Pinball1970
Valued Senior Member
Waves do not recoil they interfere
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The question of multiple dimensions in quantum mechanics:
- Thread starter quant
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Pinball1970
Valued Senior Member
Do you want me to explain it in terms of things you understand which will be something classical? That will not work.
Pinball1970
Valued Senior Member
John Butterworth explained this at a presentation this way, a wave or particle travels from A to B, the probability that it will be detected at point B will have P {B} what it does in-between? In terms of a path? No one knows. All the rest is mathematics.
Why don't you answer the question Doctor of Physics DaveC426913, instead of being so obstructionist and evasive. It is a very simple question to which you don't seem to have a clue. The question, I will repeat it, was: "What is the quantum mechanics explanation for how light travels from Point A to Point B?" A seemingly simple question which, from the tone of your posts you should easily be able to answer. IF you cant' or don't want to answer, kindly shut up because I want to know the answer! Read everything I wrote, and yes, brightness I did realise this was a quote from the double slit experiment. In the context used in my post it holds good. I repeat if you can't answer, just shut up and hold your peace I don't have time for this kind of diversionary crap.
Thanks, like a breath of fresh air, a direct answer. From what I can gather, (forgive the lengthy answer): "In classical mechanics particles are described with position and momentum in three-dimensional space. However, in quantum mechanics, particles are represented by wave functions, which are solutions to Schrodinger’s equation. These equations describe the probability amplitude for a particle’s state, but they do not exist in ordinary three dimensional space . Instead they inhabit a complex, abstract space where each particle has its own set of co-ordinates. For a single particle, the wave-function in three dimensions might be sufficient to describe the particle, but for systems with multiple particles, the situation becomes more complex. Each particle adds additional dimensions to the state space, resulting in a higher-dimensional configuration space. For example, a system of two particles would require a six-dimensional space (three dimensions for each particle). This increase in dimensionality complicates the mathematical treatment of the system, as the wave function must now account for the interactions between particles and their respective positions. The concept of entanglement also arises in this higher-dimensional space, where the states of particles become linked, such that the state of one particle cannot be described independently of the state of the other, regardless of the distance separating them. This entangled state leads to non-local correlations that challenge our classical intuitions about separability and locality in physical systems."
This content can be found in the book: "Quantum Mechanics" by Cohen-Tannoudji, Diu, and Laloe, where the properties of wave functions for systems of multiple particles and the implications of entanglement are explored and in other standard textbooks on quantum mechanics.
Before quoting multiple dimensional spaces quoted above and attributing it to Hilbert space, think about the surrounding facts: What possible reason can so many brilliant contemporary physicists have for supporting the Many World Interpretation of quantum mechanics? The reason is that they believe those multiple dimensions in Hilbert space each exist as a viable possibility (i.e., real) this being so, how can they just collapse and disappear, where do they go? The alternative is that each possibility manifests as reality in an alternate universe which is parallel to but undetectable from out Universe. This is how the Multi World Interpretation ties in with quantum mechanics and it is just another explanation given for how light propagates.
IMHO this is the ultimate pits when describing such a beautiful phenomena as light. Back to Newton and his prism. Only an opinion mind you but holding this opinion in a den of quantum mechanics supporters is worse than being Daniel in the den of lions.
I would like to thank QuarkHead for his unbiased post. In fact I think he has made the point better than I was able to do. So yes, thank you.
Isn’t quantum mechanics supposed to regard light (photons) as possessing both wave and particle property. No I think this is a deliberate diversion away from a fact namely, "optical microscopes cannot see small objects", to a supposition about what someone meant. The context becomes meaningless in the face of a fact, also, James R seems to be implying that photons have varying sizes, which could mean a photon with a 60 Hz frequency has a wave-length (size of 5,000,000 metres)
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Pinball1970
Valued Senior Member
I am less qualified in physics than Dave, James and Exchemist. You need to know that.
Pinball1970
Valued Senior Member
Recent polls suggest that this is not the favoured interpretation
DaveC426913
Valued Senior Member
Pretty sure that's not what he's implying.
exchemist
Valued Senior Member
But what you say fits my understanding certainly.
quant could be the very person to whom Feynman's famous quote was addressed: "You don't like it? Go somewhere else! To another universe where the rules are simpler, philosophically more pleasing, more psychologically easy."
