Ask an experimental physicist

This Reddit post says things like:

And then the point goes out. All at once, as if God turned off the switch. You have crossed the event horizon of the black hole.

and:

But Alice cannot see Bob either, because in order to do so, she has to turn her head toward her own past. The distortion of spacetime is so great that the spatial direction in which Bob lies relative to her is actually in her past. In technical terms, any light that comes to her from Bob will fall perpendicular to her eyeballs, regardless of which direction she turns her head.

When I read this, I believed that it was wrong (but well-written, making it more dangerous!). (However, he described Gravity Probe B's verification of the geodetic effect correctly.)

Wikipedia says:

An observer crossing a black hole event horizon can calculate the moment they've crossed it, but will not actually see or feel anything special happen at that moment. In terms of visual appearance, observers who fall into the hole perceive the black region constituting the horizon as lying at some apparent distance below them, and never experience crossing this visual horizon.[7] Other objects that had entered the horizon along the same radial path but at an earlier time would appear below the observer but still above the visual position of the horizon, and if they had fallen in recently enough the observer could exchange messages with them before either one was destroyed by the gravitational singularity.[8] Increasing tidal forces (and eventual impact with the hole's singularity) are the only locally noticeable effects.

And it cites http://jila.colorado.edu/~ajsh/insidebh/schw.html which says:

Engulfed in blackness? NO! It is a common misconception that if you fall inside the horizon of a black hole you will be engulfed in blackness. More specifically, the story is that as you fall towards the horizon, the image of the sky above concentrates into a smaller and smaller circular patch, which disappears altogether as you pass through the horizon. The misconception arises because if you lower yourself very slowly towards the horizon, firing your rockets like crazy just to stay put, then indeed your view of the outside universe will be concentrated into a small, bright circle above you. Click on the button to see what it looks like if you lower yourself slowly to the horizon. Physically, this happens because you are swimming like crazy through the inrushing flow of space (see Waterfall), and relativistic beaming concentrates and brightens the scene ahead of (above) you. See 4D Perspective for a tutorial on relativistic beaming. But this is a thoroughly unrealistic situation. You'd be daft to waste your rockets hovering just above the horizon of a black hole. If you had all that rocket power, why not do something useful with it, like take a trip across the Universe? If you nevertheless insist on hovering just above the horizon, and if by mistake you drop just slightly inside the horizon, then you can no longer stay at rest, however hard you fire your rockets: the faster-than-light flow of space into the black hole will pull you in. Whatever you choose to do, the view of the outside Universe will not disappear as you pass through the horizon.

This explanation agrees with everything I know (when hovering outside the event horizon, you are accelerating instead of being in free fall).

Can you confirm that the Reddit post was incorrect, and Wikipedia and its cited link are correct?

I have a PhD in theoretical physics (General Relativity), and I'd be happy to help out with any questions in my area.

Excellent! That happens to be a subject I'm very interested in.

Here are two questions, to start:

1. Do you have a position in the philosophical debate about whether "general covariance" has a "physical" meaning, or is merely a property of the mathematical structure of the theory?

2. How can the following (from "Mach's Principle: Anti-Epiphenomenal Physics") be true:

[I]f the whole universe was rotating around you while you stood still, you would feel a centrifugal force from the incoming gravitational waves, corresponding exactly to the centripetal force of spinning your arms while the universe stood still around you.

given that it implies that the electromagnetic force (which is what causes your voluntary movements, such as "spinning your arms around") can be transformed into gravity by a change of coordinates? (Wouldn't that make GR itself the "unified field theory" that Einstein legendarily spent the last few decades of his life searching for, supposedly in vain?)

May I ask you which is exactly your (preferred) subfield of work? What are the most important open problems in that field that you think could receive decisive insight (both theoretically and experimentally) in the next 10 years?

I've never understood how going faster can make time go slower, thereby explaining why light always appears to have the same velocity.

If I'm moving in the opposite direction to light, and if there was no time slowing down, then the light would appear to go faster than normal from my perspective. Add in the effects of time slowing down, and light appears to be going at the same speed it always does. No problem yet. But if I'm moving in the same direction as the light, and time doesn't slow down, then it would appear to be going slower than normally, so the slowing down of time should make it look even slower, not give it the speed we always observe it in.

What am I missing?

Final question: Could you please comment a bit on

http://lesswrong.com/lw/cwq/ask_an_experimental_physicist/7ba5 ?

Hi again shminux, this is my second question. First, I’m sorry if it’s going to be long-winded, I just don’t know enough to make it shorter :-)

It might be helpful if you can get your hands on the August 3 issue of Science (since you’re working at a university perhaps you can find one laying around), the article on page 536 is kind of the backdrop for my questions.

[Note: In the following, unless specified, there are no non-gravitational charges/fields/interactions, nor any quantum effects.]

(1) If I understand correctly, when two black holes merge the gravity waves radiated carry the complete information about (a) the masses of the two BHs, (b) their spins, (c) the relative alignment of the spins, and (d) the spin and momentum of the system, i.e. the exact positions and trajectories before (and implicitly during and after) the collision.

This seems to conflict with the “no-hair” theorem as well as with the “information loss” problem. (“Conflict” in the sense that I, personally can’t see how to reconcile the two.)

For instance, the various simulations I’ve seen of BH coalescence clearly show an event horizon that is obviously not characterized only by mass and spin. They quite clearly show a peanut-shape event horizon turning gradually into an ellipsoid. (With even more complicated shapes before, although there always seem to be simulation artifacts around the point where two EHs become one in every simulation I saw.) The two “lobes” of the “peanut EH” seem to indicate “clearly” that there are two point masses moving inside, which seems to contradict the statement that you can discern no structure through an EH.

(In jocular terms, I’m pretty sure one can set-up a very complex scenario involving millions of small black-holes coalescing with a big one with just the right starting positions that the EH actually is shaped like hair at some point during the multi-merger. I realize that’s abusing the words, but still, what is the “no-hair theorem” talking about, given that we can have EHs with pretty much arbitrary shape?)

In the same way, I don’t quite get the “information loss paradox” either. Take the simple scenario of an electron and a positron annihilating: in come two particles (coincidentally, they don’t have “hair” either), out come two photons, in other words a “pair” of electromagnetic waves. (Presumably, gravity waves would be generated as well, though since most physics seems to ignore those I presume I’m allowed to, as well.) There are differences, but the scenario seem very similar to black hole merger. Nobody seems to worry about any information loss in that case—basically, there isn’t, as all the information is carried by the leaving EM waves—so why exactly is it a problem with black holes? That is, what is the relevant difference?

[Note: if electrons and annihilation pose problems because of quantum effects, one can make up a completely classical scenario with similar behavior, using concepts no more silly than point masses and rigid rods. I just picked this example because it’s easy to express, and people actually think about it so “why don’t they worry about information loss” makes sense.]

