Schrödinger's hat

With systems governed by the Schrödinger equation, the Pauli exclusion principle is simply taken as a postulate, with regards to that theory, asking why is akin to asking why F=ma of Newtonian mechanics. There are reasons once you get into relativistic and non-linear theories, it is related to the principles of symmetry. I do not understand the standard model yet, and explaining this properly is going to be out of my league for at least another year. Even then I think I would struggle to put it in terms you would understand without studying a lot of maths. With regards to your second question, you're thinking of the de Broglie wavelength. This only applies to matter waves which are not bound, it also relates to the momentum more than energy (energy is related to momentum, so wavelength is related to kinetic energy in this way). The uncertainty principle does apply in a way, the states are quite well determined energetically, this means that the timing of a photon leaving during an electron transition is well determined, and the photon is consequently close to monochromatic.

By quantum object in this case I was talking about something which would be modelled reasonably accurately by a single wave-function (ie. not big enough to be collapsing its own wave-function/interacting all the time and thus averaging out quantum effects). Such as an atom, or an electron. You're right in that it's also used to describe a discretised object.

Umm, by relativists, it is. Except space-time is not Euclidian (time isn't quite the same as the other directions)

I think you're confusing a square well with an atomic 3d well. It's not so much about energy maxima, as the other quantum numbers. The Pauli exclusion principle states that two fermions can't have exactly the same state. As the energy levels increase, it opens up more variations for angular momentum and magnetic moment numbers. Spin can always be either positive or negative half, so we wind up with: n is the energy level angular momentum l can range from 0 up to n-1 magnetic moment m can range from -l to l spin can always take two values. So we have for each l value [math] (2l+1)*2 [/math] or [math]\sum_{l=0}^{n-1}2*(2*l+1)=2*n^2[/math] This is related to what values and wave functions are valid solutions to the Schrödinger equation. Hah, beat me while I was remembering how to sum a simple series. We can tell who is a chemist and who's a physicist by the time it took me to remember how atoms work. I guess, in order to avoid confusion I should talk about m a bit. The s p d f are just the chemists' annoying convention for things that should be numbers *grumbles* (there's actually a good reason involving spectrometers, and a lack of quantum physics at the time for this convention -- but I digress) Note that mississippichem said that some orbitals are degenerate. This is true if there is no magnetic field. The numbers he stated match the 2(l+1) that I was talking about -- s is l=0, so 1 state, p is l=2, 2*2+1=5 and so on-- because they are the number of different values for the magnetic moment. Understanding exactly what m is is hard and requires staring at a vector diagram for a couple of hours, but you can think of it as the way in which the angular momentum interacts with a magnetic field when it is present. Even if it there is no magnetic field, they are still different states, so the pauli exclusion principle doesn't exclude them

Umm, I'm not sure this is a great thing to make analogies between, but here goes: Voltage could be compared to temperature difference between source and destination. Where potential measures concentration of potential energy, temperature measures concentration of heat energy. The word you're looking for is thermal flux, which is equivalent in some ways to current, and in some ways to power of a circuit. Negative temperatures can in some ways be defined, but it involves a lot of quantum and isn't related to definitions based on average kinetic energy. So, negative temerature doesn't exist in the way you're thinking. You could have negative temperature difference the same way you can have negative potential difference. Another important difference is heat is always positive (you can only gather heat together, and it will want to spread out into its surroundings). Whereas charge has two signs (an electron and a proton will attract. As I said, it's possibly not a good idea to try and make an analogy between these types of systems. Especially as you go into more detail about thermodynamics/stat mech.

Don't dig too deep, eventually the concept of force moons you and runs out the door.

