mean i'm psychic????;D;D

[bindeweede]

No problem. It was only supposed to be a quick couple of paragraphs, but apparently summarising the whole of quantum physics in less than a book is harder than it first seems. Bear in mind this was written off the top of my head, so it probably won't be 100% accurate. Also, I didn't really get into different interpretation here, but many theories, and people, see various parts in different ways. If you see things that disagree with other things you are told, it is not necessarily that one is right and the other isn't, it's just that the maths can be done in several different ways which all give the same answers, but with different assumption about what is actually "real".

Well, I've read through it a few times, and I think I understand a little bit of it, but I don't think I'll be trying to delve any deeper???
Oh, and just for the record, I don't really read "Hello" magazine - just put it in for a laugh;)

[Jocky]

I was just about to say that. 8) ;D

Excellent post Cuddles. We'll have to keep that one for posterity somewhere. O0

Looks like a good basis for an article on the main UKS site to me!