This book is Creative Commons Attribution License 4. Skip to Content Go to accessibility page. University Physics Volume 3 7. My highlights. Table of contents. Chapter Review. Modern Physics. Answer Key. By the end of this section, you will be able to: Describe the physical meaning of the position-momentum uncertainty relation Explain the origins of the uncertainty principle in quantum theory Describe the physical meaning of the energy-time uncertainty relation.
Figure 7. The Uncertainty Principle Large and Small Determine the minimum uncertainties in the positions of the following objects if their speeds are known with a precision of 1. Hint : According to early experiments, the size of a hydrogen atom is approximately 0. The ground-state wave function of this system is a half wave, like that given in Example 7. Note that this function is very similar in shape to a Gaussian bell curve function. We can take the average energy of a particle described by this function E as a good estimate of the ground state energy E 0 E 0.
This average energy of a particle is related to its average of the momentum squared, which is related to its momentum uncertainty. Is the emitted radiation monochromatic? Strategy We invert Equation 7. However, the surprise comes when he narrows the slit even more and the projected light takes a horizontal form like this —.
He interprets the vertical line as revealing the particles location where momentum cannot be seen because there are no horizontal lines to show it. Then, vertical lines become horizontal lines to reveal the momentum, but then there are no horizontal lines to give information about the position.
However, in the 4th frame, the light does not conform to expectation because the light sliver appears in the horizontal orientation even though it is projected vertically. I would say that in frames the light is manifesting as a particle, but in frame 4, it is manifesting as a wave because we see diffraction occurring. However, I would interpret this experiment as demonstrating the particle-wave duality. The circular and vertical projected line is showing the particle manifestation of light because the photons are doing what you would expect point particles would do — they are traveling in straight lines from the projector to the screen.
However, when the transition occurs to a horizontal line with a vertical slit, diffraction is occurring, and the light is behaving as a wave. So, we see that the inability to know location and velocity at the same time is the same problem as not being about to observe a wave and a particle at the same time.
In Copenhagen, when one measures the wave, it collapses to a particle — so you cannot detect both particle and wave simultaneously.
The wave must be inferred from the pattern of dots on the screen in the double-slit experiment. Certainly, one can think of examples in which this problem of inability to determine location and speed can be circumvented. If an electron or other particle is shot from an electron gun to a screen, one can know the location of the particle at the point of origin the gun and the location of the particle at the point of destination the screen and the time it took the particle to travel from gun to screen.
Moreover, consider that the first terrestrial measurement of the speed of light was done by Hippolyte Fizeau in when he projected a pulsed beam of light onto a distant mirror and measured the time it took for the light to go to and return from the mirror. This occurred long before quantum theory was born, and he was able to know the location of a light beam particle and wave in three locations and determine the speed of it.
I suppose he did not get the memo coming backward in time that you cannot know the location and speed of photons at the same time. Furthermore, it is difficult to know how classical computers and now quantum computers which are supposedly in development could operate with such certainty in the midst of such uncertainty. If one defines a particle as a small piece of matter that has boundaries and a definite location in space and time, then the problem must be a measurement problem.
A particle has a definite location even though there might be a wave which occupies multiple points in space associated with it. To wit, if a particle has a distinct location, rather than multiple locations as the Copenhagen interpretation says, then it should be locatable with a beam of light of low enough frequency to hit the particle and cast a shadow on a screen. When Rutherford hit the nucleus of a gold foil atom with an alpha particle Helium nucleus , and the alpha particle was deflected, was he hitting a ghost wave or something solid protons and neutrons with a definite location?
On the other hand, when the alpha particle missed the nucleus, it passed through the electron cloud, or the electron was too small in the essentially empty space between the nucleus and the electron to affect the alpha particle.
But then Copenhagen says a particle can have a superposition of locations and only when one measures it, does the wave collapse and condense to one location. Here, Copenhagen confuses particle and wave.
A wave can be spread out over multiple points in space and have a superposition of localities, and a researcher cannot pinpoint one location where it exists — but a particle cannot occupy multiple positions -even though it might have the potential to be in multiple locations.
So, when you measure the wave, it collapses to a particle a la Copenhagen and now you have its location, but since its velocity has been changed with your measuring device, its original velocity cannot be known. What exactly is the relationship between a particle and a wave in the Copenhagen view. In one depiction I have seen, the particle is embedded in the wave and the wave function must be collapsed to determine where the particle is.
So, the particle and the wave can exist at the same time. In another depiction, the wave and particle do not exist at the same time. First, the quantum is a wave occupying many points in space, but when it hits a screen or is tampered with in some way, the wave immediately condenses to a particle. All-Wave Theories and Uncertainty The Copenhagen interpretation is more or less synonymous with quantum mechanics particle can be in a superposition of states simultaneously, the observer cannot be detached from the observed, the consciousness of the experimenter determines the outcome of the experiment, there is no mind-independent, objective reality.
Instead the universe splits so that each wave of probability becomes realized in some universe somewhere as said previously, the cat is alive in one universe, dead in the other. There are no particles in this view only disturbances in a quantum field so there is no particle-wave duality and no need to try to locate a particle and find its momentum at the same time.
The Uncertainty principle is null and void in this view since a wave is a disturbance in a field and never a point particle. Even when they see a small dot on a screen in the double-slit experiment, QFTers insist that the dot was a small wave oscillating in 3D to give the appearance of a particle. The wave has been shrunk from infinity to a localized place on the screen. Energy-Time Conjugate Another conjugate incompatibility or inverse relationship is time and energy, i.
