by AnonYMous
Why don't we see waves in larger objects then? Are these purely mathematical manipulations?
Well one interpretation is that the wave that and object makes is not a real wave; it is actually a probability wave. All systems, great and small have a mathematical probability wave function that defines their motion. Matter as a probability wave means that though we cannot know for certain where the particle will be, we can know the probability that the particle will be in one place or another, depending on the values of the wave function. This answer gives no concrete place, only possible places, and the probability that the particle will be in each of those places. This explains the phenomena of quantum tunneling; when an object can seemingly pass through a barrier it should not be able to pierce. A particle will most likely bounce off a barrier, but because all particles behave as a wave, some part of the particles probability wave could reach past the barrier itself, hence the particle has a chance of being on the other side of the barrier. This is the quantum tunneling effect so necessary in many semiconductors.
Okay, so matter can be described by mathematics as a probability wave, but we really don't understand why it behaves this way, just that it does?
Interpreting what the math means is important. In the end math needs to make sense to you, otherwise, it is literally just numbers. The basic equations of the past like Newton's laws of motion are pretty easy to grasp. You understand them concretely in your mind because they represent a physical fact you can observe. The Schrödinger wave equation maps the motion of a particle, but it gives multiple results, a wave of positions for one particle; though you actually observe one position for one particle. Therefore, the equation is not what you observe in real life. The big problem with the Schrödinger equation is the fact that there is no second part to the equation; some other mathematical pyrotechnics that will provide one concrete result from the myriad of possibilities. You see one concrete result in the real world, not a wave of results.
So what happens to the other possibilities that do not occur? Are they simply thrown out? It does seem that perhaps there is something missing in our knowledge, some part of the equation that would give us one concrete answer.
Einstein and even Schrödinger himself understood that his equation could make accurate predictions, but both believed that behind the equation, there must be some underlying effect, some information that would illuminate the next position of the particle precisely. The Schrödinger equation was just the best they could do at the time. They still believed that God did not roll dice. Yet in the nearly one hundred years since the debate began, no such information has appeared, the universe does seem to behave inherently randomly.
If there is no such information, what does the probability wave actually mean?
The Double Slit Experiment
I have been presenting these concepts in a sort of abstract mathematical way, so let me explain it to you again in the context of an actual physical situation.
If you think it will help.
I think it will. One thing I like about humans is that you can explain something in one way, and then another. That combination helps their understanding. Like seeing things from two angles gives you a better understanding of space. So you have mathematics describing particles as waves, yet you do not usually see particles as waves. The reason is that particles only behave as waves when you aren't looking.
What do you mean?
Just like the Invisible Boy in the super hero comedy 'Mystery Men', whose power is that he can become invisible, but only when no one is looking; particles behave as waves, but only when no one is looking. Hence, in order to see the wave, we need to not look at it.
--This last reference caught me by surprise and broke me out of my intense mode of analysis. It brought me back to the reality that I was speaking to someone who claimed he was from outer space.
I find it curious that an alien would be so familiar with our pop culture. Charlie Brown, Survivor, Mystery Men? I haven't even seen that movie.
Do you feel that an alien should only go around quoting Shakespeare? I have the ability to process a lot of information. When studying humans, wouldn't you think that I would be interested in what the majority of a human population find entertaining, even if that thing only had its moment and then passed away with the humans who enjoyed it? Great art may transcend paradigms, but popular art defines them. And only on rare occasion is great art completely accepted or understood in its own time. I have an interest in many types of ideas. The ideas that blaze hot and fade away, and the ideas that linger at a cool burn. Besides, when communicating with humans, it is usually more effective to use references from their current pop culture, plus some of those references are truly entertaining. In this case, the reference is very fitting. It is disappointing that you, as a long-time member of this paradigm are unaware of this very amusing reference. But even if it is of no use to you now, it may aid your understanding some evening when you are flipping through the channels on your television and 'Mystery Men' happens to be on. Perhaps you should get another cup of tea, and I will return to my story?
All right.
--He waited until I poured my tea from the teapot and continued.
There was an experiment done with light in 1799 that paradoxically allowed you to actually observe the phenomenon of not observing. It was called Young's experiment. It has since been refined, and is now repeated in almost every college physics class in the world with not only photons of light but many types of particles. It is now better known as the Double Slit Experiment.
Yes, I have read about this experiment, and it is included in many lay books about quantum theory.
What do you remember about it?
I remember it all: Single photons were fired off one by one into a chamber. The photons could go through one of two slits. One to the left and one to the right. Behind the slits was a board that absorbed the photons. Photon detectors were placed at the entrance to both slits. When experimenters looked at the pattern of the photon strikes behind the slits with detectors on, it made a definite pattern of dots behind one slit, and dots behind the other slit.
