The Mysteries of Quantum Mechanics

Transcription

1 The Mysteries of Quantum Mechanics Class 5: Quantum Behavior and Interpreta=ons Steve Bryson

2 Ques=ons?

3 The Quantum Wave Quantum Mechanics says: A par=cle s behavior is described by a wave This wave is not the waving of physical things we re not sure what it is Where the wave is strong, the par=cle is most likely to be found Where the wave does not wiggle the par=cle will not be found The frequency of the wave is high the par=cle is moving fast, where the frequency is low the par=cle is slow But only if you look for the par=cle Otherwise the wave just keeps waving Quantum mechanics is wrioen en=rely in terms of this wave Par=cles do not appear in the mathema=cs

4 The Components of a Quantum Wave What does this quantum wave tell us about a par=cle described by this wave? If I look for a posi=on the par=cle is more likely to be found where the wave is strong If I look for a speed, half the =me I will measure one speed, half the =me the other There are only two components, with the same strength and different frequency likely here not likely here

5 The Quantum Uncertainty Principle A quantum wave cannot describe a par=cle with an exact posi=on and an exact speed exact posi=on means very very localized wave exact speed means only one frequency component No wave can have both A quantum wave can have an approximate posi=on and speed Depends on the mass of the par=cle An tennis ball s posi=on uncertainty of a trillionth of a meter (size of an atomic nucleus) has a speed uncertainty of 85 billion trillionths of a meter/second An electron s posi=on uncertainty of 7.4 mm has a speed uncertainty of 7.4 meters/second Also called the Heisenberg Uncertainty Principle

6 The Quantum Rules Revisited If a quantum wave describes a par=cle, here is how to predict what you ll see in a measurement For a posi=on measurement: You are most likely to find the par=cle where the wave is strongest, less likely where it is weak, and you will not find it where the wave is not waving For a speed measurement: First, decompose the wave into its component simple waves You will measure the speed determined by the frequency of one of those components, with stronger components being more likely You will only see a speed determined by a component

7 Measurement and the Quantum Wave So measurement changes the quantum wave to match the measurement result The type of measurement determines the type of collapse Posi=on: collapse to a well- localized wave Speed: collapse to one of the pre- measurement wave s simple sine wave components According to quantum mechanics, this is a real, physical change Important enough to have a name: Collapse of the quantum wave AKA Collapse of the wave func=on But quantum mechanics does not explain how this collapse occurs Speed measurement Posi=on measurement

8 The Quantum Wave and the Double Slit The electron double slit experiment starts with an electron source What s really emioed by the electron source is electron quantum waves Those waves are what goes through the slits No electron here Electron quantum wave before the slit Electron quantum wave split by the slits Electron may be here

9 The Double Slit With a Detector Now we can understand why detec=ng which slit the electron goes through destroys the interference The quantum wave collapses to a wave just at the slit with the detected electron Note: seeing no electron at one slit is the same as detec=ng it at the other slit Only one wave means no interference! Detector Electron quantum wave split by the slits

10 How the Unmeasured Quantum Wave Evolves It depends on the star=ng wave Well localized waves spread out Simple waves stay the same

11 Two Kinds of Evolu=on of the Quantum Wave From the wave equa=on When the par=cle is lee alone Completely determinis=c not random Observa=on Causes instantaneous collapse of the wave to the wave that reflects the observa=on Exactly which wave it collapses to is random But with exactly predicted sta=s=cs based on the quantum wave before observa=on

12 Light from Atoms By 1900 it was also known that light from some gases (made from pure elements) have strange behavior Each element only emits certain colors The colors are unique to each element The paoern of colors seemed to be related to integers

13 How the Quantum Wave Describes Electrons in Atoms The quan=zed orbits of electrons in atoms comes naturally from the idea of a quantum wave To see how, we start with an electron in a box Atoms are not boxes, but this is easier to think about and includes the most important idea According to the quantum rules, the wave can only wave in the box, not outside the box Wave cannot wave here Wave can wave here Wave cannot wave here

14 What Kind of Wave Waves Only in a Box? Look at only simple waves All other waves can be made from simple waves Wave cannot wave here Wave can wave here Wave cannot wave here The wave has to be zero at the boundary of the box Only mul=ple of half- wavelengths are possible Just like a guitar string!

