Since calculus, physics, and all things-mathematics seem popular at the moment, I was wondering if any of you can crack this nut: http://www.youtube.com/watch?v=DfPeprQ7oGc
This is a neat animation that demonstrates experimental observations for when researchers try to measure whether electrons behave as particles or as waves. While electrons behave as particles when travelling through the single slit, they behave as waves when presented with two slits. Then, when you try to observe each electron to figure out which slit it goes through, it once again behaves as a particle. It’s fascinating stuff!
I’ve read about this before. One thing I don’t understand is where exactly on the two-slit setup the single electrons and photons were being fired at. Were they fired at one of the slits? At both alternately? Or neither? In the last case, were they fired at the space between the slits or to one side of them?
Furthermore, how does anyone know whether the electrons or photons hitting the screen on the other side are actually the same ones that were fired?
Regarding the “act of observing”, based on what the video says, the experiment was being observed from the beginning. What the video should say is that the experimenters forced the particle to affect something else in addition to the two-slit setup and the screen. I imagine what this something else was and where it was positioned would be important.
I think they’re fired straight at the middle, but the slits in real experiments are extremely close together. Since the quantum particles seem to display both wave and particle properties, they either can move around a bit to go through the different slits (moving horizontally in a wave-like motion), the firing range of the particle-gun is wide enough to technically encompass both slits (like shooting a barrage of marbles), or something too wacky for my mind to comprehend.
The double slit experiment is subject to debate up until today, especially because it is seemingly trivial but yields non-trivial results. Any model of quantum mechanics is tested by its implications for the double slit experiment. Now, the results are undisputable: Electrons behave as particles and they behave as waves. The question is, how does the electron decide how it will behave? Schrödinger’s solution to the problem was, based on a thought by de Broglie, his Schrödinger-equation. (Look the formula up on Wikipedia) The solutions of this equations are complex, in the mathematical sense, wave-functions, that is sinuses. If you take the square of the absolute of such a solution you get something that is interpreted as a probability-distribution that gives you the probability to find the particle at a given point in space and time. Funny thing is, for high enough energies the Schrödinger equation yields Newton’s equation of motion. Now we have some basics to get a bit of the presented experiment.
In the case that you do not, speaking in the particle picture of electrons, observe through which slit the electron goes you get, speaking in the wave picture of electrons, an equal probability distribution to find the electron at any of the two slits. You can then look at the two slits as two sources of electrons and let the two resulting functions add up, that is interfere. This yields the correct pattern on the screen.
In the case that you do, speaking in the particle picture of electrons, observe through which slit the electron goes, you get, speaking in the wave picture of electrons, one source of electrons. For big enough slits, this yields a pattern on the screen that is identical to the pattern you expect from a particle. (Big enough in this context means three or four times the de Broglie wave length lambda = h/(m*c) where h is Planck’s constant, c speed of light and m the electrons rest mass. This is completely analogous to classic waves) Now, from this point of view, we could state that the wave-like behavior of electrons is their true behavior. This is what happened when this effect was observed for light. (Which is not that hard. Punch in a very dark, thin, fairly hard piece of plastiv or paper two holes a centimeter apart whith a very sharp needle. Shine a laser on it. Enjoy the interference pattern. This might not work because of a really bad laser or because of bad holes but it can really be done.) The problem is that electrons, like light, have particle-like behavior too. For light, see photoelectric effect, for electrons, see Compton effect. Both effects are virtually impossible to explain with a wave pricture of electrons.
Now, one modern interpretation by Zeilinger is that information is the fundamental aspect of quantum physics. By measuring the slit the electrons go through you have to loose some other information that is encoded in the pattern so you have to loose the interference pattern. If you do not observe which slit is being passed, you can keep this other information and have the interference pattern on the screen. Sadly I can give no more information on this.
What the video refers to at the end is the path-integral formulation of quantum mechanics by Feynman. Basically you add up all possible probabily.functions and the result yields the correct probability function. Now there is (philosophical) debate how to interpret this formulation. Basically there is the copenhagen interpretation that there is only probability and probability is an inherent feature of quantum physics, and the Everett interpretation that there are uncountably infinite universes in which all of the possibilities in the path-integral happen but in each universe just one way is realised. Personally, I have no clue which of them is right, both sound crazy.