We can make all of our equations without unit vectors (but not without vectors), just divide and multiply by the magnitude. [math]\frac{r}{r}\hat{\mathbf{r}}=\frac{1}{r}\mathbf{r}[/math] In terms of the magnitude of a unit vector (or any vector) it relates to size. A vector is something that carries two pieces of information, direction and size. So 3km east is a vector, or 1 Newton down. We often use unit vectors when we are supplying the size information elsewhere so we'll have [math]\frac{1}{r^2}[/math] The maginutde (a scalar or number, it carries the units, too) [math]\times\hat{\mathbf{r}}[/math] the direction (in english this means 'in the direction that you measured r') It still carries a magnitude (1), but this is replaced by the other magnitude when they are multiplied (1x something=something). Another unit vector would be 1 unit east, or 'in the direction I drove' so you could have 5 km (magnitude) 'in the direction I drove'(unit vector), together they make a normal vector.

It's a way of sorting events. Without spacetime there'd just be events, no order to them. No system or way of interacting to anything. event a1 is tied to event b1 which interacts with c1 and so on but a1 also interacts with a2 etc so we pick an order call one of these sets of links up/down then left/right, there are still lnks we haven't accounted for, so forward/back, time until we run out of degrees of freedom lots of these events are boring (empty space), but one event is linked to those around it forward in time, and backward in time, we look at these links, and what types of links there are, these are the laws of physics whether all the events exist objectively, or they're created is a bit of an open question (determinism) hmm, this is hard to tease apart If you want the ontology of it (what is it, rather than what is it isomorphic to) I can't really help you. My ontology broke down just as I got past quantum town and be damned if I can get the parts to fix it.

Well, it's thermodynapics, subset of physics. It's caused by differing rates of thermal conductivity. Intermolecular force is a good start. There are other things involved (evaporation carries heat away because the fastest molecules are the ones that escape from the top surface of the liquid). Start reading here: http://en.wikipedia.org/wiki/Conduction_(heat) (Note that citing an encyclopaedia in your report is not such a grand idea, maybe head down to the library and get a textbook.) Feel free to ask some more specific questions when they come up.

Methinks you've never seen a mathematics paper.

From a quantum perspective. Force is more of an emergent concept. Or you can think of it as rate of change of energy with respect to space, much more like the classical version. There is more than one model, even within quantum theories. QM just has potential wells which are there because shut up, that's why. QFT gets more complicated, but there is a mechanism there. I don't think going into virtual particles and force carriers at the moment would be productive. I have a reasonable conceptual grasp of these, but I'm still a fair way from learning the theory properly, so I do not want to comment in case I mislead or misinform. Your model of balloons is a bit better, and it's understandable that you want to model them classically. That's what you know. Solidity is also a macroscopic construct. If the interactions between your skin and an object are more frequent/more energetic than those between parts of your body, things will feel solid. If you think about it hard, all of these macroscopic ideas will emerge from large numbers of quantum objects. In fact they have to for it to be valid. If, on the other hand, it doesn't work the other way around, I think the quantum concepts should take primacy. Thinking about a 4d universe is very difficult and counter-intuitive at first, but over time it makes more sense. QM is much the same.

There's nothing wrong with your logic, it's just what n represents. Finish this sentence. The balances will be equal 4.61 years after ________ Then this one The balances will be equal 7.61 years after ________ This is why defining our terms explicitly is important, otherwise we can be talking about two different things without noticing.

Not quite maths, but close: Heisenberg is driving down the street when he gets pulled over by a police man. The cop asks, "Do you know how fast you were going?" Heisenberg replies, "No, but I know exactly where I am."

As I was trying to explain in the chat before you wandered off. Potential difference can be positive or negative. The range is any number from negative infinity to infinity. You measure them the same way you measure any voltage difference. If your volt meter doesn't measure negative voltage, swap the leads. If you are too lazy to take the time to try and understand things properly then I can't help you any further. I just realized you could be having trouble with IRC and not receiving all the messages. If that is the case then I apologise for getting cranky, and you don't deserve it.Perhaps you can explain what you are trying to do in more detail?

You could build a Farnsworth reactor. Not really cold fusion, but the idea is to keep the ions from thermalising as long as possible and accelerate them with an electric field. It'd probably require a budget of about 50k, and some engineering expertise though.

