I was under the impression that when electroncs jump up to a higher orbit, it's a higher energy state, and they are moving about faster. And when they release energy and settle back down to a lower orbit they are slower. Is this incorrect?
No, there is really no such thing as "speed" of electrons. The electrons simply have more energy in higher energy states. The concepts of mass and kinetic energy just get melded together at atomic scales into a single quantity called just "energy." It becomes rather pointless to try to break the total energy back down into constituent pieces. - Warren
"The concepts of mass and kinetic energy just get melded together at atomic scales into a single quantity called just "energy."" Im sorry, ive never heard anything like that before. To not break it into its constituant peices would be to complicate the matter. Would you mind explaining the mechinism behind the "energy"? Energy is usually defined as the ability to do work, but this definition is a bit to vauge to explain particles with it. This is how i think: All particles have 4 forces they create. These four forces and their velocity and position would describe everything about the particle. Energy would be derived from the base properties. Could you explain this more thouroughly?
French, Your concept is great for classical particles. However, real particles don't work that way. You can't specify momentum and position explicitly at the same time. The particle simply doesn't have those characteristics at the same time. Energy and time are also non-commuting observables. If you know exactly how much energy an electron has, you have no information about the time period over which is has that energy. You can specify exactly the energy held by an electron in a certain orbital, but you cannot, if you know that energy, know the time span. If you don't know the time span, you can't know the momentum or position, either. Essentially, the electron in orbit around a nucleus can only be described by one number: its energy. You just can't break it down into pieces. If you can exactly state the energy of an electron in an atom, you have also exactly pegged its four quantum numbers (since any set of those four quantum numbers exactly defines one energy state). That's what the mathematicians would refer to as a "maximally informative set." There is no way to gain any further knowledge (like the exact momentum) of the system. Electrons are not like billiard balls - they simply don't have well-defined momenta in systems like atoms. The only number you can use to describe them is their total energy. This is what I mean when I say that the concepts of mass and kinetic energy get melded into one quantity at atomic scales. - Warren
Frencheezy, Somehow I completely missed this post: I'm quite aware of the concept of plurality. What you're missing is this: the term 'quanta' was coined by Planck to describe packets of radiation. You're welcome to call energy states in an atom 'quantum energy states,' but you are not welcome to call the energy states themselves 'quanta.' For whatever reason, the term 'quanta' is just not used that way among physicists. Quarks feel both forces. The weak force is, not surprisingly, weaker than the strong force. Quarks are the only fundamental particles that experience the weak and strong forces. The strong force in particular is complicated, because there are actually three different types of "strong charge" (which are called 'colour') each which can be positive or negative. Rather than my spouting numbers at you, you'd do well to go buy a book and investigate the matter yourself. Frankly, French, I'm proud of you. I know you were referring to doppler spreading of emission lines as temperature increases. The center frequency, of course, does not change as temperature increases. I fully expected you to try to explain the doppler spread as some new, bizarre effect of electron "speed." I'm proud of you for realizing yourself what your error was, and perhaps solving one of your own puzzles with a bit of simple, observable, real science. I'll make a real scientisit out of you yet, French. Well, there are no "repulsive" forces at play between electrons and nuclei -- that was my intent. Attractive forces (namely electromagnetism) are naturally present. Well, I wish I could explain to you why they don't -- but I can't. The bottom line is that they just don't. Nature doesn't work that way. It is not in my ability to explain why Nature works that way, as opposed to some different way. It just turns out that electrons in atoms really just don't have any characteristic you could call "speed." The charge of an electron produces a field that can observed at any distance you'd like. I'm not exactly sure how you've come to think of the size of a particle as a function of the strength of a field, but the two are very different concepts. We have experimentally proven that electrons are very, very small. The current upper bound on the electron's size is currently 10^-18 m (I may not be correct, I have looked through quite a collection of recent literature to find the exact number, but I cannot find it). It really does seem like fundamental particles are really just geometric points, even though that can't ever be proven -- all you do experimentally is set ever smaller and smaller upper bounds. - Warren
"heisenberg uncertainty principle again " Ok, the heisenberg uncertainty principle. What is the experimental proof for that? As far as I know (which isn't too far), the evidence is that when you measure something that small, whatever you measure it with (electrons, light, other small particles) bumps the object away, thus creating a problem with measurements. Is there more to this? "The mass of the electron is defined quite specifically in all my textbooks." "No, they're certainly not wrong. The mass they list is the rest mass." How was the mass measured? Electrons are never at rest as far as I know... im probably misusing the term. "because there are actually three different types of "strong charge"" Do the different colors of the strong force interact with eachother? "Well, there are no "repulsive" forces at play between electrons and nuclei " Yes, but electrons repel other electrons... "It really does seem like fundamental particles are really just geometric points" Ya, thats about what I was saying. If you don't want to consider particles as points, then the only other thing to go by is its electromagnetic field. The field does extend out pretty much forever, I always thought putting a size on a particle is a bit arbitrary.
