• Philosophy and Spirituality
    Welcome Guest
    Posting Rules Bluelight Rules
    Threads of Note Socialize
  • P&S Moderators: JackARoe | Cheshire_Kat

Quantum Mechanics, Power of thought, Reality- Truly amazing

complexPHILOSOPHY said:
Feynmann Diagrams and some reading helped give me an overal conceptual idea of the nature of quantum mechanics. I stare at mathematics all day long, wishing I could understand them.
I used to feel the same way. Trust me, it's even cooler when you can understand them -- it's well worth the effor. You can teach yourself mathematics, too, with a lot of effort and some patience. Just get a book and start working problems in it. That's very important -- working problems is how you learn things, especially at first. Depending on what background you have, I would recommend starting with an introductory book in analysis/calculus or group theory. Calculus, Vol. I by Tom Apostol is very good for the first, and Abstract Algebra by Dummitt & Foote is good for the second. Both are difficult, but they require only HS-level backgrounds to understand, and they'll give you a taste of 'real math.'
Did you read about the crazy russian dude that supposidly solved the Poincare Conjecture?
Yup; I'd like to say he's crazy, but based on the mathematicians I know he's not really that unusual. They are a weird bunch.
How crazy is Supersymmetry?
Not crazy at all. In fact, right now it's mainstream among the high-energy physics community. At the moment, I'd say a majority of the community favor SUSY. It's extremely popular. Many of the experiments etc at the LHC (the next big supercollider under construction, set to come online in 2008-9) are being designed especially to look for SUSY.

When the LHC comes online it will a 'make-or-break' moment for supersymmetry. Either the LHC will find it, and it will go from being a popular idea to an established theory -- or the LHC will find no sign of it, and it will become a rejected, fringe idea. It's possible for SUSY to be true but not detectable at the LHC, but it's extremely "unnatural" and all the nice properties and reasons for believing in SUSY will be ruined.

So a lot of us are hoping we'll find it, but at least we'll know soon one way or the other...
 
While you're around Zorn and we're talking about supersymmetry, have you looked at the textbooks by Wess and by West on SUSY? My supervisor recommends them as very good but I wouldn't mind a second opinion, particularly from a student's POV since she lectures SUSY so much of it is fairly straight forward to her now even if it isn't to peons like me ;)
 
I definately want to try my best to major in mathematics and high energy physics and supposing that I can handle the upper-level physics and mathematics courses, what 'route' would you guys suggest (types of math and physics classes to take)? If I am not directly conversating with my girlfriend or getting to fucked up, I am fixated on physics, mathematics and philosophy. I definately feel like I have the motivation and passion for devoting a majority of my time to understanding it.
 
The courses I took which were important to doing HEP, in roughly the order I took them (along with explainations since your courses won't be called the same) w ere :

1st Year
Differential Equations : Obvious. Algebra & Geometry : Introduction to groups, matrices, mappings, indices. Vector Calculus : Differential equations in multiple dimensions, vectors. Dynamics : Lots of Newtonian stuff.

2nd Year
Linear Algebra : Tons of stuff on mappings, transforms and linear operators. Special Relativity : 4-vectors, Lorentz transforms, Minkowski metric. Mathematical Methods : Solving PDEs, tensors, variational principles, fourier series. Quantum mechanics : Non-relativistic stuff, 1D Schrodinger equation, Linear operators, Bra-ket notation, Angular momentum operators. Complex methods : Calculus involving complex numbers.Electromagnetism : Obvious. Statistical physics : Canonical ensembles, thermodynamics, phase changes

3rd Year
Principles of Quantum Mechanics : Dirac formalism, Pictures, Time dependent quantum systems, canonical methods. Further complex methods : Branch cuttings, Beta/Gamma/Zeta functions, Fourier/Laplace transforms. General Relativity : Obvious. Asymptotic Methods : Asymptotic series.

4th year
Quantum Fied Theory : Relativistic quantum mechanics, Feynman diagrams, Quantisation, Gauge theory. Symmetries in Particle Physics : Tangent spaces, Lie groups/algebras, Poincare/Lorentz groups, SU(2)/SU(3) and their algebras. Further General Relativity : Charts, Lie derivatives, manifolds, space-time configurations/diagrams. Black holes : Metrics of various black holes, Penrose diagrams, Hawking radiation, Black hole mechanics. String theory : Introduction to... Advanced QFT : Renormalisation, Path integrals. The Standard Model : QCD, Spontaneous Symmetry Breaking.

Quite a few courses there and some of them are sort of 'spare', like statistical physics and further complex methods. Sure, a bit here and there in them is useful but you can get by easily without 90% of those courses. Though some of the pure courses like linear algebra seem boring as sin at the beginning, the stuff in it is so important to theoretical physics I wish I'd paid more attention to them now.
 
