Heisenberg's Uncertainty Principle EXPLAINED (for beginners)

a lot of us have heard about Heisenberg's uncertainty principle and it's an interesting concept however it's a very tricky idea to actually wrap your head around so in this video I'm going to explain exactly what the principle is and give you a way of thinking about it that will hopefully make things a lot clearer and don't worry you don't need to know any advanced level maths or physics to understand this video just some high school stuff hey what's up you lot my name is path being levels critical at this point and I make fun physics videos though I don't have to try too hard because physics is already fun now before I go into Heisenberg's uncertainty principle I just quickly wanted to mention if you enjoyed this video then please leave a thumbs up and share it with your friends don't forget to subscribe to my channel if you haven't already and hit that Bell button if you want to be notified every time I upload finally before we get into the video if you want to learn a little bit more about quantum mechanics then check out this video I made about the Schrodinger equation so Heisenberg's uncertainty principle first of all what even is it well the uncertainty principle is a concept within the framework of quantum mechanics which by the way deals with very very small objects now the principle itself says something really baffling it tells us that there is a fundamental and universal limit to how much we can know about pairs of quantities known as conjugate variables now for our purposes in this video conjugate basically means related to each other or linked together in a specific way and variables are quantities that vary or change now most commonly the uncertainty principle is described using the quantities of position and momentum momentum by the way is directly related to a particle speed it's not exactly the same thing there is a difference between speed and momentum but for this video we'll kind of use the two terms interchangeably because they're very closely related to each other with these quantities were told that the more we know about one the less we can know about the other more specifically then the uncertainty principle tells us if we take our uncertainty in position which we'll call Delta X and multiply it by the uncertainty in momentum which were called Delta P then this product when we multiply these two together is greater than or equal to H bar divided by 2 now H bar is just a constant is just a number so the right-hand side of the inequality H bar divided by 2 is also just a number but let's think about this for a second the uncertainty principle is telling us that when we multiplied the two uncertainties together this has to be greater than or equal to some number in other words the product has to be at least this number what does this mean then well it means that we cannot take the two quantities Delta X and Delta P and make them both as small as we would want them to be if we make one of them small let's say we make Delta X very small then the other quantity Delta P has to get larger so that when we multiply them together it has to be at least h-bar divided wretched why is this relevant to us then or remember that these uncertainties represent uncertainties in our measurement of the position and the momentum of a particle for example basically here's a good way of thinking about it let's say normally in the classical world we will measure the particle to be here in the quantum world is not quite so simple before we measure the particles position we have a probability distribution usually peaks at the position that we would measure classically in other words there's a very high probability that the particle is where we would measure it to be classically however it also has a probability of being somewhere else and it's the width of this probability distribution roughly speaking that defines the uncertainty in our measurement of that particles position in other words the answer C is how uncertain we are about a measurement so coming back to our original point then we cannot make both of these quantities Delta X and Delta P the uncertainties in position and momentum we cannot make them arbitrarily small we can't make one of them arbitrarily small we can't even make one of them zero in other words we know exactly where the particles let's say position is but that's at the expense of the other if the uncertainty in the particles position is zero then the uncertainty of the particles momentum has to be infinity in other words if we know exactly where that particle is with 100% certainty then we know absolutely nothing about that particles momentum or speed now there's actually a lot I haven't mentioned about the uncertainty principle I'm skimming over a lot and simplifying a lot of things and taken away the subtlety out of a lot of things as well I want us to look in some detail at where the uncertainty principle actually comes from but before we go into that let's look at a common description of the uncertainty principle that gets thrown around whenever the uncertainty principle is discussed okay so let's consider we've got a particle it's just doing these things or moving around in space being a particle how would we measure the position and speed of that particle we can't just stick a ruler down beside it it's teeny tiny it's a particle so what we have to do is to fire a light at that particle the light then bounces off that particle and gives us information about the particles position and speed or momentum now the interesting thing is at this scale at the teeny tiny scale quantum effects start to occur the light that we fire at it has quantum property now at this scale it has wave particle duality now if you haven't heard of wave particle duality pause this video and google it YouTube it Wikipedia it's a really interesting and weird concept there are a lot of good videos and explanations about it online so go check it out and then come back to this video but anyway so wave particle duality is a thing of those scales in other words when we fire a light at this object at this particle the light itself will have both particle-like and wave-like properties in other words we'll be firing photons of light now photons are particles so we're firing particles of light at the particle that we're trying to measure as