To answer Autolykos question: Such double-slit experiments are set up so that the source of the tested entity, like light or electrons, spews the “stuff” more or less evenly on the screen. It does not matter that a big part of the “stuff” is lost because it clashes against the walls because what is measured is what goes through the slits. Of course you can not be perfectly sure that the “same” electron hits the screen as is emitted, but you can know what impulse the electron has when it is emitted and you can measure the impule of an electron at the target. If the impuls is the same and the electron at the target arrives at the time it was expected to arrive, that is there is no reason to believe that an other electron hit the target than was emitted, we have to accept it is the same electron.
Regarding the last statement, it is not that much a physical statement as much as a principal. If two object are identical in all their properties they are regarded the same. This is especially true in quantum mechanics since there are so few properties that it is not anymore an abstraction but a matter of fact. Further proof is obtained if you look at Gibb’s paradox, that is if you calculate the entropy of an ideal gas before and after you remove a seperating wall between two chambers of the same gas at the same pressure, you conclude that the entropy after is greater than before, though you can restore the previous state by simply reinstalling the barrier, reducing the entropy wich is deemed impossible by the second law of thermodynamics. This problem resolves if you use Sackur-Tetrode’s equation which is obtained if you assume the particles to be indistinguishable, that is you are not able to “name-tag” the exact particles.
I started studying physics last year so I am not very advanced in my understanding but I hope that my writings helped you to understand reality better.
one thing to keep in mind is that uncertainty is in the eye of the observer, not in nature. on LessWrong.com, from which comes the article that Azure linked, they make it a point in probability theory that probability is in the mind, not in nature. this is just elementary understanding of the terms used: both uncertainty and probability refer to a type of ignorance or partial knowledge. nature knows nothing of these things; it is only rational actors that can have knowledge or ignorance.
the only possible paradoxes, just due to the elementary meaning of these words, are verbal paradoxes. a “paradox in nature” is not merely surprising and counterintuitive, it is an incoherent string of words masquerading as insight. what is really happening is there is a contradiction in the words we use to describe these phenomena, and that can ONLY be because we are being imprecise with our words.
as to the double-slit experiment, it is interesting that the fringe effect was produced almost 200 years ago…with a needle! check it out:
Zangelbert Bingledack, a quick search on lesswrong.com did not yield anything that resembles your implied point. It is a claim you should have to prove. As NNT pointed out in his books, it is irrelevant if a probabilistic description arises because of lack of knowledge of underlying parameters or because of inherent probabilistic properties. In quantum mechanics it seems the latter is the case since assuming hidden variables proves to be an incorrect description of reality, it can be ruled out experimentally by showing that Bell’s inequality holds true.
A paradox, by any reasonable definition, means “defies expectation or common sense”. A contradiction in words we use simply means we have to adjust our vocabular to describe reality, that is the premises from which we derive conclusion or examine the deductions more closely. That is the inherent feature of science: You use a given vocabulary to describe a subject until you find it unfit to describe reality and then adjust your vocabulary. But be sure to know what you are talking about and what you are criticizing.
Quite interesting thing with the needle, I have to try that one time at home. On paper as in fact.
re: paradox, every dictionary i looked at just now listed one of the top definitions as “contradiction” or “apparent contradiction”. seems you are agreeing with me anyway. my comments were directed at those who would claim nature is fundamentally contradictory (often these are non-physicists misappropriating concepts like the uncertainty principle and particle/wave “duality”).
The dictionaries I consult all entail as possibly meaning the apparent contradiction. In case of actual contradiction there is no reason to call it paradox since it is an actual contradiction and shows that the deduction or the premises are wrong. I agree that nature can not be contradictory, how would that be possible? The premise of science is to explore the laws of nature, if there is no apparent law, then we are wrong. If nature seems to contradict herself, then it is our misunderstanding of her that leads to such a conclusion.