Last edited:
^diff equations, linear algebra, vector calc, these are all 300 level math courses here. is it different there or did you start university with guns blazing?
 
qwedsa said:
^diff equations, linear algebra, vector calc, these are all 300 level math courses here. is it different there or did you start university with guns blazing?

I had the same initial impression when I read his course list. UCSD requires that you finish three semesters of Calc (Calc I,II&III), then you complete diff equations and then linear algebra. Only after you finish these, do you continue on in the higher level math courses (aside from physics -- the physics starts after Calc I).
 
qwedsa said:
^diff equations, linear algebra, vector calc, these are all 300 level math courses here. is it different there or did you start university with guns blazing?
I don't know exactly what Calc I, II and III involve in the US but my old uni assumed you know things like basic differentiation, integration, Taylor expansions, some geometry and things like induction when you get there. Those are covered in the double maths A Level course here in the UK for 17 and 18 year olds. No linear algebra is assumed but the ground work is done in the Algebra & Geometry course which involves a lot of group theory too.

Vector calc needs diff. equations and some A&G, but not too much. As long as you can do partial derivatives and integrate you can do the course in theory.

I will admit though, they did tend to throw you into it at full tilt. We covered the double maths course materal in 90 minutes of lectures, incase some people hadn't done the 2nd A Level. About 100 hours of high school lessons compressed into 1.5 lectures was the starting pace.
 
>>What exactly 'exists' in the Quantum Vaccum (If that is even the proper question to ask)?

It would be amazing to discover that this so-called vaccuum is actually filled with something, or a plethora of different things, which have a major bearing on how those things we DO perceive now behave. That's kind of what I was getting at when I compared reality as we see it to a shadow play behind a translucent screen.
It is filled with 'something,' so to speak. This is really one of the great triumphs of quantum field theory: it tells what we call the vacuum is really an incredibly complicated set of fluctuating fields. And, in fact, these vacuum fluctuations have a very real, noticeable effect on particles.

To greatly simplify, the vacuum is 'polarized' by particles, the same way ordinary metal can be polarized by a magnet. If you take a little piece of iron, it normally has no magnetization at all; it won't stick to other pieces of iron for example. But if you bring a magnet near it, the iron gets magnetically polarized and turns into a magnet itself, so it "sticks to" the original magnet! This is how magnets stick to a refrigerator, for example -- the fridge magnets polarize the nearby part of the fridge, and the two magnets stick to one another. It's also why most electromagnets are built around an iron core -- the electromagnet polarizes the iron in the center, which adds up with the electromagnetic's own magnetism to create a much stronger magnetic field. (Similarly, electric charges will electrically polarize materials surrounding them, but the polarization is opposite to the original charge, so it has the effect of making the electric field weaker.)

In a similar but much more complicated fashion, charged particles polarize the vacuum near them, which then alters their apparent charge. The effect of this vacuum polarization can either be to increase the particles' effective charge (as in the magnetic case above) or to reduce their effective charge ('shielding' them, as with electric case above.) By measuring this effective charge of a particle, and comparing it with the original "bare" charge, we can actually see the effect of the quantum vacuum!

Now you might object that we don't what the bare charge of a particle is, because we can't very well get rid of the vacuum after all, so how could we ever measure it? For most things that's true. But there's one exception: the magnetic moment (just think of this as magnetic charge, tho it's slightly different.) The magnetic moment of a particle comes from its spin, which in quantum mechanics must be either an integer or half-integer value: 0, 0.5, 1, 1.5, 2, .... (Spin has to do with how a particle looks from different angles, and it's straightforward to prove it cannot be anything other than these values.) So we know what the "true" bare value of the magnetic moment of a spin-1/2 particle, like the electron or muon, is: it's precisely 2. (Actually this is what's called the Lande g-factor; to get the magnetic moment you have to multiply it by q/4m, but that's not important.) We can see how different this is from the measured "effective" value. And we can calculate how much the vacuum polarization should change it using quantum field theory.

This has been done, and the effect of the vacuum polarization has been measured to amazing precision. I am not exaggerating when I say this is one of the most precise experiments ever done in physics. The measured and theoretically calculated values of the magnetic moment for the electron are:

2.00231930437 (expt)
2.00231930435 (theory)

and for the muon:

2.002331842 (expt)
2.002331838 (theory)

Without the effect of the vacuum, they would be precisely 2. So the QFT calculations of the vacuum's effect are right to 8 decimal places!!! It's amazing.

There are many other ways we can see the effects of the vacuum, too. For example, we can collide particles together so they approach very close to one another, so close that there's not enough space between for the 'shielding' effect of vacuum polarization to have its full effect. If they are close enough they will see each other's "bare" charges. We do indeed see this -- at very high energy collisions, the charges etc. of particles change from what they are for particles further away from one another. We say that charge, mass, coupling constants and so on "run" with energy, thanks to the effect of the vacuum. This running of parameters is extremely important in quantum field theory.