15 The Quantum Wave in a Box So the quantum wave in a box can only have certain, discrete frequencies By the quantum rules, frequency determines the speed of the electron Speed determines energy So the electron in a box can only have discrete energies If it has high energy (frequency), it can lose energy by emilng light to fall to a lower energy (frequency) The light s energy will be the difference in the electron s energy before and aeer So an electron in a box would emit only specific energies = colors of light If an electron fell from the n=4 to the n=1 frequency, the emioed light will have energy E 4 E 1

16 Electrons in Atoms Atoms are not Boxes There are no walls The electron is held in the atom by a force from the nucleus But the quantum wave equa=on can be solved for electrons with this force Hydrogen (one proton, one electron) is simplest The resul=ng three- dimensional waves are complicated Depends on the energy of the electron But only a discrete set of waves with par=cular energies solve the wave equa=on for an electron in an atom Like the electron in a box

17 Light EmiOed by Atoms The light emioed by elements is completely explained by the quantum wave of electrons in atoms The colors exactly match the predic=ons of quantum mechanics The Schrödinger equa=on gets it almost right, later versions of quantum mechanics get it right to ¼ of one billionth (!!) of the value measured

18 Atom in a Box Simula=on program for Macintosh/iPhone/ ipad only (atoms are not boxes, the box refers to the computer)

19 Where is the Electron in an Atom? Simplest case of Hydrogen: 1 electron orbi=ng 1 proton These drawings show where the quantum wave is strongest The lowest energy state is simple: the electron is near the nucleus orbit is not an obviously bad descrip=on A higher energy state has the electron in one of several different regions Nothing like an orbit

20 What Happens When the Electron Falls Down? The atom emits light Red light in this example But what did the electron do? Quantum mechanics says the change is instantaneous The electron does not move from one orbit to another orbit This does not fit well with the idea of the electron as a par=cle With a posi=on and speed in some direc=on

21 Quantum Tunneling Another important quantum behavior is tunneling: a situa=on where a classical par=cle cannot go but a quantum par=cle can The most common example is An electron crossing a gap where the electromagne=c field pushing it back is too strong for a classical par=cle This is how transistors and other semi- conductors work in your computer, smart phone, etc.

22 The Quantum Wave Allows Tunneling The quantum wave is changed, but not completely reflected by the quantum wave It is partly reflected, partly transmioed Energy barrier Before Incoming wave packet (par=cle)

23 The Quantum Wave Allows Tunneling The quantum wave is changed, but not completely reflected by the quantum wave It is partly reflected, partly transmioed Energy barrier Aeer Reflected wave TransmiOed wave

24 Did the Electron Travel Through the Barrier? The quantum rules tell you where it may be found before, during or aeer the tunneling But the quantum wave does not show the history or path of a par=cle through the barrier Energy barrier Aeer Reflected wave TransmiOed wave

25 Quantum Tunneling Simula=on From hops://phet.colorado.edu/en/ simula=on/quantum- tunneling

26 What Does it All Mean? How do we interpret the quantum wave? What does it tell us about par=cles Do par=cles have posi=ons and speeds if we don t look? Is the quantum wave fundamental, or does it only describe sta=s=cs of par=cles? For example, temperature is not fundamental: it is the average random mo=on of par=cles Does everything have a quantum wave?

27 The Classical Interpreta=ons (before 1980) Par=cles are real and the quantum wave is sta=s=cal, not really telling us about the details of individual par=cle mo=ons sta=s=cal interpreta=on, hidden variables interpreta=on The quantum wave is a way of predic=ng the sta=s=cal results of experiments and all other ques=ons are invalid Copenhagen interpreta=on The quantum wave is real and fundamental and depends on our state of knowledge consciousness interpreta=on The quantum wave and par=cle are both real, and the quantum wave pushes the par=cle around pilot wave interpreta=on The quantum wave is real, fundamental, independent of us and applies to everything many worlds The quantum wave is an incomplete descrip=on Einstein etc.

28 How We Evaluate the Interpreta=ons We ask what happens in a measurement The different interpreta=ons have different explana=ons of how the quantum wave collapses But if quantum effects only apply to very small things, how can we determine which interpreta=on makes sense? Speed measurement Posi=on measurement

29 Schrödinger's Cat Important: this is a thought experiment that no one actually does The use of cats makes it interes=ng We need to amplify the effects of quantum measurements Recall our two- component example with a speed measurement Build a box, inside which is a device that measures the speed If speed 1 is measured, fill the box with poison gas If speed 2 is measured, do nothing Put a cat in the box and press the measurement buoon but don t open the box to see what happened What does quantum mechanics say about this? Speed measurement

30 The Quantum Schrödinger's Cat Does quantum mechanics describe the en=re box including the cat? Yes: then before we look, the cat has a quantum wave that says dead and an equally strong quantum wave that says alive The quantum wave does not collapse un=l we look No: then there is a cat that is alive or dead whether we look or not when did the wave collapse What counts as an observa=on?

31 Sta=s=cal Interpreta=on Par=cles behave determinis=cally according to unknown laws The quantum wave tells us the sta=s=cs of that behavior, due to our ignorance of the actual laws hidden variables refer to parameters in those laws With each iden=cal star=ng point the same thing will always happen But we don t have the ability to start the hidden variables at the same star=ng point with each experiment, so we see sta=s=cal behavior If we repeat the cat experiment many =mes, half the =me we get dead cats and half the =me live cats, whether we look or not Quantum mechanics says nothing specific about individual experiments No collapse, just discovering what really happened Next week we ll see why this interpreta=on does not look likely

