Oooh, I haven't seen that. Awesome sauce.

 Some how my reply posted twice,so I edited it out.

 

See this is what I've always said. Quantum physics is impossible. A wave is a configuration of things-- a thing cannot be a wave. Nor can it be in many places at once, take many paths at once, or have many identities at once. A thing is a thing: it has a specific identity, a specific position, and a specific velocity. Again, we find that the law of identity is evil's enemy and its conqueror.

I am an unabashed Bohrian. I do not believe that reality is fundamentally a blurred, undifferentiated mass of acausal sludge. I will not accept the postmodernists' mutilation of science, reality, and logic. The same laws that govern the most massive planet also control the tiniest particle of matter. To say otherwise is to suggest that logic is limited to the large, and that the very small is the playground of irreality.

Who's saying otherwise? Honestly, Presupp, you must get to know the real science, there's no saying that different laws govern different magnitudes of matter, it's all governed by the same laws it's just the computational power and algorithms required to calculate the very large from the very tiny are ever so slightly beyond reach right now. **Granted that if we discovered them tomorrow then the very large might look rather fantastically different to what we've become accustomed to, however, it's pretty much assured that the laws of relative objects will still work within that framework for certain purposes.

As for your being precious about the erstwhile conclusions and axioms of logic, you should know it makes you a hypocrite for claiming that naturalism doesn't hold consistent with it's presuppositions. If 'God controls all things in the universe" is your presupposition then your God cannot function under those logical laws as even the most pedestrian logical syllogisms regarding the characteristics of the Christian theistic deity will demonstrate easily. You're being inconsistent to be precious over what uniformity your "god" must ultimately adhere to.

Quantum science on the other hand is thoroughly consistent with it's natural presupposition (which isn't much of a presupposition in the sense that it's otherwise known as just taking things as they come).

DG is an excellent tutor, read what he has written and familiarise yourself with the facts of the matter.

This is the part of your post that attacks Bohr's theory:

 

Baloney. Schrodinger's model explains nothing since it contradicts the law of identity. Bohr's model is correct. It is the only logical model, and if you cannot figure out how the observations can be made to fit it, you must try harder.

 

Yes of course matter is nothing but a haze, reality is a fog, everything is probability, nothing is true, A is not A. Makes perfect sense.

SO TRY HARDER. You can't give up just because you've run into a problem. QM is running into problems anyway, why not backtrack and give the reasonable model another shot?

 deludedgod,

Please remeve the picture of Davisson Germer experiment from your post. If you have time for disccusions, you should have time to draw a picture and not to copy one with link of the original site. 

The bounciness of electrons? Particles don't have "bounciness". There is no "illusion" of diffraction. Do you even know what diffraction is? Since you obviously don't, I shall tell you. Diffraction is an effect observed when waves pass through a gap in a boundary, this results in something called a diffraction pattern. Different waves diffract with respect to boundaries in different ways. Light has very little diffraction, sound, by contrast, is heavily diffracted. This is why

Additionally, I don't think you understand precisely what an interference pattern is, so I shall tell you. Interference occurs when two waves meet. There are two possibilities under consideration here. The two concepts belong under the general concept of superposition, which is commonly stated as this:

For some xy plane of a 2D wave, for some two waves that meet at any point in the plane, the superposition resulting is the sum of the individual y displacements of the two waves. If this results in a larger peak or trough of the wave, this is said to be constructive, if the sum displacement decreases the sum amplitude (called cancellation) the interference is said to be destructive. Diffraction and interference tend to go together because when waves diffract through gaps, the sum components interfere on the other side, producing an interference pattern

 

The wavefunction of the diffraction beam is described as follows. The structure factor describes electron scattering on the back of the plate as F, such that:

F=Σife^-2(pi)igr

We should then note that beam intensity is equal to the modulus of the square of the wavefunction (we employ the modulus here because we are solely concerned with magnitude. Since the wavefunction is said to be a nonreal answer (which means it is given in terms of complex numbers, which have an imaginary part) it isn't meaningful to refer to real valued answers with respect to the value of the wavefunction. We must talk about the modulus. Hence:

I=/ψ/²

Here, obviously /x/ is a crude approximation of modulus.

According to Heisenberg: L=h/p

This describes the wavelength of the electrons.

The wavelength of electrons can be measured by analyzing the slit interference pattern. They indicate de Broglie was correct, as was Heisenberg, electrons diffract. Particles don't. Diffraction is a property of waves.

Returning to the previous point, the firing of electrons through the slits can produce distinct patterns. The first is interference, as shown:

This results from the wave property of electrons. The slits in the diffraction experiment act as the diffraction grating. The slit-interference pattern on the double split indicates a wave property. An interference pattern indicates a wave. 

