Heisenberg’s Uncertainty Principle. Why, exactly, can you not know both the velocity and position of a particle?
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Knowing position or velocity mean you need to measure it. In term of particle, the only way to measure anything means you need to interact with it, as if a blind man had to touch its environment to know where are the walls. (by any of the 4 fundamental forces).
Each interaction mean you exchange energy with the particle. If you want a precise measurement, you need a bigger energy exchange, and thus a bigger uncertainty on the other measurement (be it position or velocity)
In order to see something, light has to hit the object and then travel to your eye.
If a particle is small enough, the simple act of being hit by a single photon of light changes the particle’s position. By the time that same photon reaches your eyeball carrying the information of where the particle was, it has moved elsewhere. So we’re only able to see where a particle WAS, but it’s impossible to know exactly where the particle is NOW, without looking again – ie, without pinging it with more photons and repeating the same problem.
On the quantum level, the simple act of observing particles changes their behavior.
The big problem is that we cannot detect a thing unless we interact with it. If there is no interaction, you cannot know it is there. We only know it is there by information we get from “touching” it (even if that “touching” uses light).
The problem is, of course, that when dealing with very small objects, the seemingly tiny energy of light is big in terms of the very tiny object. The following is a simplified way of understanding the issue.
The precision we can get in terms of the location requires very short wavelength light (the precision concerning location decreases as wavelength increases). That light is the most energetic. So, we can tell where the object is, but only if we hit it with energetic light, which moves the object and changes its direction and velocity (the energy changes its movement).
To avoid changing the movement much, we have to use low energy (large wavelength) light, but we can’t “see” small details with large wavelengths.
So, you can either see where the thing is, very well, but change its movement a lot (and not in a predictable way) OR you can have a big zone of “the thing is somewhere in there” but have little to no impact on its motion. Choice is yours.
This problem only exists on a very fine scale, things in the size range of the wavelength of light, and thus things with little to no mass.
Remember that velocity is a vector, and has a directional component.
Imagine a big pool. Someone jumps in and makes a big splash. You can easily look at the splash and say “that’s the location of the splash, that’s where the position is”. But what’s the velocity of the splash? Well, its speed is equal in all directions, so it must cancel out to zero, right? Can you meaningfully assign a velocity to the wave produced by the splash?
Now imagine the splash dissipates and the wind picks up, pushing waves across the surface of the pool. It’s much more obvious what the velocity of the waves are: they have both a speed and a direction. But where are the waves? Well, they’re everywhere.
Quantum objects typically inhabit some point on a spectrum between these two states. It’s not a matter of lacking the precision necessary to measure both qualities, the fact is that both qualities just cannot be well defined at the same time.
This isn’t a uniquely quantum property, either. This uncertainty comes directly out of the wave-like nature of quantum objects. The wave function that describes the position and momentum of particles is characterized by the sum of a series of sine waves of various frequencies and amplitudes. Critically, these waves go on forever in all four dimentions: space and time. In order tohave a well-defined position you have to add lots of high-frequency sine waves, which forces the momentum to be spread out across a large range of frequencies.
Heisenberg’s Uncertainty Principle states that it is impossible to know both the exact position and the exact velocity of a subatomic particle at the same time. The more precisely you know one of these values, the less precisely you can know the other.
This principle arises from the fact that particles can exhibit both wave-like and particle-like behavior. When we try to measure the position of a particle, we are essentially bouncing a photon off of it, which changes the particle’s velocity. Similarly, when we try to measure the velocity of a particle, we are interacting with it in a way that changes its position.
So, the more precisely we try to measure one of these values, the more we disturb the other value. This means that there is a fundamental limit to how precisely we can know both the position and velocity of a particle at the same time.
In summary, Heisenberg’s Uncertainty Principle arises from the wave-particle duality of subatomic particles, and states that it is impossible to know both the exact position and the exact velocity of a particle at the same time due to the disturbance caused by measurement.
Citations:
[1] https://scienceexchange.caltech.edu/topics/quantum-science-explained/uncertainty-principle
[2] https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Quantum_Mechanics/02._Fundamental_Concepts_of_Quantum_Mechanics/Heisenberg’s_Uncertainty_Principle
[3] https://chem.libretexts.org/Courses/Pacific_Union_College/Quantum_Chemistry/01%3A_The_Dawn_of_the_Quantum_Theory/1.09%3A_The_Heisenberg_Uncertainty_Principle
[4] https://www.britannica.com/science/uncertainty-principle
[5] https://www.khanacademy.org/science/physics/quantum-physics/quantum-numbers-and-orbitals/v/heisenberg-uncertainty-principle
[6] https://courses.lumenlearning.com/suny-physics/chapter/29-7-probability-the-heisenberg-uncertainty-principle/
There are already a lot of good explanations for rationale as to why this occurs, but just to add a bit of info for the interested: this is not at all a property inherent to quantum mechanics specifically and it is not limited to position and momentum. In a mathematical system that operates like quantum mechanics (a wave like system let’s say) you will see this type of property arise between any set of quantities that are related in the same way as position and momentum (non commutative operators).
That was one of the most mind blowing things to me when I took quantum mechanics. It seems like when you really look at the background of these common interesting facts, there’s always some really cool background to it.
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