Quantum Physics

1. Quantum Physics Dan Hooper Fermilab Saturday Morning Physics

2. Physics in 1900 The ideas of Isaac Newton continued to provide the foundations of physics Our understanding of electricity, magnetism, heat had grown steadily over the past 100-150 years From the perspective of 1900, it looked like physicists had managed to understand all of the phenomena in our world (almost…)

3. Problems with Physics in 1900 • Gravitational mass and inertial mass • Orbit of the planet Mercury • Speed of light • Power source of the Sun • Spectrum of light • Stability of atoms

4. Problems with Physics in 1900 • Gravitational mass and inertial mass • Orbit of the planet Mercury • Speed of light • Power source of the Sun • Spectrum of light • Stability of atoms Solved by Einstein’s Theory of Relativity Solved by Quantum Mechanics

5. Problems with Physics in 1900 Where does the Sun get its energy?

6. Problems with Physics in 1900 Why does light have the spectrum we observe?

7. Problems with Physics in 1900 Why don’t atoms collapse?

8. Our Understanding of Light in 1900 Circa 1900, physicists thought of light as waves of electromagnetic radiation Very successful theory - electromagnetism was the greatest accomplishment in physics since Isaac Newton

9. Our Understanding of Light in 1900 By this time, physicists had measured the spectra of light that is emitted by objects at a given temperature and in equilibrium – the blackbody spectrum The problem was that when physicists calculated what this spectrum should look like, their results did not agree with the measurements

10. Our Understanding of Light in 1900 Based on the data, the German physicist Max Planck reverse engineered a formula that matched the observed spectrum To explain why this formula worked, Planck had to conjecture that for some unknown reason, light-waves were only radiated by quantities of energy that are proportional to their frequency, E=h𝜈 Planck (and others at the time) thought this had to do with the matter that was radiating the light (as opposed to the light itself)

11. The Photoelectric Effect

14. Einstein’s Explanation of the Photoelectric Effect (1905) Einstein postulated that light waves were made up of individual pieces - called “quanta” of light (now called photons) - each with an amount of energy proportional to their frequency E=h𝜈 Low frequency light was thus, according to Einstein, made up of low energy photons that could not free electrons from the metal plate, and thus couldn’t generate electric current High frequency light, in contrast, was made up of photons with more energy, which could free electrons, creating current

15. Einstein’s Explanation of the Photoelectric Effect (1905) Einstein proposal was radical Meant that light was both a wave, and was made up of particles The quantum revolution had been born

16. Into The Atom In the early 20th century, as the nature of the atom was beginning to become understood, questions about the stability of atoms and the spectrum of light from atoms persisted

17. Louie De Broglie Niels Bohr

18. Electrons As Waves Standing waves (those with an integer number of wavelengths around the atom) are the configurations that can exist This is just like standing wave patterns on a vibrating string

21. “Quantized” Energy Levels!

22. Solutions To Atoms’ Problems Light from atoms would be emitted when an electron moved from an energetic standing wave pattern to a lower energy pattern  discrete groups of spectral lines for each type of atom!

23. Solutions To Atoms’ Problems Light from atoms would be emitted when an electron moved from an energetic standing wave pattern to a lower energy pattern  discrete patterns of spectral lines for each type of atom! For each type of atom, there is a minimum energy standing wave; electrons cannot lose any more energy from this state  the atom was stable! Lowest energy state (nowhere to go from here)

24. Particles and Waves Bohr’s model of the atom requires that electrons we not only particles, but also act like waves Louie De Broglie extended this further, and postulated that all matter has a wave-like nature In particular, De Broglie said:  = h/p In other words, De Broglie was just proposing that electrons (and other forms of matter) act like light does! p=momentum h=6.626x10-34 Joule-seconds

25. What Does it Mean to be a Wave?

26. What Does it Mean to be a Wave?

27. Are You A Wave? • According to De Broglie, yes. But only barely. • A 100 kg person walking at 1 m/s has a wavelength of ~6x10-36 m • not remotely measurable

28. Are You A Wave? • The wave-like behavior of matter becomes notable only in the sub-atomic world: • An electron (m=9x10-31kg) moving at 10,000 km/s has a wavelength of ~10-10 m • about the size of a typical atom! • Electrons are waves as big as the atoms they are part of! Our Newtonian picture of electrons orbiting a nucleus like planets orbiting the Sun is not really correct

29. Are You A Wave? Instead of electrons being in planet-like orbits, they are unchanging standing waves, “smeared out” over the volume of the atom

30. But What is “Waving”? • Water waves are made up of water molecules; peaks of the waves are where there is the most water • Sound waves are made up of atoms/molecules in high pressure and low pressure patterns • Waves on a string are the motion of atoms/molecules • Question: If photons and electrons (and other quantum particles) are waves, what is waving?

