Heisenberg Uncertainty
Created | Updated Mar 4, 2003
Werner Heisenberg was a German physicist who helped to formulate quantum mechanics in the beginning of the twentieth century.
He discovered the "Heisenberg Uncertainty Principle" in 1927.
This is a basic interpretation of the Heisenberg Uncertainty Principle.
To observe a particle, light must be reflected off the particle. At this present time in history, photons of light are the finest measuring tools a researcher has. Perhaps in the future, a different type of particle such as a graviton might be used to probe the
sub-microscopic depths. Extremely unlikely, but it is a possibility nonetheless.
To find both position and momentum of an electron, at least one photon must be utilized. Essentially the photon will bounce off the electron, then reflect back through the measuring device. For large particles, such as sand grains or buses, the measurements of position and momentum, where position means "the location" and momentum is basically the mass of the particle along with its direction and speed, the uncertainty is very small. Thus comparisons and measurements can be made with relative ease. For the smaller sub-atomic particles, the uncertainty is larger, and the location and momentum becomes more of a probability.
Observe an electron that has momentum p = mv, mass time velocity.
"Mass" can be interpreted as the amount of "stuff", or basic building blocks, an object is made of. Some scientists say that "quarks" could be the fundamental building blocks, but they are not quite sure about that. And of course, velocity is the speed and direction of the particle.
Make the measurement with photons of light that have a wavelength "lambda". Wavelength is the distance light travels for one cycle, and frequency is the number of cycles per second. For example,
visible light is around the frequency range 10^14 to 10^15 cycles per second. 10^14 is a 1 with 14 zeros, and 10^15 is a 1 with 15 zeros. 10 with an exponent that is greater than zero, will be a 1 followed by "exponent" number of zeros.
Since light in a vacuum travels at the speed of 10^8 meters per second,and the wavelength is the distance light travels for one cycle, the equation (velocity) = (wavelength) x (frequency) applies.
velocity of light in vacuum = c
lambda = wavelength = (c/frequency) equals
(10^8 meters/sec )/(10^14 cycles/sec ) equals 10^(-6) meter or
1/(1000000) meter
This equals one millionth of a meter. As the frequency of light is increased and the wavelength gets shorter, the energy increases.
For a photon of light, energy = hf, where h is the famous Plancks constant and f is frequency.
Since the wavelength of a particle is described by the DeBroglie formula as (lambda) = (Planck's constant)/(momentum), the photons wavelength is (lambda) = h/mc. mc = h/(lambda) is the photons momentum. h is Planck's constant and c is tha speed of light in vacuum. Even though photons have zero rest mass, they have mass by virtue of their kinetic energy(kinetic energy means energy of motion).
When one of these photons bounces off the electron, the electron's original momentum will be changed. This is very similar to the way billiard balls change their trajectories by bouncing off one another.
The amount of change in the electron's momentum is an probability-uncertainty (delta-mv), and will be of the same order and magnitude as the photon's momentum.
(delta-mv) is approximately equal to (h/lambda)
(delta-mv) ~= (h/lambda)
The larger the wavelength of the observing photon, the smaller the uncertainty in momentum, because it has less energy.
Because of wave-particle duality, the photon of light cannot measure the electron's position (x) with perfect accuracy.
The smaller the wavelength of light, the higher the frequency, higher the energy, and greater the accuracy in measuring the position of the electron. A reasonable estimate is one photon wavelength.
So uncertainty in position (delta-x) is greater than or equal to one photon wavelength.
(delta-x) >= (h/lambda)
The smaller the wavelength, the greater the accuracy in the measurement of the position, but as the wavelength of the photon gets shorter, its frequency increases according to the equation E = hf, and its energy and momentum increases, and the electron's momentum is changed to a greater degree by the bombarding photon, that is to say, the momentum of the electron has greater uncertainty.
By using photons of short wavelength and higher energy, the greater the accuracy in measurement of the position, but a greater uncertainty in the momentum of the electron.
By using photons of longer wavelength and lower energy, the greater the accuracy in measurement of the momentum, but a greater uncertainty in the position of the electron.
Since (delta-mv) ~= (h/lambda)
and
(delta-x) >= (lambda)
combine the two.
(delta-x)*(delta-mv) >= h
The physics books explain it as...
(delta-x)*(delta-mv) >= h/(2pi)
When considering wave-particle duality, position is a particle property and momentum is a wave property.
In conclusion, the uncertainty is basically because the attributes of position and momentum are intertwined such that the more accurately one attribute is known, the less accurately the other is known. Wave particle duality also says that nature is both continuous and discrete.
