Understanding the Heisenberg Uncertainty Principle

If you are uncertain about what the Uncertainty Principle means, maybe this article can give you another take on it.

In 1927, Werner Heisenberg published what has become known as the Heisenberg Uncertainty Principle, which significantly impacted and defined quantum mechanics from then on. In a nutshell, it states/proves, mathematically, that it is impossible to get infinite precision on a pair of complimentary properties, which depend on each other, such as speed/momentum and position/location.

This was revolutionary for a few reasons, but mostly because it said that we can never truly know all the facts about anything, especially as we try to get more precise. Classical physics lived and breathed on the idea that we could ultimately determine precisely all possible facts, and not only determine those precise facts about an object…all of them…but predict the outcome and behavior of any object ahead of time if you knew or gave all the relevant facts. For example, if you tell me how much a rock weighs, what its shape, angles, and density are, what the environmental conditions are (e.g., wind, humidity, etc.), and what force and arc you plan to throw the rock with, I can tell you where the rock will land, ahead of time, exactly every time. Or as another example, you will frequently hear that randomly flipping a penny many times will result in an even number of heads and tails over time. That is as long as you do it randomly, the penny will land heads up 50% of the time and tails up 50% of the time, or as close to those even percentages as can be accomplished in the real world. But if you flip a penny exactly the same way every time (i.e., same starting position, same applied force, same direction, same weather, etc.), it will land the same way every time without any variation, 100% of the time.

In classical physics, this is known as determinism. If you give me all the relevant facts, I can determine what’s going to happen. For thousands of years, this was the Holy Grail of all sciences – learn the facts so we can determine what’s going to happen – regardless of the science involved, be it physics, biology, or geology. As humans, we thought if we learned enough about what was going on and how it was going on, that we could not only predict a particular event with certainty, but figure out all events from the beginning of the beginning to the end of the end. We could be the masters of our domain.

And then Heisenberg came along and said it was all an imaginary, impossible goal. Not only that, but any time we measured an object, it impacted the object forever. And he proved it using math. He created a formula that so far has held up nearly 100 years and no one seriously thinks it is wrong. This creates lots of conflict because we do measure most of our world in ways that seem very deterministic. We can predict where rocks…and missiles will land. And when we use a radar gun to measure the speed of a car, horse, or baseball, it doesn’t appear to impact the speed of the object being measured. Can you imagine if you measured the speed of a race car at a NASCAR event and it impacted the speed of the car, simply because you measured it? Actually, that is exactly what happens, but the impact of our measurement upon large objects is so small and our measurement is so relatively imprecise that we don’t notice or account for it.

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For much of our world, it seems we can predict how things act and react. And measuring things doesn’t seem to impact, at least observably, anything we measure. But at the very small, sub-atomic, quantum-level, our measurements are proven to impact the things we measure and as we go to more precisely measure some properties, the measurement of other dependent properties must become less accurate. And there’s no way to fix it. There’s no way to more precisely measure both properties of a complimentary property pair (AKA complimentary variables pair) at the same time; measuring one impacts the other.

Let me explain this more.

Let’s start with a complimentary property pair. What’s that? A complimentary property pair is two properties of an object that depend on each other. The most common example is speed (often called momentum in the physics world). Speed is calculated by determining the distance travelled over time. Speed is often measured in miles per hour or miles per kilometer. The miles and hours of the speed calculation are the complimentary property pairs of the speed calculation. I can’t tell you the speed of an object without knowing the starting and measured locations and starting and measured time values. When measuring a race car’s speed, we start a time clock when the car passes some line on a surface and stop the time clock when the car passes the same line or another line we wanted. Then we divide the amount of measured time by the distance travelled in that time to get miles per hour (or whatever scale I’m using). I can’t determine speed without getting both distance and time.

What Heisenberg determined is that we can’t precisely measure both distance and time, ever more precisely at the same time. As we attempt to be more accurate on one value, the other must become measurement less precise. This occurs for all complimentary property pairs of all objects, even race cars and rocks, but the impact is unnoticeable at anything above the sub-atomic level. As mass of an object increases, the impact of the measurement of one side of the complimentary pair doesn’t as noticeably impact the other. At very small, sub-atomic scales, the impact is significant and relatively huge. And again, Heisenberg didn’t just say this and ask the world to believe him. He created a mathematical formula that has withstood nearly 100 years of independent testing that has never been contradicted.

The most common example given to demonstrate the Heisenberg principle is trying to determine the speed or position of an electron. At those sub-atomic scales, the changes in precision are very significant. An electron is moving around the nucleus of an atom nearly the light speed, but any attempt to measure the exact speed creates an inherent variance of plus or minus 1,000 kilometers per second (according to Heisenberg’s math formulas). Imagine if a car we were trying to measure the speed of differed by 1,000 kilometers per second and we didn’t know what the true value was. Our measurement would be useless.