 This is not a discussion of getting "lucky", this is not a discussion about "getting a few things right". This is a discussion about a set of mathematical descriptions of reality that have gotten everything right, everything perfectly described, everything empirically verified and everything to an accuracy far greater than any other field of science. If you were to use an electron gun to perform a double slit experiment, you would be able to predict perfectly the positions of electron contact with the plate, but more importantly, when electrons are fired in a single file through the slit, the order in which they enter is completely random. There is no way to tell the path taken by the electron. This is so heavily verified there is no dispute about it. When the gun is tuned to fire electrons one at a time, the interference pattern is that which would appear if multiple electrons had been fired simultaneously, because of electron diffraction. Electrons can be described as waves. In this, there is no room for rational doubt. If you can consider two slits in front of a mounted polarized plate where the guns fire through the slits, the electrons do not impact around the edges of the slit, as would be the case if they were particles. You can clearly see electrons diffract, there is no room for doubting

 The fact that electrons have wave-properties has been known for 80 years. However, a more important feature of path dependance of electrons was demonstrated with sensitive lab equipment. If we fire electrons in burst, the diffraction pattern is accounted for as similar to a macroscopic diffraction grating, like with a water wave, or a light wave:

The interference pattern created by the electrons being fired across the slits indicated to the physicists performing the experiment that the electrons were interfering with each other to create superposition as well as diffraction. Later in the century, the apparatus was developed to perform the same experiment with single electrons being fired through the gun, and...the same thing happens. Interference patterns result. So, as has been verified countless times, this indicates that the electron is interfering with itself, which means it is going through both slits at the same time (electron path dependance). By way, electrons aren't the only things that diffract and interfere. Protons do too. And neutrons. And atoms. Even large molecules like bucky balls can diffract, which is kind of cool when you think about it, given that a bucky ball is about 7 orders of magnitude bigger than an electron.

It's not. It's heavily empirically demonstrated. Here's a hypothetical wavefunction in a quantum system:

This wavefunction describes the quantum state. However, this is only a portion of the wavefunction, albeit by far most of the probability space. Electron tunnelling across a barrier can be predicted by knowing the quantum state of the system. It is worthy of note that as h-bar tends to zero, so does the transmission coefficient, which is why bigger objects like you or me, don't tunnel.

The process of tunnelling, of course, does not only apply to electrons. It also applies to the nucleus, which is the basis of radioactive decay. Electron tunnelling, in fact is used all the time (such as in tunnelling microscopy and in the plane of the mitochondrial membrane in the transfer of electrons between the electron carrier groups of the oxido-reductase system of the mitochondria's ATPase system.

The electron can behave as both depending on the observation of the electron crossing the slit. It can diffract in a wave pattern, or in a particle pattern. You probably will object to this but since it has been so heavily empirically verified that this would be a waste of time.

Have you ever bothered to study properties of particles or the experiments verifying the terms under discussion? Electrons are fired from the gun at high velocity through the slit. The acceleration potential is a reasonable fraction of c depending on the pd. being used. In a cathode ray tube, thermal emission of electrons via a filament causes their striking a phosphorous screen, like so:

If Bohr's model was correct, electrons would behave in a slit-diffraction gap in the exact same manner as they do in a cathode ray tube. In a tube, they As I have already pointed out, interference patterns are created by single electrons. This alone refutes your hypothesis. The guns we use for the slit experiments are so finely tuned they can fire single electrons through the slits. The screen behind the mounted slits captures electrons. Do you really think that the original founders of QM didn't think of this before you did? The double split experiments are designed in such a way that the electron is captured the moment it reaches the screen. At any rate, bouncing electrons would produce chaotic patterns, not interference patterns. The interference patterns created by the double split experiments are a form of diffraction and superposition which is mathematically directly explained by Schrodinger's equations. Whereas I can outline precisely every single measure used to rule out the alternatives you propose, you continue to vaguely defer to "sensitive measuring devices". We don't need "more sensitive measuring" devices to confirm or refute the idea that the patterns of diffraction are caused by bouncing electrons. All we have to do is point out that the patterns of electron distribution are diffraction patterns that result in superposition. Only waves diffract, ergo electrons are waves.

Because electrons are accelerated through the slit at near light speed, and they are captured upon impacting the mounted screen, this immediately rules out your "bounciness" hypothesis. Imagine firing bullets through slits in a wall into a wooden frame. Like I said, the founders of quantum mechanics considered the possibility you put forth, and they refuted it. According to Schrodinger, when you remove a single slit, the electrons should resume a particle-like pattern (like firing bullets) instead of a diffraction pattern. When there are two slits, electrons interfere and cause diffraction. Schrodinger was exactly right. When you take one slit away, the electrons pass through the gun and hit the back like bullets, just like Bohr would have predicted with his model. When you put two in, they have the properties of a wave even if only one electron is fired. Thus electrons have the property of wave-particle duality. There is no way around this. There is no rational room for denying it. It is one of the most heavily verified principles in science.