Russell E. Rierson
He discovered the "Heisenberg Uncertainty Principle" in 1927.
This is a basic interpretation of the Heisenberg Uncertainty Principle.
To observe a particle, light must be reflected off the particle. At this present time in history, photons of light are the finest measuring tools a researcher has. Perhaps in the future, a different type of particle such as a graviton might be used to probe the
sub-microscopic depths. Extremely unlikely, but it is a possibility nonetheless.
To find both position and momentum of an electron, at least one photon must be utilized. Essentially the photon will bounce off the electron, then reflect back through the measuring device. For large particles, such as sand grains or buses, the measurements of position and momentum, where position means "the location" and momentum is basically the mass of the particle along with its direction and speed, the uncertainty is very small. Thus comparisons and measurements can be made with relative ease. For the smaller sub-atomic particles, the uncertainty is larger, and the location and momentum becomes more of a probability.
Observe an electron that has momentum p = mv, mass time velocity.
"Mass" can be interpreted as the amount of "stuff", or basic building blocks, an object is made of. Some scientists say that "quarks" could be the fundamental building blocks, but they are not quite sure about that. And of course, velocity is the speed and direction of the particle.
Make the measurement with photons of light that have a wavelength "lambda". Wavelength is the distance light travels for one cycle, and frequency is the number of cycles per second. For example,
visible light is around the frequency range 10^14 to 10^15 cycles per second. 10^14 is a 1 with 14 zeros, and 10^15 is a 1 with 15 zeros. 10 with an exponent that is greater than zero, will be a 1 followed by "exponent" number of zeros.
Since light in a vacuum travels at the speed of 10^8 meters per second,and the wavelength is the distance light travels for one cycle, the equation (velocity) = (wavelength) x (frequency) applies.
velocity of light in vacuum = c
lambda = wavelength = (c/frequency) equals
(10^8 meters/sec )/(10^14 cycles/sec ) equals 10^(-6) meter or
1/(1000000) meter
This equals one millionth of a meter. As the frequency of light is increased and the wavelength gets shorter, the energy increases.
For a photon of light, energy = hf, where h is the famous Plancks constant and f is frequency.
Since the wavelength of a particle is described by the DeBroglie formula as (lambda) = (Planck's constant)/(momentum), the photons wavelength is (lambda) = h/mc. mc = h/(lambda) is the photons momentum. h is Planck's constant and c is tha speed of light in vacuum. Even though photons have zero rest mass, they have mass by virtue of their kinetic energy(kinetic energy means energy of motion).
When one of these photons bounces off the electron, the electron's original momentum will be changed. This is very similar to the way billiard balls change their trajectories by bouncing off one another.
The amount of change in the electron's momentum is an probability-uncertainty (delta-mv), and will be of the same order and magnitude as the photon's momentum.
(delta-mv) is approximately equal to (h/lambda)
(delta-mv) ~= (h/lambda)
The larger the wavelength of the observing photon, the smaller the uncertainty in momentum, because it has less energy.
Because of wave-particle duality, the photon of light cannot measure the electron's position (x) with perfect accuracy.
The smaller the wavelength of light, the higher the frequency, higher the energy, and greater the accuracy in measuring the position of the electron. A reasonable estimate is one photon wavelength.
So uncertainty in position (delta-x) is greater than or equal to one photon wavelength.
(delta-x) >= (h/lambda)
The smaller the wavelength, the greater the accuracy in the measurement of the position, but as the wavelength of the photon gets shorter, its frequency increases according to the equation E = hf, and its energy and momentum increases, and the electron's momentum is changed to a greater degree by the bombarding photon, that is to say, the momentum of the electron has greater uncertainty.
By using photons of short wavelength and higher energy, the greater the accuracy in measurement of the position, but a greater uncertainty in the momentum of the electron.
By using photons of longer wavelength and lower energy, the greater the accuracy in measurement of the momentum, but a greater uncertainty in the position of the electron.
Since (delta-mv) ~= (h/lambda)
and
(delta-x) >= (lambda)
combine the two.
(delta-x)*(delta-mv) >= h
The physics books explain it as...
(delta-x)*(delta-mv) >= h/(2pi)
When considering wave-particle duality, position is a particle property and momentum is a wave property.
In conclusion, the uncertainty is basically because the attributes of position and momentum are intertwined such that the more accurately one attribute is known, the less accurately the other is known. Wave particle duality also says that nature is both continuous and discrete.
Russell E. Rierson