Your writing is not really clear to me, so I might have misunderstood you. I hope you have less problems understanding my point.
no i agree with everything you said just now. but you are aware that many people believe, due to QM and/or its popular interpretations, that there actually can be contradictions “in nature”?
I know that many people quantum mechanics to be complicated, contradictory. Only one statement of that is true, if any. I know that those popular books present a massively simplified version of quantum theory and are thus wrong. I seek truth and hope that people will follow, in physics as in political theory and practice.
Thanks for that. I started reading it and, while interesting, Yudkowski already lost me when he started talking about “configurations” and “amplitudes”. Also, having read some of his stuff before (on his belief in the Singularity), his dogmatism about things puts me off. He commits a fundamental error of science when he claims that QM is fact. Strictly speaking, the only facts in science are observations.
It’s this apparently fundamental issue with quantum physics which leads me to suspect that (certain) experimental results have been somehow misinterpreted. I agree with Einstein that “God does not play dice with the universe”.
Is that the case even when single electrons or photons are (allegedly) emmitted one at a time?
Either way, the descriptions of the double-slit experiment that I’ve read don’t explain this. They make it sound like the electrons or photons are fired through both slits alternately or at the small space in between them. I think this only adds to the confusion when they then talk about the results.
Does measuring the impulse of the emmitted electron have an effect on it? I suspect so, as one of the things that does seem very certain in quantum physics is the Heisenberg Uncertainty Principle. On such a small scale, it seems (nearly) impossible to measure a property of a particle without somehow affecting either that property itself or another (perhaps related) property.
Assuming that the electron hitting the screen is the emmitted electron may satisfy Occam’s Razor, but only because we can’t (yet) find out more information. That doesn’t make it true.
Our intuitive understanding of objects is that they are unique with respect to position/extension in space and position in time. Depending on how you look at it, that can be as few as two properties and as many as seven. Even in the latter case, there aren’t that many.
That intuitive understanding seems to break down, however, on the subatomic or “quantum” scale. I think the reason for that, however, is that the experimental systems aren’t themselves considered entirely at that scale. Even in a simple experimental setup, there are so many subatomic particles that the level of information contained (so to speak) is staggering to calculate. Furthermore, there’s the fact that, in trying to account for all of it, through measurement/observation, it’s necessarily affected (the Heisenberg Uncertainty Principle). Maybe that’s why quantum physics contains so much pure math.
Gibb’s Paradox is very interesting. Based on your explanation of it, I suspect that the Second Law of Thermodynamics isn’t quite what we think it is. Although an ideal gas is just that, its particles would still be distinct from one another in space and time. So treating them all as identical would technically be inaccurate.
“assuming hidden variables proves to be an incorrect description of reality, it can be ruled out experimentally by showing that Bell’s inequality holds true.”
Not if the hidden variables are properties shared by pairs or multiples of particles.
It is impossible to show that there is randomness in nature, and not just ignorance in your own head.
Eh? Using an instrument to observe the photons travelling through two slits doesn’t do that. It doesn’t do that at all. This video is fine until it gets to that point. After that, it is suggesting magic. Whoever made this video has never performed this experiment. Those results were obtained by closing off one of the two slits, and then repeating the experiment by reopening one and closing the other. The interference pattern can be slightly disrupted by placing atoms near the opening of each slit in order to measure them, but observing does not change the interference pattern. If it does, then it is the fault of the instrumentation being used to observe, not the act of observing. Observation only yields uncertainties when trying to observe electrons as waves and particles at the same time. There’s a whole Principle for it. And all it says is that the more precisely the position of an electron is measured, the harder it is to measure it as a wave. To expound on that, imagine a bullet traveling through the air. You want a precise measurement of its position. You freeze it like some cheesy stop-motion puppet and measure the position. However, with the bullet suspended in time, you can determine no speed or direction that will tell you about its behavior as a mobile object.
I for one strictly seperate interpretation of equations and model for date. My primary concern is to accurately predict what you will measure. Interpreting the results is secondary.
Yes, even when just one electron is released that is the case. In terms of wave model you emit a pulse of electron wave, in terms of particle model you emit a single electron but you pass on knowing where it exactly is. The source is calibrated so that it fills an area in which both slits are included but you can not know which slit is targeted in the particle model. Compare this to my mention of information as fundamental property.