Yes it does. We can watch it do so.

I was being sarcastic. I think now may be the best time for you to shut your arrogant mouth. Up until this point I have been perfectly civil despite the fact that I could have easily abandoned that and mocked you endlessly for knowing nothing about basic physics and not having the first clue about the mathematics being discussed. You have humiliated yourself endlessly by saying the most ridiculous things and demonstrating remarkable confidence for someone with a remarkable lack of expertise. In other words, even though I have been perfectly entitled to mock you, I have not. You have mocked me. So at this point I will abandon civility and tell you bluntly that you know nothing of basic mathematics or physics (the bounciness of electrons). You know no basic quantum mechanics, yet you talk with the grandiose confidence of an expert. You have put no effort into this subject. You have not made the slightest attempt to learn the immensely complex mathematics behind modern physics. Do you know, for example, what the Schrodinger equation is? Do you know how to integrate probability spaces, employ complex pseudovectors, write eigenfunctions for quantum states, etc. ad infinitium? 

Lastly, could you stop charging me with "postmodernism", whatever that means? I hate postmodernism. Quantum mechanics is a highly rigorous, heavily verified, very, very accurate discipline of physics. It has nothing to do with postmodernism.

Returning to the weary point that electron orbitals are not quantized as Bohr stated. We have already demonstrated countless times that electron sub-orbitals are probability spaces describing two electrons due to Pauli exclusion. We have observed electrons tunnel, disappear, reappear, diffract, exist in multiple places, all in ways whose quantum states are perfectly predicted by the Schrodinger equation and its derivations. Electrons are not point charges that orbit a center of postive charge.

Hey Presup,

As Grant said to Lee at Appomattox, "You give up?"

 

Aha! But if it was an illusion, you would not know it was an illusion, so you can't say there is NO illusion. QED.

And yes, particles obviously are bouncy. We see light bouncing off of things all the time. If your model does not accomodate this, I think we now know whose is superior.

"This is why" what?

Anyway, I know precisely what diffraction is and I believe that with respect to electrons it is an illusion caused by the law of bounciness of electrons, or LBE. I have explained all of this before, and you have not acknowledged it, while I have addressed each point in your posts. DG, to be frank, I am becoming frustrated with this exchange. If you continue to choose not to express an understanding of my positions I shall have to end our discussion.

You said this already. Look, if I postulated a magical ghost who moves things around, and deduced a few things that happened to be true from properties that I ascribed to this ghost, I would not have warrant to believe in the ghost. You can get a few things right by sheer luck if your initial premises are of the proper sort. What I am saying is you may have stumbled onto formulas that get things right by luck but will eventually lead you wrong.

Stop right there. Look, for the billionth time: A thing cannot have two positions at the same time, ergo a thing cannot collide with itself. You keep denying the laws of logic to support your theories.

There are 4 problems here.

#1: For a quantum state to be described, the quantum state would have to have an identity, but you deny that these things have set identities, ergo you contradict yourself. #2: A function cannot have a portion, since a function describes a relationship between two variables with an input and output, ergo if it is truncated (or partitioned) some part must be omitted, thereby disabling the function. It either is a function, or it is not. This is the law of noncontradiction, which you must deny again to support your theory. #3: A system as a whole cannot have a "state", since a state is a property of an individual, and a system is a conglomeration of individuals. #4: Large objects obviously can tunnel, as exhibited by moles and construction equipment daily. Words have meaning, and you cannot so easily separate the concept of "tunneling" from its referents. You deny the identity of words, the laws of logic, and the nature of man's mind to support your theory.

I doubt that very much. A thing is either a thing OR a wave, not both. This is obvious from the most cursory examination of reality: waves are relationships between multiple things, and hence cannot BE things. You keep hitting this wall. Reality will not go away, so you must actually fit your reasonings within it.

Yes, as should be clear by now and as is evidenced throughout our correspondance.

 

I do not have a responsibility to explain the thought processes of the enemies of reason.

 

Obviously not, or they wouldn't bounce.

Bouncing is an orderly process, my friend, when governed by the Newtonian mechanic. You naturally deny any semblance of order. Your lack of confidence in reality is striking.

No, because the diffraction is wholly illusory, caused by the bouncing of electrons. Only more sensitive equipment will be able to confirm my model.

Light bounces, dude. Since LIGHT bounces, obviously things can bounce at the speed of LIGHT. This is what permits you to see stuff, so I am somewhat surprised that you forgot.

Argument from assertion.

Well if you want to play that game: Nuh-uh! No you caint!

I seem to recall things differently. *ahem.*

"...you have missed out on everything in physics from 1927 onwards."

 

"These are comments that could come only from people like yourself, not versed in the most basic physics."

 

"The idea that somehow these highly sensitive and extremely accurate and powerful experiments have anything to do with "postmodernism" is the height of ignorant nonsense."