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quant:
The most familiar kinds of waves - water, light, sound etc. - do not reflect off other waves of the same type. What happens instead is that the waves simply pass through one another.
Get yourself two flashlights. Turn them on and try crossing the beams. Can you see the beams reflecting off one another where they cross? Does crossing one beam with another alter the position of the spot of light from the first one that appears on the opposite wall?
For example, if a sound wave consists of two sinusoidal tones, that is a superposition of two waves. But nobody is invoking mysterious "extra dimensions" of space or time when we describe sound waves, no matter how complicated they are.
My guess is that you're wrong about this.
Do you think that photons are carriers of electric charge? If so, why?
And what has any of that got to do with free electrons and massive nuclei, exactly?
What kind of waves are you thinking about?
The most familiar kinds of waves - water, light, sound etc. - do not reflect off other waves of the same type. What happens instead is that the waves simply pass through one another.
Get yourself two flashlights. Turn them on and try crossing the beams. Can you see the beams reflecting off one another where they cross? Does crossing one beam with another alter the position of the spot of light from the first one that appears on the opposite wall?
If you agree that such things do not take place, what are you talking about?
All of physics accepts multiple dimensions - usually four of them. You directly experience those in your daily life. Physics tries to model reality.
Are you talking about Hilbert spaces or physical dimensions of space and time? Do you understand the difference?
Okay.
Not at all. A superposition is just like an addition of two waves that happens in regular old 4-D spacetime.
For example, if a sound wave consists of two sinusoidal tones, that is a superposition of two waves. But nobody is invoking mysterious "extra dimensions" of space or time when we describe sound waves, no matter how complicated they are.
Physics says that a wavefunction can represent reality. Clearly, it can, because we can do theoretical calculations using wave models that predict certain experimental outcomes which, when compared to the results of real-world experiments, turn out to be accurate. But this has no particular dependence on any one particular interpretation of quantum physics. The many worlds interpretation is equally compatible with the experimental outcomes we observe.
Please tell me the "actual facts", as you understand them.
Did you take a poll of leading contemporary physicists?
My guess is that you're wrong about this.
Are you actually just using the word "dimensions" as a substitute for "many worlds"? They aren't the same thing, you know, despite the common misuse of the word "dimension" in popular culture.
Where did you get the idea that quantum mechanics ignored the possibility of photons as being carriers of electric charge?
Do you think that photons are carriers of electric charge? If so, why?
And what has any of that got to do with free electrons and massive nuclei, exactly?
Which arguments? Why?
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I answered it back in post #24, above. Did you miss that one?
This is all fine. Notice how the author talks about "three-dimensional space" in the first sentence. Wave functions also use that three-dimensional space; after all, they predict outcomes in our real world, which has three spatial dimensions. In the following sentences, however, the author also talks about a "complex, abstract space" called "configuration space". There, he is talking about one way of thinking about a mathematical model.
For instance, let's say that you and I want to track out respective locations in the world. We might do so by wearing GPS trackers that record our respective latitudes and longitudes and how those change over time. So, at any given time, both our locations will require 4 numbers to specify: two numbers for your latitude and longitude, and another two numbers for mine. The "state" of our "location system" that we're using to track our positions has four coordinates, which mathematically we can refer to as dimensions of the state space.
We could even write down elements of the state space in the format (LAT1, LONG1, LAT2, LONG2), or similar. Each individual set of four numbers would specify one unique combination of our combined locations on Earth.
This example state space has 4 dimensions. Suppose we wanted to track 100 people in the same way. Then, we'd need a state space with 200 dimensions.
However, I hope you can see that nothing in this description affects the fact that the Earth's surface only needs two coordinates to specify a location: latitude and longitude. Nothing about the physical space is changed by the state-space description.
The bottom line here is: don't confuse abstract dimensions with physical dimensions. This appears to be a mistake you're making with quantum physics.