(2) As far as I understand, exactly what happens in (1) also happens when something that is not a black hole falls into one. Take a particle (an object with small mass, small size but too low density to have an EH of its own, no internal structure other than the mass distribution inside it) falling spirally into a BH. AFAIK, this will generate almost exactly the same kind of gravitational waves that would be generated by an in-falling (micro-) black-hole with the same mass, with the only difference being that the waves will have slightly different shape because the density of the falling particle is lower (thus the mass distribution is slightly fuzzier).

Even though the falling particle doesn’t have an EH of its own, AFAIK the effects will be similar, i.e. the black hole’s EH will also form a small bump where the particle hits it, and will then oscillate a bit and radiate gravitational waves until it settles. Like in case (1) above, all the information regarding the particle’s mass and spin should be carried by the gross amplitude and phase of the waves, and the information about the precise shape of the particle (how its mass distribution differs from a point-mass like a micro–black hole) should be carried in the small details of the wave shapes (the tiny differences from how the waves would look if it were a micro–black hole that fell).

(3) Even better, if the particle and/or black hole also has electric charge, as far as I can tell the electro-magnetic field should also contain waves, similar to the electron/positron annihilation mentioned above, that carries all relevant information about electro-magnetic state of the particles before, during and after the “merger” (well, accretion in this case) in the same way the gravitational waves carry information about mass and spin.

So, as far as I can tell, coalescence and accretion seem to behave very similarly to other phenomena where information loss isn’t (AFAIK) regarded as an issue, and do so even when other forces than gravity are involved. In other words, it seems like all the information is not lost, it’s just “reflected” back into space. I’m not saying that it’s not an issue and all physicists are idiots, I’m just asking what is the difference.

(I have seen explanations of the information loss paradox that don’t cause my brain to raise these questions, but they’re all expressed in very different terms—entropy and the like—and I couldn’t manage to translate in “usual” terms. It’s a bit like using energy conservation to determine the final state of a complex mechanical system. I don’t contradict the results, I just want help figuring out in general terms what actually happens to reach that state.)

Hi shminux, thanks for your offer!

I have some black hole questions I’ve been struggling with for a week (well, years actually, I just thought about it more than usual during the last week or so) that I couldn’t find a satisfactory explanation for. I don’t think I’m asking about really unknown things, rather all explanations I see are either pop-sci explanations that don’t go deep enough, or detailed descriptions in terms of tensor equations that are too deep for what math I remember from university. I’m hoping that you could hit closer to the sweet spot :-)

I’ll split this into two comments to simplify threading. This first one is sort of a meta question:

Take for instance FIG. 1 from http://arxiv.org/pdf/1012.4869v2.pdf or the video at http://www.sciencemag.org/content/suppl/2012/08/02/337.6094.536.DC1/1225474-s1.avi

I think I understand the what of the image. What I don’t quite get is the when and where of the thing.

That is, given that time and space bend in weird and wonderful ways around the black holes, and more importantly, they bends differently at different spots around them, what exactly are the X, Y and Z coordinates that are projected to the image plane (and, in the case of the video, the T coordinate that is “projected” on the duration of the video), given that the object in the image(s) is supposed to display the shape of time and space?

The closest I got trying to find answers:

(1) I saw Penrose diagrams of matter falling into a black hole, though I couldn’t find one of merging black holes. I couldn’t manage to imagine what one would look like, and I’m not quite sure it makes sense to ask for one: Since the X coordinate in a Penrose diagram is supposed to be distance from the singularity, I don’t see how you can put two of those, closing to each other, in one picture. Also, my brain knotted itself when trying to imagine more than one “spot” where space turns into time, interacting. On the other hand, that does look a bit like the coalescence simulations I’ve seen, so I might not be that far from the truth.

(2) I suppose the images might be space-like slices through the event, perhaps separated by equal time-like intervals at infinity in the case of the video. I don’t want to speculate more, in case I’m really far from the mark, so I’ll wait for an answer first.

(In case it helps with the answer: I do know what an integral is (including path, surface, and volume integrals), though I probably can’t do much with a complicated one mathematically. Similarly for derivatives, gradient, curl and divergence, though I have to think quite carefully to interpret the last two. If you say “manifold” and don’t have a good picture my eyes tend to glaze over, though. I sort of understand space curvature and frame-dragging, when they’re not too “sharp”, qualitatively if not quantitatively. I can visualize either of them—again, as long as they’re not “sharp” enough to completely reverse space and time dimensions; i.e., I have an approximate idea of what happens when you’re close to an event horizon, but not what goes on as you “cross” one. (Actually, I’m not sure I understand what “crossing an EH” means, again it’s the “when” and “where” the seem to be the trouble rather than the “what”; most simple explanations tend to indicate that there’s not much of a “what”, as in “nothing much happens as you cross one that doesn’t happen just before or just after”.) I can’t quite visualize a general tensor field, but when you split the Riemann tensor into tidal and frame-dragging components I can interpret the tendex and vortex lines on a well-drawn diagram if I think carefully.)

See the end of the second-last paragraph of this.

I guess it depends on what you mean by 'understanding'. I personally feel that you haven't really grasped the math if you've never used it to solve an actual problem - textbook will do, but ideally something not designed for solvability. There's a certain hard-to-convey Fingerspitzggefühl, intuition, feel-for-the-problem-domain - whatever you want to call it - that comes only with long practice. It's similar to debugging computer programs, which is a somewhat separate skill from writing them; I talk about it in some detail in this podcast and these slides.

That said, I would say you can get quite a good overview without any math; you can understand physics in the same sense I understand evolutionary biology - I know the basic principles but not the details that make up the daily work of scientists in the field.

Those two questions are completely unrelated. Popular physics books just aren't trying to convey any physics. That is their handicap, not the math. Greene could teach you a lot of physics without using math, if he tried. But there's no audience for such books.

Eliezer's quantum physics sequence impressed me with its attempt to avoid math, but it seems to have failed pretty badly.

I don't think it's going to be practical this century. The difficulty is that the same properties that let you cut the latency are the ones that make the detectors huge: Neutrinos go right through the Earth, and also right through your detector. There's really no way around this short of building the detector from unobtainium, because neutrinos interact only through the weak force, and there's a reason it's called 'weak'. The probability of a neutrino interacting with any given five meters of your detector material is really tiny, so you need a lot of them, or a huge and very dense detector, or both. Then, you can't modulate the beam; it's not an electromagnetic wave, there's no frequency or amplitude. (Well, to be strictly accurate, there is, in that neutrinos are quantum particles and therefore of course are also waves, as it were. But the relevant wavelength is so small that it's not useful; you can't build an antenna for it. For engineering purposes you really cannot model it as anything but a burst of particles, which has intensity but not amplitude.) So you're limited to Morse code or similar. Hence you lose in bandwidth what you gain in latency. Additionally, neutrinos are hard to produce in any numbers at a precise moment. You're relying on muon decays, which of course are a fundamentally random process. So the variables you're actually controlling are the direction and intensity of your muon beam, and at respectable fractions of lightspeed you just can't turn them around on a dime. Plus you get the occasional magnet quench or whatnot, and lose the beam and have to spend five minutes building it up again. So, not only are you limited to dots and dashes, you can't even generate them fast and reliably.