That is the logical result. If you have half of the photons go through one whole and half through the other, after a while, you will see a pattern of two clumps of dots on the paper behind each whole. This would be a pattern made by a particle. If you throw baseballs through two slits and against a wall behind them, the baseballs will all hit the wall in a clumped pattern in the area directly behind the slits.
Yes, and here was the strange result of the experiment: when they let the particle shoot out, but turned the detectors at both slits off, it created an interference pattern on the wall behind the slits. A pattern of particles in vertical stripes or lines, not clumps of dots. And some of these lines were not even directly behind the slits. Some photons were striking the back of the wall in places they should not even reach.
Correct, and this is an illogical result. If the scientists had their particle detectors on, detecting the photon as it moved through the slit, there was the expected regular pattern of the photons going through one whole or the other whole and striking the wall behind the slits. However, when the detectors weren't on, when no one was watching the photons, something else happened; there was a completely different pattern on the wall behind the slits, an interference pattern of light and of dark lines. This pattern happens when a wave runs into another wave. In some places the wave is amplified and you get distinct lines and in other places it is canceled out and you have dark lines. So the particles were crashing into each other, like waves, and being bounced around to places on the wall not directly behind the slits.
Yet the photons were fired off individually, one at a time, so they could not possibly collide with each other.
You see, when the scientist were measuring or observing each individual photon as it went through a slit, they got one specific result, each photon going through one whole or the other. Light as a particle. When they were not measur
ing, turning the detectors off, they got an interference pattern. Light as a wave. This is the dual nature of light. This experiment works exactly the same way with electrons or protons too. This interference pattern, with photons striking the back wall at impossible angles, could only be created if single particles were going through both slits at the same time and bouncing off each other. What that means is that when the detectors did not measure the particle, when no one was looking, it was in many places at once, in likely and unlikely locations. This is the wave nature of matter that the Schrödinger equation models.
So when measured, or observed, the photon existed in one concrete location, but when it wasn’t measured it existed in many locations.
It boils down to this: why do the results change when you aren't looking? Common sense would say that the particle is in the same place whether you are looking at it or not, yet that is not the case. So what is happening?
I have read a few different interpretations, all of them confusing. I guess the way I have thought about it is that the particle isn't anywhere until it is measured or observed and then it seems to find a concrete place to be. I do think of it as rolling dice. If you close your eyes and roll it, you are rolling all possibilities. Only when you looked to see what you are rolling would it actually become 1, 2, 3, 4, 5, or 6.
This is called wave function collapse in quantum theory. And this brings up an interesting question about the nature of reality. Do you exist in a definite world, where everything exists whether you see it or not? Or do you create your own personal world with your observations, where the only thing that actually exists is what you observe? Most religious experts and scientists would agree with the first idea: Whether with the help of God or all by itself, the world was created and exists regardless of your observation. Yet your interpretation of the experiment, that your observations create the world seems to contradict that.
It reminds me of the famous Zen koan “When a tree falls in the woods and no one hears it, does it make a sound?”
Yes, what the Buddhist monks grappled with a thousand years ago, Einstein and Bohr grappled with almost one hundred years ago, and current scientists and philosophers grapple with now.
So what is the answer?
The theory that dominated quantum mechanics for most of the 20th century was the Copenhagen interpretation originally created by Niels Bohr. He and Einstein had quite a few famous battles about it, but by Einstein's death, Bohr was widely considered the victor. Actually there are a lot of interpretations of the Copenhagen interpretation; but basically it says a thing exist in a superposition of states until it is measured or observed. Once the particle runs into an observer, a measurement or an interaction, it collapses the wave function, changing the wave into one specific result.
Yes, I have heard this theory used in new age thinking. It has been interpreted to mean that there is no world outside of your own experience. Nothing exists until you see it, so if you really desire to experience something, the world can manifest that way.
The idea certainly gives humans a sense of personal power, however, that isn't what Bohr was saying. You don't see wave patterns of falling trees, or baseballs when no human is looking. You can roll dice and not look all day, you won't get a wave of dice possibilities. This is because it is not only human observation that collapses the wave function. It does not even need to be a living being doing the observation. A particle's wave function can collapse even if it encounters another particle. The molecules in the die, and the table and your hand and the air, will observe each other and give a concrete result, whether you cover your eyes or not.
So the molecules observe each other and stop the interference pattern.
Since you don't usually think of non living things as observing, you could just say that they interact with each other. The photons in the double slit experiment interacted with the detectors as they went through the slits and they took on definite positions. Since they took on definite positions before the slits, they now made particle like marks on the wall behind the slits. The Copenhagen interpretation states that interaction with a measuring instrument or even other atoms may collapse the wave function of a system, and then give you an actual concrete result.