And the vacuum acts in more fundamental ways, too -- for example, that's where (most) mass comes from. By themselves, electrons, for example, would be massless and so travel at the speed of light. The reason they don't is because of interaction with part of the vacuum (the vacuum Higgs field.) You can think of the Higgs vacuum as "clumping" around electrons and "dragging" them and slowing them around -- much the same way as a beautiful woman walking through a crowded room might be slowed down by people gathering around her to try and to talk to her.

One more way -- if the total energy density of the vacuum is nonzero (we don't know what it is) that would act as a sort of "dark energy" (or "cosmological constant") which would cause the expansion of the universe to accelerate. This is, in fact, just what cosmologists have discovered in recent years! But no one knows yet whether the dark energy causing our universe to expand faster and faster is caused by the vacuum energy or by something else.

complexPHILOSOPHY said:
I am fairly certain that our brains are composed of 10% neurons and 90% glial cells. I am also fairly certain that neuron's through out the body, 'encode' electrobiochemical messages which are transmitted or fired from the synapse of one neuron (the area which encompasses the axon, synaptic cleft and axon terminals) to the dendrites of another neuron. Whether or not local or nonlocal groups of neurons fire in patterns, I do not know. Although I am not an expert in bio/organic chemistry, I believe that peptides are involved in 'peptide synthesis' which is involved in the formation of amino acid's and proteins.
True. The way it normally works is that an electrochemical signal called the "action potential" propagates down the length of a neuron. The action potential is a spike in voltage, which causes voltage-gated ion channels (think of them as doors in the side of the neuron which open when the voltage changes) to open up and let certain (sodium) ions into the cell. These incoming ions cause the voltage to increase even more, which opens more voltage-gated ion channels nearby, which further increases the voltage, and so on. So you get a constantly-regenerating pulse of voltage (and ion concentration) travelling down the neuron.

Once the pulse reaches the end of the neuron (the axon terminal), something different happens. There is a narrow gap, the synapse, between the end of the neuron and the next neuron. The action potential can't directly travel to the next neuron because of this gap. Instead, the neuron has a bunch of "messenger" molecules (called neurotransmitters) sitting around pre-made next to the synapse. When the action potential reaches the synapse, it causes a different set of voltage-gated channels to open up, and these channels cause the neuron to dump its neurotransmitter into the synapse. The neurotransmitter molecules then bind to receptors on the neuron at the other end of the synapse, which causes something to happen. In the simplest case they just cause that neuron to fire an action potential itself. But they can also have more complicated effects, like making that neuron easier to fire, or making it less likely to fire, or changing the frequency at which it fires, or even causing a sort of 'learning' mechanism in it to kick in.

Anyways, the most common neutrotransmitter is called glutamate, but there are many different neurotransmitters in use by different kinds of neurons -- GABA, acetylcholine, serotonin, endorphins, vasopressin, just to name a few. Some of these are "peptides" (another word for "proteins") and so are called neuropeptides -- eg, endorphins, dynorphins, vasopressin, oxytocin, neuropeptide Y, and substance P, to name a few well-known ones.

Much of GG's info about "peptides" seems dubious or bogus. Neuropeptides are involved in cognition and emotion, certainly, and many drugs work by imitating various neuropeptides (or other neurotransmitters.) But they have no special connection with acupuncture or suchlike, they don't mean emotions are stored in the bodies' tissues, and they certainly aren't in your "chakras" for God's sake.
Well, this vacuum can be thought of as a 'pool of energy' filling the entire universe which is invisible in the same way the water in a transparent pond is. In order to see the water, you throw a stone in and waves ripple out. This is exactly how we 'view' the quantum vacuum, we perturb it using high energy magnetic fields. At this level, no physical matter exists, however, virtual particles and antiparticles appear and annihilate in plank time.
Actually we see the effect of the vacuum on any particle (of course it's usually not large so to see it precise experimental conditions are needed) not just on photons (which make up magnetic fields.) Physical particles are "ripples" on the quantum fields that make up the universe. The vacuum is simply the lowest-energy state of these fields -- clasically that would mean no motion, field strength, or energy at all, but in quantum mechanics there is some even in the lowest-energy state -- and the excited states have additional waves in the fields, corresponding to one or more particles.

Also, virtual particles exist much longer than the Planck time -- generally speaking, they will exist a time T=hbar/E, where E is the "extra" (or "missing") energy of the virtual particles. Remember that in a sense "virtual particles" are just a convenient way to think of the complex quantum field interactions that are really going on. As long as those interactions are sufficiently "weak," we can represent them as taking place by the exchange of these virtual particles (doesn't work well for strong interactions). Whether you think of virtual particles as "really existing" or not is a matter of personal preference.

