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MODERN PHYSICS NICASTRO and IN THIS PRESENTATION, YOU WILL BE INTRODUCED TO THE FOLLOWING TOPICS: IN THIS PRESENTATION, YOU WILL BE INTRODUCED TO THE FOLLOWING TOPICS: 1. QUANTUM WAVE PACKETS IN THIS PRESENTATION, YOU WILL BE INTRODUCED TO THE FOLLOWING TOPICS: 1. QUANTUM WAVE PACKETS 2. UNCERTAINTY IN MEASUREMENT IN THIS PRESENTATION, YOU WILL BE INTRODUCED TO THE FOLLOWING TOPICS: 1. QUANTUM WAVE PACKETS 2. UNCERTAINTY IN MEASUREMENT 3. MEASURING POSITION IN THIS PRESENTATION, YOU WILL BE INTRODUCED TO THE FOLLOWING TOPICS: 1. QUANTUM WAVE PACKETS 2. UNCERTAINTY IN MEASUREMENT 3. MEASURING POSITION 4. MEASURING VELOCITY IN THIS PRESENTATION, YOU WILL BE INTRODUCED TO THE FOLLOWING TOPICS: 1. QUANTUM WAVE PACKETS 2. UNCERTAINTY IN MEASUREMENT 3. MEASURING POSITION 4. MEASURING VELOCITY 5. HEISENBERG UNCERTAINTY PRINCIPLE IN THIS PRESENTATION, YOU WILL BE INTRODUCED TO THE FOLLOWING TOPICS: 1. QUANTUM WAVE PACKETS 2. UNCERTAINTY IN MEASUREMENT 3. MEASURING POSITION 4. MEASURING VELOCITY 5. HEISENBERG UNCERTAINTY PRINCIPLE 6. WHY THE H.E.P. DOESN’T REALLY APPLY TO “MACROSCOPIC OBJECTS” IN THIS PRESENTATION, YOU WILL BE INTRODUCED TO THE FOLLOWING TOPICS: 1. QUANTUM WAVE PACKETS 2. UNCERTAINTY IN MEASUREMENT 3. MEASURING POSITION 4. MEASURING VELOCITY 5. HEISENBERG UNCERTAINTY PRINCIPLE 6. WHY THE H.E.P. DOESN’T REALLY APPLY TO “MACROSCOPIC OBJECTS” 7. THE COPENHAHEN INTERPRETATION OF QUANTUM THEORY IN THIS PRESENTATION, YOU WILL BE INTRODUCED TO THE FOLLOWING TOPICS: 1. QUANTUM WAVE PACKETS 2. UNCERTAINTY IN MEASUREMENT 3. MEASURING POSITION 4. MEASURING VELOCITY 5. HEISENBERG UNCERTAINTY PRINCIPLE 6. WHY THE H.E.P. DOESN’T REALLY APPLY TO “MACROSCOPIC OBJECTS” 7. THE COPENHAHEN INTERPRETATION OF QUANTUM THEORY 8. QUANTUM FLUCTUATIONS IN THE MACROSCOPIC WORLD, WHAT DOES IT MEAN TO MAKE AN OBSERVATION, OR MAKE A MEASUREMENT??? IN THE MACROSCOPIC WORLD, WHAT DOES IT MEAN TO MAKE AN OBSERVATION, OR MAKE A MEASUREMENT??? LET’S USE A BASEBALL ANALOGY: We “observe” something by receiving light waves that scatter, reflect or are emitted by objects. Our eyes absorb this energy and convert it into information that our brain processes. When the pitcher throws the ball, light rays reflect off the ball and we, with the help of our eyes and brain, are able to locate the position of the ball with a great deal of certainty. We can also determine (with some practice) the speed of the ball, and the path it will take when it reaches the plate. All this information is received because light rays reflect off of the ball. Of course, the actual speed of the ball might be measured using more sophisticated devices (radar gun, photocells, electronic timers, etc.). Our brain processes this information in about one fourth of a second, and sends signals to our muscles to swing the bat at the projected location of the ball! The baseball is “macroscopic”. The energy of the light waves interacting with the ball does not significantly effect its location, trajectory or speed. Therefore, at this level and scale, where the position and momentum of relatively large objects can be accurately measured, the world is said to be “DETERMINISTIC,” that is, capable of using basic laws of physics (i.e., Newton’s Laws of Motion) to predict future events. THIS IS CALLED . . . QUANTIZATION MEANS THAT WE CANNOT OBSERVE THE UNIVERSE WITHOUT AFFECTING IT QUANTIZATION MEANS THAT WE CANNOT OBSERVE THE UNIVERSE WITHOUT AFFECTING IT WHAT DOES THIS MEAN???? QUANTIZATION MEANS THAT WE CANNOT OBSERVE THE UNIVERSE WITHOUT AFFECTING IT WHAT DOES THIS MEAN???? At the QUANTUM (“microscopic”) level, the universe is NONDETERMINISTIC! IF WE ARE TRYING TO LOCATE AN ELECTRON, OR DETERMINE ITS MOTION (MOMENTUM), WE CAN ONLY DO THIS BY CASTING LIGHT ON IT. BEFORE THE SHEER INTENSITY OF THE LIGHT WOULD EASILY AFFECT OUR MEASUREMENT. electron AFTER ? IF WE ARE TRYING TO LOCATE AN ELECTRON, OR DETERMINE