Hi,
I was wondering if this could be explained as clear possible…
I’ve read that particles that are observed in some kind of experiment behave differently to ones that aren’t observed. Somehow they came to the conclusion that unobserved particles are in an indeterminate state (e.g. spinning clockwise and anti-clockwise simultaneously) and when they are observed, they end up in a random definite state.
I think there is also a thought experiment that involves two electrons that are brought together which causes one to have the opposite spin to the other (or something). Then they are separated far apart and one is observed. It previously was in an indeterminate state and then it goes to a random definite state. The other one instantly goes to the opposite state.
So were those particles really in some kind of mysterious inbetween state? Or were they in a definite state all along, but the observer was currently ignorant of their state?
I think I read somewhere that this inbetween state which is dependent on an “observer” is just one way of explaining the experiments…
Also, if an observer is really required, what is the cut-off limit for an observer? Is a 3 year old an observer? What about a one month old? What about an extremely premature baby? What about a foetus that has started to form a basic nervous system? What about a chimp? What about a lizard? Or an ant? Or a tree? Or a rock?
The idea that particles “are” in some state and we just don’t know it has to do with something called hidden Variable Theories, and there are some experimental results which indicate to many that HVTs can’t be correct.
Some interpretations state that there is no sense in which particles are or are not in any particular state, but rather that they yield specific information with respect to the instrument they are observed with. The state is a function of the instrument.
An observer is pretty much anything (3 year old child, natural event, etc) capable of magnifying quantum information to the level of the macro world.
the observer doesn’t have to be sentient; it could be a (suitably equipped) recording device such as a camera (unless you want to entertain the absurd notion that there isn’t actually an image on the developed film, but a superposition of two different images of which one becomes visible when you look at it.
This gave rise to Schröedinger’s and Dirac’s theory of quantum mechanics which implies that particles cannot have have **separate and well-defined **positions and velocities, but rather a “quantum state,” which is a combination of the two.
You can think of an observation as being sufficient interaction with the environment such that a particular quantum state becomes irreversible, at which point the quantum state ceases to be indefinite.
Take the famous double slit experiment. Turn on a light and shine it through two slits and you get an interference pattern of light and dark stips on a surface behind the slits. Why this happens is easy to explain. Light passing through one slit has the crests and troughs of the light wave interfere with the waves and troughs passing through the other slit. Where wave meets wave they add up and create a bright line. Where a wave and trough meet they cancel each other out so you get a dark line.
Now, do this experiment where you release only one photon every minute. One would suspect the photon must pass through only one slit. You may not be able to predict which one but it shouldn’t matter. After letting your experiment run awhile you would expect your particle detector behind the slits to display two lines (one for each slit). Oddly, this doesn’t happen. Your particle detector will show identical light and dark lines as if the light source had been on full-blast. The only explanation for this (that I’m aware of) is that the photon passed through BOTH slits and interfered with itself. Completely counter-intuitive I’ll admit but other explanations I’ve heard are just as hard to believe (e.g. that a photon in a mirror universe to our own interferes with our photon).
Still not convinced? How about Quantum Computers? While they don’t exist yet (although I think someone got one to add two numbers but I’m not sure) scientists are working on building a Quantum Computer that exploits this “I’m everywhere at once (within some limits)” idea.
The people most excited about a working quantum computer are probably the NSA. Encryption schemes are getting increasingly hard to break even with exceedingly powerful computers. There are simply so many possiblities for a computer to run through that even speedy supercomputers take a long time to hack through them all. Realize that a computer doe sjust one thing at a time in succession. So, if you need to crank through 1 billion combinations you start at 1 and run through them all (this is loosely speaking…there are other things going on that can help speed this up a bit but essentially this is what happens).
Now take a quantum computer based on what I described in the double slit experiment. Instead of following one calculation to completion and starting on the next imagine doing ALL calculations simultaneously! Since the quantum computer doesn’t follow a predefined path to an answer it essentially follows ALL paths to the answer in one go. The NSA is drooling at the prospect of getting their hands on one of these (but it will be awhile yet as they are very hard to build if indeed they are possible at all).
