Практика Shadowing: The Uncertainty Principle: What Does It Mean, How Does It Work? - Изучайте разговорный английский по видео
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If you know one thing about quantum mechanics, then that's more than most people, and it's probably that it's got something to do with the uncertainty principle.
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But just exactly what does that mean and how does it work?
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That's what we'll talk about today.
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Werner Heisenberg was the first to understand that quantum mechanics sets limits to what we can know.
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Yes, even for string theorists.
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Some properties of quantum particles can't be determined precisely at the same time.
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And it's not because we're not good at measuring, it's just how nature is.
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The best known example is the position and momentum of an object.
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You can think of the momentum as the velocity multiplied with the mass.
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This isn't correct for massless particles, but for our purposes it'll be good enough.
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Let's just pretend that massless particles don't exist, it shouldn't be too hard.
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Quantum mechanics says that you can't measure both the position and momentum precisely.
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This means if you know precisely where a particle is, you don't know which direction it's going.
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And the other way around, if you know which direction it's going, you don't know where it is.
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The position of a particle is usually denoted with x and the momentum with p.
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The uncertainty in each is marked with a large delta in front of the variable.
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So delta x is the position uncertainty and delta p is the momentum uncertainty.
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Heisenberg's uncertainty principle then says that the product of those two is always larger than a constant h -bar divided by two.
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This means if one of those uncertainties gets very small, then the other one must be very large, otherwise the inequality would be violated.
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This is where the joke about Heisenberg comes from, where he gets stopped by police who tell him how fast he was driving, and Heisenberg says, great, now I'm lost.
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But what does it mean that you can't measure the position and momentum with certainty at the same time?
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Does it mean that if you come with two detectors, a lightning strike will explode one of them?
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Well, no. The uncertainty principle doesn't say that you can't measure both of those quantities.
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It shows that you can't measure both precisely.
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If you've pinned down one, then the other will have a large spread.
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This means if you repeat the experiment, the result will be all over the place.
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It's the statistical uncertainty of this series of measurements that becomes large.
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A good example of this is letting quantum particles go through a narrow opening.
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The quantum particles act like waves, so this will create an interference pattern on the screen.
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This pattern is built up of single particles.
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The particles don't all collect in one place.
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And that's because you know the particles went through the slit, so you know something about their position.
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Then you can't tell which direction they are going.
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But of course, once a single particle hits the screen, you know which direction it went.
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What the uncertainty Uncertainty principle means is therefore that if you repeat this for many particles, then the outcome has a broad distribution.
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Another example is the relation between the uncertainty in energy and time.
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Consider you have a fluorescent sticker, the kind of stuff that glows in the dark.
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You put it into light and then, for a few hours afterwards, it'll emit light of a particular color, usually it's some shade of green.
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The way this works is that the light
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which falls on the sticker kicks off an electron from its normal energy level into a higher level.
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In most materials, the higher electron levels are extremely unstable.
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The electron falls back down immediately, and in that process the photon is emitted again.
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In fluorescent materials, however, the electrons can stay there for a few hours.
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It's called a metastable state.
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And only when the electron falls down will the light be emitted again.
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As a consequence the sticker glows for some hours.
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But just exactly how long do the electrons stay in that higher energy level?
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Ah, well, you can't say exactly.
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You can only talk about the probability of it dropping down in a certain amount of time.
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And why is that?
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It's because you know something about the energy of the electron on.
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It's sitting on this meta -stable level.
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Consequently, you can't know exactly how long it stays there.
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Such is life you can't have at all.
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This is basically also how nuclear decay works, by the way.
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Finally, the uncertainty principle has its origin in the properties of waves.
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It comes about because in quantum mechanics particles can act like waves.
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What's a wave?
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A wave is something that changes periodically in space and time.
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That could be water waves, electromagnetic waves, sound waves, or even a Mexican wave when a sports game gets boring.
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Waves have a wavelength and a frequency that's inversely proportional to the wavelength.
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The frequency tells you how much change there is in a certain period of time.