I, on the other hand, have been nothing but respectful. Perhaps your perception of my posts is more reflective of your philosophic insecurities than my tone.

It is very heavily postmodern. Heidegger himself was very heavily influenced by postmodern thought, and the theory is the basis of every major attack on reason in the last fifty years.

I think I have addressed each of those arguments already.

But there IS a de facto refusal to treat the large and small the same.

So bring it on. Name one of these alleged syllogisms.

You've just repeated everything you stated in the previous post.

As I said before, and will say over and over again:

-Electrons are captured by the screen the moment they impact it. They cannot rebound and impact the screen a second time

-Removing one slit causes a particle pattern without diffraction. If the electrons bounced, and this was responsible for diffraction as an illusion, then we would see a diffraction pattern regardless of the presence of a second slit.

-Did you even read the piece on diffraction? What don't you understand about the fact that your bounciness assertion has been ruled out? Take one slit away, and the particles impact with the back of the screen like bullets.

-When particles are accelerated at near c towards the mounted screen, they are captured immediately, like in a Cathode ray tube. Again, for the seventh time, the acceleration of electrons towards the screen is like firing a bullet. That's what electron guns do.

Don't you get it? You keep deferring to bouncing as ad hoc. You are reasoning in a circle. You presume the electrons must bounce, and so if we rule it out, there must be something wrong with the equipment, not the hypothesis. There is nothing wrong with our equipment. I'll say it again: If we take away one slit, the electrons form a particle pattern of impact. They do not bounce. If electron bouncing created the illusion of diffraction, then it would do so regardless of other slits in the experiment.

-Bouncing cannot create a diffraction. Diffraction patterns result from waves transmitting through a boundary, as outlined below, the pattern is so distinct it cannot be confused for anything else.

-Additionally, single electrons fired at the slit still produce superposition. As I said before, if a single electron is fired in a single slit, then a single point of impact is registered. If a single electron is fired and there are two slits, a diffraction pattern results. Diffraction patterns cannot be caused by rebounding particles.

The proper term is reflect. Light reflects. Like all waves, light reflects when it meets a particular boundary. However,you forget that not all boundaries induce light reflection. Some induce absorption, depending on the wavelength, which is the basis of color. This is so simple I am surprised you forget. Indeed, this is the basis of the Bohr model so I am even more surprised you forgot it. But since you didn't actually know the postulates of Bohr's model I suppose we cannot be too surprised. According to Bohr, electron promotion by energy input to a particular next quantized orbital can only be induced by the correct energy input. Thus for example, for some orbital n, if the difference in energy with n+1 is 3eV, then the energy input into the system to induce the excitation of the electron must be exactly 3eV. This is why particular surfaces reflect and absorb various wavelengths. Schrodinger also points out this principle, since the probability spaces described by VSEPR form sub-orbitals which are the basis of orbitals (albeit not quantized orbitals. That was where Bohr was wrong. He admitted the error and became a staunch defender of QM).  Electrons, as I said, are absorbed into the mounted screen and captured, just like in a cathode ray tube. The plate upon which the slit is mounted in front of is absorptive. Electrons will not reflect off it.

More sensitive equipment? Like what? We have electron guns that fire single electrons and produce the described effect. What could possibly be more sensitive than that?

That's ridiculous. Have you ever researched double slit experiments? Have you ever performed or watched them being done? You can set up your own double slit experiments using photons if you want, with a photographic plate. See what happens.

EDIT: I think this is a reasonable request. I do not think you should respond until you have performed the experiment yourself. I've done it with both light and electrons, although I don't know if you have access to an electron gun (I do), but even if you didn't, you can demonstrate identical behavior with photons. So, do it yourself, or don't come back, because you clearly know nothing about the experiment. Considering that this experiment is central to QM, your ignorance is totally inexcusable.

I am telling you precisely what happens in a double slit experiment, verified countless times, and you dismiss it as being "argument from assertion". It is clear that you are being ad hoc and deferring to your explanation despite its having been proven false, and then trying to pin it on equipment flaws. There are no flaws in the equipment. Electrons are captured immediately. The rebounding of electrons off the back plate is not permitted. The guns fire single electrons, the pattern which I described results. You cannot get more accurate, or more precise, than modern double slit experiments, which can time impact within femtoseconds and can fire single electrons. This debate is over. The effects observed are still there. The possibility that particle-like electrons are rebounding to cause diffraction pattern has been eliminated. Electrons can readily interchange between behaving as particles and waves. They can diffract and superimpose on each other and on themselves, as can photons (demonstrated by Mach-Zehnder interferometers). You cannot dismiss the results of these experiments. The founders of QM were very suprised too, as you can imagine, and tried every concievable mechanism to refute the results or to make them fit with the view that electrons are particles. Einstein put forth the electron in the box thought experiment to refute the idea of wavicle duality but he was refuted by Bohr who pointed out that he (Einstein) had forgotten to take Relativitistic kinematics into account.