ITS MOTION (MOMENTUM), WE CAN ONLY DO THIS BY CASTING LIGHT ON IT. BEFORE THE SHEER INTENSITY OF THE LIGHT WOULD EASILY AFFECT OUR MEASUREMENT. electron BUT REMEMBER, EINSTEIN SAID THAT LIGHT CONSISTS OF “PHOTONS” (LIGHT QUANTA), EACH FREQUENCY HAVING ITS OWN ENERGY (hf). AFTER ? IF WE ARE TRYING TO LOCATE AN ELECTRON, OR DETERMINE ITS MOTION (MOMENTUM), WE CAN ONLY DO THIS BY CASTING LIGHT ON IT. THE SHEER INTENSITY OF THE LIGHT WOULD EASILY AFFECT OUR MEASUREMENT. BUT REMEMBER, EINSTEIN SAID THAT LIGHT CONSISTS OF “PHOTONS” (LIGHT QUANTA), EACH FREQUENCY HAVING ITS OWN ENERGY (hf). SO, WHAT IF WE MADE THE LIGHT SO DIM THAT WE COULD SEND JUST ONE PHOTON TO DETECT THE ELECTRON? BEFORE one photon electron IF WE ARE TRYING TO LOCATE AN ELECTRON, OR DETERMINE ITS MOTION (MOMENTUM), WE CAN ONLY DO THIS BY CASTING LIGHT ON IT. THE SHEER INTENSITY OF THE LIGHT WOULD EASILY AFFECT OUR MEASUREMENT. BUT REMEMBER, EINSTEIN SAID THAT LIGHT CONSISTS OF “PHOTONS” (LIGHT QUANTA), EACH FREQUENCY HAVING ITS OWN ENERGY (hf). SO, WHAT IF WE MADE THE LIGHT SO DIM THAT WE COULD SEND JUST ONE PHOTON TO DETECT THE ELECTRON? BEFORE one photon electron RECALL THAT PHOTONS OF DIFFERENT FREQUENCIES ARE PARTICLE-LIKE IN THEIR INTERACTION WITH OTHER OBJECTS, AND THAT EACH PHOTON CONSISTS OF A TINY “WAVE PACKET” WHICH IS EITHER “COMPACT” (HIGH FREQUENCY, HIGH ENERGY), OR “SPREAD-OUT” (LOW FREQUENCY, LOW ENERGY). WAVE PACKETS NARROW *Photon well localized *Short wavelength *High frequency BROAD *Photon not localized *Long wavelength *Low frequency HEISENBERG’S “QUANTUM MICROSCOPE” Heisenberg devised this thought experiment to show how interactions between an observer and the system under observation result in unavoidable and unpredictable disturbances in the system – a phenomenon that underlies Heisenberg’s Uncertainty Principle. HEISENBERG’S “QUANTUM MICROSCOPE” Heisenberg devised this thought experiment to show how interactions between an observer and the system under observation result in unavoidable and unpredictable disturbances in the system – a phenomenon that underlies Heisenberg’s Uncertainty Principle. The experiment attempts to measure the position and velocity (or momentum) of an electron by shining light on it and detecting the scattered light. But the light has both a wave and a particle nature, and to know precisely where the light is, we need a wave packet of short-wavelength light. BEFORE detector Light source electron HEISENBERG’S “QUANTUM MICROSCOPE” Heisenberg devised this thought experiment to show how interactions between an observer and the system under observation result in unavoidable and unpredictable disturbances in the system – a phenomenon that underlies Heisenberg’s Uncertainty Principle. The experiment attempts to measure the position and velocity (or momentum) of an electron by shining light on it and detecting the scattered light. But the light has both a wave and a particle nature, and to know precisely where the light is, we need a wave packet of short-wavelength light. Using such a packet, we could determine the electron’s position with high precision. AFTER detector Light source electron ? HEISENBERG’S “QUANTUM MICROSCOPE” Heisenberg devised this thought experiment to show how interactions between an observer and the system under observation result in unavoidable and unpredictable disturbances in the system – a phenomenon that underlies Heisenberg’s Uncertainty Principle. The experiment attempts to measure the position and velocity (or momentum) of an electron by shining light on it and detecting the scattered light. But the light has both a wave and a particle nature, and to know precisely where the light is, we need a wave packet of short-wavelength light. Using such a packet, we AFTER Light source electron ? could determine the electron’s position with high precision. detector But its correspondingly high frequency (E=hf) means that the wave packet carries high energy, which