well as this because light has a wave-like behavior we can define that light with a specific wavelength now if the wavelength of the light that we're firing at the particle is short if we have a short wavelength light then we get more information about that particles position because the peaks in short wavelength light are closer together same thing with the troughs so we get more information about the whereabouts of that particle however this comes at a price remember that short wavelength particles are high-energy particles we can see this from the relationship e is equal to HC divided by lambda e is the amount of energy carried by the light H and C are both just constants just numbers we don't need to worry about it too much and lambda is the wavelength of the light so in other words E is inversely proportional to lambda so if we have short wavelength light going into our particle then the energy of that short wavelength light is large and vice versa long wavelength small energy so as we said earlier we're putting in short wavelength light into our particle we get lots of information out by the particles position however the light that we're putting in short wavelength light is high in energy so it's going to result in a kick to the particle the act of measuring it where that photon has resulted in a kick and so we know less about that particle speed or momentum now this is the explanation that gets thrown around when Heisenberg's uncertainty principle is discussed however this is not Heisenberg's uncertainty principle this is an explanation provided by Heisenberg as to why the uncertainty principle may be occurring it's not an actual description of the uncertainty principle itself as well as this it gets into a huge mess about how us measuring is making a difference in the particles position or momentum and bla bla bla bla bla let's not get into that and it also raises the question well why are we using light at all can't we think of a better way to measure the particles position and momentum that would entirely subvert this problem well that's the problem with this explanation it's not the Heisenberg uncertainty principle it's just a possible explanation as to why occurs instead let's look at one of the ways of understanding where the principle actually comes from now the way that I'm going to discuss of looking at the uncertainty principle will involve learning a little bit of maths specifically we'll be looking at a topic known as Fourier transforms however don't worry I'll explain the basics of Fourier transforms using just pictures and English we won't need to know any complicated maths or even go into any complicated maths so Fourier transforms are based on a fairly simple concept the idea is that lots of different functions mathematical functions can be broken down into building block functions confused let me give you an analogy to help to find a good analogy we need to look at another area of mathematics specifically vectors now for those of you that have studied vectors in any level of detail you'll know that vectors have size and direction so this arrow is a representation of a vector it starts at a certain point and it finishes at a certain point it has a certain size how long the vector is and it has a certain direction the direction in which the arrow is pointing now many of you will know that we can take this vector and break it down into components we can choose to break it up for example into its horizontal component and its vertical component so let's say that our original vector was a size of five units long now how long one unit is doesn't matter it could be a millimeter it could be a centimeter it could be a killer meter it could even be a yard for my American friends out there it doesn't matter but let's say our vector that we're looking at is five units long now we can choose to break it up into its horizontal and vertical components like I said in this case the horizontal component is three units long and the vertical component is four units long now the horizontal and vertical components are at 90 degrees to each other the technical word for this is they're orthogonal to each other which means that the triangle that we've just drawn is a right angle triangle and hence we can apply Pythagoras's theorem to ensure that the lengths of the sides of the horizontal component the vertical component and the original vector do actually work out try it for yourself apply Pythagoras's theorem to the side lengths of this triangle anyway so basically what we've done is we've taken this vector the original vector that's 5 units long and broken it down into a horizontal component which is three units long and a vertical component which is four units long so basically we've taken our vector and broken it down into sensible building blocks the sensible building blocks being a unit long vector in the horizontal direction and a unit long vector in the vertical direction we've got three in the horizontal and four in the vertical just like that which break a function up into sensible building blocks made up of different functions specifically the functions that we'll be using as building blocks will be sine waves of different frequencies they're also unit sine waves by the way because their amplitudes are one and basically what we can do is to take our function and break it down into different amounts of sine waves at different frequencies just like how we took our vector and broke it down into different amounts of horizontal vector and vertical vector in this analogy our original vector is our original function the sine wave at one frequency is one of our sensible unit vectors the sine wave another frequency is another one of our sensible unit vectors and so on and so forth if we want five units of this sine wave we just multiply its amplitude by five then we add it to another sine wave with a different frequency that's the analogy by the way interestingly the sine waves of different frequencies are defined as being orthogonal to each other just like how we add the horizontal unit vectors and the vertical unit vectors being orthogonal to each other however the definition of orthogonal in this case is different they're not at 90 degrees to each other but there's a really clever definition which I won't go into just take my word for it that they're orthogonal also if you don't know