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If you have a perfectly regular sound wave, then it would sound like a beep at one particular frequency.
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But most sound signals aren't that simple.
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For example, here's me singing an A.
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This isn't just one frequency.
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You can take this sound apart and you'll find that, for one thing, I'm not a computer chip, so I don't exactly hit the A.
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But also, the way the human voice box works, it has a lot of higher harmonics.
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This breakdown of sound into all the frequencies it contains is called a spectrum.
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This doesn't only work for sound, but for every distribution of anything really.
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You can calculate a spectrum of the distribution of people in a room if you want to, and I'm sure somewhere there are businesses doing just that.
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But a more relevant example for us is light.
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If you have light of one particular wavelength, then that'd be one particular color,
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and the spectrum of this light would have one single peak at one particular frequency.
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Technically, for the spectrum to be exactly one frequency, the light wave would have to keep on waving forever.
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We never deal with that in reality.
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In reality, the light we deal with is bunched.
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It passes by within a certain window of time.
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First it wasn't there, then it was there, now it isn't there again.
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Like money on my bank account.
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Physicists call this a wave packet.
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How do you pack waves?
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Especially without getting wet?
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The curious thing about waves is that they can interfere both constructively and destructively.
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If they interfere constructively, they add up.
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If they interfere destructively, they can cancel each other out.
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If you overlay many of them in just the right way, you can do this so that outside of some region of space and time, the interference is almost completely destructive,
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and you are left with a constructive interference in just a small region.
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A wave packet is an overlay of different wavelengths and therefore an overlay of different frequencies with the correct offset.
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Such an overlay, by the way, is called a superposition.
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Sounds familiar?
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Yes, we do use superpositions in quantum mechanics.
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And this is where the word comes from.
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It comes from adding different wavelengths together.
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You superpose them.
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Okay, now here's the thing.
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As we just saw, we have two ways to describe the same wave packet.
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You can either say it's this distribution in time, wasn't there, was there, isn't there again,
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or you can say it's this distribution of frequencies with these offsets.
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They both describe the same thing, the same wave packet.
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There is a mathematical procedure to calculate one from the other.
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It's called a Fourier transformation.
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Put in a distribution in time, the Fourier transformation will give you the spectrum.
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Put in the spectrum, the Fourier transformation will give you the distribution in time.
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Here's the kicker.
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If the one distribution is sharply peaked, say you have a flash of light that's just a brief moment in time,
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then that means that it must contain a lot of different frequencies.
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The spectrum is very spread out.
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And the opposite is also true.
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If you have something with a very narrow frequency, then it must be spread out in space.
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Now you can ask, what's the relation between the spread in these two distributions, the one in time and the one in frequency?
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And would you know it, they're related to each other by an inequality that looks pretty much like the uncertainty principle.
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Whoa, but wait, this had nothing to do with quantum mechanics.
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We were just talking about spectral analysis.
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So what is going on?
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What's going on is that while this looks like the uncertainty principle, it's not.
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This is a property of waves.
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It relates a spread in time with the spread in frequency.
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To get Heisenberg's uncertainty principle, you further have to identify a frequency with an energy.
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Or if you do it in space, you have to identify the wave vector with the momentum.
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And this is where the H bar gets in.
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We learned this from no other than Albert Einstein.
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Yes, that guy again.
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He pops up more than toast in a student house.
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It's actually what he won the Nobel Prize for.
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No, seriously.
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Albert Einstein didn't win the Nobel Prize for special or general relativity.
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He wanted for putting h -bar in the right place.
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And the way he figured it out was from an observation called the photoelectric effect.
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If light shines on a metal plate, that can kick electrons out of the plate.
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One can measure this because it creates a current, so it's electric.
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This is why it's called the photoelectric effect.
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But for this to work, the frequency of the light must be above a certain threshold.
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If the frequency stays below the threshold, but you increase the brightness of the light, nothing happens.
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This was very confusing to scientists in the 19th century.
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They could understand that it takes energy above a certain threshold to kick out an electron.
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But if you think that light is a wave, then it's the brightness that measures this energy.