imparts momentum to the electron in an unpredictable way, disturbing its velocity. HEISENBERG’S “QUANTUM MICROSCOPE” Heisenberg devised this thought experiment to show how interactions between an observer and the system under observation result in unavoidable and unpredictable disturbances in the system – a phenomenon that underlies Heisenberg’s Uncertainty Principle. But the light has both a wave and a particle nature, and to know precisely where the light is, we need a wave packet of short-wavelength light. RESULT: Good precision of its location, uncertainty about its velocity. AFTER detector Light source electron ? HEISENBERG’S “QUANTUM MICROSCOPE” SO, WHAT IF WE USE A LOW-ENERGY PHOTON? By using a low energy photons have a broad wave packet form (more “spread out”), so it’s not precisely localized. BEFORE detector Light source electron HEISENBERG’S “QUANTUM MICROSCOPE” SO, WHAT IF WE USE A LOW-ENERGY PHOTON? By using a low energy photons have a broad wave packet form (more “spread out”), so it’s not precisely localized. RESULT: the experiment measures velocity (momentum) precisely, but its position remains uncertain. AFTER detector Light source electron ? HEISENBERG’S “QUANTUM MICROSCOPE” BOTTOM LINE: THE STANDARD INTERPRETATION OF QUANTUM PHYSICS IMPLIES THAT IT IS MEANINGLESS TO TALK ABOUT A SUBATOMIC PARTICLE AS HAVING SIMULTANEOUSLY BOTH A WELL-DEFINED VELOCITY AND A WELL-DEFINED POSITION. HEISENBERG’S “QUANTUM MICROSCOPE” BOTTOM LINE: THE STANDARD INTERPRETATION OF QUANTUM PHYSICS IMPLIES THAT IT IS MEANINGLESS TO TALK ABOUT A SUBATOMIC PARTICLE AS HAVING SIMULTANEOUSLY BOTH A WELL-DEFINED VELOCITY AND A WELL-DEFINED POSITION. THIS IS THE “HEISENBERG UNCERTAINTY PRINCIPLE”. MATHEMATICALLY THIS CAN BE STATED: MATHEMATICALLY THIS CAN BE STATED: The uncertainty in velocity momentum (remember P = mv) The uncertainty in position Planck’s Constant WHAT THIS MEANS The uncertainty in velocity momentum (remember P = mv) Planck’s Constant The uncertainty in position AS AND AS ∞ 0 0 ∞ This uncertainty leads to many strange things. For example, in a Quantum Mechanical world, I cannot then predict where a particle will be with 100 % certainty. I can only speak in terms of probabilities. For example, I can say that an atom will be at some location with a 99 % probability, but there will be a 1 % probability it will be somewhere else (in fact, there will be a small but finite probability that it will be found across the Universe). This is strange. This uncertainty leads to many strange things. For example, in a Quantum Mechanical world, I cannot then predict where a particle will be with 100 % certainty. I can only speak in terms of probabilities. For example, I can say that an atom will be at some location with a 99 % probability, but there will be a 1 % probability it will be somewhere else (in fact, there will be a small but finite probability that it will be found across the Universe). This is strange. BUT WHY DON’T WE OBSERVE THIS IN THE MACROSCOPIC WORLD? IF WE RESTATE THIS EQUATION, USING THE PRODUCT mv FOR MOMENTUM, THEN m Δv Δx = h Δv Δx = h m WHICH MEANS THAT THE LARGER THE MASS, THE SMALLER THE UNCERTAINTY. THAT’S WHY MACROSCOPIC MASSES HAVE ALMOST NO UNCERTAINTY!!! A SECOND FORM OF THE UNCERTAINTY PRINCIPLE IS which perhaps has an even greater impact on our understanding of the behavior of matter, involves the measurement of the energy of a particle, and the time available to make the measurement. The shorter the time available, the less accurate the energy measurement is. If ΔE is the uncertainty in the results of our energy measurement, and Δt the time we had to make the measurement, then ΔE and Δt are related by the variation above. A SECOND FORM OF THE UNCERTAINTY PRINCIPLE IS which perhaps has an even greater impact on our understanding of the behavior of matter, involves the measurement of the energy of a particle, and the time available to make the measurement. The