exactly what I mean by sine waves at different frequencies pause this video and check out the Internet and explanation for the frequencies of waves however let's carry on so we've taken our original function and we've broken it down into building block functions now this is a really tricky concept so feel free to replay this part of the video until you understand exactly what I'm talking about if it's still not clear please please please feel free to drop me a comment below and I'll try and clarify as much as I can in the comments otherwise feel free to check out Fourier transforms on the internet though I should warn you they're quite complicated anyway so the thing that's of interest to us when we break down a function into its constituent sine waves is that the sine waves that we break them down into are at different frequencies the reason for this is that we can do something really clever let's say we have a function which we can break down into two units of one frequency and one unit of another frequency and nothing else what we can do is to make a new plot a new function on the X or the horizontal axis will be the frequencies of the components that we've broken our function into and all the vertical axis will be how much of each component we have so like we said in our function we had two units of the first frequency so we'll plot at the first frequency along the horizontal axis two units up and we had one use of the second frequency now we have no other frequency sine waves in our original function so for every other frequency on our new plot the amount will now at this point what we've done is we've made a new plot we've made a new function this new function is known as a Fourier transform of our original function we'll link it to the Heisenberg uncertainty principle in a second but before we do that there's an interesting thing to note about Fourier transforms if our original function is really really wide on its horizontal axis and the Fourier transform of that function is going to be really really narrow this is a property of Fourier transforms for example let's just take a normal sine wave it's a pure sine wave so it only has one frequency so when we break it down into its constituent components well its constitute component is just itself we've got one frequency one sine wave one pure sine wave now a sine wave stretches on forever in the horizontal direction because it's a pure sine wave it goes on forever in this direction and in this direction now if we were to plot its Fourier transform it looks something like this because its components its building blocks are just made up of one frequency sine wave the frequency of the original sine wave in this case and it has no other sine wave frequency components so our original function a sine wave infinitely wide as a Fourier transform that's infinitely narrow it's peaked at one frequency and it has a value of zero at every other frequency so it's infinitely narrow so a wide original function results in a narrow Fourier transform and this is true the other way around as well by the way if you have a narrow original function you get a wide Fourier transform okay so let's bring this back and Link it to Heisenberg's uncertainty principle to do this we first need to remember what we said earlier about a particles position and momentum being described by a probability distribution in other words we have a certain probability of a particles position being in a range of values and the same is true for its momentum now these probability distributions are known as wave functions so the wave function for a particles position basically tells us the probability with which we'll find the particle in a certain position and the same is true for the momentum now here's the clincher the wave function for a particles momentum is the Fourier transform of the wave function for the particles position in other words if the wave function for a particles position is wide so we have less information about it because it could be in a large range of values then the wave function of the particles momentum is very narrow in other words we know a lot more about it we are a lot more certain about the momentum because it could be in a very small range of values and again the opposite applies as well narrow position wavefunction wide momentum wavefunction the more we know about a particles position Nerra wavefunction could be a small range of values the less we automatically know about its momentum and this is how we can understand Heisenberg's uncertainty principle it is a fundamental property of the universe it has got nothing to do with our measurement apparatus our current technology or our intelligence levels it's just a property of the universe and according to quantum mechanics there's no way of getting around that and with all of that being said I hope that explanation was clear but I'm gonna stop the video here because it's getting really really long if there's something you don't understand that I haven't made very clear please feel free to leave a comment down below if i've also made an error point yeah let me know the comments below and I'll try and fix it in the description or in the comments or something like that now with all that being said if this videos helped you understand the Heisenberg uncertainty principle a little bit better then please leave a thumbs up also share this video with anyone you think might find it interesting or useful but yeah thank you so much for watching I hope you enjoyed it feel free to subscribe to my channel if you haven't already if you're interested in more content like this I make lots of fun physics videos and I'm hoping to do a lot more very very soon leave me a comment down below telling me what area of physics you want me to cover next as well as any problem areas of physics that you might be struggling with let me know down below anyway thanks so much for watching I'm gonna end the video here buh buh buh buh bye [Music]

Channel: Parth G

Views: 61,322

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Keywords: Heisenberg's Uncertainty Principle, Heisenberg's Uncertainty Principle Explained, Uncertainty Principle Explained, Uncertainty Principle Derivation, Heisenberg's Uncertainty Principle Class 11, Quantum Physics, Physics, Parth G

Id: iZ96TuP_veY

Length: 14min 42sec (882 seconds)

Published: Sun Dec 16 2018