All that said, what application other than finance really needs better latency than you get by going at lightspeed through orbit? And while it's true that people would make money off that, I don't see any particular social return to it. Liquidity is a fine thing, but I cannot fathom that it matters to have it on millisecond scales - seconds should be just fine, and we're already way beyond that just with lightspeed the long way around. As for blackout zones, are you thinking of cellphones? I suggest that this is a bad idea. To get a reliable signal in a man-portable detector you would have to have a very intense neutrino burst indeed; and then you'd also get a reliable signal in the body of the guy holding it. We detect neutrinos by the secondary radiation they cause. I haven't worked the numbers, but even if cancers were rare enough to put up with, think of the lawsuits.

Here's another article saying basically the same thing I say below, but with extra flair.

There isn't a unified "string theory controversy".

The battle-tested part of fundamental physics consists of one big intricate quantum field theory (the standard model, with all the quarks, leptons etc) and one non-quantum theory of gravity (general relativity). To go deeper, one wishes to explain the properties of the standard model (why those particles and those forces, why various "accidental symmetries" etc), and also to find a quantum theory of gravity. String theory is supposed to do both of these, but it also gets attacked on both fronts.

Rather than producing a unique prediction for the geometry of the extra dimensions, leading to unique and thus sharply falsifiable predictions for the particles and forces, present-day string theory can be defined on an enormous, possibly infinite number of backgrounds. And even with this enormous range of vacua to choose from, it's still considered an achievement just to find something with a qualitative resemblance to the standard model. Computing e.g. the exact mass of the "electron" in one of these stringy standard models is still out of reach.

Here is a random example of a relatively recent work of string phenomenology, to give you an idea of what is considered progress. The abstract starts by saying that certain vacua are known which give rise to "the exact MSSM spectrum". The MSSM is the standard model plus minimal supersymmetry. Then they point out that these vacua will also have to have an extra electromagnetism-like force ("gauged U(1)_B-L"). We don't see such a force, so therefore the "B-L" photons must be heavy, and the gist of the paper is to point out that this can be achieved if one of the neutrino superpartners acts like a Higgs field (by "acquiring a vacuum expectation value"). In fact this paper doesn't contain string calculations per se; it's an argument at the level of quantum field theory, that the field-theory limit of these string models is potentially consistent with experiment.

That might not sound exciting, but in fact it's characteristic, not just of string phenomenology, but of theoretical particle physics in general. Progress is incremental. Grand unified theories don't explain the masses of the particles, but they can explain the charges. String theory hasn't yet explained the masses, but it has the potential to do so, in that they will be set by the stabilized size and shape of the extra dimensions. The topology of the extra dimensions is (currently) a model-building choice, but once that choice is made, the masses should follow, they're not free parameters as in field theory.

As for what might determine the topology of the extra dimensions, anthropic selection is a popular answer these days - and that has become another source of dissatisfaction for string theory's critics, because it looks like another step back from predictivity. Except in very special cases like the cosmological constant, where a large value makes any kind of physical structure impossible, there's enormous scope for handwaving explanations here... Actually, there are arguments that the different vacua of the "landscape" should be connected by quantum tunneling, so the vacuum we are in may be a long-lived metastable vacuum arrived at after many transitions in the primordial universe. But even if that's true, it doesn't tell you whether the number of metastable minima in the landscape is one or a googol. This is an aspect of string theory which is even harder than calculating the particle masses in a particular vacuum, judging by the amount of attention it gets. The empirical side of string theory is still dominated by incrementally refining the level of qualitative approximation to the standard model (including the standard cosmological model, "lambda CDM") that is possible.

As for quantum gravity, the situation is somewhat different. String theory offers a particular solution to the problems of quantum gravity, like accounting for black hole entropy, preserving unitarity during Hawking evaporation, and making graviton behavior calculable. I'd say it is technically far ahead of any rival quantum gravity theory, but none of that stuff is observable. So approaches to quantum gravity which are much less impressive, but also much simpler, continue to have supporters.

I don't do formal Bayes or Kolmogorov on a daily basis; in particle physics Bayes usually appears in deriving confidence limits. Still, I'm reasonably familiar with the formalism. As for string theory, my jest in the OP is quite accurate: I dunno nuffin'. I do have some friends who do string-theoretical calculations, but I've never been able to shake out an answer to the question of what, exactly, they're calculating. My basic view of string theory has remained unchanged for several years: Come back when you have experimental predictions in an energy or luminosity range we'll actually reach in the next decade or two. Kthxbye.

The controversy is, I suppose, that there's a bunch of very excited theorists who have found all these problems they can sic their grad students on, problems which are hard enough to be interesting but still solvable in a few years of work; but they haven't found any way of making, y'know, actual predictions of what will happen in current or planned experiments if their theory is correct. So the question is, is this a waste of perfectly good brains that ought to be doing something useful? The answer seems to me to be a value judgement, so I don't think you can resolve it at a glance.

What on earth is the String Theory controversy about, and is it resolvable at a glance like QM's MWI?

I wonder how you resolve the MWI "at a glance". There are strong opinions on both sides, and no convincing (to the other side) argument to resolve the disagreement. (This statement is an indisputable experimental fact.) If you mean that you are convinced by the arguments from your own camp, then I doubt that it counts as a resolution.

Also, the Occam's razor is nearly always used by physicists informally, not calculationally (partly because Kolmogorov complexity is not computable).

As for the string theory, I don't know how to use Bayes to evaluate it. On one hand, this model gives some hope of eventually finding something workable, since it provided a number of tantalizing hints, such as the holographic principle and various dualities. On the other hand, every testable prediction it has ever made has been successfully falsified. Unfortunately, there are few other competing theories. My guess is that if something better comes along, it will yield the string theory in some approximation.

I am a graduate student in experimental particle physics, working on the CMS experiment at the LHC. Right now, my research work mainly involves simulations of the calorimeters (detectors which measure the energy deposited by particles as they traverse the material and create "showers" of secondary particles). The main simulation tool I use is software called GEANT, which stands for GEometry ANd Tracking. (Particle physicists have a special talent for tortured acronyms.) This is a Monte Carlo simulation, i.e. one that uses random numbers. The current version of the software is Geant4, which is how I will refer to it.

The simulation environment does have an explicit description of the detector. Geant4 has a geometry system which allows the user to define objects with specific material properties, size, and position in the overall simulated "world". A lot of work is done to ensure the accuracy of the detector setup (with respect to the actual, physical detector) in the main CMS simulation software. Right now, I am working on a simplified model with a less complicated geometry, necessary for testing upgrades to the calorimeters. The simplified geometry makes it easier to swap in new materials and designs.

Geant4 also has various physics lists which describe the various scattering and interaction processes that particles will undergo when they traverse a material. Different models are used for different energy ranges. The choice of physics list can make a significant difference in the results of the simulation. Like the geometry setup, the physics lists can be modified and tuned for better agreement with experimental data or to introduce new models. The user can specify how long the program should keep track of particles, as well as a minimum energy cutoff for secondary particles (generated in showers).