Measuring the impulse of the electron forbids you to know its position certainly on the same axis by a certain amount. Some interpret this as you destroying the other property, some interpret this as you knowing some information but forgetting about the rest. Either way it is a fundamental property. Anyway, if you are allegedly emitting one electron you know, to a certain degree, what energy it has and thus the absolute value of its impulse, but not where it is going. If you knew it, you knew which road it would take and thus get the pattern of classic particles reaching the screen.
In current models of particles there are so few properties of a particle that it is actually possible to say in this model that two particles are induistingishable. Discussing whether the electron that reaches the screen is the same that is emitted or not is, pardon me, idiotic. Assuming this is the simplest hypothesis, explains the data perfectly and fits all the data in all other experiments. For further proof, see below what I write to Gibb’s paradox.
Again, the above may not be true, equations are, for me, only there to describe data. Their interpretation is secondary. Whether or not this is “true” in any sense is irrelevant. Something is for me true if it explains the data. For example, saying that earth’s gravity potential on the surface is g=9,81m/s^2 is not more or less wrong or right than Newton’s equations or even Einstein’s equations on the surface of the earth.
In popular discussions of quantum physics one has to keep in mind that the authors not necessarily distuingish between empirical results, old models of quantum physics and new models of quantum physics. Again as anology the laws of gravitation: Newton was not wrong, he was right in the above mentioned sense for systems with relatively low low mass. For systems with high mass Einstein’s equations are correct. For systems with low mass, Einstein’s equations yield Newton’s equations. But in our modern understanding, the alleged “meaning” of Einstein’s equation is more correct than that of Newton’s equation.* It is similar in quantum mechanics where old models of quantum mechanics like Bohr’s model of hydrogen are accurate in describing certain aspects of quantum mechanics but fail completely in other respects. Newer models have to explain everything older models explained too but introduce new concepts which shed new light on old phenomena.
Now, you talk about our intuitive understanding but it is not that simple. For example you can take two objects and squeeze them really hard. What is it that resists against fusing the two objects? In quantum mechanics the answer is that fermions resist because they can not exist at the same point in space** while also being identical in all other respects. “In all other respects” really means just a few known properties and there no single experiment that shows fermions at the point in space while being identical in all this known properties. Fermions are particles with half-integer spin, the signature of it being one of the before mentioned properties, like electrons. Particles with integer spin are bosons and are not excluded from the same spot in space, like atoms. The latter is the reason you can create Bose-Einstein-condensates.
The above should only demonstrate that there really is a reason to assume that we know alle fundamental properties in which particles are distuingishable. If should also proof that in quantum physics some properties of the macroscopic world are a bit more natural than previously known.
Your argumentation regarding Gibb’s paradox is correct in the logical sense. Either the second law of thermodynamics is wrong, falsely interpreted, or particles are in fact indistuingishable. The latter is more probable, so in my understanding of “truth” more true. If you describe a system of particles with their wave functions and switch two of those particles, fermions and bosons do not change their respective absolute values but the former change the sign of their wave function.*** So changing two particles does not change the behavior of the system as a whole, therefore the two particles are not distuingishable.
Now to understand the second law of thermodynamics, I will give it straight in one formulation. “Entropy in a closed system stays constant or increases.” Entropy, loosely speaking, is a measure of how many microscopic states yield the same macroscopic state. Macroscopic means total energy, sum of impulses microscopic means impulses and locations of particle. If you calculate this for an ideal gas, that is a fluid where there is no interaction beetween particles other that direct crashes and the particles have nearly no expansion, and look at the above mentioned situation you get Gibb’s paradox. You should not be able to reduce entropy in the closed system by just putting in a barrier. The thing is, in consctructing the formula to calculate entropy in an ideal gas you assume you can distuingish the particles, switching two particles gives you a new microscopic to the same macroscopic state. But as I mentioned above, you can resolve the paradox by assuming you can not distuingish the particles. Quantum physics gives further proof, switching two particles yields no new microscopic state, at least in the case of bosons.