This seems to make some sense.
It does, but it has some major problems. One problem is that relativity shows that no point in space, no point in time, and no observer is unique or better than any other. Yet some observers collapse the wave function, and some do not. You can easily have an object made of many particles behave like a wave in the double slit experiment. The Copenhagen interpretation seems to imply that some observers collapse the function, and some do not, these effects do not happen, say in baseballs, which have billions of atoms, but do happen in some larger structures, some large enough to be seen with the naked eye. It does not explain which observer is good enough to collapse a system into reality. The other issue is that the Schrödinger equation accurately provides a wave of results. You can interpret it as saying that that none of the results actually exists and one happens to pop into existence when observed. Or you can interpret it as saying that all possibilities are somehow superimposed on top of each other and when observed all the possibilities simply disappear, except for one. To me, neither interpretation is satisfactory.
What do you think?
I think that Bohr's Copenhagen interpretation, bores me. In the Bohr interpretation, the Schrödinger equation’s results are strictly hypothetical, there are many results but only one version actually exists. Why should one version win over others that could actually be more likely? And why do some observers collapse the wave into reality and some do not. It seems to me that the whole thing is a very complicated attempt to keep the world very simple. I think the reason it was initially popular was because the other possible interpretation of the results of the Schrödinger equation opens up an infinitely large can of worms that was virtually unimaginable back then.
The Garden of Forking Paths
So what is the other possibility?
The other possibility is that the Schrödinger equation simply describes what actually happens to a system, the results are not possible locations, but actual locations. When a particle moves to the next coordinate in space-time, it moves to all the locations described by the Schrödinger equation.
But if all these possibilities do actually occur, what you are saying is that the particle will be in many places at once. We do not see particles in many places at once.
Yes, because you are only capable of observing one of these results. When you experience one of the possibilities, the other possibilities do not cease to exist. They still exist, you simply cannot observe them. Your consciousness is singular; it observes one possibility. Once it observes one, it cannot observe the others. Though you cannot perceive the other positions of the system consciously, you can see them mathematically because math transcends the senses. These other possibilities are represented in the mathematical equations of quantum mechanics. So you see, Einstein was right, God does not play dice. He rolls 1,2,3,4,5 and 6, all of them, though you are only capable of observing one of those rolls.
But where exactly are these other rolls, these other results?
They manifest in a different dimension of the universe. Rather, what your scientists now call, the multiverse. A universe that encompasses other universes.
You are speaking of parallel worlds.
Yes.
Well why didn't you say so earlier, I am familiar with the idea, though mostly from science fiction books and movies.
Parallel universes do make for many great science fiction plots. But I wanted you to know the scientific reasoning behind the idea, to truly understand the concept. And while the idea has been around for quite a while in fiction, like the beautiful writings of Jorge Luis Borges, it is not a new idea to science either. The idea of parallel universes has been around for over fifty years in the scientific community. The first scientist to propose it was Hugh Everett the third
. He called it the Many Worlds Interpretation of Quantum Mechanics. It may seem like a crazier idea to you than Bohr's one result universe, but actually it is simple compared to the complexity of the Copenhagen interpretation. All things follow the Schrödinger equation, period. Everett even presented the theory to Bohr in 1959. Of course he was misunderstood and ignored at the time.
Was his theory taken seriously by other scientists?
Not immediately, though by the end of his life Everett was considered a bit of a star in the scientific community. You see, the human imagination is always playing around with many worlds, what could have been and what could be, and that is only natural, because many worlds are a structural part of the multiverse. As an observer of many worlds, to me a single variation universe seems so plain, so uninspired.
It does sound interesting, but is hard for me to believe that many universes exist out there that I cannot see.
Think again of your concept of the spatial dimension; you exist in a location in space, and though you have the power to see other locations, you cannot see all locations in space. Yet you still know other locations exist and you can use your imagination to see far of places: whales in the ocean, the peak of Mount Everest, or the rings of Saturn. Now think of your concept of time. At any single moment, you exist in one coordinate of time. You cannot directly see any of the other coordinates of time, but I hope you now understand that they too exist, and you can use your imagination to recreate them as well. The situation is the same with the dimension of universe variations. You are only capable of observing one possibility, one universe. Yet you constantly use your imagination to see other possibilities. Hence it is not the limits of God, or mathematics, or even your imagination that bind you to one single world, it is the limits of your consciousness. The universe you are observing is just one variation of a possibly infinite number of universes. But you do not have the ability to observe all of these universes simultaneously. Your consciousness can only observe a single variation, a single slice, and in that sense, you seem to me, like Charlie Brown seems to you; flat.