Yes it is. But it produces a very different effect from diffraction. If we allowed an electron to bounce across a reflective screen, we would see a distinct dispersal pattern, like the marks left by squash balls in a squash court. The points of impact left by the ricochet would be all over the screen. As I said before, the effect produced by electron diffraction is distinct.

PS: Since the acceleration is close to c, electron motion from the gun is actually described by Relativity, not Newtonian mechanics. Newtonian mechanics would be unable to explain the the acceleration of the electron out of the gun, since it does not obey Newton's laws.

If we mounted a slit in front of the screen and allowed a wave to transmit through the boundary, we would get a pattern very much unlike that described above. Diffraction patterns are quite different to impact patterns producing by ricocheting particles. For light diffraction, there is inverse proportionality between distance of diffraction from the slit, and the intensity. Similar descriptions hold for electrons. This cannot be produced by bouncing. As I already said before, and will say again the wavefunction explains this perfectly:

We should then note that beam intensity is equal to the modulus of the square of the wavefunction (we employ the modulus here because we are solely concerned with magnitude. Since the wavefunction is said to be a nonreal answer (which means it is given in terms of complex numbers, which have an imaginary part) it isn't meaningful to refer to real valued answers with respect to the value of the wavefunction. We must talk about the modulus. Hence:

I=/ψ/²

Hence. given that the intensity is the square of the modulus of the wavefunction, we see a pattern of diffraction that is not the same as the pattern which would be produced by bouncing. Firstly, as the slit widens, the pattern is destroyed. If the electrons ricocheted across the mounted screen, this would not be observed. If one of two slit is removed, the pattern is destroyed. Again, this would not be observed under your proposal. This is all irrelevant anyway since the mounted screen captures the electrons. Once the screen captures electrons, they lose the kinetic energy gained by the gun acceleration, so they wouldn't rebound, similar to a cathode ray tube. Finally, intensity is inversely proportional to distance from the slit (as you can see from the formula). This again, indicates a wave.

Imagine a steel wall with a gap in it mounted in front of a second steel wall. Imagine you fire a gun through the slit and allow the bullet to ricochet around. What do you expect to find in terms of impact? Now consider firing bullets through a gap into a second mounted wall made of wood. What do you expect to find in the latter case? Bullets embed in wood, so you will find a dispersal pattern consistent with firing bullets through the gap. Electron gun firing is analogous to the second scenario, in that the mounted screen captures electrons. However, as I said before, with two slits, you see diffraction, a very distinct and recognizable pattern indicating wave-properties, even with only one electron.

 

I laughed so hard I almost choked when I read this. Do you know what tunnelling means in the context of quantum mechanics? When a mole tunnels, they are merely displacing dirt, when an electron tunnels, it directly violates a law of classical mechanics by penetrating a barrier with a higher impedance than the kinetic energy of the particle. Two distinct concepts. Don't confuse them.

A common example of tunnelling in the quantum sense is employed in the oxido-reductase system that transfers electrons from NADH to O2 to generate ATP in the plane of the inner membrane of the mitochondria. The system has four large components:

The protein components each contain the electron carrier groups that allow for electron transfer between a set of precisely positioned faces of the polypeptide chains which hold the electron carrier groups. The reduction potentials of the groups are such that the affinity for electrons increases through the chain (or, in more technical, there is a drop in reduction potential). This ensures no short-circuiting can occur, since the energy of the electron downgrades with each transfer because it is mechanochemically coupled to the pumping of protons out of the mitochondrial matrix, which is an energetically unfavorable conformation change in the protein. Because of this, electrons need to "jump" between a carrier group and the next in a manner which is not possible under classical particle descriptions of electron motion. The two most common carrier groups are heme and iron-sulfur centers. The electrons jump between the carrier groups, from one to the next in a unidirectional fashion just described. The Oxido-reductase system would not function if it were not for the ability of the electrons to tunnel. There are other similar examples (radiation is a form of tunnelling, albeit of protons and neutrons). This is not possible under the classical model of nuclear binding. You can do the math yourself and find out how much energy is needed for an He4 to escape from a large nucleus.

You can do the math yourself and prove it. Just use the formula ∆E=c^2∆m, but be sure to use SI units or you will get confused. Remember that c^2=9x10^16ms^-1 and the kinetic energy of an escaped alpha particle is 5.84 MeV, and that the factor of conversion between eV and J is 1.6x10^-19, and that the conversion between amu and kg is 1.66053878x10^-27 kg.