While QM does invoke ontological status between waves and particles, it doesn't necessarily invoke mysticism. QM embodies the philosophy of Holism, the antithesis of atomism.
It CERTAINLY doesn't involve any sort of mysticism! Far from it. The connection between waves & particles isn't mysterious at all, though we often unfortunately make it sound so. In fact, electrons, photons, etc. are neither waves nor particles. Instead they are quantum waves (or excitations of quantum fields, to be more accurate.) These quantum waves behave according to the rules of quantum mechanics (quantum field theory, to be more accurate) which are very complex and very weird but well-known. It turns out that in certain conditions, quantum waves act very much like regular waves. In other conditions, quantum waves act very much like regular particles. Sometimes they act like neither. This is what people mean when we say things are "both" particles and waves -- both are approximations and are each useful in different circumstances, though sometimes you have to use the full rules of quantum mecahincs.

I wouldn't say that QM is especially "holistic." True, particles can be entagled and correlated across vast distances in a bizarre manner. But the working philosophy of physicists studying QM/QFT/etc is still reductionism, still splitting things up into simple pieces and figuring out how each one of them works. In fact QFT is a fully "local" theory -- events cannot causally affect things far away except by sending them signals, which travel no faster than the speed of light.
 
AlphaNumeric said:
While you're around Zorn and we're talking about supersymmetry, have you looked at the textbooks by Wess and by West on SUSY? My supervisor recommends them as very good but I wouldn't mind a second opinion, particularly from a student's POV since she lectures SUSY so much of it is fairly straight forward to her now even if it isn't to peons like me ;)
Wess & West? Haven't heard of it. I used Baer & Tata which is very good -- it's got a strong phenomenological bent to it tho, so it's more appropriate for a phenomenologist than a pure theorist. Drees et al is OK, too, though not as good IMO. Weinberg's QFT vol. 3 is IMO very good for theory (everything Weinberg does is disgustingly good) though I've only gone through little bits of it.
 
zorn said:
The connection between waves & particles isn't mysterious at all, though we often unfortunately make it sound so. In fact, electrons, photons, etc. are neither waves nor particles. Instead they are quantum waves (or excitations of quantum fields, to be more accurate.) These quantum waves behave according to the rules of quantum mechanics (quantum field theory, to be more accurate) which are very complex and very weird but well-known. It turns out that in certain conditions, quantum waves act very much like regular waves. In other conditions, quantum waves act very much like regular particles. Sometimes they act like neither. This is what people mean when we say things are "both" particles and waves -- both are approximations and are each useful in different circumstances, though sometimes you have to use the full rules of quantum mecahincs.
zorn, with this idea of the quantum particles, can you explain what goes on when the electrons supposedly 'interfere with themselves' (when you fire them through the two slits one at a time and they form an interference pattern)
 
On the original topic of the thread: I haven't seen wtbdwk; and I think I would rather gnaw off a testacle than watch it. Every one of my friends who have seen it (a few of them physics grad students too) have said it's a horrible, terrible, painfully wrong distortion of science in the service of sheer moonbat-crazy looniness. I've heard that the one or two actual physicists who appeared in the film were pissed as hell at the way they were used -- they would explain some real physical phenomena in detail, then the filmmakers would pick one wacky-sounding line, take it completely out of context, and make it sound like they were talking about Jane Housewife summoning voodoo Atlantean spirit-warriors in her kitchen.

Ugh. It's hard for me to emphasize how much I despise this cheesy, half-baked, muddled, fuzzy New-Age intellectual-drooling-masquerading-as-a-belief-system. Getting high and then mashing together every "spiritual" or "Eastern" or "mystical" thing you've heard into some vile farrago where like, yeah, man, the Atlanteans totally ascended to the Fifth Dimension, cuz they brought the energies of their chakras into alignment with the quantum frequencies of the cosmos -- bleach! -- this is not a good idea. Turn on the BS meter, exercise some intellectual quality control! We're talking about channeling Ramtha the ancient spirit-warrior from Atlantis for Chrissakes! How much more idiotic can you get?

<ahem> Anyways...
complexPHILOSOPHY said:
This gives us our current, best understanding of the universe (aside from gravity, which general relativity explains to the decimal point but QM is trying to explain) and gives way for QET (Quantum Electrodynamics - The Electroweak Force or The Electromagnetic Force and the Weak Force), QCD (Quantum Chromodynamics - The Color Force or Strong Nuclear Force). These are all intrinsic to Quantum Field Theory.
I'd say it a little differently. Quantum field theory is the general 'formalism' or theory we use to describe nature. QED, QCD, and GSW electroweak theory are all examples of quantum field theories -- QED is the quantum field theory containing just electrons, positrons, photons, and the electromagnetic interaction between them, for example. When you roll them all up together, and include all the known particle types, you have what's called the Standard Model. Right now, the Standard Model explains virtually all experiments in particle physics (and the rest of physics for that matter, except for gravity.)
What this does tell us, is that we can no longer reduce complex macroscopic systems into fundamental microscopic particles and then explain the macroscopic systems in terms of possessing the characteristics of the microscopic particles. We must instead, view complex systems as emergent systems, possessing emergent properties not present in the system or level before it.
I don't think that QFT means this; QFT has no particular connection with emergent systems. We can explain macroscopic systems by reference to more fundamental laws acting on their constituent particles -- quantum field theory reduces to quantum mechanics in one limit, which reduces to classical mechanics in another limit, which explains the motion of a billiard ball, for example.