The Many Worlds interpretation of quantum mechanics has no special connection with Hilbert spaces or abstract dimensions. It literally proposes multiple separate physical universes, which is a completely different thing. This is in contrast to the Copenhagen interpretation, which merely says that wavefunctions change in a certain way when measurements are made, without spawning new universes.
They don't collapse of disappear or go anywhere. A particular model will use a certain number of abstract dimensions. Your question is like asking where our latitude and longitude coordinate data disappears to.
I'm not at all clear on what your opinion is on how light propagates.
Can you explain?
Demonstrably, certain experiments show that light has wave-like properties (e.g. the two-slit interference experiment), while other experiments show that light has particle-like properties (e.g. the photoelectric effect).
Quantum mechanics accounts for all of these phenomena using a single model.
Do you deny that light has wavelike properties? Do you deny that light has particle-like properties? If you don't deny one or both of these things, tell me how you account for the experimental observations. Start with the two experiments I just mentioned, if you like.
What are you talking about? What "fact" are you referring to?
Nobody is disputing that optical microscopes have limits to their resolving power. Nobody is disputing that those limits are related to the wavelength of the light used. Unless you are disputing this. Are you? If not, then what are you talking about?
I don't think that the concept of the "size" of a photon is particularly useful. In what circumstance would it become important to know the "size" of a photon? Interactions of photons with matter, for instance, can be characterised by referring to such features as the wavelength of the photon, or its frequency, or its energy or momentum, without ever referencing a "size".
My previous point is that you, quant, seem to have confused "size" (as in particle diameter, or similar) with wavelength. The two are not the same thing.
Do you understand this point?
By the way, the frequency and wavelength of a photon are related by
$$c=f\lambda$$
where c is the speed of light, f is the frequency and lambda is the wavelength. The same equation applies for classical electromagnetic waves.
Exactly, and then only if they are closely related in terms of frequency and wave-length, recall how difficult it was to jam signals in the second World War. Also, since waves do not recoil but only interfere, how does this whole question of photon emission arise? No recoil? What about the conservation of energy and momentum? Further, the rate of photon emission has proven to be at least in the hundred terahertz range, as definitively proved by the new optical atomic clocks. How do two waves, the incoming electromagnetic wave, and the electron wave-function 'interfere with each other to produce this kind of photon emission? A large part of quantum mechanics has to be taken on blind faith, and a deep belief in the absolute veracity of the mathematical systems used. How can one use imaginary numbers and get a real result? Its like saying 'pigs can fly'. The truth is pigs cannot fly, the trot around on their little trotters. Just that the circumstance exists where I can state: " Pigs can fly." Does not mean that they actually do fly!
Pity they don't demonstrate particle properties when used in a microscope!
No, and in fact in my work, it is very evident that a photon possesses both properties, it is a symbiosis of a wave and a particle, not like the ridiculous com0plementarity theory where a photon can be either a wave or a particle, just not at the same time. That's really asking to be kicked. If you ask me.
Exactly what I said, optical wave-lengths are too large to see objects more than 200nm - 300 nm small. Therefore size does matter. If it didn't the wave-length should not matter and it should be possible to view even sub-atomic particles through an ordinary microscope. If this problem exists at the level of a microscope, it must surely exist in atomic processes such as photon absorption and emission.
Good God man, the whole phenomenon of light is based on such a mechanism, i.e., electron (classical radius, Electron cloud wave function or whatever) absorbing and emitting photons. When the size difference is 178 million, surely that is cause for investigation and concern?
No, Sir, it is yoou who are confusing the issue. Let us accept for a moment that you are right, and that the light enters the atom in the form of a photon. How is it supposed to interact with your electron cloud or wave- function, it will pass straight through the wave-function without any interaction. Or are you saying thgat at the time the photon enters the atom, the electron wave-function is 'detected' (i.le., becomes a particle) ? In which case your whole quantum mechanics theory is wrong, because it doesn't say that. Would you if you were in a position to do so, like to amend that?
No. Waves interfere even when they aren't close in terms of frequency and wavelength. They obey the principle of superposition. Whenever they share the same space, they just add up, in effect.
That was before my time, I'm afraid. What do you recall from that time?
Photons have momentum. When an atom absorbs or emits a photon, the atom recoils, to conserve momentum.