It isn't actually a "measurement effect," though by and large it's taught as if it is just a result of humans not having good machinery yet. The principle is in fact verified with every measurement made of the 3D components of spin vectors (you can only know one at a time). It's also verified with a simple double-polaroid experiment. There are, in fact, loads of experiments whose results depend critically on the HU effect. Well, no particles are ever "at rest" simply because if they were, you'd know their position and momentum simultaneously, which is a no-no. Even at absolute zero, the particles still "move." The mass and energy of the electron are equivalent. All you have to do is produce a free electron of known kinetic energy (by accelerating it through a known electric potential in a cathode ray tube, for example), and then observe its motion through a magnetic field, in a bubble chamber or photographic emulsion. The electrons curl in the field, and make wide circles when they're moving fast, and small circles when they're moving slowly. The curvature of the track is directly proportional to momentum, which is another way to state energy. If you know how much kinetic energy you gave the electron, and you know how much momentum it has afterwards, you know how much mass it would have at rest. Yes, in fact, they do. Like colors repel; unlike colors attract. Certainly, but it's a second-order effect. Besides, in hydrogen, there's only one! Please Register or Log in to view the hidden image! That's an astute observation. - Warren
"measurement made of the 3D components of spin vectors (you can only know one at a time)" Is there a quick elaboration on this? "The electrons curl in the field, and make wide circles when they're moving fast, and small circles when they're moving slowly. " THE ELECTRONS!? I thought you said electrons don't have speed?... "Like colors repel; unlike colors attract. " Huh, so like three different charges instead of magnatisms two. "Besides, in hydrogen, there's only one!" So how is hydrogen's electron held in orbit?
Hmmm... I don't think I can do it very quickly. Spin can be measured in three different axes -- in one of three different directions. Measurement on one axis destroys all information about the other two. There are situations in which two particles can interact, such that their spins are subsequently related, and the spin of one is measured. The spin on the other is forced into agreement. This is known as the Einstein-Rosen-Podolsky paradox, and subsequently begat Bell's theorem. None of this would be be observed without the Heisenberg principle. Good catch; I was using terms a little loosely. That looseness happens sometimes when you get comfortable with the subject, but it can confuse people who are new to the terminology. In similar fashion, many physicists can be overheard talking about how some particles are heavier than others -- and that word, heavier, is loaded with an entirely different context than the one familiar to most people. It's jargon. What is really indicated by particle tracks is momentum, not velocity. Not speed. Electrons have energy -- a combination of rest-mass and kinetic energy, all behaving in accordance with general relativity. Momentum is essentially another name for energy. The electron's total energy is all that you can measure directly, and that's what is shown in particle tracks. More energetic particles curve less in the same magnetic field. Two particles, with different masses, but identical energies (one with more kinetic energy), could actually show the same track. When you throw GR into the mix, the whole concept of rest-mass + relativistic mass + kinetic energy gets too confusing, and people just refer to total energy. Precisely. Please Register or Log in to view the hidden image! Because it turns out that Nature discretizes the energy states in potential wells, as we've discussed in depth. - Warren
"Measurement on one axis destroys all information about the other two. " That sound a bit like the idea that if you try to measure something small, the measurement changes the particle. If that were the case, couldn't we calculate how much our measurement changed the spin/movement of it? "What is really indicated by particle tracks is momentum, not velocity. " That makes a lot more sense. But if all electrons have the same mass (we would assume), then electrons with different momentums would have to have different speeds...
To those who have not taken on the challenge of understanding the mathematics of quantum theory, it is often believed that it's just a "measurement effect," one that can be eliminated by building better and better measurement devices. However, mathematically, the particle simply doesn't have any two non-commuting observables (like position and momentum) simultaneously. The particle exists in a mixture ("superposition") of states. Measuring one property nails down a particular subset of states, all of which have maximal uncertainty about the other property. It isn't just an error due to the "crudeness" of human measurement -- the particle fundamentally can have either a precise momentum, or a precise position -- but not both. Therein lies the rub. Electrons don't all have the same mass, in accordance with general relativty. Particles gain mass as they move faster. What is mass? Mass is two things: 1) Mass represents the resistance of a particle to being accelerated. More mass -> higher resistance. 2) Mass curves space, and causes the ficticious force called "gravity" to be felt. Many particles have "rest mass," which is basically an innate resistance to acceleration, and an innate ability to curve space. Particles with high velocities become more massive -- they bend space more, and become even more resistant to acceleration. So momentum, or total energy, is not proportional to velocity at high energies. It's different. Please Register or Log in to view the hidden image! - Warren
Uh oh were getting into relativity here. I'd love to discuss that if you are. "The particle exists in a mixture ("superposition") of states. " ya iv heard of superposition. I hate to be the idiot but can you elaborate? "Particles gain mass as they move faster." That would assume electrons "move faster" than something else... I doubt that was an other loose use of speed. "the particle fundamentally can have either a precise momentum" That goes against everything I think of science as. I so much rather have my errorful theory for myself than accept something with uncertainties and shadow properties. Don't take offense, I can understanding them as if they were rules of a different universe, but as for accepting them in this universe, it can't happen now, im too stubborn. Of course as I understand more, my theory will probably look very similar to accepted theories. Well... what do you think about that stuff about different observers disagreeing about simultanuity?