An often frustrating part of Geant4 simulations is that the computing time scales roughly linearly with the number of particles and the energy of the particles. One can mitigate this problem to some extent by running in parallel, e.g. submitting 10 jobs with 1000 events each, instead of one job with 10000 events. (Rolf talks about parallelization here.) However, as we keep getting more events with higher energies at the LHC, computing time becomes more of an issue.

Because of this, there is an ongoing effort in "fast simulation." To do a faster simulation than Geant4, we can come up with parameterizations that reproduce some essential characteristics of particle showers. Specifically, we parameterize the distribution of energy deposited in the material in both the longitudinal and transverse directions. (For example, the longitudinal distribution is often parameterized as a gamma distribution.) The development of these parameterizations can be complicated, but once we have an algorithm, the simulation just requires evaluating the functions at each step. Fast simulation essentially occurs above the particle level, which is what makes it faster. A caveat: this is much easier for electromagnetic showers (which involve only electrons and photons, and only a few main processes for high energies) than for hadronic showers (which involve numerous hadrons and processes, because the strong force plays a crucial role, and therefore the energy distributions fluctuate quite a bit).

What I have given here is an overview of the simulation study of detectors; in all of this, we send single particles through the detector material. We do the same thing in real life, with a "test beam", so that we can compare to data. The actual collisions at the LHC, however, produce events far more complex than a single particle test beam. We simulate those events, too (Rolf discusses some of that below), and there are even more complications involved. I am not as knowledgeable there (yet), and this post is long enough as it is, so I will hold off on elaborating. I hope this has given you some insight into modern particle simulations!

So the reason we simulate things is, basically, to tell us things about the detector, for example its efficiency. If you observe 10 events of type X after 100k collisions, and you want to know the actual rate, you have to know your reconstruction efficiency with respect to that kind of event - if it's fifty percent (and that would be high in many cases) then you actually had 20 physical events (plus or minus 6, obviously) and that's the number you use in calculating whatever parameter you're trying to measure. So you write Monte Carlo simulations, saying "Ok, the D* goes to D0 and pi+ with 67.4% probability, then the D0 goes to Kspipi with 5% probability and such-and-such an angular distribution, then the Ks goes to pions pretty exclusively with this lifetime, then the pions are long-lived enough that they hit the detector, and it has such-and-such a response in this area." In effect we don't really deal with quantum mechanics at all, we don't do anything with the collapse. (Talking here about experiments - there are theorists who do, for example, grid calculations of strong-force interactions and try to predict the value of the proton mass from first principles.) Quantum mechanics only comes in to inform our choice of angular distributions. (Edit: Let me rephrase that. We don't really simulate the collapse; we say instead, "Ok, there's an X% chance of this, so roll a pseudorandom number between zero and one; if less than X, that's the outcome we're going with. We don't deal with the transition, as it were, from wave functions to particles.) The actual work is in 'swimming' the long-lived decay products through our simulation of the detector. The idea is to produce information in the same format as your real data, for example "voltage spike in channel 627 at timestamp 18", and then run the same reconstruction software on it as on real data. The difference is that you know exactly what was produced, so you can go back and look at the generated distributions and see if, for example, your efficiency drops in particular regions of phase space. Usually it does, for example if one particle is slow, or especially of course if it flies down the beampipe and doesn't hit the active parts of the detector.

Calibrating these simulations is a fairly major task that consumes a lot of physicist time and attention. We look at known events; at BaBar, for example, we would occasionally shut off the accelerator and let the detector run, and use the resulting cosmic-ray data for calibration. It helps that there are really only five particles that are long-lived enough to reach the detector, namely pion, kaon, neutron, electron, and proton; so we can study how these particles interact with matter and use that information in the simulations.

Another reason for simulating is to do blind studies. For example, suppose you want to measure the rate at which particle X decays to A+B+C. You need some selection criteria to throw away the background. The hihger your signal-to-noise ratio, the more accurately you can measure the rate, within some limits - there's a tradeoff in that the more events you have, the better the measurement. So you want to find the sweet spot between 0 data of 100% purity and 100% of the data at 2% purity. (Purity, incidentally, is usually defined as signal/(signal+background).) But you usually don't want to study the effects of your selections directly on data, because there's a risk of biasing yourself - for example, in the direction of agreement with a previous measurement of the same quantity. (Millikan's oil drops are the classic example, although simulations weren't involved.) So you tune your cuts on Monte Carlo events, and then when you're happy with them you go see if there's any actual signal in the data. This sort of thing is one reason physicists are reasonably good about publishing negative results, as in "Search for X"; it could be very embarrassing to work three years on a channel and then be unable to publish because there's no signal in the data. In such a case the conclusion is "If there had been data of such-and-such a level, we would have seen it (with 95% probability); we didn't; so we conclude that the process, if it occurs, has a rate lower than X".

Proton decay has not been observed, but even if it happens, it needn't be an obstacle to life, as such. For humans in anything remotely like our present form you need protons, but not for life in general. Entropy, however, is a problem. All life depends on having an energy gradient of some form or other; in our case, basically the difference between the temperature of the Sun and that of interstellar space. Now, second thermo can be stated as "All energy gradients decrease over a sufficiently long time"; so eventually, for any given form of life, the gradient it works off is no longer sharp enough to support it. However, what you can do is to constantly redesign life so that it will be able to live off the gradients that will exist in the next epoch. You would be trying to run the amount and speed of life down on an asymptotic curve that was nevertheless just slightly faster than the curve towards total entropy. At every epoch you would be shedding life and complexity; your civilisation (or ecology) would be growing constantly smaller, which is of course a rather alien thing for twenty-first century Westerners to consider. However, the idea is that by growing constantly smaller you never hit the wall where the gradient just cannot support your current complexity anymore, and instantly collapse to zero. An asymptote that never hits zero is, presumably, better than a curve of any shape that hits the wall and crashes - at least this is true if your goal is longevity; of course, pure survival is not the only goal of humans, so there's a value judgement to be made there. You might decide that it's better not to throw anyone out of the lifeboat and all starve together, rather than keep going at the price of endless sacrifice and endless shrinking. And, of course, if we can extrapolate to such incredibly distant beings at all, there's going to be quarrels over exactly who gets thrown out, and the resulting conflict might well make the asymptote shrink drastically, or collapse, as resources are used to fight instead of survive. To survive literally forever you need to be lucky every time; entropy only needs to be lucky once.

That said, even with total entropy you get the occasional quantum fluctuation that creates a small, local gradient again - in fact, arbitrarily large gradients if you wait arbitrarily long times; if somehow you were able to survive the period between such events, you could indeed live for ever. In fact, if you are able to wait long enough you will see a quantum fluctuation the size of the Big Bang. The problem is, of course, that a human, and probably life more generally as well, is extremely low-entropy compared to the sort of universe you get at 10^1000 years. In fact, interstellar space from our era would look rather low-entropy compared to that stuff. So the difficulty is to protect yourself against the, as it were, sucking vacuum that tries to rip the low entropy out of your body, without using up your reserves of energy on self-repair.