Both work just fine with photons. In fact, even in the classical electromagnetic wave description of light, the waves carry momentum.
The rate of photon emission from what? It can vary a lot, depending the source.
Incoming electromagnetic wave? Emission is outgoing, not incoming. What are you talking about?
Not at all. We can experimentally test it. You should check out some experimental results. In fact, were it not for experiments, we wouldn't have quantum theory today.
Quantum mechanics is science, not religion. Ergo, no faith required. Instead, we use evidence.
The proof is in the pudding. The maths makes predictions, which we can test against real-world experiments. There's no need to "believe in" the maths. We can objectively ask questions like: does the math make predictions that match experimental outcomes? If the answer is "yes", then the theory must be doing okay.
What, exactly, do you mean by "real result". Are you using the word "real" in the mathematical sense, to distinguish "real numbers" from "imaginary numbers", or are you using "real" in a colloquial sense to mean something like real-world answers to problems?
Either way, there are lots of applications of imaginary numbers that lead to results that are "real" in both the mathematical and real-world senses of that word. No flying pigs required.
Have you ever studied complex numbers, quant? It sounds like maybe you haven't.
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Horses for courses. The features of photons that you will observe depend on the type of observations you make.
Great! When are you going to show us your work?
Why? Is there a problem?
But "size" is different from wavelength. Do you understand my point about that, or not? You keep repeating the same error, even after I helpfully explained the issue to you. Why is that?
It does! For instance, an atom will only absorb or emit light at specific wavelengths. You've heard of emission spectra, I assume (?)
Where does the "size" of a photon come into any of that?
I think we don't need to worry about it. The "size" of a photon doesn't seem to be a useful or necessary concept. Like I said.
Can you point me to any standard physics reference that refers to the "size" of a photon?
So, just to confirm: you agree with me that the "size" of a photon and its wavelength are two different things? Or do you think they are the same thing?
Tell me: how do you calculate the "size" of a photon? Show me your maths.
So, we're talking about an atom potentially absorbing the photon, for example?
Maybe. On the other hand, if the spacing between atom energy levels is just right, the photon might be absorbed by the atom. The relevant comparison, in this case, is between the energy of the photon (which is related to its wavelength, not its "size") and the quantised energy levels of the atom.
The quantum description of something like a photon doesn't involve the photon changing from a wave to particle, or vice versa. Rather, the photon has both particle-like and wave-like properties.
But yes, atomic absorption can be used to "detect" photons. That's how the camera in your cell phone works, to pick an example at random. It's also how the retina in your eye works, to pick another example at random.
Have you consider that maybe your whole quantum mechanics theory might be wrong, and not mine?
Do you think it's at all possible that there are some things you don't understand about quantum mechanics?
Where did you learn your quantum mechanics? Did you take a course, or are you self taught?
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exchemist
Valued Senior Member
Quite. What quant seems to miss, presumably due to his lack of mathematical background, is that it is not the "particles" that are said to inhabit a multidimensional space in QM but the equations that represent them (i.e. the maths, not the things themselves) and, furthermore this space is an abstract (because mathematical not physical) space.
But I'm glad at least you have now smoked out his misunderstanding on this point, which is just as we had thought.
Next up? The classical electron radius, perhaps? I see he has returned to this (artificial and fictitious) construction yet again. Good luck!
Pinball1970
Valued Senior Member
The multi dimensional thing could have come from either pop sci - Another dimension like aliens or something or connected with string theory.Quite. What quant seems to miss, presumably due to his lack of mathematical background, is that it is not the "particles" that are said to inhabit a multidimensional space in QM but the equations that represent them (i.e. the maths, not the things themselves) and, furthermore this space is an abstract (because mathematical not physical) space.
But I'm glad at least you have now smoked out his misunderstanding on this point, which is just as we had thought.
Next up? The classical electron radius, perhaps? I see he has returned to this (artificial and fictitious) construction yet again. Good luck!
String theory works in 10 or 11 dimensions from memory, our regular dimensions each orthogonal to the other. String has 6 or so compactified (Calabi - Yau)
A lot of misconceptions going on with Quant.