shorter the time available, the less accurate the energy measurement is. If ΔE is the uncertainty in the results of our energy measurement, and Δt the time we had to make the measurement, then ΔE and Δt are related by the variation above. LET’S LOOK AT AN EXAMPLE: A device that has become increasingly important in research, particularly in the study of fast reactions in molecules and atoms, is the pulsed laser. The lasers we have used in various experiments are all continuous beam lasers. The beam is at least as long as the distance from the laser to the wall. A device that has become increasingly important in research, particularly in the study of fast reactions in molecules and atoms, is the pulsed laser. The lasers we have used in various experiments are all continuous beam lasers. The beam is at least as long as the distance from the laser to the wall. The beam is at least as long as the distance from the laser to the wall. If we had a laser that we could turn on and off in one nanosecond, the pulse would be 1 foot or 30 cm long and contain 30cm 6 x 10– 5 cm/wavelength = 5 x 105wavelengths Even a picosecond laser pulse which is 1000 times shorter, contains 500 wavelengths. Some of the recent pulsed lasers can produce a pulse 500 times shorter than that, only 2 femtoseconds (2 x 10– 15 seconds) long. These lasers emit a pulse that is only one wavelength long. If we had a laser that we could turn on and off in one nanosecond, the pulse would be 1 foot or 30 cm long and contain 30cm 6 x 10– 5 cm/wavelength = 5 x 105wavelengths Even a picosecond laser pulse which is 1000 times shorter, contains 500 wavelengths. Some of the recent pulsed lasers can produce a pulse 500 times shorter than that, only 2 femtoseconds (2 x 10– 15 seconds) long. These lasers emit a pulse that is only one wavelength long. If we want to measure the energy of the photons in such a pulse, we only have 2 femtoseconds to make the measurement because that is how long the pulse takes to go by us. In the notation of the uncertainty principle Δt = 2 x 10–15 sec = 2 femtoseconds this is the time available to measure the energy of the photons in our laser pulse Let us suppose that the laser produces red photons whose wavelength is 6.2 x 10– 5 cm, about the wavelength of the laser we have been using. According to our usual formula for calculating the energy of the photons in such a laser beam we have Ephoton = 12.4 x 10– 5 eV cm 6.2 x 10– 5 cm = 2eV Now let us use the uncertainty principle in the form ΔE ≥ h Δt to calculate the uncertainty in any measurement we would make the energy of the photons in the 2 femtosecond laser beam. We have ΔE ≥ h Δt ≥ 6.63 x 10– 34 J sec 2 X 10– 15 sec ≥ 3.31 x 10– 19 J Converting ΔE from J to electron volts, we get ΔE ≥ 3.31 x 10– 19 J 2 eV The uncertainty in any energy measurement we make of these photons is as great as the energy itself! 1.6 Å~ 10– 19 J/eV ≈ If we try to measure the energy of these photons, we expect the answers to range from E – ΔE = 0 eV up to E + ΔE = 4 eV . The uncertainty in energy is a consequence of the energy/time variation of the Uncertainty Principle. The interaction time is known to a high degree of precision. If we try to measure the energy of these photons, we expect the answers to range from E – ΔE = 0 eV up to E + ΔE = 4 eV . The uncertainty in energy is a consequence of the energy/time variation of the Uncertainty Principle. The interaction time is known to a high degree of precision. The same variation is vital in the field of QUANTUM ELECTRODYNAMICS, where an apparent violation of energy conservation can be rationalized by an interaction time within the uncertainty limits imposed. This leads to the “creation” of “VIRTUAL PARTICLES” that last for a very short time, but can explain the energies produced in a quantum process. Such events are known as “QUANTUM FLUCTUATIONS” and they form the basis for our understanding of particle interactions. A