Overall, I'd say it doesn't look utterly hopeless, although it is subject to a Fermi paradox: If survival over arbitrary timescales is possible, why don't we see any survivors from previous BB-level events? If my account is correct, it seems unlikely that ours is the first such fluctuation.

Not an answer, but there is a beautiful short sci-fi story by Isaac Asimov that touches on this theme called "The last question". I don't know if it is okay to provide a link but it isn't hard to find online.

I took a physics course in my International Baccalaureate program in high school - if you're not familiar with IB, it's sort of the European version of AP - and it really resonated with me. There's just a lot of cool stuff in physics; we did things like building electric motors using these ancient military-surplus magnets that had once been installed in radars for coastal fortresses. Then when I went on to college, I took some math courses and some physics courses, and found I liked the physics better. In the summer of 2003 (I think) I went to CERN as a summer student, and had an absolute blast even though the actual work I was doing wasn't so very advanced. (I wrote a C interface to an ancient Fortran simulation program that had been kicking around since it was literally on punchcards. Of course the scientist who assigned me the task could have done it himself in a week, while it took me all summer, but that saved him a week and taught me some real coding, so it was a good deal for both of us.) So I sort of followed the path of least resistance from that point. I ended up doing my Master's degree on BaBar data. Then for my PhD I wanted to do it outside Norway, so it was basically a question of connections: My advisor knew someone who was looking for a grad student, wrote me a recommendation, and I moved to the US and started my PhD. Then, when it was time to choose a thesis topic, I actually, at first, chose something completely different, involving neutrinos and reconstructing a particular decay chain from missing energy and some constraints. It turned out we couldn't get a meaningful measurement with the data we had, there were too many random events that would fake the signal. So I switched to charm mixing, which (with perhaps the teensiest touch of hindsight bias) I now actually find more interesting anyway.

As you can see, 'decide' may be a somewhat strong word in this context; I've basically worked on what my advisors have suggested, and found it interesting enough not to quit. I suspect I could have worked on practically any problem with much the same results.

Well, if we do find it there are presumably Nobel prizes to be handed out to whoever developed the correct variant. If we don't, I most earnestly hope we find something else, so someone else gets to go to Stockholm. In either case I expect the grant money will keep flowing; there are always precision measurements to be made. Or were you asking about practical applications? I can't say I see any, but then they always do seem to come as a surprise.

I think their problems will be rather different from ours. We simulate particle collisions literally at the level of electrons (well, with some parametrisations for the interactions of decay products with detector material); I think it will be a while before we have the computer power to treat cells as anything but black boxes, and of course cells are huge on the scale of particle physics (as are atoms). That said, I suspect that the major issues will be in parallelising their simulation algorithms (for speed) and storing the output (so you don't have to run it again). Consider that at BaBar we used to think that ten times as much simulated data as real data was a good ratio, and 2 times was an informal minimum. But at BaBar we had an average of eleven tracks per event. At LHCb the average multiplicity is on the order of thousands, and it's become impossible to generate even as much simulated as real data, at least in every channel. You run out of both simulation resources and storage space. If you're simulating a whole brain, you've got way more objects, even taking atoms as the level of simulation. So you want speed so your grad students aren't sitting about for a week waiting for the current simulation to finish so they can tweak one parameter based on the result; and you get speed from parallelising and caching. "A week" is not hyperbole, by the way; for my thesis I parallelised fits because, with twenty CPUs crunching the same data, I could get a result overnight; at that rate I did graduate eventually. Running on one CPU, each fit would take two weeks or so, and I'd still be 'working' on it (that is, mainly reading webcomics), except of course that the funding would have run out some time ago.

There are various possibilities depending on the energy of the particles.

An antineutron has valence quarks , , . A proton has valence quarks u, u, d. There are two quark-antiquark pairs here: u + and d + . In the simplest case, these annihilate electromagnetically: each pair produces two photons. The leftover u + becomes a positively-charged pion.

The pi+ will most often decay to an antimuon + muon neutrino, and the antimuon will most often decay to a positron + electron neutrino + muon antineutrino. (It should be noted that muons have a relatively long lifetime, so the antimuon is likely to travel a long distance before decaying, depending on its energy. The pi+ decays much more quickly.)

There are many other paths the interaction can take, though. The quark-antiquark pairs can interact through the strong force, producing more hadrons. They can also interact through the weak force, producing other hadrons or leptons. And, of course, there are different alternative decay paths for the annihilation products that will occur in some fraction of events. As the energy of the initial particles increases, more final states become available. Energy can be converted to mass, so more energy means heavier products are allowed.

Edit: thanks to wedrifid for the reminder of LaTeX image embedding.

![](http://www.codecogs.com/png.latex?\\bar\{u\},%20\\bar\{d\},%20\\bar\{d\})

Very complicated things.

Both the antineutron and the proton are soups of gluons and virtual quarks of all kinds surrounding the three valence quarks Dreaded_Anomaly mentions; all of which interact by the strong force. The result is exceedingly intractable. Almost anything that doesn't actually violate a conservation law can come out of this collision. The most common case, nonetheless, is pions - lots of pions.

This is also the most common outcome from neutron-proton and neutron-antiproton collisions; the underlying quark interactions aren't all that different.

What happens when an antineutron interacts with a proton?

Good question.

I'm going to tender the guess that you get a kaboom (energy release equivalent to the mass of two protons) and a left over positron and neutrino spat out kind of fast.

Well no, it seems to me that there is a real physical process apart from our understanding of it. It's true that if you had enough information about a random piece of near-vacuum you could extract energy from it, but where does that information come from? You sort of have to inject it into the problem by a wave of the hand. So, to put it differently, if entropy is ignorance, then the laws of thermodynamics should be reformulated as "Ignorance in a closed system always increases". It doesn't really help, if you see what I mean.

It depends on why I want to re-prove it. If I'm transported in a time machine back to, say, 1905, and want to demonstrate the existence of the atomic nucleus, then sure, I know how to run Rutherford's experiment, and I think I could derive enough basic scattering theory to demonstrate that the result isn't compatible with the mass being spread out through the whole atom. Even if I forgot that the nucleus exists, but remembered that the question of the mass distribution internal to an atom is an interesting one, the same applies. But to re-derive that the question is interesting, that would be tough. I think similar comments apply to most of the Standard Model: I am more or less aware of the basic experiments that demonstrated the existence of the quarks and whatnot, although in some cases the engineering would be a much bigger challenge than Rutherford's tabletop setup. Getting the math would be much harder; I don't think I have enough mathematical intuition to rederive quantum field theory. In fact I haven't thought about renormalisation since I forgot all about it after the exam, so absent gods forbid I should have to shake the infinities out. I think my role would be to describe and run the experiments, and let the theorists come up with the math.

Unless you count spinoffs, I don't really see any. Big accelerator projects tend to be on the cutting edge of, for example magnet technology, or even a bit beyond. For example, the fused-silica photon-guide bars of the DIRC, Detector of Internally Reflected Cherenkov light, in the BaBar detector, were made to specifications that were a little beyond what the technology of the late nineties could actually manage. The company made a loss delivering them. Even now, we're talking about recycling the bars for the SuperB experiment rather than having new ones made. Similarly the magnets, and their cooling systems, of the LHC (both accelerator and detectors) are some of the most powerful on Earth. The huge datasets also tend to require new analysis methods, which is to say, algorithms and database handling; but here I have to caution that the methods in question might only be new to particle physicists, who after all aren't formally trained in programming and such. (Although perhaps we should be.)