It's another one of those mathematical systems. Essentially, you can describe a particle by a function. To predict the value of an observable (such as momentum, or position) you can apply an operator to the function. The value of the observable is an eigenvalue of the operator. The generic eigenvalue equation is: A-hat * phi = a * phi where A-hat is an operator, a is an eigenvalue, and phi is the eigenfunction that corresponds to a. Particles have wavefunctions which are combinations of potentially large numbers of individual phi, each representing one possible value of the observable. Essentially, the wavefunction exists as a vector in a space (called a Hilbert space) spanned by a set of eigenfunctions representing pure states, each of which corresponds to a possible value of the observable. To determine the expected value of the observable, you convolute the wavefunction with the observable's operator in a mathematical device shown in a notation by Dirac as: < A > = < psi | A-hat * psi > where A is the observable, < A > is the expected value of the observable, psi is the wavefunction, A-hat is the operator corresponding to the observable, and < | > is the Dirac notation of the convolution integral. In integral form, the expression looks like: < A > = integral ( conjugate of psi * A-hat * psi ) I apologize for not being capable of making this more clear. In english, the superposition principle says that the state of a particle is a weighted combination of all the states corresponding to all possible outcomes of a measurement. Evaluation of the convolution integral given above will give the expected value of the observable. To determine the probability of a given value of the observable, you look at the projection of the wavefunction onto the individual pure state functions. The squared modulus of each projection is the real probability. I'm sure I've just made this clear as mud. No, I mean: higher relatively velocities cause higher measurements of mass. Yep, it's one of those stumbling blocks that you'll either overcome and become an empirical scientist, or continue rejecting and become a crackpot. The choice is totally yours. You've come to think of the world as little billiard balls, with precisely defined energies, momenta, velocities, etc... as classical particles. Unfortunately, all of our observations of the subatomic world are inconsistent with the billiard ball view. You won't be alone if you won't accept quantum mechanics -- good ol' Albert Einstein himself was disgusted by the whole thing and said, stubbornly, that "God does not play dice." Albert, of course, didn't have the privelege of modern experimental results. This is a standard conclusion of relativity. There is no such thing as absolute simultaneity. - Warren
"I'm sure I've just made this clear as mud." Right, if I get interested ill look it up. "No, I mean: higher relatively velocities" Whenever I mention speed, i always mean relative speed. I get that relative concept, so its kind of redundant to say relative speed in place of speed. Thus for electrons to have different masses from relativistic speed differeces, they would have to be moving at different -relative- speeds. ""God does not play dice." " I think like that. I think einstein relized probabilities, but he had a different way for explaining them. He would probably say that probabilities account for our inability to predict perfectly what would happen. What does happen is precisely defined but may be a bit beyond our prediction capabilities. Having the uncertainty princible makes probabilities a must. "There is no such thing as absolute simultaneity." How is that possible. I've discussed this and my opponent said that simultaneity is different ONLY in different frames of reference. He also said a frame of reference was just a different point of view. I thought that a frame of reference was a distinct relativistic property determined by relative speeds and accelerations and such. I'm still not convinced that things can ACTUALLY be simultanious in one frame and not another.
No, Einstein favored the classical view of billiard balls - the same view you prefer. The view is incompatible with observation, and Einstein spent much of his later life trying to find a way to explain the observations in such a way that didn't require probabilities. Remember, quantum mechanics makes probability a central feature of the Universe's operation. Einstein didn't like that. As much as he was a creator of quantum mechanics, he was one of its detractors. This is correct. - Warren
"Thus for electrons to have different masses from relativistic speed differeces, they would have to be moving at different -relative- speeds. " Id like to reitterate that since you ignored it. "No, Einstein favored the classical view of billiard balls " Thats what I meant. But im sure enstein could grasp the concept of probability, thus he would have to explain it somehow. That "somehow" was to say that it is our lack of information that forces us to use past information to predict the future. -simultaneity is different ONLY in different frames of reference.- "that is correct." Could you give an example of when this is the case? Another thing, I have been wondering how you define speed. Is it the change in distance between the two objects or is it the limit of the change in distance? Like if a train is going past you in a straight line, and you are standing 40 feet away from the tracks, the trains distance from you will change slower and slower, then faster and faster, the point of change being the trains closet point to you. hopfully that made sence