Λ(1520) particle can be “created” if the total energy (in the center of mass system) of the incoming particles equals the rest mass energy of the Λ(1520). A 2 eV photon suddenly creates a positronelectron pair. A short time later the pair annihilates, leaving a 2 eV photon. In the long term, energy is conserved Quantum fluctuation. The uncertainty principle allows such an object to suddenly appear, and then disappear. BUT ANOTHER ASPECT OF QUANTUM THEORY IS THAT PARTICLES, LIKE ELECTRONS, HAVE NO REAL PHYSICAL SHAPE (LIKE A BASEBALL), AND HAVE A WAVE-LIKE PROPERTY (NOT A PHYSICAL WAVE LIKE A WATER OR SOUND WAVE). THIS WAVE-LIKE PROPERTY, A CONSEQUENCE OF WAVE-PARTICLE COMPLIMENTARITY, SUGGESTS THAT THE ELECTRON IS MOST LIKELY WHERE THE WAVES ARE “STRONGER”(LARGER AMPLITUDES). SO, INSTEAD OF BEING A “HARD PARTICLE”, IT IS A PROBABILISTIC WAVE WHICH INDICATES THE “LIKELIHOOD” OF THE ELECTRON’S PRESENCE IN SPACE. BUT ANOTHER ASPECT OF QUANTUM THEORY IS THAT PARTICLES, LIKE ELECTRONS, HAVE NO REAL PHYSICAL SHAPE (LIKE A BASEBALL), AND HAVE A WAVE-LIKE PROPERTY (NOT A PHYSICAL WAVE LIKE A WATER OR SOUND WAVE). THIS WAVE-LIKE PROPERTY, A CONSEQUENCE OF WAVE-PARTICLE COMPLIMENTARITY, SUGGESTS THAT THE ELECTRON IS MOST LIKELY WHERE THE WAVES ARE “STRONGER”(LARGER AMPLITUDES). SO, INSTEAD OF BEING A “HARD PARTICLE”, IT IS A PROBABILISTIC WAVE WHICH INDICATES THE “LIKELIHOOD” OF THE ELECTRON’S PRESENCE IN SPACE. French physicist Louis deBroglie, in 1929, suggested that if waves can have particle properties, then particles should have wave properties. The smaller the particle, the more pronounced are its wave properties. SO, AN ELECTRONS SHOULD HAVE DISTINCT WAVELIKE PROPERTIES, LIKE FREQUENCY AND WAVELENGTH! SO, AN ELECTRONS SHOULD HAVE DISTINCT WAVELIKE PROPERTIES, LIKE FREQUENCY AND WAVELENGTH! Planck’s Constant “deBroglie Wavelength velocity mass THIS WOULD ANSWER THE QUESTION ABOUT WHY ELECTRONS DO NOT LOSE ENERGY IN THEIR POSITION AROUND THE NUCLEUS OF AN ATOM, AND THEREFORE WHY ATOMS EXIST!!! IF AN ELECTRON, ENCIRCLING THE NUCLEUS OF ITS ATOM, HAS AN EXACT MULTIPLE (n) OF WAVES, IT WOULD BE IN A STANDING WAVE PATTERN AROUND THAT NUCLEUS. IF AN ELECTRON, ENCIRCLING THE NUCLEUS OF ITS ATOM, HAS AN EXACT MULTIPLE (n) OF WAVES, IT WOULD BE IN A STANDING WAVE PATTERN AROUND THAT NUCLEUS. (YOU REMEMBER STANDING WAVE PATTERNS FROM OUR 1ST SEMESTER WORK IN WAVE THEORY.) Length of SWP with six nodes If this standing wave were twisted into a “circular” pattern, so that the circumference Were exactly this length, then you would see something like this: This would represent one possible “shell” location for electrons around a nucleus. This would represent one possible “shell” location for electrons around a nucleus. IT WOULD ALSO SERVE TO PREDICT THE SIZES OF “ALLOWABLE” SHELLS WHERE ELECTRONS MAY BE FOUND (AT A DISTANCE “r” FROM THE NUCLEUS). SINCE IT WOULD REPRESENT A “STANDING WAVE PATTERN,” ENERGY WOULD NOT BE LOST, BUT “RECYCLED” WITHIN THE WAVE ITSELF. IT WOULD ALSO SERVE TO PREDICT THE SIZES OF “ALLOWABLE” SHELLS WHERE ELECTRONS MAY BE FOUND (AT A DISTANCE “r” FROM THE NUCLEUS). HERE’S A DEMONSTRATION OF deBROGLIE WAVE PRODUCED BY OSCILLATING A HOOP AT RESONANT FREQUENCIES. Bohr’s atom showed electrons as particles similar to planets going around the sun. de Broglie’s atom treats electrons more as waves with wave patterns that fit symmetrically within the atom. In both cases, the energy levels of the electrons must go up by an incremental quantity (quantum). Both of these played a role in the modern theory of the atom and the structure of the electrons. As elements were built by adding one proton and one electron at a time, the electrons would find a position and shape that maximized their distance from each other (from repulsion) yet kept them as close as possible to the positive nucleus (attraction). The way they positioned themselves followed a fairly basic pattern known as its quantum number.