There, I've just provided you with all the data to prove that an alpha particle emitted from the nucleus directly violates a law of classical physics overcoming the kinetic energy barrier confining it to the nucleus, and that this is therefore by definition an example of tunnelling. Gamow pointed this out first, since if you calculate correctly, you should realize alpha particles are confined to the nucleus by a potential well and therefore do not escape by classical means of overcoming a kinetic energy barrier. Once outside the potential well, the nucleus exerts great force on the particle due to repelling charge which causes it to move at a speed of approximately 1.5x10^4ms^-1. However, until then it is trapped. However, if you do the mathematics correctly using the Schrodinger equation for prediction of the transmission coefficient, you should find that the probability of a helium nucleus tunnelling out corresponds to the rate of decay depending on the isotope stability (which is determined by the proton/neutron ratio). Thus a helium nucleus directly violates a law of mechanics, at least classical mechanics, and overcomes a kinetic energy impedence. This is not a violation of conservation of energy, since the total energy remains unchanged when the alpha particle exits the nucleus, it is however, a violation of the classical principle of activation energy. It can only be explained under QM.

Naturally, I expect you to confirm this for yourself, although the mathematics behind quantum tunnelling are highly intricate, since you are an expert on this subject, that should not be a problem.

To prove this to yourself, I suggest you choose several isotopes, calculate the potential wells.  The V on the x axis refers to the hill potential.

For this you must calculate the turning points of the kinetic energy barriers if considered under classical mechanics. The turning points, you will find, are those points where the gradient of the function are zero. Once that is done, you can consider finding the coefficient predicted by quantum tunnelling. You can refer to the graph, but first you must find V which. For accuracy, however, to find T I suggest this equation use this equation:

T = {e^{-2/int_{x_1}^{x_2} dx /sqrt{{2m}/{hbar^2} / V(x) - E )}}}/{ 1 + {1}/{4} e^{-2/int_{x_1}^{x_2} dx /sqrt/{2m)

Check your calculations and come back to me. You should find that radiation is impossible under your description, but predicted with perfection by Gamow and Schrodinger. If the above is impenetrable to you, I offer you the following help:

T=Transmission coefficient

e=exponential factor

int=integral

The bound integral is expressed as int_x_1^x_2. This means the bound integral between x1 and x2, where x1 and x2 are the turning points of the potential hill.

sqrt=square root

V(x)=potential hill

m=mass

hbar=Reduced Planck's constant (or if you prefer: Fermi-Dirac constant)

You should note that a potential hill is the opposite of a potential well. A potential well is the problem faced by an alpha particle in a large nucleus. The potential well is the area surrounding an area of minimum energy. If a body is said to be "trapped" in a potential well then it cannot convert its potential energy to another form (usually kinetic). Once an alpha particle has escaped, it is outside the potential well and it is highly energetically favorable for the energy to be converted to kinetic energy. A potential hill is the opposite. It is the area surrounding a local maxima of potential energy. On one side of the barrier, a particle is said to be in a well and on the other it is said to be  on a hill. The values for the hill and the well potentials you need to calculate using mass-energy equivalence. Once done, you can find T and then you can compare the probability of tunnelling to the rate of decay for that isotope and see how they match. Since I've done these calculations myself, I can tell you they do. Prove it to yourself, I've given you all the tools.

Well, electrons do, so do photons (evidenced by Mach-Zehnder interferometers). At any rate, electrons are not particles. Your assertion would certainly be true if they were, but they are not. Electrons have wave properties.

Like I said, that depends on how you treat wavefunction collapse. It depends on the interpretation of QM being taken. Right now, I remind you, we are arguing about whether electron orbitals are quantized. As I have said before, they are not. According to some quantum physicists, there is no such thing as a wavefunction beyond a mere description of an electron, whereas others like de Broglie state that a wavefunction is a real property of an electron.

PS: Every time you talk about "vindicating Bohr" you shoot yourself in the foot as Bohr was one of the lead proponents of QM. The staunch opponent of QM was Einstein, at least until Bohr refuted him with the electron in a box thought experiment.

Somebody needs a little mathematical tutorial. Do you know what a complex number is? A complex has a real and imaginary component. An imaginary components refers to a second axis on what used to be called (about 500 years ago) the number line and is now called the number plane. The imaginary unit, i is simply defined as r(-1). Thus a complex number, for example, is 4i+7. In this case, the real component refers to 7. A nonreal answer is said to be a function which delivers an output which has an imaginary component. However, when you square an imaginary unit, the nonreal component disappears. That is why we refer to the square of the modulus of the wavefunction. This is because i²=-1, which is a real-valued answer.

EDIT

It appears someone needs two math tutorials. Wavefunctions are generalized in complex space. The square of the wavefunction refers to the probability density of a particular space with respect to the electron. Thus, in referring to a part of the function, we do not mean a mathematical component of the function in the sense of a "truncated" function (in this case the Schrodinger equation), rather we mean a bind on the range, describing a particular component of the probability space as opposed to the entire probability space. The function is identical, but when we say a "part" of the output we refer to a bind on the range. Since you are an expert on this subject, you presumably know that within complex space, there is a surjection map between the complex Hilbert space under description and complex numbers (which is the codomain, the range being probability amplitudes). A bind on the range of the probability function will not retain the property of surjection mapping, thus will not describe the whole probability space. That is the only difference.

