Print PDF
Favorite
Email
Disclaimer 1: The following represent preliminary results. I have yet to perform a proper statistical analysis. I myself am convinced that what I write here is purely speculative until I set up proper data collection and perform the requisite mathematics. Please refrain from telling anyone that anything presented here is "fact" until I can defend such a statement.
Disclaimer 2: This project is not safe for a wide variety of reasons. If you insist on attempting it, please observe adequate safety procedures. I am not qualified to recommend anything specific, so please perform extensive research. Your safety is your responsibility.
What I am describing here are my attempts to demonstrate the Copenhagen Interpretation of Quantum Mechanics. This does not prove other interpretations as incorrect, it only proves that the Copenhagen Interpretation is useful for explaining the behavior of this device. For lack of a better name, I name this device a "Copenhagen Interpreter". Rather ironically given it's name, if successful the device will produce nothing but provably inutterable nonsense.
The Copenhagen Interpretation was developed by Bohr and Heisenberg. Simply put (by wikipedia):
[It] rejects questions like "where was the particle before I measured its position" as meaningless. The measurement process randomly picks out exactly one of the many possibilities allowed for by the state's wave function.
What I will try and accomplish here is to build a "small" device that measures a system which may exist with some probability as a number of discrete states. Further, the state the system will exist in at time "N" cannot be predicted even given perfect perfect knowledge of the system, infinite computing power and infinite time. In other words, if the source can sustain maximum possible entropy, this device will be a nice demonstration of the Copenhagen Interpretation at work.
Being mortal, I don't have perfect knowledge of the system, infinite computing power or infinite time. What I do have is statistics, which is as close to any of these distasteful things as I care to get.
For fellow stats geeks, I'll be using P=0.01 throughout this experiment.
Disclaimer 2: This project is not safe for a wide variety of reasons. If you insist on attempting it, please observe adequate safety procedures. I am not qualified to recommend anything specific, so please perform extensive research. Your safety is your responsibility.
What I am describing here are my attempts to demonstrate the Copenhagen Interpretation of Quantum Mechanics. This does not prove other interpretations as incorrect, it only proves that the Copenhagen Interpretation is useful for explaining the behavior of this device. For lack of a better name, I name this device a "Copenhagen Interpreter". Rather ironically given it's name, if successful the device will produce nothing but provably inutterable nonsense.
The Copenhagen Interpretation was developed by Bohr and Heisenberg. Simply put (by wikipedia):
[It] rejects questions like "where was the particle before I measured its position" as meaningless. The measurement process randomly picks out exactly one of the many possibilities allowed for by the state's wave function.
What I will try and accomplish here is to build a "small" device that measures a system which may exist with some probability as a number of discrete states. Further, the state the system will exist in at time "N" cannot be predicted even given perfect perfect knowledge of the system, infinite computing power and infinite time. In other words, if the source can sustain maximum possible entropy, this device will be a nice demonstration of the Copenhagen Interpretation at work.
Being mortal, I don't have perfect knowledge of the system, infinite computing power or infinite time. What I do have is statistics, which is as close to any of these distasteful things as I care to get.
For fellow stats geeks, I'll be using P=0.01 throughout this experiment.
Remove these ads by
Signing UpStep 1Entropy Source
To begin we need a source of entropy. Not just any source... flipping coins, rolling dice, or observing the behavior of certain celebrities is not sufficiently random. Coin flips, dice rolls, and celebrity drug rehab are what we might call "large systems", which the Copenhagen Interpretation suggests are best described by classical physics.
The source of entropy for our purposes must be "small".
A source where quantum tunneling occurs seemed to me like a good place to start, as it only occurs on a small scale. As a consequence of the Heisenberg Uncertainty Principle, we cannot know for certain both where a particle is, and how fast it is moving (Note: this will be far from a complete treatment of the topic). As the measurement error decreases with respect to velocity, it increases with respect to position and vice versa. Therefore, if there exists a particle and a potential well, we cannot be certain the particle is within the well while being certain that it is traveling below the escape velocity for that well... it's all a matter of probability. (My reasoning may be incorrect here: please correct me if so)
Alpha decay is caused by quantum tunneling. If we have some macroscopic amount of an alpha-emitter, measuring alpha decay meets our criteria for a "small source", since it represents an individual atom decaying. Furthermore, knowledge about the particles within an atom useful in predicting alpha decay cannot be determined due to the nature of quantum tunneling vis. The Uncertainty Principle... So even given perfect knowledge of the system, and infinite time, you could never do better than pure chance when trying to determine the time of the next measured decay.
