Homemade Quantum Laser Micrometer (Nestor's Micrometer)

Okay I don’t want to scare any of you away. This experiment is actually really simple, but the concepts behind it are somewhat confusing at first (it is quantum physics after all). Basically we know that matter behaves “solid” like a single point if it’s a really big glob of it, but the smaller the glob gets the more it behaves like a “wave.” Normally when people think “wave” they think of ocean waves or sound waves. When the word “wave” is used here, it means simply that like ripples in a pond, if a wavelike particle were moving, where it would be at any given time after it started moving would be anywhere and everywhere along a “ripple” that radiates outward from the source where it began moving. The picture above shows what I mean. That’s one of the “spooky” quantum effects we will illustrate.

Since we know that matter (things) should only be in one place at once, not two, the instant that one of the ripples hits another object, thus “interacting” with the universe, the wavelike behavior of the blob of matter disappears and begins to act like it’s in one spot (“solid”) again. So in other words if the ripple bumps into something or we try to see the blob acting like it’s in many spots at the same time the blob says to itself “oh no! They’re catching on to me… I’m going to act like I’m in one spot again.”

Even though stuff acts like this, we can still catch it behaving like it’s in many spots at the same time and acting like a wave. The “double slit” experiment is how we do this. If we pass blobs of stuff through two slits and it creates a pattern of two bands of hits on the back of the wall we know that it’s acting like a solid particle. If it makes a pattern with many bands of hits on the back of the wall we know that it’s acting wavelike.
 

Okay now get a laser pointer, tape, super glue, two staples, a rubber band, some cardboard, a string, a piece of paper, a pencil, a measuring tape, and a hair. If you have more than one color laser pointer then do this experiment with both colors! Any color will work. As for the hair color, black works best. If you don’t have black hair it will still work, but when you find the width of the hair, it won’t be quite as accurate.

Okay. First thing is to use the staples and a little piece of cardboard to make something to hold the piece of hair up. You can make the hair vertical or horizontal, it doesn’t really matter, but the point is for the hair to be straight and above the ground. The hair behaves like two slits. Stuff can go to the area above the hair or below the hair, but not through the hair because the hair blocks it much like with two slits stuff can go in one slit or the other but is blocked by something in-between the two slits.

In this experiment the “stuff” we are shooting through the two slits is light. Now is light made up of waves or photon particles? Well the answer is both. Photons are extremely small so they can behave like a wave or a solid particle like we discussed before. Wrap the rubber band around the “on” button of the laser so it shines continuously and you don’t have to hold the button. Now tape your “slits” to the end of a table and shine the laser at the hair. You might be seeing the wave pattern on the wall already! If that’s all you wanted to see than you don’t have to do anything else.
Now we are going to use this pattern to find the width of that little hair, then after mysteriously erase information from the universe (in author's notes). Use a piece of cardboard to make a little stand for the laser so it shines at the hair and you don’t have to hold it there. Tape it down.

The farther your setup is from the wall, the more accurate your measurements will be so it might be wise to scoot the table back a bit. Get the string and tape it to the spot on the wall at the middle brightest part of the pattern and pull the string to where your laser is hitting the hair. Cut the string there and measure its length, then take the string off from the wall where you taped it.

Tape the piece of paper you have to the wall where the pattern is, then use your pencil to mark the middle of each of the bands. It might be wise to wear some shades while doing this (you will see why when you try it).

Keep in mind that the more intense the laser, the shorter the wavelength, and the more distance between the hair and the back wall, the more accurate the measurement will be of the hair in the end (the easier you will be able to measure accurately).

I did all of the math for you, so all you have to do now is just plug all of the measurements you made into my little formula and you will get the width of your tiny little hair! You will need to know the wavelength of your laser. It usually has on the laser a little sticker saying the wavelength in nanometers “nm.” Since color depends on wavelength, a green laser pointer will have a different wavelength than a red one. Make sure that you convert all units to meters. The equation will be off by several orders of magnitude if you do not! If you just wanted to find the width of your hair you’re done with the experiment! Most human hairs are anywhere from 0.00001 meters to 0.0002 meters. The apparatus that you have built is thus a “Quantum Micrometer” (Nestor’s Micrometer).