Another thing from thermodynamics is that every degree of freedom carries some energy. If particles had some degree of freedom we di not know about we should expect to get wrong values for their energy. The simples case is the classic ideal gas which energy is E=3/2k_bT, where k_b is Boltzmann’s constant and T temperature. This comes from knowing that the particles of an ideal gas have three degrees of freedom, moving in every three spacial direction.
One last thing, that should have been the first. Speaking of particles is not really meaningful in quantum physics. This is not because there are no particles****, the fotoelectric effect at my level of understanding can only be explained if you assume photons to be particles, but because most people assume that particle means that electrons and co are really tiny billiard balls. They are not. Their behavior can only be explained in some freakish mixture of wave and particle behavior that comes from the probabilistic description of quantum physics.
Newton for example assumed the effect of gravity to be instant. In Einstein’s equation the effect of gravity travels with speed of light. Equivalence of gravitational and inertial mass is not explained in Newton’s model.
** Point in space in this case means a cell in phase space. For all purposes of this discussion read “point in space” as really small space between two particles.
*** This was first found experimentally in electrons orbiting atoms and was dubbed Pauli principle. The more general statement is found below.
**** There is discussion about no-particle physics where every phenomenom is explained without using the idea of particles but I am not yet at that level of understanding to research that.
Baxter,
I have to read up on that.
So? The equations describe the data splendidly.
Valject,
I have to read up on the claims in your post.
P.S.: I know that my reasoning here and there is a bit sloppy. I work on it. If you have questions, ask.
To be honest, I’m not sure how this addresses my suspicion. However, I’d like to point out that dealing in probabilities necessarily means not dealing in accurate predictions.
How can one not know which slit is targeted? Either the electron is launched toward a slit or it isn’t. That doesn’t mean it will (not) go through the slit, as there are many other variables at work, but I don’t see how the person who set up the apparatus cannot know where it’s aiming.
I fail to see how either of those interpretations makes any logical sense. Just because the information can be known doesn’t mean it will be known.
We’re using different meanings for “indistinguishable” (and “equivalent”) then. You seem to be using it in the sense of “interchangeable”. Hence considerations of spatial and temporal positions are irrelevant to you. But not to me.
Epicycles were also sufficient to describe data… for a while.
I hope you see my point. As far as I’m concerned, science is a tool for understanding how things really are (i.e. truth). It’s not simply about finding some mechanism to fit the data. This is why I consider ideas such as “cosmic inflation”, “dark matter”, “dark energy”, “string theory”, etc. to be the modern equivalent of epicycles. Of course, I can’t disprove them, but then again I can’t disprove that there could be a microscopic teapot orbiting the Sun between Earth and Mars.
If Eliezer Yudkowsky’s explanation of quantum mechanics is any indication, the newer models seem even more baffling than the old. But maybe that’s just me.
I don’t see how your exposition on fermions and bosons shows how “it’s not that simple”. Can you please explain?
The questioning mind would look at fermions and wonder why they can’t exist at the same point in space. “That’s just the way they are” seems like a highly unsatisfying answer.
Also, I was under the impression that objects do not always readily fuse together due to electromagnetic repulsion. Of course, one can ask where the electromagnetic repulsion comes from, and I think that’s an interesting question.
I didn’t think anything was ever proven in science – only in logic.
Again, it depends on what you mean by “particles are in fact indistinguishable”, doesn’t it? What makes you believe that to be more probable? Based on my meaning for “indistinguishable”, as outlined above, I’d consider it far less probable – in fact, I’d consider it logically impossible.
Particles can be (mathematically) interchangeable, sure. But if, at a given point in time, you have one particle at one point in space and another particle at another point, you can’t logically say that there’s no difference between them whatsoever.
What are your definitions for “microscopic state” and “macroscopic state”?
Why does the paradox have to be resolved that way? Why can’t one simply say that the second law of thermodynamics is imprecise or not all it appears to be? I don’t understand the inherent difficulty here – it seems like sheer unwillingness to me.
What do you mean by “degree of freedom” and “carry energy”?
So we’re back to square one: whether God plays dice with the universe. I still agree with Einstain that God does not. Believing the converse seems to mean abandoning the foundational principles of science.