Now in practice certainly there are emergent properties at various levels that can't be usefully predicted from the more fundamental theories. Even though "in theory" the equations of QFT tell us all we need to know to understand say superconductors, in fact it's impossible to solve the equations of QFT in all but the simplest case. So to understand superconductors we have to study them on their own level, using pieces of quantum mechanics where we can and filling in the rest through experiment and study. The fact that all properties of macroscopic objects can be logically reduced to fundamental microscopic theories does not mean that those macroscopic properties can be reduced to microscopic ones in any useful, epistemological sense.
- How come, when we seek to measure a particles momentum, we fix its position and when we measure its position, we fix its momentum?
This isn't really right -- when we measure position of a particle, we fix its position, but the act of measurement causes its momentum to become uncertain. The reason 'why' is well-understood in the rules of QM -- it's because position and momentum are not commuting operators; either one fully describes its part of a state and leaves no room for the other -- but 'why' the rules of QM are like that is not something that's explained.
- Why does the simple act of detection, collapse the wave function into a particle?
Right, this is called the problem of measurement and is a big question.
- Why do quantum entities demonstrate a double-aspect appearance (waves of potential and at the same time, particles of actualization)?
This comes straight out of the rules of QM. Photons (or electrons, or other particles) are quantum waves. Roughly speaking, they are waves, but they have a fixed 'minimum size.' Photons of frequency f have energy E=h*f with h being Planck's constant, for example. These little minimum-size 'packets' are called quanta; this is where the word 'quantum' comes from. Also, when we do a measure on a quantum wave, we always find either a whole quanta or none at all -- never only part of it. For example when we measure the position of an electron, we never see it spread out over space even if that electron's quantum wave is spread out over space. Instead, we always find one whole electron at one fixed position.

The spread of the electron's quantum wavefunction tells us the probability of finding the electron at various places when we do the measurement. If an electron wavefunction is compressed in just one small area, a sharp peak, we would always find that electron there when we measured its position. OTOH, if its wavefunction spreads out over a large space, then we could find the electron anywhere when we measured its location -- sometimes we would find it at one end, sometimes the other. The larger the wavefunction is in a given region, the higher probability there is of finding the electron there when we make a measurement.

This weird and complicated behavior of quantum waves gives rise to both the ordinary "particle" and ordinary "wave" behaviors, just in different circumstances. When a particle's wavefunction is squashed into a small region (especially easy if the particle is massive) then it moves along as a tight "wavepacket," basically a localized pulse of ripples in a very small area. As long as the packet is small enough, this looks very similar to how an ordinary particle moves, a blob moving in a straight line. You could only see that it's a wave if you looked close enough to see the packet is made up of ripples; for most purposes it doesn't matter. And if the wavepacket collides with other wavepackets or walls often, so that its position is "measured" often, it stays localized in a small region and its wavefunction doesn't have a chance to spread out much. In other words, under these circumstances the quantum wave acts just like an ordinary particle!

OTOH, suppose we create a strong electromagnetic wave of frequency f. Even "weak" waves by macroscopic standards are so strong that the energy in a tiny part of the wave is much greater than the energy E=h*f in each photon (unless f is ridiculously huge.) So even a weak, tiny electromagnetic wave is made up of billions upon billions of photons. Here, each photon's wavefunction is spread out over a large area (the whole wave), and so we see it behave like a wave. The true wave behavior of the quantum wave is evident, not hidden as it is if the waves are incredibly tiny and compressed into a packet.

And, what's more, the quantum behavior is hidden here! Since the wave is made up of zillions of photons, the fact that photons are measured in discrete lumps is irrelevant. Sure, the field strength can only changed by fixed lumps (corresponding to adding 1, or 2, or 3, etc... photons) -- but what does it matter if the field has to be 2.000000000000 tesla or 2.00000000000001 tesla or 2.00000000000002 tesla or 2.00000000000003 tesla? For all practical purposes it looks continuous, not quantum. And the fact that when we observe photons we observe the whole photon in one place is also irrelevant. Even the weakest measurement will involve absorbing, say, a million photons. While each photon is always in one place, those million photons scattered around can cover the whole wave. So when we measure the electromagnetic field, we see it spread out, as usual for a wave. Under these circumstances, the quantum behavior of the photons' quantum waves is hidden and they act just like an ordinary wave!