It goes the same way as location-momentum - the more you know about the time, the less you know about the energy and vice versa. Again, is this a measurement problem or does a particle not have a certain energy at a certain time?
To say that a particle does not have a certain energy at a definite time seems like an oxymoron. It would seem much more logical to say we cannot know how much energy a particle had at a definite time because of the shortcomings of our measurement. Einstein had the perfect thought experiment to refute this energy-time conjugate. He imagined a radioactive clock that emits light randomly attached to weight scale— all suspended from a ceiling.
When the clock emits a photon, the scale would register a loss of mass and the time would be recorded instantly; thus, one would know the energy level and time simultaneously. Bohr became visibly upset with this thought experiment because he believed it undermined the validity of quantum theory.
Hence one cannot know exactly when the energy was lost because of the limitation of the speed of light and degree of gravity. For example, if the measurement is recorded by an experimenter, there is a certain amount of time that elapses between the event carried by light and the visual perception of the event.
If one accepts relativity, the clock and the scale are traveling through space at the same speed, and they are in the same level of gravity, so the clock is doing the recording, not an observer who has to wait for the light from the clock to reach her eye. Certainly, Bohr, the primary author of the Copenhagen interpretation, believed that time-energy was a measurement problem because the observer changes the variables of time and energy by the act of observation.
Therefore, every quantum conjugate problem is a measurement problem because the observer is part of the experiment and therefore affects the outcome.
For example, it is hard to believe that an astronomer looking at starlight that was emitted a thousand lightyears ago could affect that star in any way.
However, John Wheeler apparently believed that the astronomer affects the star and that his influence goes backwards in time according to the quantum eraser double-slit experiment Folger Such an idea strains the level of credibility and the boundaries of science in my book, but it comes directly from the Copenhagen playbook that the observer always affects the object of study. Now contrast this passive observation looking at starlight with active observation where the researcher hits a particle with high-frequency light and knocks it off its trajectory.
Certainly, the researcher would affect the object of study is this case of active, participant observation. Despite this absurdity in the Copenhagen interpretation revealed by Schrodinger, the Copenhagen interpretation is still the dominant view in quantum theory according to Sean Carrol As mentioned earlier, Carrol says that many physicists are defecting from the Copenhagen to the Many Worlds Interpretation, an even more absurd interpretation which is being called a theory by people like David Deutsch Newer Interpretations of Uncertainty and the Copenhagen Interpretation For those who want to deny that Heisenberg thought of the uncertainty principle as a measurement problem, Jussi Lindgren and Jukka Liukkonen would beg to differ.
Moreover, in their study, Lindgren and Liukkonen concluded that the correlation between a location and momentum, i. In other words, there is an objective reality independent of the observer where location and momentum are linked at the same time. The results suggest that there is no logical reason for the results to be dependent on the person conducting the measurement. They contend that there is nothing that suggests that the consciousness of the person in some psychic way would create a certain reality or outcome.
Hence, their interpretation of quantum mechanics supports classical scientific principles and brings rationality to quantum theory. It is interesting that it took about years for some physicists to say what independent researchers, with no vested interest in a theory, have been saying, using rational, scientific realism, from the first time they encountered quantum physics and the Uncertainty Principle. One should keep in mind that the founders of quantum theory were heavily influenced by Eastern mysticism.
Both Bohr and Heisenberg had gurus who helped them develop their theories according to Fritjof Capra. David Bohm also had a guru that helped him develop his theories. While Eastern mysticism may be interesting in a philosophical sense, it is contrary to the scientific method where hypotheses must be falsifiable. Science does not need mysticism and mysticism does not need science, but man needs both.
Mysticism belongs in the realm of religion and the arts and perhaps the humanities, but not science. Conclusions and Summary 1. The meaning of the Heisenberg Uncertainty Principle hinges largely on the definition of a particle and wave. In this paper, a particle is a piece of subatomic matter-energy mattergy. Although it is usually part of an atom, it can exist independently as well. It can take the form of plasma, gas, liquid or solid depending on the level of heat energy and can be condensed to a solid mass in low energy situations.
It exists in a definite place at a definite time — it cannot be in multiple places at the same time. Waves can occupy multiple points in space and may be associated with a particle, but a true particle cannot. A particle can, however, have the potential of occupying multiple places at different times but can actually occupy only one place at a time.
However, the potentiality of occupying many different states can exist at one time. Big Bang theorists say that in the early universe, there was only radiation photons , and as the universe expanded and cooled, all the particles in the Standard Model were condensed from the radiation, therefore, the photon must be the basic indivisible unit of matter energy as defined by Planck.
Copenhagen indicates that there is a particle-wave duality, but Quantum Field Theorists and Many Worlds advocates say that there are only waves, no particles. This theory is forced into the trap of saying that our senses deceive us when we interact with hard matter held together by the strong nuclear force and electromagnetism.
If there are no particles, only waves, then Quantum Field Theory would have nothing to say about the Uncertainty Principle which acknowledges the existence of particles. The velocity of a quantum particle cannot usually be determined in the classical way of locating the particle in at least two points in space and measuring the time it takes for the particle to traverse from one point to the other because determining the location of the particle affects its velocity.
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