So, to the extent that such engineering advances might make their way into other fields, take your choice. But as for the actual science, I think it is as close to knowledge for the sake of knowledge as you're going to get.

A few years ago, I heard about a very penetrating scanner for shipping containers, that used muons, which are second-generation particles, analogous to charm, but for leptons. I don't know whether it's still promising or not.

I don't know of any other applications for second- or third-generation particles. They all have so much shorter lifetimes than muons, it's hard to do anything with them.

How often do you invoke spectral gap theorems to choose dimensionality for your data, if ever?

I have never done so; in fact I'm not sure what it means. Could you expand a bit?

Carbon nanotubes in space elevators: Nicolas Pugno showed that the strenght of macroscale CNs is reduced to a theoretical limit of 30 gigapascal, with a needed strenght of 62 GPa for some desings... Whats the state of the art in tensile strenght of macro-scale CNs? Any other thoughts related to materials for space elevators?

This might be out in left field, but:

Can water be pumped through carbon nanotubes? If so, has anyone tried? If they have, has anyone tried running an electric current through a water-filled nanotube? How about a magnetic current? How about light? How about sound?

Can carbon nanotubes be used as an antenna? If they can be filled with water, could they then be used more effectively as an antenna?

I haven't actually read a popular-science book in physics for quite some time, so I can't really answer your question.The phrase "The God Particle" always makes me wince, it's exactly the sort of hyperbole that leads to howling misunderstandings of what physics is about. It's not Lederman's fault, though.

I've seen the magnet-in-tube experiment done with an ordinary conductor, which is actually more interesting to watch: If you want to see a magnet falling freely, you can use an ordinary cardboard tube! As for superconductors, it could be the solid-state guys have one lying around, but I haven't asked. You'd have to cool it to liquid-helium temperatures, or liquid nitrogen if you have a cool modern one, so I don't know that you'd actually be able to see the magnet fall.

The coolest tabletop experiment I've personally done (not counting taking a screwdriver to the BaBar detector) is building cloud chambers and watching the cosmic rays pass through.

Sorry, I missed your post. As shminux says, new concepts take time to mature; the first musket was a much poorer weapon than the last crossbow. Then you have to consider that this sort of engineering problem tends intrinsically to move a bit slower than areas that can be advanced by data analysis. Tweaking your software is faster than taking a screwdriver to your prototype, and can be done even by freshly-minted grad students with no particular risk of turning a million dollars of equipment into very expensive and slightly radioactive junk. It is of course possible for an inexperienced grad student to wipe out his local copy of the data which he has filtered using his custom software, and have to redo the filtering (example is completely hypothetical and certainly nothing to do with me), thus costing himself a week of work and the experiment a week of computer-farm time. But that is tolerable. For engineering work you want experienced folk.

It's a growing field. One of my roommates is working on plasma waveguides, a related technology.

I'm not an experimental physicist, but from what I know, the whole concept is relatively new and it takes time to get it to the point where it can compete with the technologies that had been perfected over many decades. With the groups at SLAC, CERN and Max Planck Institute (among others) working on it, we should expect to see some progress within a decade or so.

Well, it depends on what you mean by "nothing but". You can obviously (in principle) make a logic gate of photon beams, but I don't see how you can make a stable apparatus of nothing but photons. You have to generate the light somehow.

NB: Sometimes the qualifier "in principle" is stronger than other times. This one is, I feel, quite strong.

It's an intriguing idea, a pure photon-based gate based on elastic scattering of photons, however I don't see how such a system would function, even in principle. Feel free to elaborate. Also, presumably constructing an equivalent electron- or neutron-based gate would be easier.

'Observation' is a shorthand (for historical reasons) for 'interaction with a different system', for example a detector or a human; but a rock will do as well. I would actually suggest you read the Quantum Mechanics Sequence on this point, Eliezer's explanation is quite good.

The different cases of an observation are different components of the wavefunction (component in the vector sense, in a approximately-infinite dimensional space called Hilbert Space). Observation is the point where the different cases can never come back together and interfere. This normally happens because two components differ in ways that are so widespread that only a thermodynamically small (effectively 0) component of each of them will resolve and contribute to interference against the other.

This process is called Decoherence.

Have you ever run into geometric algebra or people who think geometric algebra would be the greatest thing ever for making the spatial calculation aspects of physics easier to deal with?

I can't say I have, no. Sorry! I'm afraid I couldn't make much of the Wiki article; it lost me at "Clifford algebra". Both definitions could do with a specific example, like perhaps "Three-vectors under cross products are an example of such an algebra", supposing of course that that's true.

Why can't you build an electromagnetic version of a Tipler cylinder? Are electromagnetism and gravity fundamentally different?

Well yes, to the best of our knowledge they are: Electromagnetic charge doesn't bend space-time in the same way that gravitational charge (ie mass) does. However, finding a description that unifies electromagnetism (and the weak and strong forces) with gravity is one of the major goals of modern physics; it could be the case that, when we have that theory, we'll be able to describe an electromagnetic version of a Tipler cylinder, or more generally to say how spacetime bends in the presence of electric charge, if it does.

How does quantum configuration space work when dealing with systems that don't conserve particles (such as particle-antiparticle annihilation)? It's not like you could just apply Schrödinger's equation to the sum of configuration spaces of different dimensions, and expect amplitude to flow between those configuration spaces.

You have reached the point where quantum mechanics becomes quantum field theory. I don't know if you are familiar with the Hamiltonian formulation of classical mechanics? It's basically a way of encapsulating constraints on a system by making the variables reflect the actual degrees of freedom. So to drop the constraint of conservation of particle number you just write a Hamiltonian that has number of particles as a degree of freedom; in fact, the number of particles at every point in position-momentum space is a degree of freedom. Then you set up the allowed interactions and integrate over the possible paths. Feynman diagrams are graphical shorthands for such integrals.

A while ago I had a timelss physics question that I don't feel I got a satisfactory answer to. Short version: does time asymmetry mean that you can't make the timeless wave-function only have a real part?

I'm afraid I can't help you there; I don't even understand why reversing the time cancels the imaginary parts. Is there a particular reason the T operator should multiply by a constant phase? That said, to the best of the current knowledge the wave function is indeed symmetric under CPT, so if your approach works at all, it should work if you apply CPT instead of T reversal.

What is your opinion of the Deutsch-Wallace claimed solution to the probability problems in MWI?

Now we're getting into the philosophy of QM, which is not my strength. However, I have to say that their solution doesn't appeal to that part of me that judges theories elegant or not. Decision theory is a very high-level phenomenon; to try to reason from that back to the near-fundamental level of quantum mechanics - well, it just doesn't feel right. I think the connection ought to be the other way. Of course this is a very subjective sort of argument; take it for what it's worth.

