Predictions of Quantum Mechanics

[mijopaalmc]

I was recently discussing the many-worlds interpretation of quantum mechanics (henceforth MWIQM) with a friend. It turns out that he is upset that people on the internet who believe in the MWIQM mock him for believing in God. He apparently thinks the God hypothesis is as plausible the MWIQM, as he views both as unfalsifiable and unable to make naturalistic predictions about the world. In fact, he goes so far as to say he believes all QM is bunk.

I have pointed out to him that QM is one of the most well-verified theories about the universe we have. For instance, it either predicts or explains, among other things, blackbody radiation, the photoelectric effect, the yellow sodium doublet, and semiconductor band gap theory.

He happens to be a much more practical person than I, so some of the predictions or explanations of QM I mentioned above are a bit arcane (from the point of view of a person who has taken no more than a college-level general physics course).

My question to you is therefore:

Does anyone know of some more accessible material on the predictions or explanations of QM that I can direct him to, assuming that he is honestly interested in expanding his knowledge of QM?

 

[The Man]

Try searching for QED Quantum Electro-Dynamics and QCD Quantum Chromo-Dynamics, two of the fundamental quantum theories that comprise what is now known as the standard model. I have always considered myself as a subscriber to the Copenhagen interpretation of quantum physics. I never gave the many worlds interpretation much credence, until I read an article in the December 2007 edition of Scientific American about Hugh Everett and his many worlds interpretation. I must say that it is very well presented and gives some fine experimental considerations. It has certainly made me pause to rethink that I may have been premature in dismissing the many worlds interpretation without full consideration. Perhaps researching Hugh Everett might give you the information you are looking for? The interpretations of QM may be debatable but its reality and application to modern technology are not.

http://en.wikipedia.org/wiki/Quantum_tunneling

Quantum tunneling was later applied to other situations, such as the cold emission of electrons, and perhaps most importantly semiconductor and superconductor physics. Phenomena such as field emission, important to flash memory, are explained by quantum tunneling.

http://en.wikipedia.org/wiki/Flash_memory

To erase a NOR flash cell (resetting it to the "1" state), a large voltage of the opposite polarity is applied between the CG and drain, pulling the electrons off the FG through quantum tunneling.

So if your friend uses a flash drive, when rewriting or erasing that drive it may involve QM.

 

[edd]

I was recently discussing the many-worlds interpretation of quantum mechanics (henceforth MWIQM) with a friend. It turns out that he is upset that people on the internet who believe in the MWIQM mock him for believing in God. He apparently thinks the God hypothesis is as plausible the MWIQM, as he views both as unfalsifiable and unable to make naturalistic predictions about the world. In fact, he goes so far as to say he believes all QM is bunk.

There is rather a fundamental problem here (well two, if you count the problem of him thinking all QM is bunk). Each of the interpretations of QM is basically giving a philosophical backdrop to the mathematics of QM. The mathematical predictions are very well tested, but how do you choose between alternative explanations of those predictions?

It's very difficult, and probably depends ultimately on sacrificing at least one common sense notion, and which bit of common sense you give up is maybe a matter of personal taste.

Now, if you choose to believe MW is bunk you'd have to pick an alternative which predicts exactly the same observable results. I think it's very difficult to come up with a theologically useful God who has exactly the same effect on the observable universe as an atheistic alternative.

I think to chase after the accuracy of QM is the wrong route to take. One needs to point out that if God exists there should be some evidence of it over its competitors. It is very difficult to come up with any prediction of MW that is not also predicted by one of its competitors.

If he actually believes all QM is bunk, then I'd probably try to find a Stern Gerlach apparatus or something to show him. No substitute for having quantum mechanics staring you in the face.

 

[INRM]

What's blackbody radiation?

 

[sol invictus]

Many consider the transistor to be the greatest invention of the 20th century. Without it the world would be a very different place (you wouldn't be reading this message, for example).

So why not ask your friend how to build a computer without using quantum mechanics?

 

[edd]

Black body radiation - what you'd expect a perfectly black body to give off as radiation (perfectly black being something that absorbs radiation of all frequencies perfectly). There's few examples - in the lab you build a 'black body' by basically having a box with a small hole in it - all the radiation bouncing around the inside eventually gets pretty close to a black body spectrum. And the cosmic microwave background is stunningly close to a perfect black body spectrum.

