Quantum Mechanics: The Uncertainty Principle
Ανέβηκε στις 23 Ιαν 2010
http://www.facebook.com/ScienceReason ... Quantum Mechanics (Chapter 4): The Heisenberg Uncertainty Principle.
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1. A Brief History Of Quantum Mechanics
http://www.youtube.com/watch?v=B7pACq...
2. The Structure Of Atoms
http://www.youtube.com/watch?v=-YYBCN...
3. Wave Function And Wave-Particle Duality
http://www.youtube.com/watch?v=7GTCus...
4. The Uncertainty Principle
http://www.youtube.com/watch?v=Fw6dI7...
5. The Spin Of Fundamental Particles
6. Quantum Entanglement
---
In
quantum mechanics, the Heisenberg uncertainty principle states that
certain pairs of physical properties, like position and momentum, cannot
both be known to arbitrary precision. That is, the more precisely one
property is known, the less precisely the other can be known.
This
statement has been interpreted in two different ways. According to
Heisenberg its meaning is that it is impossible to determine
simultaneously both the position and velocity of an electron or any
other particle with any great degree of accuracy or certainty.
According
to others (for instance Ballentine) this is not a statement about the
limitations of a researcher's ability to measure particular quantities
of a system, but it is a statement about the nature of the system itself
as described by the equations of quantum mechanics.
In quantum
physics, a particle is described by a wave packet, which gives rise to
this phenomenon. Consider the measurement of the absolute position of a
particle. It could be anywhere the particle's wave packet has non-zero
amplitude, meaning the position is uncertain - it could be almost
anywhere along the wave packet.
To obtain an accurate reading of
position, this wave packet must be 'compressed' as much as possible,
meaning it must be made up of increasing numbers of sine waves added
together. The momentum of the particle is proportional to the wavelength
of one of these waves, but it could be any of them. So a more accurate
position measurementby adding together more wavesmeans the momentum
measurement becomes less accurate (and vice versa).
The only kind
of wave with a definite position is concentrated at one point, and such
a wave has an indefinite wavelength (and therefore an indefinite
momentum). Conversely, the only kind of wave with a definite wavelength
is an infinite regular periodic oscillation over all space, which has no
definite position.
So in quantum mechanics, there can be no
states that describe a particle with both a definite position and a
definite momentum. The more precise the position, the less precise the
momentum.
The uncertainty principle can be restated in terms of
measurements, which involves collapse of the wavefunction. When the
position is measured, the wavefunction collapses to a narrow bump near
the measured value, and the momentum wavefunction becomes spread out.
The
particle's momentum is left uncertain by an amount inversely
proportional to the accuracy of the position measurement. The amount of
left-over uncertainty can never be reduced below the limit set by the
uncertainty principle, no matter what the measurement process.
This
means that the uncertainty principle is related to the observer effect,
with which it is often conflated. The uncertainty principle sets a
lower limit to how small the momentum disturbance in an accurate
position experiment can be, and vice versa for momentum experiments.
• http://en.wikipedia.org/wiki/Uncertai...
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The Cassiopeia Project - making science simple!
The
Cassiopeia Project is an effort to make high quality science videos
available to everyone. If you can visualize it, then understanding is
not far behind.
• http://www.cassiopeiaproject.com
.
---
Please SUBSCRIBE to Science & Reason:
• http://www.youtube.com/Best0fScience
• http://www.youtube.com/ScienceTV
• http://www.youtube.com/FFreeThinker
---
1. A Brief History Of Quantum Mechanics
http://www.youtube.com/watch?v=B7pACq...
2. The Structure Of Atoms
http://www.youtube.com/watch?v=-YYBCN...
3. Wave Function And Wave-Particle Duality
http://www.youtube.com/watch?v=7GTCus...
4. The Uncertainty Principle
http://www.youtube.com/watch?v=Fw6dI7...
5. The Spin Of Fundamental Particles
6. Quantum Entanglement
---
In
quantum mechanics, the Heisenberg uncertainty principle states that
certain pairs of physical properties, like position and momentum, cannot
both be known to arbitrary precision. That is, the more precisely one
property is known, the less precisely the other can be known.
This
statement has been interpreted in two different ways. According to
Heisenberg its meaning is that it is impossible to determine
simultaneously both the position and velocity of an electron or any
other particle with any great degree of accuracy or certainty.
According
to others (for instance Ballentine) this is not a statement about the
limitations of a researcher's ability to measure particular quantities
of a system, but it is a statement about the nature of the system itself
as described by the equations of quantum mechanics.
In quantum
physics, a particle is described by a wave packet, which gives rise to
this phenomenon. Consider the measurement of the absolute position of a
particle. It could be anywhere the particle's wave packet has non-zero
amplitude, meaning the position is uncertain - it could be almost
anywhere along the wave packet.
To obtain an accurate reading of
position, this wave packet must be 'compressed' as much as possible,
meaning it must be made up of increasing numbers of sine waves added
together. The momentum of the particle is proportional to the wavelength
of one of these waves, but it could be any of them. So a more accurate
position measurementby adding together more wavesmeans the momentum
measurement becomes less accurate (and vice versa).
The only kind
of wave with a definite position is concentrated at one point, and such
a wave has an indefinite wavelength (and therefore an indefinite
momentum). Conversely, the only kind of wave with a definite wavelength
is an infinite regular periodic oscillation over all space, which has no
definite position.
So in quantum mechanics, there can be no
states that describe a particle with both a definite position and a
definite momentum. The more precise the position, the less precise the
momentum.
The uncertainty principle can be restated in terms of
measurements, which involves collapse of the wavefunction. When the
position is measured, the wavefunction collapses to a narrow bump near
the measured value, and the momentum wavefunction becomes spread out.
The
particle's momentum is left uncertain by an amount inversely
proportional to the accuracy of the position measurement. The amount of
left-over uncertainty can never be reduced below the limit set by the
uncertainty principle, no matter what the measurement process.
This
means that the uncertainty principle is related to the observer effect,
with which it is often conflated. The uncertainty principle sets a
lower limit to how small the momentum disturbance in an accurate
position experiment can be, and vice versa for momentum experiments.
• http://en.wikipedia.org/wiki/Uncertai...
---
The Cassiopeia Project - making science simple!
The
Cassiopeia Project is an effort to make high quality science videos
available to everyone. If you can visualize it, then understanding is
not far behind.
• http://www.cassiopeiaproject.com
.
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