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You're getting a little off topic with the black holes, but paradoxically to the layperson, exactly the opposite of what you said is what happens near the event horizons. It's the smaller black hole that stretches things more, not the larger black hole as you suggest. The reason is because the event horizon is so much further from the center of a larger black hole, the stretching effect is reduced.
Originally posted by bobbobulau
The denser matter of the smaller black hole would stretch at a similar rate because it would maintain some form of gravitational force of the small black hole but smaller particles, say quantum in size, would stretch further because gravitational force in the larger black hole would have a stronger effect on it than gravitational resistance produced by the smaller black hole. The smaller particles would have a longer wave pattern because it stretches further.
According to the de Broglie hypothesis, every object in our Universe is a wave, a situation which gives rise to this phenomenon. Consider the measurement of the position of a particle. The particle's wave packet has non-zero amplitude, meaning that the position is uncertain – it could be almost anywhere along the wave packet. To obtain an accurate reading of position, this wave packet must be 'compressed' as much as possible, meaning it must be made up of increasing numbers of sine waves added together. The momentum of the particle is proportional to the wavenumber of one of these waves, but it could be any of them. So a more precise position measurement – by adding together more waves – means that the momentum measurement becomes less precise (and vice versa).
But they don't determine whether you define what you observe as having wave-like or particle-like properties.
An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. The term may also refer to the physical region defined by the function where the electron is likely to be.
Within a physical context atomic orbitals are the basic building blocks of the electron cloud model (alternatively referred to as the wave mechanics model or atomic orbital model), a modern framework for describing the placement of electrons in an atom. In this model, the atom consists of a nucleus surrounded by orbiting electrons. These electrons exist in atomic orbitals, which are a set of quantum states of the negatively charged electrons trapped in the electrical field generated by the positively charged nucleus. The electron cloud model can only be described by quantum mechanics, in which the electrons are most accurately described as standing waves surrounding the nucleus.
Another, apparently quite distinct, theory was produced by E. Schrodinger. This is a "wave mechanics" from which the truth of the classical mechanics for large-scale phenomena can, as a limiting case, be as easily derived as geometrical optics. In this theory, a certain quantity ψ which satisfies the so-called Schrodinger wave-equation, appears, but is omitted again in the final results which can be directly tested. Schrodinger himself interpreted ψ as the measure of the electrical density at each point - an interpretation which does not seem to be practicable.
On the other hand, Max Born's interpretation in which the value of ψ at one point is considered to be the measure of the probability that a corpuscle or a light-quantum is to be found there, is more acceptable.
Accordingly, that which is propagated in waves is not physical reality, but the measure of a probability. To this we must add that the propagation of the ψ waves does not take place in ordinary space, but in the so-called configuration space, a mere graphical, auxiliary structure of as many dimensions as there are independent co-ordinates. The whole thing is an extremely abstract method of estimating the probability of the occurrence of certain events - and not a model.
The ideas of de Broglie and Schrodinger originally arose from a desire to reduce all the corpuscular characteristics of nature to those of waves, and thus to regard corpuscles and their motion as illusory, so to speak; or as the points at which trains of waves interfere in a very peculiar way (the so-called wave packets). Max Born's view, on the contrary, would seem to be an attempt to regard only the corpuscles and quanta as real and the waves merely auxiliary constructions. The question as to which theory is the correct one has no physical meaning. In any case, the distinction between quanta moving with the velocity of light and corpuscles moving at a lesser velocity, remains. The latter have a so-called stationary mass, which the former do not possess.
Want to take a stab at applying it to entanglement? How do two particles, separated at birth (theoretically by any distance), manage to always maintain an identical state instantaneously? That one gives me fits.
I don't really mean how, I mean how can it be demonstrated to occur by the behavior of waves.
But they’re also waves, right? Then what are they waving in?
It’s interesting, isn’t it? That has hung people up ever since the time of Clerk Maxwell, and it’s the missing piece of intuition that we need to develop in young people. The electron isn’t the disturbance of something else. It is its own thing. The electron is the thing that’s wiggling, and the wave is the electron. It is its own medium. You don’t need something for it to be in, because if you did it would be buffeted about and all messed up. So the only pure way to have a wave is for it to be its own medium. The electron isn’t something that has a fixed physical shape. Waves propagate outwards, and they can be large or small. That’s what waves do.
So how big is an electron?
It expands to fit the container it’s in. That may be a positive charge that’ s attracting it—a hydrogen atom—or the walls of a conductor. A piece of wire is a container for electrons. They simply fill out the piece of wire. That’s what all waves do. If you try to gather them into a smaller space, the energy level goes up. That’s what these Copenhagen guys call the Heisenberg uncertainty principle. But there’s nothing uncertain about it. It’s just a property of waves. Confine them, and you have more wavelengths in a given space, and that means a higher frequency and higher energy. But a quantum wave also tends to go to the state of lowest energy, so it will expand as long as you let it. You can make an electron that’s ten feet across, there’s no problem with that. It’s its own medium, right? And it gets to be less and less dense as you let it expand. People regularly do experiments with neutrons that are a foot across.
A ten-foot electron! Amazing!
It could be a mile. The electrons in my superconducting magnet are that long.
A mile-long electron! That alters our picture of the world—most people’s minds think about atoms as tiny solar systems.
Right, that’s what I was brought up on—this little grain of something. Now it’s true that if you take a proton and you put it together with an electron, you get something that we call a hydrogen atom. But what that is, in fact, is a self-consistent solution of the two waves interacting with each other. They want to be close together because one’s positive and the other is negative, and when they get closer that makes the energy lower. But if they get too close they wiggle too much and that makes the energy higher. So there’s a place where they are just right, and that’s what determines the size of the hydrogen atom. And that optimum is a self-consistent solution of the Schrodinger equation.