32 Copenhagen Interpreta=on We only have access to the large- scale classical realm The quantum realm is not accessible The quantum wave can only tell us the sta=s=cal results of experiments with the quantum realm As detected by large- scale, classical measurement devices That is all we can see The measurement device determines the wave vs. par=cle behavior Ques=ons about what really happens in the quantum realm are invalid So you can t talk about what happened to the cat unless you open the box and look, and half the =me you ll find a live cat

33 Copenhagen Interpreta=on The Copenhagen interpreta=on is historically very popular for at least two reasons It was pushed hard by Bohr and Heisenberg It allowed physicists to concentrate on solving physics problems without worrying about what is going on But this interpreta=on caused dissa=sfac=on Where is the boundary between classical and quantum? Humans have to be on the classical side, but what about cats? What about rocks? Does the moon exist only when I look at it? Albert Einstein There is no account of how/why the quantum wave collapses aeer a classical measurement Are we really not allowed to talk about the microscopic details? It is difficult to reconcile this with what physicists actually do

34 Consciousness Interpreta=on The quantum wave is real, and collapses when a conscious person performs an experiment So the cat is both dead and alive un=l a person opens the box. Then one appears and the other vanishes The cat s quantum wave collapses when you look This interpreta=on was suggested by a small number of prominent physicists It is no longer taken seriously Too vague, not physically useful, poorly mo=vated

35 Pilot Wave Interpreta=on The quantum wave exerts something like a force on real par=cles, which changes how they move Both the par=cle and wave mo=on are completely determinis=c Probabilis=c aspects come from an inability to precisely set the quantum wave the same for each =me an experiment is repeated This is another kind of hidden variable theory Next week we ll see problems with any hidden variable theory So the cat is really dead or alive before you look, with an even chance each way

36 The Many Worlds Interpreta=on The quantum wave is real, and applies to everything even you Before you open the box, the cat s quantum wave has two components: one with a live cat and one with a dead cat Aeer you open the box, your quantum wave has two components, one with a live cat and one with a dead cat You yourself are an uncollapsed quantum wave The quantum wave never collapses!

37 The Many Worlds Interpreta=on Then why do we always find a dead cat or a live cat, never both? The mathema=cs of quantum mechanics says With every observa=on the quantum wave splits into components determined by that observa=on Those components of the quantum wave never interact This means that the you that sees the live cat is unaware of the you that sees the dead cat

38 The Many Worlds Interpreta=on The many worlds interpreta=on is some=mes described as assuming mul=ple copies of the universe This is wrong: this interpreta=on simply takes the mathema=cs at face value It is the other interpreta=ons that assume that the quantum wave must collapse The many worlds approach is the only approach that allows a quantum descrip=on of the en=re universe Many worlds has gained popularity in recent years Especially as larger and larger systems are constructed that show uncollapsed quantum waves But many worlds says there is a split with every observa=on, where any interac=on between par=cles acts as an observa=on That s a lot of splits

39 The Situa=on Before the 1980s The debate between the various interpreta=ons was considered more philosophy than physics Only well- established physicists could talk about them without damaging their careers What changed in the 80s is the ability to experimentally detect differences between some of the interpreta=ons These experiments have significantly sharpened our understanding of quantum mechanics The ability to perform these experiments was due to the insight of (yet again) Albert Einstein

40 The Einstein- Podolsky- Rosen Paradox (1935) Quantum mechanics says that a par=cle cannot have both an exact posi=on and exact speed at the same =me But there are circumstances when two par=cles behave in related ways Specifically, some=mes an unmoving par=cle decays into two iden=cal par=cles that fly apart The sum of their mo=ons must be zero (conserva=on of momentum), so if I measure the speed of one I know the speed of the other

41 The Einstein- Podolsky- Rosen Paradox (1935) EPR says: measure the speed of one par=cle, then measure the posi=on of the other Then I know the posi=on and speed of the second par=cle! This cannot be described by a quantum wave!! Therefore quantum mechanics is incomplete! EPR paper =tle: Can Quantum- Mechanical Descrip=on of Physical Reality be Considered Complete? Defini=on of reality: If you can predict, with certainty, the value of a measured physical parameter, then that parameter corresponds to an element of reality EPR showed how to predict with certainty the speed and posi=on of a par=cle

42 The Copenhagen Response Bohr: it came down upon us as a bolt from the blue Bohr s reply contained only one equa=on it was a medita=on on reality The two par=cles are ini=ally described by a single quantum wave the specifies the speed of both par=cles Inherited from the quantum wave of the original par=cle that split apart The two par=cles are entangled The posi=on measurement of one of the waves breaks the entanglement and collapses that par=cle s quantum wave into a posi=on wave It is invalid to ascribe reality to anything in the microscopic realm

43 The EPR Debate Neither side accepted the other s arguments What was needed was experiment But in realis=c experiments you can t measure speed and posi=on exactly enough to beat the quantum uncertainty principle In the 1940s, anyway What is needed is some other quantum behavior that is easier to measure This turns out to be something called spin In the 1980s spin is used to show that entanglement is real, and that the EPR defini=on of reality does not seem to apply to reality

44 Next Week Spin Bell s Theorem Measuring Entanglement