Steevey, your post doesn't really have much to do with what I was trying to say. Thanks anyway. Also, you seem to be conflating quantum computing and quantum teleportation. lemur Well quantum mechanics and QED are models applicable to individual objects. That being said, the results they give are not deterministic. They will state exactly what interactions are possible for the objects they are describing, but the results will always be probabilities. Any experiment you do will follow one of the possibilities it describes, but you don't know which one. If you do a lot of experiments, the number of times you get each result will match the probabilities of the theory. Once we get into QFT it's a bit different. I do not think I could explain it to you in any way which would give you the correct impression, especially as I have no more than a passing association with it myself. There are other areas of quantum physics where calculating the individual wave functions is prohibitive -- namely anything involving macroscopic quantities -- and so we use statistical methods and simplification more in the way you were complaining of (not quite, as the statistics are applied to the mathematical model, not generated from experiment) On Bohr and the cat: Oh yes. I forgot to mention. A very common view among physicists (about 30% of the ones I have discussed it with in depth, although this is not a very good sample size) is to have no english story at all, the story they tell is entirely in mathematics. They don't care what the ontological status of the cat is, or whether it's Copenhagen or many worlds. They just use the maths. The statistics and mathematics used in other sciences are there for a very good reason. On top of integrity issues, it's very very easy to trick yourself when performing experiments by modelling your situation with simplified mathematical objects you can reason with a process which greatly lessens the involvement of your own biases and perceptions of the system. This process is part of what I keep talking about. Scientists use whichever model or story is the simplest for the accuracy and specificity of the predictions they are trying to make. I think that part of your problem may be that some science involves correlation (when variable a is changed, variable b changes too) but not mechanism (variable a is linked to these chemical processes, which induce this behavior, changing the environment to one which decreases variable b). Sometimes if a science is new, or we are examining very complex systems (like humans) then we can find the former, but we cannot think of a good story (mechanism) to go with it. Or sometimes we have stories, but singling one of them out and calling it correct would be premature, and non-genuine. Quantum theory is, for the most part, very tight and inter-linked conceptually. There's a clear mechanism involving the other parts for each effect described. There are a few exceptions to this (why are the universal constants the numbers they are? We only determined them empirically, or why does measurement do what it does?), but not too many.

Agreed. It's hard to explain how these things may be learned in a way completely unlike the way I learned them. I think we're getting a bit closer to understanding each other here. This is exactly what we do with the mathematics. The symbols, the numbers, the rules of algebra, they're all just tools for critical reasoning and extrapolation. You could think about the same concepts without them, but from the point of view of someone who is used to thinking with mathematics this seems cumbersome and silly. In linear models it's equally valid to think of each particle as having its own wave function, or the collection having a wave function (again, multiple stories work sometimes, don't get fixated on one ontology if you try to think about these things or you'll go mad). I'm still learning and I haven't done much with multiparticle wave functions yet, but here goes. Electrons don't always (often?) work in this way as there are interaction terms. Instead you have one big wave function for all the electrons. In this case they all occupy all the space, if there's an interaction the wave function is altered. Let's say the atom is ionized by a gamma ray. There'll be a large spike in probability the wave function at one point, and a corresponding drop in probability in one of the modes of the wavefunction. This electron will fly off and eventually get far enough away from the atom that you can consider them separate wave functions without too much error. I'm glossing over (and don't fully understand) things like entanglement, and the transfer of spin here. Depending on your model, even the gamma ray was part of the wave function, and this is just the way it all evolved. At no point is it quite right to think of the electron as a little hard ball, or particle. To elaborate further, the a wave function exists over all space. It's a field, it's just more in some places than others. So our little electron is everywhere, but mostly somewhere. Our models usually go to 0 probability at some point and we represent different things as different wave functions. This is a simplification. Sparkling is a reasonable metaphor for a wave-function which is being interacted with, although this type of interaction doesn't really apply to atomic orbitals. Each sparkle being an interaction, after which the wave function smears out again until it is in a steady state. Again, the idea of dancing or jumping doesn't fit. Additionally it doesn't appear and disappear, it's always the same type of thing, and it's always everywhere (just mostly somewhere). In terms of quantum objects which have some momentum, the way they move is much more akin to a ripple travelling in a pond. The idea of an electron rotating doesn't make sense, that's not the kind of thing an electron is (again, your story involves something like a ball). There are some ways in which it is like an electron going around in circles, but more in which it isn't. I've only scraped the surface of relativistic models, and still don't really have any comprehension of spin. There's another thread on this which is currently active. There are much more detailed and accurate explanations there than anything I can provide.

