gib65

Consider this alternate form of the double-slit experiment:

Instead of one photon emitter firing single photons (one after the other) at two slits, suppose you had two photon emitters, one direct at each slit. In other words, the photons emitted by each one go directly to their corresponding slit, and only get the opportunity to interfere with the other after they've passed through the slits (and you have them setup to fire photons at exactly the same time).

What will happen?

1) Will an interference pattern emerge, just like in the single emitter case?

2) Assuming the answer to 1) is "yes", when the photon finally hits the screen and collapses into a point-like form, will there still be two of them, or will there be only one like in the single emitter case?

I'm trying to think of a type of chemical reaction that involves a rock and some other substance. What kind of rocks are most susceptible to chemical reactions and with what substances do they typically react? Acids? Oxygen? What would be a relatively quick reaction?

Purple=red+blue

Intersection colour=purple+red+yellow=red+red+blue+yellow

red+blue+yellow=black

Interersection colour= black+red=dark red

 

Just guessing.

I think you just invented a new branch of mathematics.

Take a look at this image, produced by me in Photoshop:

I began with the two lower circles. The are red (left) and yellow (right) at 50% opacity. At their intersection, they produce orange. Then I took another circle and placed it overtop (purple) again at 50% opacity to produced red (well, kinda pink - considering the opacity) at the intersection of it and the previous intersection.

Now my question is this: how does one explain the re-emergence of red (or pink?) when red was used to begin with. That is, if we go with the theory that red is one of the primary colors (so it is fundamental), then it shouldn't be possible to re-create it as a composite of other colors. Yet, it seems like it has been re-created from orange and purple. Of course, I had to use yellow as well, which isn't a primary color, but theoretically it's a mix of red and green which are primary.

I'm not claiming to have disprooven the RGB theory of color, I'm just asking how this is explained. Is it a matter of composite colors cancelling out (so the purple circle and derived orange intersection cancel each other out (partially) leaving behind that portion corresponding to the original red)? But then why did the original red and yellow combine in an additive manner in the first intersection?

I heard that the strong force which holds the quarks together in protons and neutrons is unbreakable. That is, one cannot tear the quarks in, say, a proton apart no matter how hard one tries. Is this true? If it is, then how did scientists ever figure out that protons and neutrons were made of quarks (AFAIK scientists figure out what a particle is made of by breaking it apart in an accelerator)?

So do you mean to tell me that this stuff is like "heavy ghosts"? It doesn't interact with ordinary matter yet it succumbs to the force of gravity? So what would a handful of this stuff do if it was near the surface of the Earth? Would it plummet right through the ground and head straight for the center of the Earth?

If I had a clump of dark matter in my hand, what would it look like? Would it be black or invisible?

This is a good question for Marvin.

I'm just wondering if this theory is debated at all, or if there's any solid proof. I've heard theories saying that the BB was the result of two "branes" colliding, in which case there'd have to be space and time all ready.

So it has to do with distance - so "local" means "close to" in this context.

What does the "local" part of local hidden variables mean? Does it mean local to the thing you're measuring or does it mean "having a location"? Or does it means something else entirely?

The context of frequency is in transitions; if you put an atom in a superposition of 2 states, you can say it's oscillating at the frequency difference between those states.

 

The Bohr model has electrons as standing waves. Even in that flawed picture, one wouldn't necessarily talk about an orbital frequency.

OK, so let's say the frequencies of the two states were 10 MHz and 13 MHz (I have no idea if this is to scale ), then the atom could be said to be oscillating at 3 MHz?

Take a hydrogen atom into consideration. We can say that its frequency is how many times per second (or nanosecond?) its electron orbits the nucleus. This makes sense according to the Rutherford model, but what about in the case of the standard model. As I understanding it, the standard model has electrons surrounding the nucleus as "electron clouds" - that is, they don't literally orbit the nucleus. Therefore, is it still correct to say that the atom has a frequency? Is the electron still undergoing so many ___s per second? And what are those ___s?

It doesn't exclude the QM principle, though, so it has no ability to falsify one or the other. The so-called support isn't exclusive, and in science, it needs to be.

Well, I don't think it would falsify the QM principle outright. What it would falsify, in my mind, is the idea that the distribution of the particle's position is unaffected by the state of the barrier or the particle's energy, which is something the "borrowing" theory would want falsified.

Height meaning energy, or something related (like a potential), just as height in a kinematic sense relates to potential (gh) or potential energy (mgh).

 

Particles in confinement have quantized energy levels. The ground (lowest) state has some minimum kinetic energy.

See, to me that supports the idea that the particle is somehow "tunneling" through the barrier. It doesn't proove it, it supports it. I don't know how to imagine that without denying the wave/particle duality of the particle, but it does suggest that there's something funny going on whereby the particle needs extra energy in order to be found on the other side of the barrier (or for the likelihood of finding it there to go up).

That's just what I gather from it. I don't know the math very well and I'm not as familiar with this phenomenon as others, so maybe other have better ways of explaining it.

The barrier height is important because it dictates where the bottom the barrier is, so the level of the lowest energy level of the particle.

What do you mean by this? Maybe I've misunderstood "barrier height". Does it mean how tall the barrier is (like we would say a wall is 5 feet tall, 10 feet tall, 15 feet tall, etc.), or what position the barrier is at (like we would say a painting on the wall is 5 feet up, 10 feet up, 15 feet up, etc.)?

Also, what does "level of the lowest energy level" mean?

Why?

 

Where in the theory does this borrowing come from?

 

If you work through the maths you can clearly see how the energy and barrier height change the probabilities.

I'm not denying that the math says this.