The significance here is that classical mechanics cannot predict this spectrum - and when I say can't predict it it's one of those 'not even wrong' situations - see http://en.wikipedia.org/wiki/Ultraviolet_catastrophe
It's crucial that the energy is given off in discrete packets or you end up predicting an infinite power output.

 

[Cuddles]

He apparently thinks the God hypothesis is as plausible the MWIQM, as he views both as unfalsifiable and unable to make naturalistic predictions about the world.

And he's right. As Edd says, many worlds, and most other interpretations, are nothing more than philosophy. Quantum mechanics can certainly make predicitions and is very much falsifiable, but most of the speculation about why it happens is completely unfounded, and usually involves fairly major violations of Occam's razor and often various physical laws. Many worlds, for example, requires the creation of at least one entire new universe every time any two particles interact. It's hard to imagine an idea that involves introducing more unecessary entities, as well as requiring the creation of rather a lot of matter and energy. Other interpretations are generally not much better. The important point is that none of them have any evidence whatsoever to actually support them, otherwise all the different views wouldn't exist. It's generally best not to get into discussions about which interpretation is best, because at the moment it can never be more than idle speculation.

However, the claim that all quantum mechanics is bunk is clearly wrong. I would have thought the things you point out are fairly good examples of predictions QM makes. As Sol points out, semiconductors are pretty much the foundation of the modern world. It doesn't get much more practical than that. Things like this may not seem especially practical, but they're a pretty good demonstration of what you can do with quantum mechanics.

 

[sol invictus]

As Edd says, many worlds, and most other interpretations, are nothing more than philosophy. Quantum mechanics can certainly make predicitions and is very much falsifiable, but most of the speculation about why it happens is completely unfounded, and usually involves fairly major violations of Occam's razor and often various physical laws.

I don't fully agree with you on that. Some progress actually has been made in the last decade on these questions, on valid theoretical grounds. And in principle many worlds is testable, either with a numerical simulation or possibly in a real experiment - it's just really, really hard.

As Sol points out, semiconductors are pretty much the foundation of the modern world. It doesn't get much more practical than that. Things like this may not seem especially practical, but they're a pretty good demonstration of what you can do with quantum mechanics.

One could also mention nuclear power, nuclear weapons, almost all of modern chemistry, all of modern physics, some biology, the sun, the existence of stars and planets and galaxies, the existence of matter, the cosmic microwave background, quantum computing, etc.

So I guess this "friend" thinks all of that is bunk, too?

 

[mijopaalmc]

I thank you all for your responses, but my main problem is that I don't know how to simply explain the concepts of quantum mechanics and how they give rise to most of modern technology to someone who has most likely only taken a college-level general physics course, if that.

For instance, from what I understand of band gap theory, the band gap arises from the energy difference between the bonding molecular (roughly the valance band) orbitals and the antibonding molecular orbitals (roughly the conduction band), which arise from summing over the energy states in which all or most of the wave functions of the atomic orbitals are symmetric with respect to one another and the energy states in which all or most of the wave functions of the atomic orbitals are antisymmetric with respect to one another. If the valance band and the conduction band overlap, the material is a conductor. If the valance band and the conduction band are separated by a difference within (I'm guessing here) an order of magnitude of kT (~2.4 kJ/mole and 298K), the material is a semiconductor, and a current can be stimulated to flow by a high enough voltage across the material. If the valance band and the conduction band are separated by a difference greater an order of magnitude of kT , the material is an insulator.

Now, I don't think that I would try to explain the derivation of band gap theory from quantum mechanics to him this way. (I would probably lose him at "molecular orbital".) Thus, I am wondering how to explain it and other quantum mechanically derived technologies in a more conceptual yet still somewhat accurate way.

 

[Ziggurat]

For instance, from what I understand of band gap theory, the band gap arises from the energy difference between the bonding molecular (roughly the valance band) orbitals and the antibonding molecular orbitals (roughly the conduction band), which arise from summing over the energy states in which all or most of the wave functions of the atomic orbitals are symmetric with respect to one another and the energy states in which all or most of the wave functions of the atomic orbitals are antisymmetric with respect to one another.

That's not really correct. Bonding versus anti-bonding is a useful distinction for small numbers of orbitals. But in a solid, what you should be thinking about isn't an orbital splitting into a bonding and antibonding band, but into a single band (where the antibonding state equivalent would be at the top of the band and the bonding state equivalent would be the bottom of the band)

If the valance band and the conduction band overlap, the material is a conductor.