The first time that I did this experiment with my friend Pedro, the calculations were a bit off (the hair was measured to be one order magnitude higher than it was supposed to be). We could not figure out exactly why this was, as we had used formulas found online modeling the double-slit experiment, and it did not describe many things observed. For example, the first bright spot was seen to be slightly larger than all of the others, and the formulas found online did not predict this. It turns out that many formulas online are only approximations and not ideal models of the double-slit interference pattern, often relying on an assumption that all of the maximums (the centers of the bright spots) are equidistant from one another. This is false. To fix this, we derived a new formula where a distance d can be measured as accurately as possible. This particular derivation, expressing distance as a function of n, lambda, x, and L, if you are generous enough to provide honorable mention, I call the "Nestor-Amaral Equation" or the "Nestor-Amaral Derivation."

Don't be impeded by math, all you have to do is plug the numbers in! Keep in mind that when I say "maximum," I mean the center  of a bright spot. In addition, the variable "x" is the distance from the center of the largest bright spot (the middle of the pattern) to the center of the outermost bright spot, and the variable "n" is how many bright spots, not counting the centermost one.

If math and convoluted explanations scare you or you are already confused read no more.
You’re still here? If you want to know a bit more I’ll give you a bit of more information on quantum mechanics explained for anyone to understand and explain the Quantum Eraser Experiment too.. First of all, the property of blobs of things to be in multiple spots at once is called “superposition .” The pattern that you saw with many bands of light was called an “interference pattern ” because the light interferes with itself (that is, the little ripples are bumping into themselves and thus interacting).

1.) The De-Broglie Relationship
The reason that matter behaves this way isn’t something as spooky as you might assume at first. It just illustrates that the only reason that we see things in one spot is because our wave of potential places to be (our superposition of possible states, or ripples, etc) is collapsed when we interact with something. Big things have a bigger influence/interaction with the universe than smaller things. For example, if you take an electron, it is surrounded by empty space so it is free to be in multiple spots at the same time. The universe doesn’t store information about its location because it doesn’t need to because it doesn’t interact with anything. We know that the universe is lazy and only does what it has to, taking the easiest possible way out of anything (conserving mass, etc). Now if we have a baseball, it isn’t surrounded by empty space. It’s surrounded by gas molecules bumping off of it, light hitting it, and people watching it. The behavior of the ball’s past rules out possibilities of it being in multiple places because of the information enclosed in the effect that it had on its environment (like air drafts that the ball causes, it smashing into a window, people’s memories of the ball, sound waves, etc). Stuff isn't somewhere until it has to be somewhere.
    Now there is a relationship between how big a blob of matter is, its speed, and its wavelength (how “wavelike” it is). This relationship is called the “De-Brolie Relationship ” and basically means that a blob’s wavelength equals Planck’s constant over momentum. You can find Planck’s constant online and momentum is simply the mass of an object times its velocity. Thus you can find how “wavelike” you are, a baseball is, a grain of sand or even an electron.

2.) Relativistic Mass
Some of you sharp readers may have noticed that since momentum equals mass times velocity, and that a photon’s mass is zero, its momentum must then be zero and so its wavelength is infinite. Well, not exactly. A photon has no “rest mass ” but has a “relativistic mass .” The difference between the two types of mass is that no matter what your velocity is, rest mass will always be the same, but not necessarily relativistic mass, which is a result of the effects of general relativity.
    In fact, the equation for the De-Broglie wavelength is only half true, much like most formulas given in High School physics classes are only half true. What I mean by this, is that general relativity must be taken into account. Most of the time general relativity is omitted from equations is because it is only really noticeable once you get close to the speed of light.
    The “real” De-Broglie wavelength is calculated as (Planck’s Constant/(Rest Mass x Velocity)) x sqrt(1 – (Velocity Squared/The Speed of Light Squared)). Notice that the only thing we added to the equation is the multiplication of a square root with a bunch of stuff in it. The thing we multiplied by is called the “Lorentz Factor ” and the closer you get to the speed of light, the closer to zero it gets.
    Notice that when we plug everything into this modified formula, we get 0/0. When one gets “0/0” that pretty much always is the math’s way of saying “sorry there might be an answer, but you have to use another way to get it if there is.” This situation is different than when you get a number over zero (infinity) or zero over something (zero).
    The way that we get the real answer is to of course assume that photons have a relativistic mass and to use another formula. Energy = Planck’s Constant x The Speed of Light In a Vacuum / The Wavelength. Now you could just as easily use the little sticker on the laser pointers to find the wavelength and use that to calculate energy. Frequency is calculated as 1 / Wavelength so you can use that relationship to calculate frequency too.