So we find, using the rules of QM, that quantum waves behave like classical particles in certain conditions (localized, high-energy/high-mass wavepackets), and behave like classical waves in other conditions (large coherent waves, zillions of quanta involved.) That's where the "double-aspect" behavior comes in. Of course sometimes neither condition applies and the full quantum behavior is evident -- the quantum wave spreads out and evolves like a wave, and only can have certain values, like a wave. But when measured it shows up in one place like a particle.
- Why does nonlocality appear to exist (particles can interact instantaneously as though space was nonexistent)?
Nonlocality doesn't exist, as far as we know. QFT is a fully local theory (QM is not, but that's because it's wrong.) There is some weirdness in quantum theory in that measurement of one object can simultaneously affect another entangled object far, far away. This is part of the structure of quantum theory and cannot be used to send signals or violate locality (causality.) It is strange, though, and leads to interesting speculation about the nature of space & time.
 
qwedsa said:
zorn, with this idea of the quantum particles, can you explain what goes on when the electrons supposedly 'interfere with themselves' (when you fire them through the two slits one at a time and they form an interference pattern)
I can try. They do interfere with themselves, in fact. When you launch an electron at the slits, it's not 'measured' until it actually hits the screen on the far side (or the wall with the slits in it). So before then, its quantum wavefunction of the electron propagates like an ordinary wave. Now, to see a diffraction pattern, the electron's wavefunction must be wide enough to cover both slits (if the two slits are too far apart, then you just get particle-like behavior.)

What happens is the wavefunction propagates like a wave up to the wall with the slits. Impact with the wall "measures" the electron, and as before, either the whole electron hits the wall somewhere (in which case it's blocked and doesn't pass through the slits at all) or else the whole electron makes it past the wall. Assuming the wavefunction makes it past the wall, it goes through both slits since it's wide enough to cover both of them, just like a wave. It propagates forward to the screen, interfering with itself, just like a wave. Once it hits the screen, it's 'measured' again and this time it's always stopped since there's no holes in the screen.

In a position measurement, we always find the whole electron at a fixed location, so we see one bright dot appear one place on the screen. Where it appears is random, but the electron wavefunction just at the screen gives the probability of it appearing in each place. Since the wavefunction is large in some places (constructive interference) and small in others (destructive interference) it has a high probability of appearing in certain fringes and low probability of appearing between them. You can't tell anything from one hit, but if you keep shooting electrons through, they will hit the high-probability fringes more frequently and the low-probability ones less often. So, dot-by-dot, you'll fill in a classic interference pattern on the screen.

If you put measuring devices on the slits, though, to see "which" slit a particular electron passed through, you are performing a position measurement on each electron when it passes through the slits. You always see a whole electron when you measure, so either the left or the right detector fires each time. Since this measurement 'collapses' the electron wavefunction to the measured value, the electron wavefunction becomes localized in the slit it was measured at. So it only comes from one slit, and there is no interference pattern seen.

complexPHILOSOPHY said:
I definately want to try my best to major in mathematics and high energy physics and supposing that I can handle the upper-level physics and mathematics courses, what 'route' would you guys suggest (types of math and physics classes to take)? If I am not directly conversating with my girlfriend or getting to fucked up, I am fixated on physics, mathematics and philosophy. I definately feel like I have the motivation and passion for devoting a majority of my time to understanding it.
Great! :) Alphanumeric's list is a good one, though very fast-paced -- if you get through all that coursework in four years you are hard-core. I didn't take quantum field theory or GR until grad school and I'm no slouch. Anyways, the best thing to do is to look in your course catalog for the math & physics majors (or talk to profs/advisors in those departments.) There's usually a pretty standard 'track' that takes up most of your time through the first three years -- especially if you take both math & physics courses, which I highly recommend.

I'll give the standard set of courses I think you should take below. This isn't exactly what I took as an undergrad (I took a few more) but a sort of an ideal core list that IMHO you should cover in an ideal world. On top of this, you can add anything that particularly interests you or which seems to be taught by a good professor. Don't worry if you can't get all this stuff -- a lot of physicists don't take a lot of the stuff I list under 3rd & 4th year until grad school. As general adivce, first, I strongly recommend you take as much math as possible, as quickly as possible. It will be hard but it's very rewarding and a strong background in math is invaluable in more advanced physics. The amount of math used in physics balloons incredibly once you get to really advanced high-energy stuff -- a strong, broad background will not only make your life much easier then, you will feel that you really understand the physics much better than if you hadn't covered the relevant fields of mathematics. I've never met a physics PhD students who thought they took too much math, but I know lots who say they wish they had taken more.

In particular, pay special attention to linear algebra early on: you will live and breathe linear algebra and calculus as a physicist. Linear algebra's bigger brothers, functional analysis and especially anything to do with Lie groups, are good if you can find the time for them. A good grounding in real & complex analysis is important but can wait till your third or fourth year. I'll list some others below.