This is much better, but there is still something misleading in the way I am interpreting what you say. I am by no means an expert on this subject, but thinking of the results of the two measurements as causally related oversimplifies the situation. A key point is that information cannot be transmitted by this effect. On top of that, the concept of 'when the one particle is measured' is not quite valid. In a relativistic world there is only: An event (or here and now) Future Past Other The present isn't a valid concept. My understanding of this is limited, perhaps someone more knowledgeable knows what I'm trying to say?

While this may be important, I don't really see how this is relevant. Regardless of any disability, ability, knowledge, skill or ignorance: Either I will be able to help/be helped by and communicate with someone or not. If they lack knowledge that I have, I will either be have sufficient and correct skills to teach them, or not. I wish to deal with one, or a few individuals, any labels which they or others apply to themselves are irrelevant until they provide information which helps us communicate.

I think we first need to find some evidence that we are conscious. In what way are we distinct from machines? In every discussion I've seen so far the definitions have been vague or circular.

That statement wasn't intended to be universal. We could elaborate to closed, isolated system, but then the mathematical formulation would have to be expanded too. Mathematics is just a way of representing certain classes of things and the rules for their interaction. Often we need to classify and define these objects. English is exceedingly useful here. I'm not saying we should not use English statements, just that we should use all of the tools at our disposal. Edit: Also, I used n for my summation and i for my index. Shows how much attention I'm paying. To be decrease the ambiguity to your standards, without any context or set of definitions I'd have to write a book. You are also just reinforcing my point. The stories are hard to tell in an objective way. I tried to tell you my story without mathematics and you don't get it. This is because my story is hard to communicate, mathematics is not for those who understand it. Science has an agreed upon set of definitions for most of these terms. The definitions include description and mathematics, throwing away one of our tools for no good reason is silly. You could argue that physicists are throwing away tools by using mathematics, but it's simply that they could see how to apply one tool and not the other. If I want to undo a nut and I have a spanner and a screwdriver, I use the spanner. There might be a more efficient way to do it with the screwdriver, I don't know, I can try the screwdriver but it would take a long time and would be awkward and full of problems. I only know how to use the spanner efficiently for this task, it's not like I have any hatred or bias against screwdriver users. Yes, you have, you're thinking of it as a collection of particles (or something else I don't understand), this is inadequate. The word move doesn't apply here, dancing is misleading too. Suggesting points and fields are the same type of thing is also wrong. My story is that the electron is occupying the whole wavefunction all the time, only just after, or during interactions is it restricted to a subset of this space, there are other stories that fit the maths. It is a subtle and difficult concept, in my experience the best way to get an intuitive understanding of things that act in this way is to play with them, or accurate models of them. The models require maths to be accurate, this is why we study maths before trying to understand a wavefunction. I know plenty of people who have a shockingly inadequate and inaccurate intuitive understanding of momentum. In many cases they can make predictions, but when situations that are not common for them come up they are confused or mystified. This is even more common with magnetism (many people have no intuition). Through examples, playing with toys, making predictions and looking at the outcomes we can slowly build an intuition of these things. We cannot build an intuition of magnetism solely from concepts outside EM, it requires new ones. Spin is no different, it is hard to interact with so a lot of our tools for building intuition are gone. This is an oversimplification of the situation, there is something wrong with thinking of the wavefunction collapse as an effect. I do not understand fully, I am not sure if anyone understands measurement. This is a case where we have some maths and no story to go with it.

