Brain Teasers
Fraudulent Inventor
Professor Lipshultz was showing off his new inventions to a prospective investor. He told the investor that he had developed machines which would allow scientists to study the motion of gas molecules. His explanation of the machines was as follows:
"The first unit will take in any gas and completely dry it, removing all traces of liquid. Right now it is removing water vapor from air...and now you can see the "DRY" light has come on.
The second unit removes all but one molecule from the chamber. There you see the "READY" light, indicating that only a single molecule remains.
The third unit will analyze the contents of the chamber, determining exactly what chemicals are in the chamber, and in what quantity. And as you can see on the screen, the unit indicates 'Air: 1 molecule'.
The final machine will trace the exact path that the molecule takes as it bounces around the chamber. The path is represented by the lines on this computer screen."
"I'm sorry," said the investor, "but you're obviously lying to me. I can accept the fact that three of the four machines COULD work as you say, but one of them is obviously a fake."
Which machine was the fake?
"The first unit will take in any gas and completely dry it, removing all traces of liquid. Right now it is removing water vapor from air...and now you can see the "DRY" light has come on.
The second unit removes all but one molecule from the chamber. There you see the "READY" light, indicating that only a single molecule remains.
The third unit will analyze the contents of the chamber, determining exactly what chemicals are in the chamber, and in what quantity. And as you can see on the screen, the unit indicates 'Air: 1 molecule'.
The final machine will trace the exact path that the molecule takes as it bounces around the chamber. The path is represented by the lines on this computer screen."
"I'm sorry," said the investor, "but you're obviously lying to me. I can accept the fact that three of the four machines COULD work as you say, but one of them is obviously a fake."
Which machine was the fake?
Hint
What exactly is in the chamber at each step?Answer
The third unit, which analyzed the contents of the chamber, is definitely a fake. "Air" is a name that we give to the combination of gasses that make up our atmosphere. It is made up of oxygen, nitrogen, carbon dioxide, and trace amounts of several other chemicals. Because of this, there is no such thing as one molecule of air. Assuming that there is only one molecule in the chamber, it would either be oxygen, nitrogen, or one of the other chemicals. A piece of analysis equipment would never call it "air".Hide Hint Show Hint Hide Answer Show Answer
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Comments
Wow... I actually got one of your science teasers... I astound myself! ;P Nicely put together Bob.
Perhaps also the first one was a fake as it took in gases and removed all traces of "liquid". Water vapour is a gas! A nice idea for the teaser!
While vapors are commonly thought of as gasses, there are actually distinct differences between the two. Water vapor can be considered to be a liquid dissolved in air.
very nicely worded you write some of the best teasers. Well done
Great teaser.
water vapor cannot be considered a liquid dissolved in air otherwise so could most gas.
The last machine is also an impossibility. The very act of measuring the speed and position of a molecule requires some form of interaction with it to actually detect how it is moving. This usually has little impact on a larger scale, but when you're talking about something as small as a single molecule, even the "impact" of a photon of light will add energy to it, and thus change the velocity from that point onwards. Because of this, it is only really possible to measure the position OR the speed of particles at a particular moment in time. Not both. Anything after the initial reading can only be a prediction until another measurement can be made, at which time the velocity of the particle will again be altered.
water vapor is a liquid is not any better than one molecule of air
Hoder, while I agree with your whole photon interaction analysis, I don't think it's enough to call the last machine an impossibility. I'm sure that in the future someone will develop a way to follow a molecule without altering its course (or at least only altering it a negligible amount). Just because we don't know how to do it now doesn't make it an impossibility. However, since there is absolutely no such thing as "one molecule of air" (by definition), then that is a true impossibility. That's this cowboy's opinion, anyway.
My photon interaction explanation was only an example. There is no way to measure anything without an interaction of some kind (think about it). While in most cases this has little to no (visible) effect on the measurement or what is being measured, this can not be held true on a molecular scale.
I don't think there is such a thing as "a negligible amount" when you're talking about something like this. Even the smallest of small changes would be enough to alter the results significantly.
Sorry if I'm coming across too critical, I don't mean to be picky. It's still a good teaser.
I don't think there is such a thing as "a negligible amount" when you're talking about something like this. Even the smallest of small changes would be enough to alter the results significantly.
Sorry if I'm coming across too critical, I don't mean to be picky. It's still a good teaser.