1st year:
Basic physics -- classical mechanics and electromagnetism, usually out of a glossy mass-market textbook like Serway or Halliday&Resnick.
Calculus (including vector/multivariable calculus) if you need it, or linear algebra & differential equations if you already have the calc.
Group theory / abstract algebra -- if you have time

2nd year:
Quantum mechanics -- first course, usually texts like Liboff or Griffiths
Electricity & magnetism -- first course, texts like Griffiths or Purcell
Classical mechanics -- first course, Marion & Thornton common text
Waves -- Sometimes this is folded into other courses, sometimes it's separate
Special relativity -- sometimes folded into other courses, usually uses French or Taylor&Wheeler
Linear algebra, Differential equations -- if you didn't take them 1st year
Statistics & probability -- a pain, but you will need to know it

3rd/4th year:
Classical mechanics (for real) -- almost always using Goldstein. Grad-level.
Electromagnetism (for real) -- almost always using Jackson. Grad-level.
Statistical mechanics -- usually there's two classes in this (intro and advanced/grad-level), all you really need for high-energy is the first one but the advanced one is a nice bonus if you have ime
Real analysis -- Rudin is a common text.
Complex analysis
Group theory / abstract algebra -- if you haven't had time to take it before.
Mathematical methods of physics -- Every univ has this class, take it as soon as you have the prereqs for it.
Various math classes -- This is a good time to try and fit in any classes on Lie groups, functional analysis, or linear algebra-related topics you can find. Also useful, but less so: differential geometry & toplogy. Personally I very much enjoyed classes in 1) set theory, 2) mathematical logic, and 3) advanced abstract algebra, but none of these are particularly useful for physics (all math makes you smarter, so they are useful in that sense.)
Various physics classes -- This is when you start to specialize (if you have time, don't worry many don't) and take classes in areas of physics that interest you. For high-energy, definitely take particle physics -- you will learn to do "simple" QFT calculations using Feynman diagrams, though you won't understand what you're doing until you take a real QFT class. QFT is a great class but it is very very hard so don't feel you have to squeeze it in as an undergrad -- few do. There's usually a class in computational/numerical methods in physics, basically how to program computer simulations/solvers for physics problems -- take this, you WILL need to know how to program.

-----

Here is a nice little page on John Baez's (mathematical physicist) site on 'how to learn physics & mathematics' -- pretty good, and lots of book recommendations.

http://math.ucr.edu/home/baez/books.html
 
Last edited:
Thanks for your clarification on the quantum vaccuum, Zorn. I've read through all of your descriptions of QFT and tried to picture it all happening. I'm going to try to describe what I see in my head -- can you tell me if I'm on the right track?

Ever see those displays where a crowd people stand in a rectangle, each person holding up a square of cardboard? Usually the squares, when all held up together, make up some kind of design when viewed from afar. You'll see this thing at sporting events in the US, and even more spectacularly at the Mass Games they like to hold in North Korea. Anyhow, wave effects can be created when people spin their cardboad squares in just the right sequence.

I'm picturing the whole universe as being like those squares, except in 3D. A particle of matter is just a group of these units spinning, while the quantum vaccuum is made up of these spinnable units which are motionless at the time.
 
zorn said:
Wess & West? Haven't heard of it.
No, they are two seperate books, one by Wess and another by West. I've got Weinberg's Quantum Theory of Fields I but both my supervisor and I agree it's got horrible notation. Sure, he's very comprehensive but doesn't supress indices ever and some of the equations are just ugly as a result. Sometimes you can sacrifice a little decription for some elegance!
zorn said:
In particular, pay special attention to linear algebra early on: you will live and breathe linear algebra and calculus as a physicist. Linear algebra's bigger brothers, functional analysis and especially anything to do with Lie groups, are good if you can find the time for them. A good grounding in real & complex analysis is important but can wait till your third or fourth year. I'll list some others below.
Complex, like Zorn says, there's some mathematical things you must know to do theoretical physics. Linear algebra is the HUGE one. You also must be comfortable with working in the complex plane for integration, working in multiple variables and related things like variational principles involving Lagrangians and actions. Some 'applied' courses are essentially a physicists spin on extremely pure topics. My 'Symmetries in Particle Physics' course was basically 'Representation Theory for physicists'. It was ALL about proving group relations with only a small amount related to actual physics. You'd do a huge proof of something then have a tag line "This is how quarks are arranged" at the end. :\

Not sure how useful they might be but I've got plenty of typed up PDF lecture notes I've 'borrowed' from lectures or fellow students (or done myself) which you can have a look at if you want. Obviously 4th year stuff wouldn't mean much to you but some of the 1st or 2nd year material is accessible to people familiar with a bit of calculus.
 
zorn said:
I wouldn't say that QM is especially "holistic." True, particles can be entagled and correlated across vast distances in a bizarre manner. But the working philosophy of physicists studying QM/QFT/etc is still reductionism, still splitting things up into simple pieces and figuring out how each one of them works.

Doesn't QM include certain ontological commitments to the role of the observer, i.e. the problem of measurement, which seem to make it a rather poor reductionist theory?