The particle needs a certain amount of energy to penetrate the barrier (or maybe leap over the barrier if height has something to do with it). It gets this energy spontaneously and the amount of energy it gets is random. I'm assuming this is the way it works because ASAIK, according to QM, energy is one of the variables that can be uncertain. The probabilities are that the greater the energy, the less likely it will be that the particle will get it. The higher the barrier, the more energy the particle needs to "leap over" it, and since the acquisition of high energy is less likely to happen than low energy, it will be less likely that the particle will leap over the barrier, and thus the less likely it will be found on the other side of the barrier.

If the "borrowing" concept was not correct, the barrier height shouldn't have anything to do with the likelihood of finding the particle on the other side. Nor should its energy. The particle's position is distributed over its waveform, some of which reaches passed the barrier. It is not clear how this distribution is affected by barrier height or energy. There is no reason to predict that a higher barrier or lower energy will change the probability distribution of the particle's position. There should always be the same likelihood that the particle might be found on the other side of the barrier.

The QM probability depends on particle energy and barrier height.

If this is a fact, then I take it experiments have been done to verify it. I'd say these experiments are exactly the kind I was trying to describe in my last post (not word-for-word, but close enough). If particle energy and barrier height do have an effect on the QM probability, as you say, then to me this proves favorable for the "borrowing" theory.

I thought of an experiment that might be able to tell us whether the particle really is passing through the barrier in virtue of having acquired the necessary energy spontaneously: see if a correlation can be detected between the probability of finding the particle outside the barrier (after determining that it is inside) and the "penetrability" of the barrier itself. By "penetrability", I mean, the amount of energy it would take the particle to penetrate it if it were to rely on the processes of classical mechanics only. You could adjust the penetrability by the density of the barrier's material, or the type of material, or its temperature, or whatever else would affect the amount of energy needed to penetrate it. If, in doing so, you can affect the probability of finding the particle on the other side - namely, decreasing it as a function of increasing the barrier's penetrability - this supports the theory that the particle is acquiring extra energy spontaneously and using it to pass through the barrier. The assumption this experiment makes is that the more energy needed, the less likely are the chances that the particle will get that much energy spontaneously, and therefore the less likely it is to penetrate the barrier

The interaction of the other electrons affects the sprectra

So could we say, then, that the particular lines that we see in the spectra depend on the atomic number?

Also, what is 'Z'?

There are different spectral lines for each element, right? These spectral lines are explained by the Bohr model of the atom, right? That is, the Bohr model says that electrons drop from one energy level to another, and these drops are accompanied by the emission of photons carrying an amount of energy equal to the difference between the two energy levels. Because there are only a few such energy levels, the electrons can only emit photons of certain energy amounts (i.e. only certain wavelengths/frequencies). These wavelengths/frequencies are what cause the spectral lines.

Here's my question: since each element creates different spectral lines, the energy difference between each level can't be the same for all elements, can it? For example, suppose you burnt hydrogen gas, and one spectral line is created by a photon emitted from an electron that dropped from energy level n=2 to energy level n=1. Now suppose you burnt helium gas, and one spectrial line, which has to be a different one from those of hydrogen, is created by a photon emitted from an electron that dropped from the same energy levels n=2 to n=1. It's the same energy levels but a different spectral line. This means the photons emitted in each case must carry different energy amounts, and this means the difference in energy between energy levels must not be the same from one element to another. Is this true?

It really is amazing what a surge of fruits and vegetables and vitamins can do for your energy levels.

HA! I should try binging on a whole bunch of vitamins one day and see how I feel

Thanks for the answers.

Now a follow up question:

How does this fit into energy "quanta"? What I mean is, according to quantum mechanics, energy only comes in multiples of E=fh, but if f can vary continuously (because the objects emitting it can be moving away at any arbitrary speed), then does this conflict with the central idea behind quantum mechanics?

My understanding of energy quanta is simply that it comes in discrete indivisible packets (called photons), but the amount of energy carried by these photons isn't necessarily limited to specific amounts themselves. So if f can vary in a smooth continuous way, the photons making up the radiation whose frequency is f should also be allowed to vary in a smooth continuous way (in the context of a frame of reference, of course). Is this sound reasoning?

Energy is a frame-dependent quantity. Within a frame, energy is conserved, but the value of a given energy depends on the frame.

So "frame-dependent" is the word I'm looking for (as opposed to the "dilation" of energy), correct?

The minimum energy carried by a wave of electromagnetic radiation is given by E=fh, right? When an object emitting radiation moves away from us, the radiation emitted in our direction is red-shifted, right? But doesn't that imply that frequency (f) should decrease? Therefore, does the minimum energy of the radiation decrease when it red-shifts?

(If the answer is yes, I'm assuming energy is one of those dilating variables that relativity predicts - like time, length, mass, etc. - of course, "dilating" would be the wrong word in this case).

My point was a little more sophisticated. Even if you fix n=1, you can still get any energy E from E=nhf=hf, by chosing f = E/h. The point is, that you need some mechanism/reason why f is not arbitrary. Actually, the reason is that f is fixed by the mode or the change of orbital. Or possibly easier: f is fixed by the wavelengths of the light. So you cannot say that light could only carry energy in discrete packages (because I can mix frequencies f to make it fit), but you can e.g. say that light with a wavelength of 600 nm can only carry discrete amounts (because you fixed the frequency with the wavelength). I'm not sure if the fixation of the frequency, its importance and the reason why it is fixed is obvious to you or not. But you didn't seem to stress the point sufficiently (I might have overread it, also).

I'm not 100% familiar with modes or changes in orbitals, but you did make me think about the absolute velocity of light (which pretty much fixes frequency for a given observer). I would either need to mention this (which brings in whole new ball of wax vis-a-vis relativity) or talk about wavelength as you said.