In the measurement of an electron’s position and speed, the problem is that any measurement of one of the complimentary properties inversely, undeniably, unstoppably impacts the precision of the measurement of the other and impacts the object/properties themselves. This is because of the light (i.e., photons) needed to measure speed of an electron must increase in energy the faster and more accurately you want the speed measurement to be. And that energy hits the electron, like a cue ball hitting another cue ball, and impacts the electron, impacting its momentum and path.

Let’s suppose we are trying to time a race car around a race track using a watch and video-capturing camera. In order to measure the car’s speed/time, we need distance over time. Let’s assume the distance is always one exact oval, starting on the same line and measured again when the car touches the beginning of the same line. Depending on how accurately I want to measure the speed of the car when it crosses the finish line, requires that my timing device and photo measurement device be accurate to the level of accuracy and precision I desire. For example, if I use a watch that doesn’t have a second hand (time only changes every minute), my timing could only be accurate to the minute. And if my video-taking device only took video frames once a minute, it might not capture the car crossing the finish line. I might be able to say the car crossed the finish line in between two particular minutes, but not more accurate than that.

But let’s suppose I want to capture the time of the car to the nearest second. My watch would need to count out seconds and my video-taking camera would need to capture frames at least once a second, if not faster. Continuing on, suppose I wanted to capture the car to the millionth of a second (0.000001). My watch and video would need to include measurements to a millionth of a second or faster. At the macro level, this doesn’t impact the large race car enough to be detectable by the normal measurement devices we use to time race cars. But at the sub-atomic, electron level, high precision measurements require a lot of photons (or electrons). Imagine if our race car was running around the track and was suddenly hit by millions of tire-sized billiard balls. And the faster the car went, the more billiard balls that hit it. That would certainly impact the speed and trajectory of the car. That’s Heisenberg’s Uncertainty Principle in action.

Let’s for a moment revisit the complimentary pairs and go back to trying to measure our theoretical race car using a timer and camera. As anyone can attest to, as you try to get a perfect “photo finish” of cars (or horses, etc.), the objects being measured become blurry as they cross the line. This isn’t because the objects themselves are becoming blurry, but because they are moving with momentum as the video frame captures the image. If you want to capture the objects without any blurriness, you have to take faster video frames…faster and faster until the object in a single frame doesn’t move perceptibly at all between frames. If you were able to take very fast video frames, the object would appear to stand still. The increasing number of frames needed to get more precise measurements could be likened to the increase in number of photons, electrons, or shortened wavelengths (higher energy) needed to take a more precise image of a sub-atomic particle or property.

If you were just looking at one picture without any context, you might even assume the car isn’t moving at all. For all intents and purposes, the car would have zero motion shown in that picture. From the one picture alone, you couldn’t tell whether the car was going 100mph at the time or just parked on the line. Because at the time, even between individual frames, there would be very little change in distance or speed. It would appear as if time and the object stopped. Same thing at the sub-atomic, quantum level, except for the fact that the photons would be hitting the electron like rapidly fired, tire-sized cue balls would be hitting the car.

Here’s another example. Suppose I want to take a picture of a dozen roses with my camera. I can set up my camera and take a bunch of pictures of a dozen roses at the same time. But suppose I wanted to get a close up of the inside of one rose (stigma, style, filament, etc.) along with showing all the small pollen particles that might be inside. To do that, even using the same camera, you would need to change the focus of the camera. The camera lens would need to make the diameter of the lens (i.e., aperture) smaller to focus on the inside of a single rose. If the lens could also show you the other roses, they would likely be blurry because the focus of its attention (and light) is on the inside of a single rose. You cannot get both an incredible shot of the inside of all roses of the dozen at the same time that is comparatively at the same level of detail of a close-up of a single rose. You have to decide, do I take a great picture of a dozen roses, in less detail, or do I get incredible detail of the inside of one rose? You can’t do both. A camera lens can’t both take a wide picture and a magnified, focused picture at the same time. That’s complimentary pairs. But in this example the focus of the camera is concentrating its available energy (i.e. photons) on a close-up picture of the inside of a flower is similar to the shorter wavelengths needed to more precisely take a measurement of a particle or particular property.

Note: Any time anyone tries to use macro examples, such as I do with race cars and roses, and attempt to compare them to events at the quantum level, it’s going to be an imperfect comparison. Forgive the imperfections of my allegories.

Although location and momentum are the most frequently mentioned complimentary particle pairs, there are many others. Wikipedia (https://en.wikipedia.org/wiki/Complementarity_(physics)) lists these known complimentary pairs:

·        Position and momentum

·        Energy and duration

·        Spin on different axes

·        Wave and particle-related properties

·        Value of a field and its change (at a certain position)

·        Entanglement and coherence

·        Photon polarization

According to Heisenberg’s Uncertainty Principle and its math, as you go more precisely to one side of the pair, you influence the precision of the other part and natural value of the involved object forever. This has huge ramifications for our world, in general, and in quantum computers and quantum information sciences. For example, it makes the forensic analysis of quantum computers and other devices significantly more difficult than it is today. I’ll cover that topic, the challenges of forensic analysis of quantum devices soon.