I would disagree. The mathematics is simply one representation. I don't think anyone really knows the universe. The mathematical representation is certainly a very descriptive and beautiful one, and it is the closest to the true workings of the universe. Also, one can perform the mathematics without understanding it the way you do (or sometimes at all). I think about things slightly differently depending on whether describe the situation with multivectors, or tensors. Very differently if I am using a relativistic formulation rather than non. You could argue that the relativistic model is the correct one, but in many situations the Newtonian one is more descriptive. I could also use the same argument about any theory, all present theories diverge somewhere and I think the likelyhood that we will never find any holes in whatever the next iteration is is vanishing. As someone mentioned earlier. QM breaks down in strongly curved space, and we don't have anything really ready to replace it. Sometimes a mathematical model will translate into a story in English in more than one way. (see neo-Lorentzian aether theories, I think they break pretty hard as soon as you mention gravity, but the point remains that it's another story that can be told about a flat universe with the same maths as SR) Again, I don't think these are absolutely necessary. Some understanding of the quantum world can be achieved without a formal mathematical understanding of these, but the process of learning (and teaching) would be incredibly laborious and far less efficient than the mathematical route. There would have to be some representation of these concepts. Much as anyone who has ridden a bicycle over hills has some representation of the concepts of gradient, and potential well.

Anything which is sufficiently well defined and unambiguous is equivalent to mathematics. We could take: The total momentum of a system does not change. or [math]\frac{d}{dx}\sum_{n} p_i = 0[/math] They contain the same information. It just happens that the more complicated the thing we want to talk about, the more complicated and specific the words. There are plenty of concepts that are simple in one language, but describing them is a long and arduous task in another. You need to be clearer in what you mean. If 'makes sense' means you can understand it right now then this statement is absurd. Just because an individual cannot comprehend a given theory doesn't make it useless. If 'makes sense' means that the theory is logically consistent, and consistent with experiment then QM already passes. The circumstances in our models are never achieved. There's no such thing as flat space, a non-zero velocity where relativistic effects are not present or an ideal gas. That doesn't make newtonian mechanics or PV=nRT useless. None of our models are correct, they're approximations. If any of our models were exact, we wouldn't need elaborate experiments, we could just predict, for example, the next thing you are going to post on this forum, to check them. I agree that the cat example is absurd, that would never happen. A cat would collapse into alive or dead because it would interact with things. It's too big. Thinking about the cat too much is akin to thinking that 1000 years should have passed at home when I went to the shops because of relativistic effects. It's a parable. Double slit we looked at the two classical possibilities: The electron is a particle, a little ball-like object. The electron is a wave, like a ripple. We rejected these and came up with a third explanation The electron is a wave function, an object a bit like a ripple and a ball If parts of the wave function get out of phase, it interferes with itself producing patterns of high and low likelyhood of interaction. If the wavefunction wasn't collapsed, the question 'did the electron pass through the left slit?' is nonsense, it doesn't have a truth value. Sometimes we just have to accept concepts which were previously completely alien and unintuitive. This kind of thing can only be built through experience and interaction. As it's pretty hard to have a meaningful interaction with objects where quantum properties are important, one way to experience it is through our models. Sadly this is difficult without being able to do the mechanics and the mathematics. I have some ideas involving the way integrals are done in QED, and letting go of the idea of free will (I see no evidence one way or another that it is needed. Our models work just as well if we decrease t as if we increase it) which may allow me to tell a story about measurement, like I have stories for gravity, or relativity or whatever. These ideas are not well formed, and I have a long way to go before I understand the theory properly, so I will not try to explain it. One other thing to think about, is all your stories about the world are just that, stories. We make models and stories about the world to get a better grasp of reality, but none of them are all that likely to be true, many of them are already proved to be false. A crystal isn't a bunch of balls held together by sticks. Spacetime isn't a hyperbolic (3,1) vector space. You don't even touch things, it's just electromagnetic repulsion. We may discover something soon that allows us to tell a much better story about QM, or make better predictions, or both. That doesn't mean current theory is any less right, or useful (and it's very, very good). This brings me back to EM. The Lorentz Transforms were developed before Einstein's time, and your questions about QM mirror a lot of the questions about Maxwell's equations from the late 19th century. There are other stories (warning: such things attract many crackpots and I have not examined this specific formulation in detail for flaws) we can tell about a universe which follows such mathematics, but they have their own problems, and require their own assumptions an counter-intuitive objects. I'd suggest reading a bit about the history of EM and development of relativity. Many physicist come to accept that: Whatever the real story is, it's probably not the one we are using. We know the mathematics is right and so we follow it where it leads, refining it where needed, and we tell ourselves whatever story is most useful at the time (be that particles, waves, balls on sticks, or clouds of probability). Edit: combined posts to save space, this one is getting pretty epic We don't just have the maths, spin has a story too, it's just hard to tell the whole thing without the maths. It's a fundamental quantity, it provides some angular momentum, and interacts with charge. Elaborating on one of my earlier points...somewhere. Sometimes we need to introduce a new character to our stories. Spin is a little bit like angular momentum. The same way a wave function is a bit like a wave and a particle. Trying to think about it in a way that relates to what I am familiar with in the macroscopic world doesn't work properly and hurts, but when it comes down to it, if you think about momentum, or mass, or position too hard they are no less abstract. I am reminded of this: http://abstrusegoose.com/342

