Why does determining the position of an electron decrease the certainty of its velocity?

Question

Why does determining the position of an electron decrease the certainty of its velocity?

Answer 1

That's a very good question. Heisenberg's uncertainty principle as you know says you can't know the velocity and position of an electron.



I used to mentally reword the principle to say WE can't with EXISTING TECHNOLOGY ACTIVELY measure both the position and velocity of an electron. This is totally wrong but it helped me hold on to the principle until I understood it better.



Okay let's take a quick look at atomic structure. We learnt early on that atoms were made of protons neutrons and electrons and the electrons orbited the nucleus in shells like the planets orbit the sun. This is what is known as Bohr's model and it's a great way to visualise an atom when we're first learning. However in reality these sub atomic particles behave as much like waves as they do particles and the electrons don't actually orbit the nucleus of an atom but rather they could be anywhere around the atom but are most likely to be found in sometimes exotic shaped probability distribution diagrams known as "orbitals". However, it is the fact that electrons, protons neutrons and photons etc behave as much like waves as they do particles that is at the foundation of this uncertainty principle.



Firstly let me clarify what the uncertainty principle is saying. It is possible to know both the position and velocity of any sub atomic particle but the more accurately you can know the position, the less accurately you can know the velocity and vice versa.



Without going into any maths, just try to consider a boat on the ocean, let's say it's a huge ocean liner. The waves on the ocean liner make very little change to it's momentum or its position, in the same way objects we can see with our unaided eyes are not affected by any noticeable amount by the light reflecting off them which we can use to measure stuff like their position and their velocity. When we get to measurements of extreme accuracy on extremely small objects like electrons every time a photon hits it, the impact it makes on its position or velocity is relatively huge. Using my ocean analogy again think of a guy in a life jacket bobbing up and down on the wave. Now remember those waves are the light that we use to measure the position and velocity of the sub atomic particle (e.g. the guy in the life jacket). Every time a wave crashes into him his position and velocity are changed. Thus observing the electron changes its position and velocity. Now if we choose a wave that has very low energy thus giving us a high degree of certainty as to the sub atomic particle's position the low energy wave must have a large wavelength and therefore the position of the particle is not accurately measured. Similarly if we use say a light beam with a very tiny wavelength so that we can resolve the position with incredible accuracy we make a huge difference to the velocity of that sub atomic particle since very low wavelength light has very high energy. Hence the more accurately you try to measure the velocity the less accurately you can know the position and vice versa. This is in fact true of everything but for all practical purposes the uncertainty principle only becomes important when we are dealing with very small things like sub atomic particles.



So you see this correlation between accuracy of measurement of position and velocity is down to the inverse correlation between energy and wavelength of waves and not due to the technological limitations of the researcher.



If it's any consolation this uncertainty principle was extremely controversial and Neils Bohr and Albert Einstein debated it for quite some time and it was precisely this quantum uncertainty that prompted Einstein to give his famous quote "God does not play dice".

Answer 2

Because of the methods used to determine the position of it. And, even if we were to find "better methods", they still could not surpass the accuracy limit according to the Heisenberg Uncertainty Principle, because that principle is based upon the best theoretically possible methods for detection.



We are confused by this because it is super easy to determine position, velocity, mass, and momentum of any object easily held in our hands, and the Heisenberg Uncertainty Principle, if we try to apply it to a typical baseball, will produce uncertainties which are too small to even worry about.





For objects smaller than the atom though, the method you determine its position and momentum can be problematic.



Low frequency long wavelength light rays are subjected significantly to diffraction phenomena, whereby the resulting photon's detection location could really indicate a range of positions for the electron, rather than just one certain position.



You can combat this by selecting higher frequency light with shorter wavelength and making diffraction less significant. However if you select too high of a frequency for this purpose, you will "beat it to death" and disturb it away from its path.





So, you need to select light, or whatever your observing method may be, within a very sensitive wavelength range to get even the fundamentally highest accuracy results. And, those fundamentally highest accuracy results are subjected to the Heisenberg Uncertainty Principle, as an upper limit for precision capabilities.

Answer 3

Because measuring an electron position requires to 'illuminate' it in some way, and/or to extract a bit of energy from it to drive the sensor. The little energy given and/or taken away will influence the speed it has.

Answer 4

Heisenberg's uncertainty principle... you cannot simultaneously know the position and momentum of an electron. momentum = mass * velocity. so if you know position, you essentially can't know velocity