If the outer orbital is full (as in zinc), then band overlap can turn it into a metal, but more commonly for metals, the outer orbital is only partially full, so the outer band is only partially occupied. In that case, band overlap is unnecessary for conduction.

 

[Fredrik]

Many worlds, for example, requires the creation of at least one entire new universe every time any two particles interact.

I believe that this is just a (very common) misunderstanding of the MWI. It's certainly possible that I'm the one who have misunderstood it, but I'm going to try to explain what I believe the MWI really says.

In all interpretations, the state of a physical system is represented by a vector in a Hilbert space. In interpretations other than the MWI, that system never includes you. You only use this formalism to describe other things than yourself. The other interpretations also say that the state vector evolves according to the Schrödinger equation, until a measurement is performed. Then the measurement projects the state vector onto a proper subspace, and we have a new vector that represents the state of the system after the measurement. Which subspace the vector gets projected onto is unpredictable, but we can calculate the probabilities of the alternatives.

The MWI on the other hand says that we can represent the state of the entire universe as a vector in a Hilbert space. Penrose calls this space "the omnium". According to the MWI, the state vector always evolves according to the Schrödinger equation, and never gets projected onto a proper subspace. In the MWI, a measurement is just an interaction with a unitary time evolution like everything else, that through some mechanicsm (possibly decoherence), give certain orthogonal subspaces a significance of their own. In other words, this mystery mechanism just selects a preferred basis of the omnium.

So all those "worlds" don't get created when a measurement is performed. They are orthogonal subspaces that were always there, but after the measurement they get interpreted as different worlds, instead of as degrees of freedom in "the" world.

It seems to me that if this is true, it implies that the mystery mechanism must make sure that a physical system that is complicated enough to process information before the measurement (e.g. a human brain) can't continue to do so afterwards. Instead, the projections of the vector representing the state of this physical system onto the orthogonal subspaces selected by the mystery mechanism, would now describe systems that are somehow capable of processing information.

The vector representing the state of such a system would itself be a projection of the state vector of the universe onto a tiny (by comparison, but possibly still infinite-dimensional) subspace of the omnium. Since a measurement selects a preferred basis of the omnium, it also selects a preferred basis of that subspace. Before the measurement, "you" are a vector in that subspace. After the measurement, there are several "yous", each being a vector in one of the different subspaces (of the "tiny" subspace) defined by the preferred basis.

I hope that made sense. It's hard to explain this stuff.

I have never read anything about the MWI that explained these things in detail, so I don't really know if this is how the "MWI experts" (if there is such a thing) think of the MWI. I basically just read a few lines about the MWI in "The road to reality" and a few other places, and came up with the rest myself. I am however sure that the "core" of the MWI is the assertion that unitary time evolution is all there is.

 

[Fredrik]

Does anyone know of some more accessible material on the predictions or explanations of QM that I can direct him to, assuming that he is honestly interested in expanding his knowledge of QM?

I don't know if he's interested enough to read a book, but I have to recommend "QED: The strange theory of light and matter" by Richard Feynman. It's a short book (probably no more than 100 pages) that explains a lot of quantum mechanics without using any math. It mostly talks about how quantum mechanics explains optics, but it also talks about the double slit experiment and a few other things that may seem more "quantum strange" than optics.

 

[Dancing David]

I think the place to start would be in the explanation of the frequency emission and absorption of light. The fact that atoms can only absorb certain frequencies is apparent is spectra of stars and the emission phenomena is part of a sodium lamp.

This then begs the question, why only those discrete frequencies?

Which gets to the quanta issue. The 'orbits' of electrons are not like planetary orbits, you do not get a scaled 'orbit' related to the energy of the electron. Add a little energy and it is slightly larger, etc... Yet in electrons you can only move from one state to another with a gap in between.

So that is the idea of the quanta in many ways.

The tunneling would be the next one, of which some how the word diode comes to mind.

Then the crucial one.

The Coulomb law, charged particles of the same charge will repel each other as the inverse of the distance between them. So like charges will have a very high if not infinite repulsion as they approach each other.

How then does nuclear fusion occur?

Even at high temperatures and high energies two protons will not fuse. The more you squeeze them the harder they repel each other, so you could have infinite pressure and infinite temperature to create fusions. Infinities canceling out?

Yet we know that fusion at the core of the sun occurs at a not so infinite temperature.