At the end of the day, creating a theory which is both functional and intuitively comprehensible is a much stricter requirement than something which is merely functional. That being said, I don't think that an intuitive understanding of quantum physics is unattainable. At least to the degree that I intuitively understand anything. I by no means claim to have such an understanding, but with further thought and improvements in pedagogical methods I do not see why it cannot be achieved. I have a few textbooks on electromagnetism written early last century, and I think I am justified in saying that their authors' intuitive understanding of electromagnetism was far less well developed than that of the average first or second year undergraduate. The structure of the theory of EM has not really changed since then, but the ontology -- the analogies and the stories we tell ourselves -- involved has advanced. In addition to this, people are exposed to concepts such as fields from an early age, toys have magnets in them. Concepts which were abstract and counter-intuitive -- accessible only through mechanics and mathematics -- then have become much easier to comprehend. Of course I am glossing over the development and spread of relativity, and numerous other relevant points, but I do not feel this is important for what I am trying to communicate. There are as many people around with an intuitive understanding of EM that is based on a relativistic ontology as not. Coming back to intuitive QM, there are some parts that are intuitively accessible. Over time, I have learned to think of things as a probability distribution (I coopt the mathematical words as labels for intuitive objects because I have no other), an electron (or any other object) is an intuitive object which is neither wavelike, nor particle like. Letting go of thinking of the statement 'the electron is here' as having a definite truth value is important for this. The thing I am having the most difficulty with is measurement theory (what exactly is an interaction and why?). One important point here is that there is no such thing as a passive measurement. We think of observing or seeing as something which does not involve the system, but this is untrue. Measurement in quantum physics is much more akin to reaching out and touching something. You cannot know anything about a system without interacting with it. You have to hit it with a photon, or an electron or something else. This is what collapses the wave-function. This only answers one of myriad question about what a measurement is, and I am simplifying an already incomplete understanding of the theory in order to communicate it in English. I think another important question to ask ourselves is: what does it mean for a concept to be intuitive? I think that as these concepts become more and more ingrained in the public mindset, and children grow up with stories, and toys (I've often pondered over making computer games where quantum concepts are important) which involve these concepts we will start to encounter people for whom Heisenberg's uncertainty principle is as obvious and elementary as the idea that a ball will fall when we drop it. Look up Feynman's works. He was often interested in making concepts more intuitive.