3.) Spooky Action at a Distance
Almost everybody has heard that the speed of light is "the fastest anything can go," or in other words is the "universal speed limit." This is true for information too. For example, if I were to email you, and you were one light year away, there is no possible way that you can receive my message any sooner than one year. This concept works for forces too. For a force to work, such as magnetism, gravity, or anything else, there is a sort of "telephone call" that happens between the object that exerts the force and the receiving mass. The boundary on the propagation of information to the speed at which light propagates is called the information/event's "light cone ." The information that is transmitted and received between both masses manifests itself in what are known as "virtual particles ." Virtual particles are the messages that are sent and received that cause masses to respond to forces the way that they are supposed to. 
    Now, if we know that nothing can effect anything else faster than the speed of light, then we have come across an apparent problem when we take quantum mechanics into account. For example, if two particles are in superposition with one another, and one particle is a light year away from the other particle, interacting with one instantly effects the other. This apparently allows for "faster than light communication " and Einstein labeled it "spooky action at a distance ," however this only illustrates an incomplete understanding of the scenario and can be explained by means of quantum field theories (apparently, many claim).

4.) Heisenberg's Uncertainty Principle and the Quantum Eraser
One last concept that is interesting is “Heisenberg’s Uncertainty Principle ” which measures exactly how uncertain a measurement is about the position or momentum of a particle. In a nutshell, the maximum difference between the measured position of a particle and its actual position (uncertainty in position) times the maximum difference between the measured momentum of a particle and its actual momentum must always be greater or equal to Planck’s constant divided by two pi. The uncertainty principle is the reason that measurements of the hair become more inaccurate as we increase wavelength. Increasing wavelength (decreasing frequency) gives a larger inaccuracy of position, but decreasing wavelength (increasing frequency) gives a larger inaccuracy of velocity.
    If you want to do this additional part of the experiment and demonstrate the effect of the little photons when you try to “see” them in multiple places at once, having them suddenly acting like solid particles again instead of waves then lets continue on. What we are going to do is make information about which slit each photon went through available, thus collapsing the wavelike behavior of the photons and then making them behave like solid particles again, finally, erase that information so that the photons behave like waves again, demonstrating that where a photon or small particle is at any time is only decided at the moment it interacts with the universe (is observed or bumps into something). 
For this, you will need a piece of polarizing film and a clip. You can get the polarizing film from inside of a little LCD screen or 3D glasses from some theaters.
    Now cut the polarizing film into three equal-sized pieces. Turn one piece 90 degrees and put it behind one of the other pieces. It should make the back turn dark and block light. Clamp the two pieces of film right next to each other and tape the hair (or EXTREMELY small piece of string) right exactly where the seam between the two pieces of film are. We will use the third piece of film in a bit.
    How polarization works is that light oriented in only a certain way can pass through a polarizing film. The orientation that is allowed to pass through depends on the orientation of the film. That is the reason that we saw no light coming through two polarizing filters oriented perpendicular to one another. Light polarized once into one orientation cannot pass through the second filter because it is turned perpendicular and is thus not the correct orientation.
    Anyways so if we shine the laser at the hair again we see that the wavelike pattern isn’t there anymore because by polarizing the light from each side of the hair, we make information available about which side the photons went through. Before, the photons were going through both at the same time, but now that they “know” you are watching them and polarizing them, thus tagging them and making it possible to find out which side they “really” went through, they only go through one and the pattern is gone.
You can selectively block out photons coming from one side of the hair or the other by turning the third piece of polarization paper 90 degrees or 180 degrees.
    If we want to get this wavelike pattern back again, we have to somehow erase this “tag” on the photons. We have to erase the information about which photon is polarized in what orientation. The way that we do this is we take the third piece of polarizing film and turn it 45 degrees. This lets some of the light from both sides of the hair come through, and thus we can no longer find out which side any of the photons went through and the ability described previously to selectively block out photons from one side or the other is gone. So the wavelike pattern should reappear because the photons “know” that they are no longer being “watched.” The experiment that you have just performed is sometimes called the “Quantum Eraser Experiment .”

5.) What I will do with my laser cutter from the EPILOG ROCKS Contest
As a mad scientist and engineer a laser cutter would be very useful! I always like to tinker around, but usually I am stuck using only household materials. The laser cutter will be a good precision tool to use in the design of future gadgets that I am working on such as an audio modulated tesla coil, displays, RC flying machines, robots, and more. I would like to begin a start-up company and use much of the proceeds to help others. The laser cutter would no doubt be a valuable asset.

    Anyways I hope you enjoyed my tutorial. Check out my youtube channel for more mad science tutorials you can do at home using only household materials!