Probability waves
The idea of the probability wave was a pivotal insight by Max Born in 1926. He said, you have experimental evidence that waves play a role and experimental evidence that probabilities play a role, so perhaps what we are dealing with is a probability wave [1]. So in analysing the motion of a particle, we should think of it in the context of a wave undulating from here to there. In the double slit, the bright and dark bands on the screen represent a pattern of high and low values that according to quantum mechanics corresponds with a pattern of high and low probabilities for where the electron will land. Locations where the wave’s values are large, near its peaks and troughs, are locations where the particle is likely to be found. Where the probability wave’s values are small are locations where the particle is unlikely to be found. Each electron’s probability wave passes through both slits, and it is the union of these two partial waves that dictates the probabilities for where the electrons (or photons, neutrinos, muons, quarks – every fundamental particle) land. So, that is why the second slit affects the results:
Bright regions occur where the waves reinforce each other, yielding much agitation, and dark regions where the waves cancel yielding no agitation. So each particle is associated with a wave, and decades of experiments have shown that on average each particle has the same probability of being found at any given location In any single measurement, one can’t predict where any given electron will be, but if we substitute for one experiment the statistical distribution of many measurements, the regularity speaks to the likelihood or probability of finding an electron at any particular location. Thus quantum mechanics says that because electrons come in waves, an electron wave must be interpreted from the standpoint of probability, a bit like trying to determine the position of a submerged rock by the movement of the water which betrays its position, resulting in us being able to determine the rock’s position only to within a margin of error equal to the length of the wave cycles, that is, the wave’s wavelength[2].
It is possible to fire one electron at a time at the split screen, but even by firing one electron at a time over a period of time, a wave-like interference pattern is built up on the screen just the same as it would have had the photons been fired in a stream. Remember that an electron and indeed all particles are both particles and waves, and if you plot the electron’s course, you take out its wavelike properties and reduce it to a particle, so the interference pattern on the screen disappears[3].
On one view, the same probability wave picture can be said to emerge not only for all of nature’s fundamental particles, but also for macroscopic objects such as bullets, cricket balls, planets and stars as well. But in the case of macroscopic objects, the wave will be narrowly peaked, there being nearly a 100% probability that they will be located where the object is peaked and a miniscule probability (a shade over 0%) that it is anywhere else[4].
On the other hand, the probability wave for a microscopic object, say a single particle, is typically widespread, and the smaller the object, the more spread out its probability wave typically is, in other words with substantial probabilities of it being at a variety of locations, a totally foreign concept in a Newtonian world. So where macroscopic objects are concerned, quantum theory offers only the most minimal refinement to Newton’s laws which may be said to predict almost precisely the trajectory of macroscopic objects.
The reason the detection of wavelength behaviour is not readily apparent when dealing with macroscopic objects is due to the smallness of Planck’s constant, and the wavelength of the matter waves associated with such everyday objects is very tiny. In order to reproduce wavelike interference effects, the separation of the two slits must be about the same size as the wavelength of the objects (photons or electrons) that are doing the interfering, and consequently it is not possible to devise an experiment that will show interference with bullets or indeed any other macroscopic or everyday object[5].
[1] Greene (2011), 197. See also next page.
[2] Greene (2000), 113.
[3] Greene (2005), Ch 7; Jessica Griggs, “To be quantum is to be uncertain”, New Scientist, 23 June 2012, op cit, 8.
[4] Greene (2011), 199; Greene (2000), 106.
[5] Tony Hey and Patrick Walters, The New Quantum Universe, (2003), 36.
It is possible to fire one electron at a time at the split screen, but even by firing one electron at a time over a period of time, a wave-like interference pattern is built up on the screen just the same as it would have had the photons been fired in a stream. Remember that an electron and indeed all particles are both particles and waves, and if you plot the electron’s course, you take out its wavelike properties and reduce it to a particle, so the interference pattern on the screen disappears[3].
On one view, the same probability wave picture can be said to emerge not only for all of nature’s fundamental particles, but also for macroscopic objects such as bullets, cricket balls, planets and stars as well. But in the case of macroscopic objects, the wave will be narrowly peaked, there being nearly a 100% probability that they will be located where the object is peaked and a miniscule probability (a shade over 0%) that it is anywhere else[4].
On the other hand, the probability wave for a microscopic object, say a single particle, is typically widespread, and the smaller the object, the more spread out its probability wave typically is, in other words with substantial probabilities of it being at a variety of locations, a totally foreign concept in a Newtonian world. So where macroscopic objects are concerned, quantum theory offers only the most minimal refinement to Newton’s laws which may be said to predict almost precisely the trajectory of macroscopic objects.
The reason the detection of wavelength behaviour is not readily apparent when dealing with macroscopic objects is due to the smallness of Planck’s constant, and the wavelength of the matter waves associated with such everyday objects is very tiny. In order to reproduce wavelike interference effects, the separation of the two slits must be about the same size as the wavelength of the objects (photons or electrons) that are doing the interfering, and consequently it is not possible to devise an experiment that will show interference with bullets or indeed any other macroscopic or everyday object[5].
[1] Greene (2011), 197. See also next page.
[2] Greene (2000), 113.
[3] Greene (2005), Ch 7; Jessica Griggs, “To be quantum is to be uncertain”, New Scientist, 23 June 2012, op cit, 8.
[4] Greene (2011), 199; Greene (2000), 106.
[5] Tony Hey and Patrick Walters, The New Quantum Universe, (2003), 36.