Why? Because the protons are waveforms! If they were strictly classical particles they would never fuse. But because they are waveforms there is a chance that the two particles will appear next to each other under the high pressure/temperature. Then they don't have to worry about Coulomb’s law because the strong nuclear force (? I think) takes over and fusion occurs.

Then to demonstrate that particles really are waves there is nothing like Bose-Einstein Condensate.

 

[Dilb]

How then does nuclear fusion occur?

Even at high temperatures and high energies two protons will not fuse. The more you squeeze them the harder they repel each other, so you could have infinite pressure and infinite temperature to create fusions. Infinities canceling out?

The important thing about fusion is the strong nuclear force. If you get protons close enough, eventually they start being attracted to each other rather than repelled. The potential is like a very deep well at the top of a mountain. The problem is that classical particles would need enough energy to get all the way up the mountain, which would occur (with any regularity) at temperatures much higher than inside the sun. It certainly wouldn't take infinite temperatures.

If you don't include the nuclear force at first then you've described a problem where charges shouldn't ever fuse, because they have no reason to.

 

[Ziggurat]

The important thing about fusion is the strong nuclear force. If you get protons close enough, eventually they start being attracted to each other rather than repelled.

There's also a proton-neutron and a neutron-neutron attraction via the strong nuclear force. These are critical as well, since without neutrons, the electric repulsion is too strong for proton-only nuclei to remain bound.

 

[pgwenthold]

jeez, there are so many QM effects that are strictly QM that it is almost impossible to even start. There are detailed QM models that quantitatively handle a lot of stuff. For example, start with the fact that the IE of hydrogen atom is 13.6 eV. Exactly predicted by quantum mechanics from first principles (then again, it is also predicted by the Bohr model of the atom, so not the best example)

Then again, there is

1) As mentioned above, quantization of states - the fact that atoms and molecules even have line spectra in the first place is solely explainable in QM and not at all by classical mechanics. Think of rotational spectra, for example. Imagine the concept that a spinning top can only spin at certain frequencies, and never at rates in-between. That makes no sense, but is part and parcel of QM. The idea of quantized rotations is one that always fascinates me.

2) Electron spin is a completely QM concept, having no corrollary in classical mechanics. Try to explain magnetism without QM

3) You want a real prediction? Bose-Einstein condensation. Long predicted by QM, only observed 10 years ago.

These are just a few.

 

[Almo]

I agree about Stern-Gerlach. That experiment is really weird, and shows the collapse of the wavefunction thing rather well. It's the one that showed me we really need QM to take care of some rather basic things.

 

[Fredrik]

Does anyone know of some more accessible material on the predictions or explanations of QM that I can direct him to, assuming that he is honestly interested in expanding his knowledge of QM?

The replies don't seem to give the OP what he was asking for. Except mine. My recommendation rocks. Anyone disagree or have a better one?

It's been a while since I read "The emperor's new mind" by Roger Penrose, but I think that also has one of the best non-mathematical explanations of QM.

I don't know any online resources, except Physics Forums I guess, but that's just a place where he can ask questions. It's not a place where someone has already explained everything.

 

[Modified]

The tunneling would be the next one, of which some how the word diode comes to mind.

Probably because of quantum tunneling diodes.

 

[Cuddles]

I believe that this is just a (very common) misunderstanding of the MWI. It's certainly possible that I'm the one who have misunderstood it, but I'm going to try to explain what I believe the MWI really says.

I think you're confusing several different interpretations there. Many worlds does exactly what it says on the tin - there are many worlds. The idea you seem to be describing is a more modern one that says that the whole universe can be represented as a point in a phase space and that time occurs as a result of the probability distribution of that point. As far as I'm aware, many worlds specifically refers to the idea that each interaction results in all possible outcomes happening, but in seperate universes which spring into being as a result of the interaction.

It's essentially just a problem with taking mathematics literally. As an analogy, you can calculate the motion of a particle by considering all possible routes and summing them up, but that does not mean that it actually does take all possible routes, any more than using imaginary numbers to calculate something means that they really do exist. This is a common complaint about theoretical physicists, since some of them have a habit of assuming that anything that happens in the maths also happens in the real world, even though this is often obviously not the case.

However, to get things slightly back on topic, this really illustrates the point in the OP. We can speculate about all these different interpretations precisely because we really have no idea which, if any, are actually correct. Many worlds really is little better than God, because the maths stands on its own regardless of which one you think is true. I won't say it is no better, because there is at least the possibility that many worlds, and other interpretations, will be falisfiable in the future.