Now it could be that what are traditionally called “particles” are themselves emergent phenomena, arising out of yet smaller and more basic phenomena. Is anyone investigating what the latter could be?
I appreciate your questioning, this furthers my understanding.
You suspect “wrong” interpretations of quantum physics leading to wrong interpretations of experiments. I want to show that it is possible to get to the “accurate” equations without interpreting quantum mechanics. Whether or not I accept the copenhagen or the many-worlds-interpretation does not play any role in the equations, they are the same in both cases.
Look at a garden hose. The water is distributed over a certain area. If you follow one more or less random water molecule you do not know where this molecule will go. I you do not like that picture, look at a gun. Firing several times will show that the bullets are distributed over an area, though they come from the same source. If you think that is far-fetched look at a lamp. In all cases the source is properly adjusted but you can not know where exactly the individual pieces will land.
We already know empirically that the uncertainty of knowing the impulse del p and the unceirtanty of knowing the location del q are in relation with Planck’s constant as del p * del q >= h/(4pi). This is the equation, now we get so the interpretations.
Intepretation one: You measure the location of the particle with a photon. By emitting a photon on the particle, you change it’s impulse and vice versa. This is destroying the other value. Now the difference to classical physics is that it is not possible to do the other measurement better than the first. The product of both uncertainties has to obey the above relation.
Interpretation two: It is restricted how much you may know about the particle. But I have to read up more on this, interesting in this context is the quantum eraser.
There is a difference between “indistingishable” and “the same”. Clearly two objects at different points in space at the same time are different objects, anything else would be silly. But they are indistuingishable in that they can be exchanged without me, or anyone for that matter, noticing.
Epicycles are correct if you look at the solar system from the earth’s point of view.* It is wrong though to say that earth is attracting all other bodies, but this is resembled in the beautiful equations of gravity.
I see your point. I completely understand it. But I want you to understand that I see it as impossible to find “truth” in science, or anywhere else for that matter. True is what fits the data, full stop. I too am not very fond of dark matter and the like but there are different hypotheses or models to explain the data. It is only that dark matter is favored by government grants and is more popular because it is more mysterious than say modified newtonian dynamics.
But I think whether or not science finds truth or not is worth a seperate thread.
Quantum physics is not easy. Simpler models have been proposed but they all fail in describing the data. I always speak from a logical point of view. So when I say that a new hypothesis is more simple than the old, I mean it in the logical sense. The new hypothesis can of course be more unintuitive.
By now you may have guessed, I want to be a theoretical physicist.
My exposition shows that what is intuitive in classic physics may be more intuitive in the logical sense in quantum mechanics.
“Just the way they are” would be the same answer for macroscopic objects, would it? At some point you just get to “that is the way it is”, Münchhausen’s trilemma.
Electric repulsion is one of the possibilities. But the statement with fermions is more general.
I wanted to proof the assertion “With our current models, phenomena are sometimes better understood in quantum physics than in classic physics”.
My whole post is dedicated to the fact why it is very meaningful to look at particles as indistuingishable. See above. If particles were completely identical there would be no sense in talking about number of particles.
Microscopic state: A set of impulses of particles, their spin, vibrations, etc. Macroscopic state: Total energy of the system, etc.
There is no inherent difficulty in changing the second law of thermodynamics, it simply is meaningless to do so. In any other case the second law yields correct results. The proposed fix can be perfectly justified in quantum physics. Similarily, I can not see why you should change the law, it seems just to be unwillingness to accept that particles are in fact indistuingishable.
Degree of freedom means just the set of parameters that can be changed without affecting the other parameters in the set. For example the three spatial dimensions give three degrees of freedom to move. Impuls in every three directions means energy and thus there is energy in every degree of freedom.
We will always get back to square one. What are theese foundational principles of science that are violated?
Look at my footnotes, shown as stars.
As a side note, if you look at an elliptical orbit and do a Fourier approximation, you get the exact epicycles that were proposed centuries ago. Fourier approximation here simply means adding up circles of the right size iafter a rule that makes certain that the result is the original ellipse.