So, we will use a 0.9 microcurie sample of Americium-241. It's readily available, legal to own in my area, and not likely to kill me.
The source of entropy for our purposes must be "small".
A source where quantum tunneling occurs seemed to me like a good place to start, as it only occurs on a small scale. As a consequence of the Heisenberg Uncertainty Principle, we cannot know for certain both where a particle is, and how fast it is moving (Note: this will be far from a complete treatment of the topic). As the measurement error decreases with respect to velocity, it increases with respect to position and vice versa. Therefore, if there exists a particle and a potential well, we cannot be certain the particle is within the well while being certain that it is traveling below the escape velocity for that well... it's all a matter of probability. (My reasoning may be incorrect here: please correct me if so)
Alpha decay is caused by quantum tunneling. If we have some macroscopic amount of an alpha-emitter, measuring alpha decay meets our criteria for a "small source", since it represents an individual atom decaying. Furthermore, knowledge about the particles within an atom useful in predicting alpha decay cannot be determined due to the nature of quantum tunneling vis. The Uncertainty Principle... So even given perfect knowledge of the system, and infinite time, you could never do better than pure chance when trying to determine the time of the next measured decay.
So, we will use a 0.9 microcurie sample of Americium-241. It's readily available, legal to own in my area, and not likely to kill me.
| « Previous Step | Download PDFView All Steps | Next Step » |
I tested the output in Linux with the NIST test suite: http://csrc.nist.gov/groups/ST/toolkit/rng/index.html
The results were pretty good. Random data has a predictable failure rate for tests for non-randomness (as strange as that sounds). The observed failure rate was not significantly different than the expected rate.
Here's a non-quantum example: Assume coin flips are random. You have foolishly bet your friend that if a particular coin flip lands heads, you will give him 2$, and if it lands tails, you gain 1$ from him. As soon as the coin is tossed, you have on average lost fifty cents: (0.5)*(-2)+(0.5)*(1)=0.5, even though it is impossible for you to actually have lost this amount, because when the coin lands it is either tails or heads.
My assertion is that Schrodinger's cat is not *actually* both alive and dead, just as the bottle of cyanide is not actually both broken and unbroken. However, because we are dealing with probability theory, and both states of the cat are equally likely, (0.5)*(living)+(0.5)*(dead)=equally living and dead. Both of these are examples of how probabilistic models of reality do not ever correspond to the result of any given real incident.
A real life example: I study trees. I have measured the diameter of many trees, and discovered that the arithmetic mean value is some number, say 23 centimeters. This is meaningless on its own until I also tell you that the 95% confidence interval for that estimate is from say... 22.5 to 23.5 centimeters. We "know" that there is in fact a "real" mean value... but not only is it not necessary for any actual tree to have that diameter... but the real mean value is (sometimes equally) likely to be either greater or less than our estimated value.
Similarly, if we were (in rather poor taste I think) run Schrodinger's thought experiment in real life ten thousand times... we would have approximately 5000 live and 5000 dead cats. At no point in reality is any cat really alive and dead except on paper...
Probabilistic models do not describe what the status of any actual event will be while it is happening, only the average final outcome of the event if it is run many times. The Copenhagen Interpretation is interesting because it is a demonstration of a system in which the *only* models that predict behavior are probabilistic ones. Furthermore, it may suggest that the only models that predict anything are probabilistic, and that the "reliability" of classical physics is only a result of the many combined probabilistic events in macroscopic systems. As a side note, you then have Chaos Theory which asserts that extremely large, complex systems are also probabilistic... a beautiful and inconvenient symmetry, don't you think?
...And there you have my Copenhagen Interpretation Interpretation.
Some specially designed silicon diode detectors have been made with the active volume (the depleted region) very close to the surface of the detector and have an extremely thin window so that alpha particles can enter the active volume and deposit all their energy there. The charge collected is a measure of the energy of the alpha particle, and these detectors are common for alpha particle spectroscopy. One of the most common types of such detectors is called a surface barrier detector. The detectors are usually used with multichannel analyzers. Some silicon detectors have thicker active volumes and are used for beta particle energy analysis. - www.hps.org