You’re not kidding. According to the site on quantum computing I linked above a quantum computer could be capable of factoring numbers as large as 10[sup]200[/sup] in seconds! For comparison I think there are something like 10[sup]80[/sup] particles estimated to exist in the entire universe. There is no way in hell our government will let that into the hands of ordinary people. I suppose it would trickle down eventually but I wouldn’t hold your breath.
[sub] Eyes glassing over at the thought of a Quantum Quake Server [/sub]
actually simple quantum computers based on NMR spins have been made. See the latest New Scientist for more details.
Heisenberg’s uncertainty principle as quoted in Hawkings book is not the underlying reason for quantum uncertainty, as it doesn’t worry about whether the particle was in a predetermined state before measuring, the measuring disturbs the system either way.
I don’t think their electron applet works properly though… the electrons seem to make any pattern even when I make the speed go to the maximum (I have a Duron 800 so my computer should be able to handle it) The electrons always go around the center.
I followed the links from there to here: G.P. Thompson
Particles ARE Waves!
It talks about an electron beam rather than individual electrons. So it could be possible the electrons are just interacting with each other.
In the applet’s website it said that Dr. Feynman used the analogy of a machine-gun - that if electrons were particles then they might just collide into one another.
But electrons have the same charge and would repel each other… did any scientists think of that? Maybe their charge caused them to repel each other rather than they existing as waves in some instances. The interference pattern could be a pattern that emerges because of the pattern of collisions. The pattern is spread out because the electrons wouldn’t be firing out exactly in line. Now that I think about it, I thought the distribution would look more like a bell curve - there shouldn’t be any dark patches. I don’t get how there are lots of strips that seem to be in total darkness.
Anyway, just about particles with an indetermine state - i.e. they’re a “wave function” that hasn’t collapsed yet. (or something)… how do they get into that state? I mean say an electron was in an indeterminate state and then it was measured and it randomly had a clockwise spin. How can you get it back to an indeterminate state again? Maybe applying radiation to it? Or do they randomly go into an indeterminate state every now and then? I just want to understand how measurement and indeterminant states of particles relate to each other.
The particles are essentially always in an indeterminate state. When you measure one you are just taking a snapshot, so to speak, of the particle at that moment.
Quantum Mechanics is about probability. If I emit a particle I can start drawing out where that particle may be over time. The greater the time period the less certainty I have of finding it in any given place or velocity. When this is charted out it looks like a cone. There are upper and lower limits to where the particle can be. You can’t have a speed of zero and you can’t have a speed faster than light speed. As time moves forward the cone widens allowing my particle to be somewhere inside of that cone (outside of the cone would indicate a speed faster than light which isn’t possible).
Now say you measure the particle. The “wave function collapse” means we know that the particle is no longer in any given spot but at that spot with a given velocity. Prior to that all we could do was assign a probability that the particle might be in any given place if we measure it. Prior to that the particle is essentially in all places allowed by the probability cone (called a World Cone IIRC). How precisely we can know the particle’s location and speed are limited by the Heisenberg Uncertainty Principle so no matter what we can’t be 100% certain where and how fast the particle is moving no matter how hard we look. Immediately following your measurement the particle starts a new probability cone from the place where we pegged the particle.
In short you need to distinguish between what is actually happening between the times we look and what is happening when we look. Science, in a way, is a search for predictability. The more you know about a thing the better you can predict what will happen in the future. Quantum Mechanics almost becomes a statistical analysis of possible outcomes because its very nature is unpredictable.
If this seems crazy I’m not surprised but experiments have backed this up again and again. For instance, some scientists tried to fool Heisenberg’s Uncertainty Principle. They took a particle and cooled it to very very close to absolute zero where all atomic motion ceases (actually reaching absolute zero is not possible). In this fashion one might guess that you will now be able to know the particle’s location (under the microscope so to speak) and its speed (zero or very nearly) with a precision not allowed by Heisenberg’s principle. Unfortunately the Universe was hip to this trick and formed something called a Bose-Einstein Condensate. When the researchers looked down at the particle what they saw was a smeared out particle FAR bigger than its original size (although the particle didn’t really grow). To know more precisely one thing about a particle (between speed and location) is to know less about the other aspect. Since the researchers knew the speed with a high degree of precision (very nearly zero) they couldn’t know the location very well and the smeared out particle just happened to be fuzzy enough to maintain the uncertainty called for in Heisenberg’s principle.