So that you do not get confused:

Wavefunction:

Domain=Possible quantum states in Hilbert Space

Range=probability amplitude values

Codomain=Complex numbers

Wavefunction squared:

Domain=Possible quantum states in Hilbert states

Range=Probability density values

Codomain=Real numbers

Probability density in quantum mechanics is said to be normalizable. This means the sum probabilities of the particle occupying a particular real space must be 1. Thus, when we talk about normalization of a wave-function, we refer to the fact that under a bound integral, the probability of the electron occupying the space being talked about will be less than one. According to some, the probability space for an electron is the entire universe and therefore to normalize a wavefunction, we must place no restrictions whatsoever on the space it could occupy at any given time. This is what I mean when I say "part" of the function. I mean (and it should be obvious when you think about it) part of the range.

 

It appears someone needs a little physics tutorial too. Do you know what a quantum state is? In physics, a "state" is a property of a system. In thermodynamics we refer to macroscopic states and microscopic states. In QM, a quantum state refers to complete mathematical description of any multi-vector quantum system. Please stop conflating simple everyday terminology with that terminology used in physics, or you will continue to look ridiculous.

Lastly, do not tell me you have been perfectly respectful. It is nothing but the height of arrogance to talk with the authority of an expert on a subject you have never studied, to dismiss quantum mechanics when you would be unable to recognize wavefunction equations, integrate probability spaces, generalize complex vectors, or interpret a Feynmann diagram. It is the height of arrogance to talk like this when it is clear you are unfamiliar with basic terms like complex number, tunnelling, quantum state, eigenvalue, fine structure constant, Hilbert space, etc. etc.. All these terms and concepts have thus far cropped up and are pertinent to the discussion. So what makes you think you can hold such a discussion without knowing them? It is the height of arrogance to talk with grandiose confidence about Bohr's model when I had to tell you Bohr's postulates. So, please, do not tell me you have been perfectly respectful.

DG is doing a fantastic job of schooling your physics, already. I'm hoping you'll take the time to read through all of his posts cause unlike him I have a habit of jumping to the inference at every turn, so I don't really do textbook accounts and DG does great ones anyway.

Do you have a problem with what relative identity infers about your God, or don't you? I don't care if you answer, as I said. I just like pointing out that God is dirt and impertinently charging other theists with not being able to handle it.

You ignored virtually my entire post, you ignored all of my points in the previous post and the ones in this post. You never "adressed" anything, you just deferred back to your bouncing explanation which I just demonstrated false again. Please do not waste my time by walking in and pretending to be an authority in a subject you know nothing about. You didn't even read my entire post.

At this point, you are now trolling in the thread. Please don't troll. It's against forum rules.

I read your post. You did not introduce new points.

Apologies.

DG has really tried to make this clear to you Presupp, and I admire his tenacity. Now, I'm going to try and simplify this for you as much as I can.

 

*Buzz* !Wrong!

Electrons are "things" was a proposition of naturalism, which has been experimentally falsified. If electrons were discrete 'things' they would obey the logical laws that govern discrete objects.

It's relatively easy to test if electrons will act as though that they are discrete objects because it only takes a little energy to make them jump about their orbitals or separate from an atomic nucleus altogether. Given the right conditions you can launch an electron from its orbital like a rocket from a little launch pad and observe what it does in a space gap. The rules that govern its motion, if it is a discrete object, are thoroughly well established and it's easy enough to recognise a result governed by those laws.

However, given enough gaps to play in an electron will refuse to behave as a 'discrete thing'. with the erstwhile success of atomic theory electrons not behaving like discrete objects, sometimes, was, of course, very unexpected and the controls were, naturally, questioned and cross-examined.

As such.. for instance... you can close one of the slits and see plenty of evidence that discrete electron paths 'bouncing or not bouncing' can not accrue diffraction or interference patterns, and you can keep both slits open and detect the electron at the slit to ensure that you know whether it goes through one slit or both, and when you do, again, there is plenty of evidence that discrete electron paths, bouncing or not bouncing, can not accrue diffraction or interference patterns.

Once the controls have been well cross-examined you have one alternative to consider - the proposition was wrong - electrons display a non-discrete nature.

That is where we are with that.

 

A couple of things? I call straw manning! the extensive and extraordinary success of QM is hardly represented by "a couple of things".

In any case, however, of course I can grant you that it doesn't mean the theory is 'correct' it means that there is a strong correlation between the theory and the reality it is describing and when you have this you have much cause to respect the propositions of the theory, regardless of whatever insult those propositions present to your sensibilities.

