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• The Heisenberg Uncertainty Principle is one of a handful of ideas

• from quantum physics to expand into general pop culture.

• It says that you can never simultaneously know the exact position

• and the exact speed of an object and shows up as a metaphor in everything

• from literary criticism to sports commentary.

• Uncertainty is often explained as a result of measurement,

• that the act of measuring an object's position changes its speed, or vice versa.

• The real origin is much deeper and more amazing.

• The Uncertainty Principle exists because everything in the universe

• behaves like both a particle and a wave at the same time.

• In quantum mechanics, the exact position and exact speed of an object

• have no meaning.

• To understand this,

• we need to think about what it means to behave like a particle or a wave.

• Particles, by definition, exist in a single place at any instant in time.

• We can represent this by a graph showing the probability of finding

• the object at a particular place, which looks like a spike,

• 100% at one specific position, and zero everywhere else.

• Waves, on the other hand, are disturbances spread out in space,

• like ripples covering the surface of a pond.

• We can clearly identify features of the wave pattern as a whole,

• most importantly, its wavelength,

• which is the distance between two neighboring peaks,

• or two neighboring valleys.

• But we can't assign it a single position.

• It has a good probability of being in lots of different places.

• Wavelength is essential for quantum physics

• because an object's wavelength is related to its momentum,

• mass times velocity.

• A fast-moving object has lots of momentum,

• which corresponds to a very short wavelength.

• A heavy object has lots of momentum even if it's not moving very fast,

• which again means a very short wavelength.

• This is why we don't notice the wave nature of everyday objects.

• If you toss a baseball up in the air,

• its wavelength is a billionth of a trillionth of a trillionth of a meter,

• far too tiny to ever detect.

• Small things, like atoms or electrons though,

• can have wavelengths big enough to measure in physics experiments.

• So, if we have a pure wave, we can measure its wavelength,

• and thus its momentum, but it has no position.

• We can know a particles position very well,

• but it doesn't have a wavelength, so we don't know its momentum.

• To get a particle with both position and momentum,

• we need to mix the two pictures

• to make a graph that has waves, but only in a small area.

• How can we do this?

• By combining waves with different wavelengths,

• which means giving our quantum object some possibility of having different momenta.

• When we add two waves, we find that there are places

• where the peaks line up, making a bigger wave,

• and other places where the peaks of one fill in the valleys of the other.

• The result has regions where we see waves

• separated by regions of nothing at all.

• If we add a third wave,

• the regions where the waves cancel out get bigger,

• a fourth and they get bigger still, with the wavier regions becoming narrower.

• If we keep adding waves, we can make a wave packet

• with a clear wavelength in one small region.

• That's a quantum object with both wave and particle nature,

• but to accomplish this, we had to lose certainty

• about both position and momentum.

• The positions isn't restricted to a single point.

• There's a good probability of finding it within some range

• of the center of the wave packet,

• and we made the wave packet by adding lots of waves,

• which means there's some probability of finding it

• with the momentum corresponding to any one of those.

• Both position and momentum are now uncertain,

• and the uncertainties are connected.

• If you want to reduce the position uncertainty

• by making a smaller wave packet, you need to add more waves,

• which means a bigger momentum uncertainty.

• If you want to know the momentum better, you need a bigger wave packet,

• which means a bigger position uncertainty.

• That's the Heisenberg Uncertainty Principle,

• first stated by German physicist Werner Heisenberg back in 1927.

• This uncertainty isn't a matter of measuring well or badly,

• but an inevitable result of combining particle and wave nature.

• The Uncertainty Principle isn't just a practical limit on measurment.

• It's a limit on what properties an object can have,

• built into the fundamental structure of the universe itself.

The Heisenberg Uncertainty Principle is one of a handful of ideas

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B2 US TED-Ed wave momentum wavelength uncertainty position

# 【TED-Ed】What is the Heisenberg Uncertainty Principle? - Chad Orzel

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稲葉白兎 posted on 2015/03/14
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