In fact QFT is a fully "local" theory -- events cannot causally affect things far away except by sending them signals, which travel no faster than the speed of light.

What about entanglement then? Or is the position that because no information is transmitted there's no causal power...? I was under the impression that this was still open to debate.
 
zorn said:
I can try. They do interfere with themselves, in fact. When you launch an electron at the slits, it's not 'measured' until it actually hits the screen on the far side (or the wall with the slits in it). So before then, its quantum wavefunction of the electron propagates like an ordinary wave. Now, to see a diffraction pattern, the electron's wavefunction must be wide enough to cover both slits (if the two slits are too far apart, then you just get particle-like behavior.)

What happens is the wavefunction propagates like a wave up to the wall with the slits. Impact with the wall "measures" the electron, and as before, either the whole electron hits the wall somewhere (in which case it's blocked and doesn't pass through the slits at all) or else the whole electron makes it past the wall. Assuming the wavefunction makes it past the wall, it goes through both slits since it's wide enough to cover both of them, just like a wave. It propagates forward to the screen, interfering with itself, just like a wave. Once it hits the screen, it's 'measured' again and this time it's always stopped since there's no holes in the screen.

In a position measurement, we always find the whole electron at a fixed location, so we see one bright dot appear one place on the screen. Where it appears is random, but the electron wavefunction just at the screen gives the probability of it appearing in each place. Since the wavefunction is large in some places (constructive interference) and small in others (destructive interference) it has a high probability of appearing in certain fringes and low probability of appearing between them. You can't tell anything from one hit, but if you keep shooting electrons through, they will hit the high-probability fringes more frequently and the low-probability ones less often. So, dot-by-dot, you'll fill in a classic interference pattern on the screen.

If you put measuring devices on the slits, though, to see "which" slit a particular electron passed through, you are performing a position measurement on each electron when it passes through the slits. You always see a whole electron when you measure, so either the left or the right detector fires each time. Since this measurement 'collapses' the electron wavefunction to the measured value, the electron wavefunction becomes localized in the slit it was measured at. So it only comes from one slit, and there is no interference pattern seen.
it sounds as if a particle is carrying a wave with it? when the particle part is stopped, the wave travelling with it dies out. is this an accurate model?
 
^^^ Naa -- there's neither a particle nor a wave (in the ordinary senses), just the wavefunction. That propagates like a wave, until it is 'measured' -- then it 'collapses' down to the result of the measurement.
specialspack said:
Doesn't QM include certain ontological commitments to the role of the observer, i.e. the problem of measurement, which seem to make it a rather poor reductionist theory?
Why should that have any bearing on whether it's a 'reductionist' theory? The committment to the role of the observer boils down to the issue of measurement, which does not necessarily require any sort of 'observer.' That is, if I hook up a measurement device to an experiement but smash the readout/display of that device -- so no observer could ever know what the measurement was, or even if it was on -- that still counts as a ' measurement.' While this is strange, it doesn't make the theory non-reductionist in any sense. Perhaps you mean something different than I do by the word?
What about entanglement then? Or is the position that because no information is transmitted there's no causal power...? I was under the impression that this was still open to debate.
Right, causality is not affected by entanglement because there's no actual way to transmit information using it. For example, two distant observers can affect what the other sees using entanglement (cf violation of Bell's inequalities) but they can't tell that they're doing so until they travel back together and compare notes. There's a huge, and extremely interesting, literature on problems in "quantum information" that relates to this. You can come up with all sorts of clever & counterintuitive things that people can do with entangled information, but every time you think you might have some method to send a signal FTL it turns out that you can't -- there is an almost-miraculous cancellation or effect which keeps everything causal. I don't know if there's a general proof that one can never use entanglement to send FTL signals (there might be) but certainly the issue has been extremely well-studied and it always turns out you can't.
 
zorn said:
Why should that have any bearing on whether it's a 'reductionist' theory? The committment to the role of the observer boils down to the issue of measurement, which does not necessarily require any sort of 'observer.' That is, if I hook up a measurement device to an experiement but smash the readout/display of that device -- so no observer could ever know what the measurement was, or even if it was on -- that still counts as a ' measurement.' While this is strange, it doesn't make the theory non-reductionist in any sense. Perhaps you mean something different than I do by the word?

The metaphysical position that the essence of all complex things can be reduced and explained by the nature of the parts that make them up.

The idea that higher level items (observers, measuring devices) can influence the nature of sub-micro level items, would seem to cut across the heirarchy, thus not being true reductionism. Unless you can reduce the observer/measuring device to sub atomic or quantum elements?

What distinguishes a "measuring device" from other kinds of natural phenomena?
 
^when we say that a higher-level item does something, what's happening is all of its constituent parts are doing the act. when causality goes from top to bottom, it goes from bottom to top at the same time so the reductionism still works fine
 
Top