I've been around Braingle for a long time, there, hoder. Even if you were being overly critical, it wouldn't be the first time someone tried to pick apart one of my teasers. Don't worry about it. I do, however, defend my teasers to the death, so I'll add one more thing and then let it go: When you're watching a drag race and they tell you that the winner's official speed was 256.273 miles per hour, no one is concerned about the fact that the radio(?) waves used to measure the car's speed slowed it down just a tad when they crashed into it, because the "tad" amounts to what, a billionth of a mile per hour or so? My point is that someone COULD discover a particle of some kind that contains 1 one billionth of the energy or mass of a photon, and then they COULD develop a machine to use this particle to track a single oxygen molecule bouncing around a container. It's POSSIBLE. Maybe highly unlikely, but possible.
Comments sure do loose their value, when previous ones are removed, I m assuming from being offensive.
Jul 30, 2005
FYI: A particle known as a Higgs particle, as predicted by supersymmetric string theory, is one that could possibly be used to track the motion of a single atom.
Jul 30, 2005
FYI: A particle known as a Higgs particle, as predicted by supersymmetric string theory, is one that could possibly be used to track the motion of a single atom.
Nice, easy teaser. Why complicate it with photon interaction analysis? It's a pretend, make-believe machine.
Bobbrt, there's no need to wait for a new particle to be discovered. A photon can be generated with a billionth the momentum of an air molecule.
That would, indeed, allow you to get around the Observor Effect (as explained by hoder). However, it wouldn't give exact measurements.
The Observor Effect is often confused with the Uncertainty Principle. The latter is derived from the most basic laws of quantum physics (e.g., the wave-particle duality of everything). It is an unbeatable sort of catch-22. A higher-energy photon will give you a nice clean "bounce" off the air molecule, and thus an accurate position, but it will alter the molecule's momentum. A lower-energy photon will give you a better measure of momentum, but it will behave more like a wave, propogating through the molecule, and thus telling you little or nothing about the molecule's position.
I'm sure you're familiar with this in the classic question "why is the sky blue?" Blue light has a shorter wavelength, and acts more particle-ish, bouncing off the air molecules in the atmosphere Red light has a longer wavelength (less energy & momentum) and is more likely to pass through the air. Also, the photon itself has to be measured by some device, compounding the error.
Unless Lipshultz is looking at a noble gas, he's almost certainly isolated a diatomic molecule. These experience "dumbbell" collisions with the container wall, which radically alter their momentum. And whereas the momentum and position errors may be acceptable for some purposes (I calculated a minimum "balanced error" for diatomic nitrogen as +/- .0476 mm position and +/- .0476 mm/s velocity), the measurement error on angular momentum and angular position will always be such that the result of collisions cannot be predicted meaningfully.
The third machine is also somewhat questionable because of the lines on the computer screen. Air molecules at room temperature travel several hundred meters per second. That's a lot of criss-crossing lines, assuming the container is something that fits on the top of an ordinary table. A good monitor might be able to display that, it there's no way the human eye could follow it.
At any rate, it's your riddle, and the second machine is a fraud, too. So I guessed #2 & #3, gave myself full credit, and fun writing this. I can't really complain.
Cheers.
That would, indeed, allow you to get around the Observor Effect (as explained by hoder). However, it wouldn't give exact measurements.
The Observor Effect is often confused with the Uncertainty Principle. The latter is derived from the most basic laws of quantum physics (e.g., the wave-particle duality of everything). It is an unbeatable sort of catch-22. A higher-energy photon will give you a nice clean "bounce" off the air molecule, and thus an accurate position, but it will alter the molecule's momentum. A lower-energy photon will give you a better measure of momentum, but it will behave more like a wave, propogating through the molecule, and thus telling you little or nothing about the molecule's position.
I'm sure you're familiar with this in the classic question "why is the sky blue?" Blue light has a shorter wavelength, and acts more particle-ish, bouncing off the air molecules in the atmosphere Red light has a longer wavelength (less energy & momentum) and is more likely to pass through the air. Also, the photon itself has to be measured by some device, compounding the error.
Unless Lipshultz is looking at a noble gas, he's almost certainly isolated a diatomic molecule. These experience "dumbbell" collisions with the container wall, which radically alter their momentum. And whereas the momentum and position errors may be acceptable for some purposes (I calculated a minimum "balanced error" for diatomic nitrogen as +/- .0476 mm position and +/- .0476 mm/s velocity), the measurement error on angular momentum and angular position will always be such that the result of collisions cannot be predicted meaningfully.
The third machine is also somewhat questionable because of the lines on the computer screen. Air molecules at room temperature travel several hundred meters per second. That's a lot of criss-crossing lines, assuming the container is something that fits on the top of an ordinary table. A good monitor might be able to display that, it there's no way the human eye could follow it.
At any rate, it's your riddle, and the second machine is a fraud, too. So I guessed #2 & #3, gave myself full credit, and fun writing this. I can't really complain.
Cheers.
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