Also are you satisfied with decoherence as means to get preferred basis?

I'm not really familiar enough with this argument to comment; sorry!

Lastly: do you see any problems with extending MWI to QFT (relativity issues) ?

Nu, QM and QFT alike are not yet reconciled with general relativity; but as for special relativity, QFT is generally constructed to incorporate it from the ground up, unlike QM which starts with the nonrelativistic Schrodinger equation and only introduces Dirac at a later stage. So if there's a relativity problem it applies equally to QM. Apart from that, it's all operators in the end; QFT just generalises to the case where the number of particles is not conserved.

The mass of sun is decreasing every second, due to nuclear fusion inside the sun (I'm not speaking of particles escaping the sun gravity, but of the conversion of mass to energy during nuclear fusion).

IMO “conversion of mass to energy” is a very misleading way to put it. Mass can have two meanings in relativity: the relativistic mass of an object is just its energy over the speed of light squared (and it depends on the frame of reference you measure it in), whereas its invariant mass is the square root of the energy squared minus the momentum squared (modulo factors of c), and it's the same in all frames of references, and coincides with the relativistic mass in the centre-of-mass frame (the one in which the momentum is zero). The former usage has fallen out of favour in the last few decades (since it is just the energy measured with different units -- and most theorists use units where c = 1 anyway), so in recent ‘serious’ text mass means “invariant mass”, and so it will in the rest of this post.

Note that the mass of a system isn't the sum of the masses of its parts, unless its parts are stationary with respect to each other and don't interact. It also includes contributions from the kinetic and potential energies of its parts.

The reason why the Sun loses mass is that particles escape it; if they didn't, the loss in potential energy would be compensated by the increase in total energy. The mass of an isolated system cannot change (since neither its energy nor its momentum can). If you enclosed the Sun in a perfect spherical mirror (well, one which would reflect neutrinos as well), from outside the mirror, in a first approximation, you couldn't tell what's going on inside. The total energy of everything would stay the same.

Now, if the Sun gets lighter, the planets do drift away so they have more (i.e. less negative) potential energy, but this is compensated by the kinetic energy of particles escaping the Sun... or something. I'm not an expert in general relativity, and I hear that it's non-trivial to define the total energy of a system when gravity is non-negligible, but the local conservation of energy and momentum does still apply. (Is there any theoretical physicist specializing in gravitation around?)

As for 2., that's the energy of the electromagnetic field. (The electromagnetic field can also store angular momentum, which can leading to even more confusing situations if you don't realize that, e.g. the puzzle in The Feynman Lectures on Physics 2, 17-4.)

I'm not Rolf (nor am I strictly speaking a physicist), but:

1. There isn't really a distinction between mass and energy. They are interconvertible (e.g., in nuclear fusion), and the gravitational effect of a given quantity of energy is the same as that of the equivalent mass.

2. There is potential energy in the magnetic field. That energy changes as magnets, lumps of iron, etc., move around. If you have a magnet and a lump of iron, and you move the iron away from the magnet, you're increasing the energy stored in the magnetic field (which is why you need to exert some force to pull them apart). If the magnet later pulls the lump of iron back towards it, the kinetic energy for that matches the reduction in potential energy stored in the magnetic field. And yes, making a magnet takes energy.

[EDITED to add: And, by the way, no they aren't silly questions.]

They are not silly questions, I asked them myself (at least the one about the Sun) when I was a student. However, it seems army1987 got there before I did. So, yep, when converting from mass-energy to kinetic energy, the total bending of spacetime doesn't change. Then the photon heads out of the solar system, ever-so-slightly changing the orbits of the planets.

As for magnets, the energy is stored either in their internal structure, ie the domains in a classic iron magnet; or in the magnetic field density. I think these are equivalent formulations. An interesting experiment would be to make a magnet move a lot of stuff and see if it got weaker over time, as this theory predicts.

Well, it's theory, which is not my strong suit; these are just first impressions on casual perusal. It is not obvious nonsense. It is not completely clear to me what is the advantage over plain Copenhagen-style collapse. It makes no mention of even special relativity - it uses the Schrodinger rather than Dirac equation; but usually extending to Dirac is not very difficult. The approach of letting phases have significance appeals to me on the intuitive level that finds elegance in theories; having this unphysical variable hanging about has always annoyed me. In Theorem 3 it is shown that only the pointer states can maintain a perfect correlation, which is all very well, but why assume perfect correlation? If it's one-minus-epsilon, then presumably nobody would notice for sufficiently small epsilon. Overall, it's interesting but not obviously revolutionary. But really, you want a theorist for this sort of thing.

I don't have time to read it right now, but I suggest that unless it accounts for how a charge density can be complex, it doesn't really help. The problem is not to come up with some physical interpretation of the wave mechanics; if that were all, the problem would have been solved in the twenties. The difficulty is to explain the complex metric.

What happens if Eve copies the photon, and waits until Bob reads it before she does?

Not my field, but it seems to me that it should be the same thing that happens if Bob tries to read the photon after Eve has already done so. You can only read the quantum information off once. Now, an interesting question is, what happens if Eve goes off into space at near lightspeed, and reads the photon at a time such that the information "Bob has read the photon" hasn't had time to get to her spaceship? If I understand correctly, it doesn't matter! This scenario is just a variant of the Bell's-inequality experiment.

Also, you referred to virtual particles as a convenient fiction when responding to someone else. I assumed that they were akin to a particle being in a place with more potential energy than there is energy in a system during quantum tunneling. The particle is real. It's just that due to the fact that the kinetic energy is negative, it behaves in a way that makes the waveform small at any real distance. Was I completely off base?

So firstly, in quantum tunneling the particle never occupies the forbidden area. It goes from one allowed area to another without occupying the space between; hence the phrase "quantum leap". Of course this is not so difficult to imagine when you think of a probability cloud rather than a particle; if you think of a system with parts ABC, where B is forbidden but A and C are allowed, then there is at any time a zero probability of finding the particle in B, but a nonzero probability to find it in A and C. This is true even if at some earlier time you find it in A, because, so to speak, the wave function can go where the particle can't. So, yes, if you ever found the particle in B its kinetic energy would be negative, but in fact that doesn't happen. So now we come to matters of taste: The wave function does exist within B; is this a mathematical fiction, because no experiment will find the particle there, or is it real since it explains how you can find the particle at C?

Then, back to virtual particles. The mass of a virtual particle can be negative; it is really unclear to me what it would even mean to observe such a thing. Therefore I think of them as a convenient fiction. But they are certainly a very helpful fiction, so, you know, take your choice.

Also, should I have just edited my old post instead of adding a new one?

I don't think so, the number of comments here is so large that it would be very easy to miss an edit.

Ok, that's a lot of questions. I'll do my best, but I have to tell you that your quest is, in my opinion, a bit quixotic.

What is the reason for the existence of the theory of the charm quark (or any generation 2-3 quark)? What are some results of experiments that necessitate the existence of a charm quark?