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So why would turning up the brightness not kick out electrons?
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Along came Einstein and he said that's because light is made of chunks of energy.
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We now call those chunks photons.
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To kick out an electron, the energy of the photon has to be above a threshold, not the total energy of the light.
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The total energy of the light is the sum of the energy of all those photons.
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But the energy in each photon is proportional to the frequency.
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Therefore, if you want to know the total energy of the light, you take the number of photons and multiply it with their frequency,
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and now you need a constant to convert the frequency into an energy.
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That constant is Planck's constant, h.
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And the h with the bar, that's called the reduced Planck's constant and is h divided by two times pi.
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It's more commonly used in quantum mechanics because, like my uncle, it makes a lot of pi's disappear, so it's more convenient.
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Why is it called Planck's constant and not Einstein's constant?
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Good question, but I'll leave this for another video.
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Let's instead step back here and ask what all this means now.
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We've seen that what's seemingly so weird about the uncertainty principle, that there are two quantities that you can't measure precisely at the same time,
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has really nothing to do with quantum mechanics.
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It's just a property of waves.
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What quantum mechanics does for you is to make this a property of particles.
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And for that to work, you have to relate time with energy and space with momentum.
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If you're uncertain about any of this, then you're doing it right.
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We have also seen that the uncertainty principle doesn't mean you can't measure those quantities precisely in one round of an experiment,
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but that means if you repeat the experiment you get a large statistical distribution for at least one of those quantities.
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But then couldn't it be that the quantum particle actually had this property before it was measured, you just didn't know what it was?
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Rather than doing this weird thing where it's in several states at the same time until you look at it
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and poof it decides on one?
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Yes indeed.
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That's what is called a hidden variables model, and it's how Einstein thought quantum mechanics really works.
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He didn't like spooky action at a distance, and he was certain about his principles.
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Watching YouTube videos is great, especially if they're about such fun topics as quantum mechanics.
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But if you want to really understand the topic, then you have to actively engage with the material.
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A great place to do that is Brilliant, who have been sponsoring this video.
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On Brilliant, you find courses on a large variety of subjects in science and mathematics.
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The great thing about their courses is that they're all interactive with visualizations and follow -up questions, so you can check your understanding right away.
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This is why I like to look things up on Brilliant.
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It's fast, it's easy, and it tells me what I need to know.
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And they are constantly expanding their content.
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To understand better what I talked about in this video, check out for example my course about quantum mechanics.
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It gives you an introduction to interference, superpositions and entanglement, and of course the uncertainty principle.
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It begins from the very basics so you don't need to bring any background knowledge.
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And after that, you can continue maybe with their course on quantum objects or quantum computing or wherever your curiosity drives you.
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If you're interested in trying Brilliant out, use our link brilliant .org slash sabine
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and sign up for a free trial where you'll get to try out everything Brilliant has to offer for a whole week.
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The first 200 subscribers using this link will also get 20 % off the annual premium subscription.
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Thanks for watching.
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See you next week.
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Лексика и советы по произношению к этому уроку
В этом видео 182 предложений и 2366 слов для шедоуинга. Речь длится 14:44. Говорящий говорит в естественном темпе, около 161 слов в минуту, близком к повседневной речи. Только 81% слов входят в 3000 самых частых слов английского языка, поэтому лексика сложная.