31. Waves of… Probability? At first, no one really knew what to make of the wave-like nature of matter. Then, in 1925, Max Born made the bold claim that to make sense of quantum waves, we had no choice to interpret them in terms of probabilty The shape of a quantum wave (called the wavefunction) tells us in what state it is likely that we will find the system to be in if we were to measure it

32. Quantum Waves And Probability Consider the simple example of a particle-wave confined in a box Just like musical notes in a flute or trombone Increasing energy corresponds to higher frequency Very similar to Bohr levels in atoms

33. Quantum Waves And Probability Consider the simple example of a particle-wave confined in a box Each of these configurations describes how likely it is for the particle to be found at different locations within the box Highest probability at most positive and negative points; lowest probabilty at zero - this is called the particle’s “wavefunction” Most Likely Least Likely

34. Quantum Waves And Probability Many quantities have probabilities that are described by the wavefunction - location, velocity, energy, time Particles are not, generally speaking, at one place at one time, nor are they moving with a singular velocity, or possess a singular quantity of energy Events do not even happen at precisely one time All of these quantities are described probabilistically according to the laws of quantum mechanics

35. The Double Slit Experiment If we shoot (non-wavelike) particles through two slits in a barrier, and watch how they accumulate on a far surface...

36. The Double Slit Experiment If we shoot (non-wavelike) particles through two slits in a barrier, and watch how they accumulate on a far surface, we get the same pattern that we would have gotten if we shot particles through one slit at a time and added them up + =

37. The Double Slit Experiment If we shoot (non-wavelike) particles through two slits in a barrier, and watch how they accumulate on a far surface, we get the same pattern that we would have gotten if we shot particles through one slit at a time and added them up The same is not true for waves passing through the double slit; the two waves interfere with each other

38. The Double Slit Experiment Which way do electrons and photons behave? Like particles? Like waves? Like something else?

39. The Double Slit Experiment Which way do electrons and photons behave? Like particles? Like waves? Like something else?

40. Moral of the Experiment: Even Individual Particle-Waves Interfere With Each Other! Unlike waves made of sound, water, sound, or on a string, quantum particle-waves cannot be described as patterns with more or fewer molecules Instead, we have no choice but to think of quantum particle-waves are patterns of probability

41. The Heisenberg Uncertainty Principle In 1927, Werner Heisenberg generalized this quantum fuzziness into what is now known as the uncertainty principle: x p > h/4 The more precisely the location of an object is known, the more uncertainty must be present in its momentum, and vice versa A similar relationship holds for time and energy: E t > h/4

42. Implications Of The Uncertainty Principle Things that were absolutely impossible in classical (pre-quantum) physics, are possible according to quantum mechanics For example, consider dropping a ball into a hole in the ground; According to classical physics, the ball will bounce around within the hole, but will never bounce out of the hole unless something pushes it

43. Implications Of The Uncertainty Principle Things that were absolutely impossible in classical (pre-quantum) physics, are possible according to quantum mechanics For example, consider dropping a ball into a hole in the ground; According to classical physics, the ball will bounce around within the hole, but will never bounce out of the hole unless something pushes it But according to Heisenberg, the energy of the ball is not precisely fixed, which means that the ball might have enough energy to get out of the hole; but only for a short period of time, t > h/(4 E) You can also think of it this way: since the momentum of the ball is not perfectly well known, the ball has a finite probability of escaping, although not very far out of the hole, x > h/(4 p) E

44. Implications Of The Uncertainty Principle Impossible-to-cross barriers in classical physics and breached all of the time in quantum physics This effect, known as tunneling, can be thought of as exceeding the barrier’s minimum energy E for a short period of time t, or as exceeding the minimum momentum needed to exceed the barrier p, for a short distance x

45. Part II

46. Part II Quantum Weirdness

47. A Thought Experiment Lets imagine that we have an unstable atom. We know it will decay, but do not know exactly when. In fact there is no way to predict when it will happen. We only know the probability of it happening at different times in the future: The moment at which the decay takes place is smeared out over time. Probability of Decay Time

48. A Thought Experiment If we watch the atom carefully, we can quickly learn when it decays But if instead, we were to place the atom in an impenetrable box, then we won’t know until we open the box whether the atom had decayed or not yet

49. A Thought Experiment If we watch the atom carefully, we can quickly learn when it decays But if instead, we were to place the atom in an impenetrable box, then we won’t know until we open the box whether the atom had decayed or not yet Until then, the atom is described by a wavefunction, part of which has already decayed, and part of which has not. In other words, until we open the box to check, the atom is a superposition of both intact and decayed states Probability of Decay Time

50. A Thought Experiment Now lets imagine that our decayed/not yet decayed atom had been placed next to a device that releases poison whenever the decay takes place. Until we open the box, the poison is a superposition of both released and unreleased states