If any of the stuff above bothers you on some fundamental level don’t feel bad. Quantum Mechanics does that to most people who look too closely at it.
I tread gingerly in the Quantum Mechanics fields but doesn’t the “Pilot Wave” hypothesis remove the need for the observer function? Traveling backwards in time seems a trivial assumption compared to the ultimate observer super Deity outside the Universe collapsing its Wave Function.
Sorry for the hijack, but I’m trying to figure out why this would be a problem. I don’t know enough about encryption I guess, but if 200-digit numbers can be factored easily, why not just use 1000-digit numbers? Or 10000-digit numbers?
I’m no crytography expert either but I have an teeny-tiny sense of what is going on with it.
I don’t think it is a matter of just picking larger numbers to encrypt your files with. At least, there are issues with using bigger numbers. While cracking an encoded file is significantly harder than encoding it in the first place it still takes work for a computer to encrypt a file (or decrypt if it knows the key). Just using today’s most heavy duty publically available encryption schemes at their highest settings will cause a fast PC to churn for a few minutes. While that may not be so bad in the interests of security your problems increase the bigger you go.
DES, a commonly used encryption scheme, allows for something on the order of 10[sup]17[/sup] possible keys. Moving that to 10[sup]200[/sup] would be insanely difficult for today’s PCs to just encrypt if it is even possible for a standard PC to manipulate a number that big (no scientific notation here…all digits must be accounted for).
Also realize that they said a number with 10[sup]200[/sup] combinations would takes seconds for a quantum computer to crunch. Presumably 10[sup]500[/sup] or 10[sup]1000[/sup] wouldn’t be too far out of reach. The nature of a quantum computer makes it a relatively trivial thing to keep climbing up that ladder (assuming a workable machine is ever developed).
Still, I will agree that where there’s a will there is a countermeasure. One might suspect that if cracking today’s encryption schemes becomes trivial than new encryption schemes are likely to be developed. Certainly some schemes such as one-time pads would remain unbreakable even by a quantum computer so all is not necessarily open to perusal by the feds (although a one-time pad is a cumbersome and difficult to implement method if you have a lot of communication or lengthy communications to deal with).
FYI, the a number with 10[sup]200[/sup] digits is not a number with 200 digits. It’s a number with 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 digits. A 1 followed by 200 zeros. A very, very large number.
For example, if I said a number had 10[sup]6[/sup] digits, that means the number would have a million digits (1,000,000), not 6. A 1024 bit encryption would be on the order of 10[sup]3[/sup].
To give an idea of what is required to crack something like this
To give further weight to what is happening here this web site mentions the EFF’s supercomputer and 100,000 other computers were churning through 245 billion keys per second! Mind you this was to crack a 56-bit key (it was also a few years ago and computer speeds have increased since then but so have key lengths). Thus, a quantum computer being able to hack something bigger than a 512-bit key in seconds is quite an achievement if it performs as advertised.
It may be worth noting that many ( VNUNET.COM ) now consider 1024-bit RSA encryption to be compromised. For a mere billion dollars or so you can put together a computer to hack 1024-bit keys. Better still, you can build it from publicly available equipment.
Depending on what you are hacking $1 billion may be cheap.
Ah, but there’s the rub. Is not the film ultimately composed of quantum particles? And what about your eyes and your optic nerve?
What’s the only thing that isn’t composed of quantum particles? The conscious mind?
Until a measurement’s made it’s all just one big superposed wave function . And the measurement must be made by something that isn’t subject to being superposed.
There’s an interestig article in this month’s Discover magazine on this very issue: Does the Universe Exist If We’re Not Looking? Some argue that because quantum states only become determinate through observation, it is the fact of observation by conscious beings that makes the Universe exist. (My summary - please don’t hurt me… :eek: )
Also, one of the mind experiments it mentions really emphasises the weirdness of quantum stuff: if you run the two-slit experiment on a cosmic scale, using the gravitational effect of galaxies on photons, then the path that the photon takes will change depending on the way that it is observed on Earth. But to do that, the observation in effect reaches back in time and changes the path the photon took a billion years ago. (Again, my summary :eek: )