Ключевая лексика этого видео
15 слов из видео, которые стоит выучить, с произношением и значением:
| Слово | Произношение | Значение |
|---|---|---|
| frequency существительное | /ˈfɹiːkwənsi/ | частота́ |
| quantum существительное | /ˈkwɑntəm/ | коли́чество |
| uncertainty существительное | /ʌnˈsɜːtənti/ | неуве́ренность, сомне́ние |
| particle существительное | /ˈpɑɹtək(ə)l/ | части́ца, крупи́ца |
| principle существительное | /ˈpɹɪn.sɪ.pəl/ | при́нцип |
| mechanic существительное | /mɪˈkænɪk/ | меха́ник |
| momentum существительное | /ˌmə(ʊ)ˈmɛntəm/ | и́мпульс, коли́чество движе́ния |
| spectrum существительное | /ˈspɛktɹəm/ | спектр, диапазо́н |
| electron существительное | /ɪˈlɛk.tɹɑn/ | электро́н |
| precisely наречие | /pɹɪˈsaɪs.li/ | то́чно |
| quantity существительное | /ˈkwɑn(t)ɪti/ | коли́чество |
| threshold существительное | /ˈθɹɛʃ(h)oʊld/ | поро́г |
| interference существительное | /ˌɪntəɹˈfɪɹɪns/ | вмеша́тельство, поме́ха |
| packet существительное | /ˈpæk.ɪt/ | паке́т, па́чка |
| experiment существительное | /ɪkˈspɛɹ.ə.mənt/ | экспериме́нт, о́пыт |
Фразовые глаголы, которые вы услышите
| Слово | Произношение | Значение |
|---|---|---|
| kick out глагол | вышвы́ривать, вы́швырнуть | |
| fall down глагол | /fɔl ˈdaʊn/ | па́дать, упа́сть |
| get off глагол | спуска́ться, спусти́ться | |
| try out глагол | про́бовать, попро́бовать | |
| turn up глагол | объявляться, находи́ться |
Произношение, на которое стоит обратить внимание
Говорящий использует 51 сокращённых и редуцированных форм, например can't, don't, isn't. Произносите их коротко, так, как слышите.
- Звуки «th»: threshold /ˈθɹɛʃ(h)oʊld/, mathematics /mæθ(.ə)ˈmæt.ɪks/, mathematical /ˌmæθ(.ə)ˈmæt.ɪ.kəl/, wavelength /ˈweɪvˌlɛŋ(k)θ/, theorist /ˈθiːəɹəst/
- Звуки «sh» и «zh»: threshold /ˈθɹɛʃ(h)oʊld/, transformation /ˌtɹæns.fɔɹˈmeɪ.ʃən/, relation /ɹɪˈleɪʃ(ə)n/, flash /flæʃ/, shine /ʃaɪn/
- Длинные слова — следите за ударением: uncertainty /ʌnˈsɜːtənti/, momentum /ˌmə(ʊ)ˈmɛntəm/, interference /ˌɪntəɹˈfɪɹɪns/, experiment /ɪkˈspɛɹ.ə.mənt/, transformation /ˌtɹæns.fɔɹˈmeɪ.ʃən/
Как заниматься с этим видео
- Прослушайте всё видео один раз молча и выпишите незнакомые слова.
- Начните со скорости 0,75×, повторяйте предложение за предложением и вернитесь к обычной скорости, когда станет легко.
- Запишите себя и сравните с оригиналом, обращая внимание на такие слова, как frequency, quantum, uncertainty.
Грамматика в этом видео
Конструкции, которые говорящий использует чаще всего, с точными словами из видео:
| Конструкция | В видео |
|---|---|
| Пассивный залог be + причастие прошедшего времени — важно, что происходит, а не кто это делает | is usually denoted · is marked · would be violated |
| Present Perfect have/has + причастие прошедшего времени — прошлое действие, важное сейчас | you've pinned · We've seen · have also seen |
Что такое техника Shadowing?
Shadowing — это научно обоснованная техника изучения языка, изначально разработанная для подготовки профессиональных переводчиков и популяризированная полиглотом доктором Александром Аргуэльесом. Метод прост, но эффективен: вы слушаете аудио на английском от носителей языка и немедленно повторяете вслух — как тень, следующая за говорящим с задержкой в 1–2 секунды. В отличие от пассивного прослушивания или грамматических упражнений, Shadowing заставляет мозг и мышцы рта одновременно обрабатывать и воспроизводить реальные речевые паттерны. Исследования показывают, что это значительно улучшает точность произношения, интонацию, ритм, связную речь, понимание на слух и беглость речи — что делает его одним из самых эффективных методов для подготовки к IELTS Speaking и реального общения на английском.