Create a free Team What is Teams? Learn more. Why is what Heisenberg's uncertainty principle describes true? Ask Question. Asked 6 years, 5 months ago. Active 4 years, 5 months ago. Viewed 2k times. EDIT In response to the comments about 'why' being a poor question to ask in physics: It would be equally useful to know how we observed Heisenberg's uncertainty principle.
I suspect I'm thinking about this the wrong way. Improve this question. Hal Hal 2 2 gold badges 8 8 silver badges 16 16 bronze badges. From a mathematical perspective: The Fourier transform. Momentum and Position are related by a Fourier transform and there we have a theorem that a 'narrow' distribution in real space is a 'wide' distribution in frequency space and vice versa.
Have a look here: physics. None of these can be explained in as simple terms as the Fourier transform. Add a comment. Active Oldest Votes. Improve this answer. Sebastian Riese Sebastian Riese 8, 2 2 gold badges 25 25 silver badges 44 44 bronze badges. Heisenberg's idea of how the measurement disturbance leads to the principle is inuitive, yet we understand today that it is false.
An early incarnation of the uncertainty principle appeared in a paper by Heisenberg, a German physicist who was working at Niels Bohr 's institute in Copenhagen at the time, titled " On the Perceptual Content of Quantum Theoretical Kinematics and Mechanics ". The more familiar form of the equation came a few years later when he had further refined his thoughts in subsequent lectures and papers.
Among its many counter-intuitive ideas, quantum theory proposed that energy was not continuous but instead came in discrete packets quanta and that light could be described as both a wave and a stream of these. In fleshing out this radical worldview, Heisenberg discovered a problem in the way that the basic physical properties of a particle in a quantum system could be measured. In one of his regular letters to a colleague, Wolfgang Pauli, he presented the inklings of an idea that has since became a fundamental part of the quantum description of the world.
The uncertainty principle says that we cannot measure the position x and the momentum p of a particle with absolute precision. The more accurately we know one of these values, the less accurately we know the other. Multiplying together the errors in the measurements of these values the errors are represented by the triangle symbol in front of each property, the Greek letter "delta" has to give a number greater than or equal to half of a constant called "h-bar".
Planck's constant is an important number in quantum theory, a way to measure the granularity of the world at its smallest scales and it has the value 6. One way to think about the uncertainty principle is as an extension of how we see and measure things in the everyday world.
You can read these words because particles of light, photons, have bounced off the screen or paper and reached your eyes. Each photon on that path carries with it some information about the surface it has bounced from, at the speed of light. Seeing a subatomic particle, such as an electron, is not so simple. You might similarly bounce a photon off it and then hope to detect that photon with an instrument.
But chances are that the photon will impart some momentum to the electron as it hits it and change the path of the particle you are trying to measure.
Or else, given that quantum particles often move so fast, the electron may no longer be in the place it was when the photon originally bounced off it. Either way, your observation of either position or momentum will be inaccurate and, more important, the act of observation affects the particle being observed. The uncertainty principle is at the heart of many things that we observe but cannot explain using classical non-quantum physics. Newtonian physics placed no limits on how better procedures and techniques could reduce measurement uncertainty so that it was conceivable that with proper care and accuracy all information could be defined.
Heisenberg made the bold proposition that there is a lower limit to this precision making our knowledge of a particle inherently uncertain. More specifically, if one knows the precise momentum of the particle, it is impossible to know the precise position, and vice versa. This relationship also applies to energy and time, in that one cannot measure the precise energy of a system in a finite amount of time.
More clearly:. Aside from the mathematical definitions, one can make sense of this by imagining that the more carefully one tries to measure position, the more disruption there is to the system, resulting in changes in momentum. For example compare the effect that measuring the position has on the momentum of an electron versus a tennis ball. These photon particles have a measurable mass and velocity, and come into contact with the electron and tennis ball in order to achieve a value in their position.
When the photon contacts the electron, a portion of its momentum is transferred and the electron will now move relative to this value depending on the ratio of their mass. The larger tennis ball when measured will have a transfer of momentum from the photons as well, but the effect will be lessened because its mass is several orders of magnitude larger than the photon.
To give a more practical description, picture a tank and a bicycle colliding with one another, the tank portraying the tennis ball and the bicycle that of the photon.
The sheer mass of the tank although it may be traveling at a much slower speed will increase its momentum much higher than that of the bicycle in effect forcing the bicycle in the opposite direction. All Quantum behavior follows this principle and it is important in determining spectral line widths, as the uncertainty in energy of a system corresponds to a line width seen in regions of the light spectrum explored in Spectroscopy.
It is hard to imagine not being able to know exactly where a particle is at a given moment. It seems intuitive that if a particle exists in space, then we can point to where it is; however, the Heisenberg Uncertainty Principle clearly shows otherwise. This is because of the wave-like nature of a particle. A particle is spread out over space so that there simply is not a precise location that it occupies, but instead occupies a range of positions.
Similarly, the momentum cannot be precisely known since a particle consists of a packet of waves, each of which have their own momentum so that at best it can be said that a particle has a range of momentum. Let's consider if quantum variables could be measured exactly. A wave that has a perfectly measurable position is collapsed onto a single point with an indefinite wavelength and therefore indefinite momentum according to de Broglie's equation.
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