 

Here you are demonstrating a basic misunderstanding of Quantum Theory, this is not an argument against QM at all. QM agrees with you, we have the collapse postulate which states heuristically that for physical significance an electron takes a specific position and velocity and the Heisenberg uncertainty principle which states that our observation interaction is too disruptive to that state for us to determine it completely. This is all overshadowed by the measurement problem which is basically the evidence that physical significance imparts physical significance, somehow, from one quantum state to another.

As for electrons leaping from one place to another without cause, there is a cause! The electron is already there! The cause is the wave evolution which places the electron in multiple potential states, a physically significant state is simply one of those. It is apparent, reiterating the measurement problem, that physical significance imparts physical significance from one quantum object to another, therefore if there is physical significance to a quantum leap it occurs, its cause is the evolution of the wavefunction of the electron, the reality we are accustomed to is the result.

Yes, I see them. That's quite a nice effect. I also note that the slit created by your thumb and finger acts like a divergent optical focus, which is why you should see a concave image of whatever you are looking at. That effect is the result of the curvature of your finger and thumb as they form a slit, they curve inward slightly, resulting in a concave lens. The latter effect is more easily observed if you are staring at a screen with words on it (like I am now). You have to move your makeshift slit back and forth a bit to get that effect, because like all lenses, the one made by your fingers has a specific focal length.

I didn't know I could see an interference pattern so easily! It works on LCD monitors too. Thanks for sharing!

 

Okay, except that it would have to do this faster than light, as the change occurs at the speed of light. I think this is still impossible from your standpoint. correct? Did you even look at the experiment?

Here's another one for you: Elitzur-Vaidman bomb-tester

In case you're not feeling very link-clicky, here's the breakdown:

If this is not a problem for your idea then, by all means, explain why we're wrong to use this principle to perform computations without actually running the computer. Then explain why, if we're all so wrong about this quantum mechanics stuff, it predicts things so well anyway.

 

Hello,

 

I just finished reading John D. Jackson’s short book, “Mathematics for Quantum Mechanics: Introductory Survey of Operators, Eigenvalues and Linear Vector Spaces”

   Also in the 8 weeks, basically since I began this thread, I have read all the following:

   “Molecular Quantum Mechanics”… Friedman/Atkins
 “On the Quantum Theory of Line Spectra” Niels Bohr
 and a slightly older book “Space-Time Structure” Erwin Schrödinger.


   Can anyone with some insight to: OP/quantum study/probability spaces/Schrödinger/Planck/Bohr/VSPER theory/etc. recommend some excellent books that will give me a better framework for my knowledge in these areas?

 

How are you with the college maths, Wonko? Your list suggests that you aren't inclined  to shy away from technical material and if that's the case you should try Penrose's Road to Reality. It's a thumping big brick of a book and there's lots of maths to plough through to get into it but in my opinion it's probably one of the most comprehensive books available for what you've stated you're after - a framework for knowledge in these areas.

If you aren't looking for something requiring so much commitment at the opposite end of the spectrum Marcus Chown has published some entertaining and accessible books on physics, as has Lee Smolin.

And for the chemistry I used to access an excellent online textbook with interactive panels and contextual discussion to make the concepts more accessible, this book is the reason for every good grade I got in my early chemistry classes.

- took me a little while to find it again- http://www.wwnorton.com/college/chemistry/gilbert/home.htm the molecular shape tutorial is chapter #7 and VSEPR is here

 

Eloise,

Thank you for the information. My college math was sparse to adequate, but I have self-taught away from college by borrowing textbooks from friends and especially the library system available to me as well as a few purchases. Sometimes I do have to look things up online when I can't quite follow the book(s) but I am willing to learn anything. Even if I  have to re-read the same page or paragraph five times. I don't know why I didn't find this stuff very interesting a couple of decades ago during my college. It's probably why my grades were fair to poor on some of it.  

Penrose will be at the top of my new list now. I'll also add Chown and Smolin as an easier read is, on some days, just perfect.

I will also access the online textbook and the other links.

Thanks again for taking the time to help me out.

 

Vector calculus is also called "multivariable calculus". As such, any material on vector calculus presupposes the student has good knowledge of single variable and fundamental calculus. So if the pages in the given link are confusing, you might want to start with this first:

http://www.libraryofmath.com/calculus.html

You'll notice that this page covers everything the other link did (divergence, curl, Jacobians, Gaussian spheres, triple integrals, surface integrals, flux, etc.) but also has a lot of introductory material. I recommend reading all the introductory material on LOM, but I think the first link is more clear on the more complex calculus, also it spends more time on the deriviations, which are more important than the formulae.

If you don't like getting online learning material from multiple different sources and trying to integrate them all together, then all the applied mathematics you could ever possibly want ( everything from calculus to combinatorics and discrete probability, complex algebra etc.) is bundled together in this 2320 page monster from the wonderful and sacroscant institution of CalTech:

http://www.cacr.caltech.edu/~sean/applied_math.pdf

*prints it*