Basically the strange quark is motivated by the existence of kaons, charm quarks by the D family of mesons (well, historically the J/psi, but I'm more familiar with the D mesons), and beauty quarks by the B family. As for truth quarks, mainly considerations of symmetry. Let's take kaons, the argument being the same for the other families. If the kaon were to decay by the strong force, it would be extremely short-lived, because it could go pretty immediately to two pions; there would certainly be no question of seeing it in a tracking detector, the typical timescale of strong decays being 10^-23 seconds. Even at lightspeed you don't get far in that time! We therefore conclude that there is some conservation principle preventing the strong decay, and that the force by which the kaon decays does not respect this conservation principle. Hence we postulate a strange quark, whose flavour (strangeness) is conserved by the strong force (so, no strange-to-up (or down) transition at strong-force speeds) but not by the weak force.

I should note that quark theory has successfully predicted the existence of particles before they were observed; you might Google "Eightfold Path" if you're not familiar with this history, or have a look at the PDG's review. (Actually, on closer inspection I see that the review is intending for working physicists familiar with the history - it's not an introduction to the Eightfold Path, per se. Probably Google would serve you better.)

Which of the known hadrons can be directly observed in any way, as opposed to theorized as a mathematical in-between or as a trigger for some directly observable decay?

For this I have to digress into cross-sections. Suppose you are colliding an electron and a positron beam, and you set up a detector at some particular angle to the beam - for example, you can imagine the detector looking straight down at the collision point:

___detector

e+ -----> collision <------- e-

Now, the cross-section (which obviously is a function of the angle) can be thought of as the probability that you'll see something in the detector. If electron and positron just glance off each other without annihilating (at relativistic speeds this can easily happen - they have to get pretty close to interact, and our control of the beams is only so good), we call that Bhabha scattering, and it has a particular cross-section structure. For obvious reasons, the cross-section is highest at small angles; that is, it is really quite unlikely for the electron and positron to dance past each other in the exact way that throws them out at a ninety-degree angle to their previous paths; but it's pretty easy for them to give each other a one-degree kick. If you calculate the cross-section at some particular angle as a function of the total beam energy, you'll see that the higher the energy, the lower the cross-section, and indeed experiment confirms this.

What if the electron and positron do annihilate, creating a virtual photon that then decays to some other pair of particles - for example, a charm-anticharm pair? Well, again, the cross-section is highest near the beam (basically to conserve the angular momentum - you have to do spin math) and decreases with energy.

So we have this cross-section that decreases monotonically with energy. However, as you run your beam energy up, at very specific energies you will see a sharp increase and drop-off, in a classic Breit-Wigner shape. In other words, at some particular energy it suddenly becomes much more likely that your decay products get kicked away from the beam. Why is that? We refer to these bumps in the spectrum as resonances, and explain them by appealing to bound states - particles, in other words. What happens is that with an intermediate bound state, there are additional Feynman paths that open up between the initial state "electron and positron" and the final state "hit in detector at angle X". Additional paths through parameter space gives you additional probability unless you're very unlucky with the phases, hence the bump in the cross-section - the final state becomes more likely. (Additionally, for reasons of spin math that I won't go into here, the decay products from a bound state of two quarks are produced much more isotropically than back-to-back quark-antiquark pairs.)

Here's a different way of looking at it. Suppose you have a detector that encloses the collision space, so you can reconstruct most of the decay products; and you decide to take all pion pairs and calculate "If these two particles came from a common decay, what was the mass of the particle that decayed?" Then this spectrum will basically be flat, but you will get an occasional peak at specific masses. Again, we explain this by appeal to a bound state.

It occurs to me that this may not actually differ from what you call "mathematical in-betweens"; I have answered as though this phrase refers to virtual particles, which are indeed a bit of a convenient fiction. Anyway, this is why we believe in the various hadrons and mesons.

(I'm getting "comment too long" errors; splitting my answer here.)

I had to split my answer in two, and clumsily posted them in the wrong order - some of this refers to an 'above' which is actually below. I suggest reading in chronological rather than page order. :)

Am I right in thinking that the tau lepton is only theorized in order to explain an in-between decay state?

Well no, you get a specific resonance in hadron energy spectra, as described above.

If you don't know, do you know of anything related to any other fermions (or hadrons) that only exist as a theoretical in-between?

There's the notorious sigma and kappa resonances, which are basically there only to explain a structure in the pion-pion and pion-kaon scattering spectrum. Belief in these as particles proper, rather than some feature of the dynamics, is not widespread outside the groups that first saw them. (I have a photoshopped WWII poster somewhere, captioned "Is YOUR resonance needed? Unnecessary particles clutter up the Standard Model!) I see the PDG doesn't even list them in its "needs confirmation" section. I'm aware of them basically because I used them in my thesis just as a way to vary the model and see how the result varied - I had all the machinery for setting up particles, so a more-or-less fictional particle with some motivation from what others have seen was a convenient way of varying the structure.

How were the masses of the tau lepton and the top quark determined? If the methods are different for the charm quark, how was the mass of the charm quark determined?

So quark masses are a vexed subject. The problem is that you cannot catch a quark on its own, it's always swimming in a virtual soup of gluons and quarks. So all quark masses are determined, basically, by taking some model of the strong interaction and trying to back-calculate the observed hadron and meson masses. And since the strong interaction is insanely computationally intractable, you can't get a very good answer.

For the tau lepton it's rather simpler: Wait for one to decay to charged hadrons, calculate the four-momentum of the mother particle, and get the peak of the mass distribution as described above.

Does the weak interaction cause any sort of movement, or hold anything together, or does it only act as a trigger for decay?

I don't believe anyone has observed a bound state mediated purely by the weak force. In fact one of the particles in such a state would have to be a neutrino, since otherwise there would be other forces involved; and observing a neutrino is hard enough without adding the requirement that it be a bound state. However, I suppose that in inverse-beta-decay, or neutrino capture, the weak force causes some movement at the final movement, to the extent that it's meaningful to speak of movement at these scales.

Why is it considered a field energy?

Because it can be quantised into carrier bosons, presumably.

When detecting gamma radiation, how much background is there to extract from?

This is really hard to give a general answer for. In the BaBar detector, photons are reconstructed by the EMC, the electromagnetic calorimeter. My rule of thumb for this instrument is that photons with energy less than 30 MeV are worthless; such energies can easily be faked by the electronic noise and ambient radiation. Above 100 MeV you have to be fairly unlucky for an EMC hit to be background. I don't know if this is helpful; perhaps you can give me a better idea of the context of your question?

Does the process of extracting from the background require performing hundreds of iterations of the experiment?

Again, this is really dependent on context. Can you be more specific about what sort of experiment you're asking about?

Since you know quite a lot about it, and since the majority of my knowledge comes from Wikipedia, what does "fitting distributions in multiple dimensions" mean? What is the possibility of error of this process?

Have a look at my answer to magfrump. As for errors, our search algorithm does rely on the log-probability function being reasonably smooth, and can give misleading answers if that's not true. It can get caught in local minima; we try to avoid this by starting from several different points and checking that we converge to the same place. In some cases the assumption of symmetric errors can mislead you, so we often look at asymmetric errors as well. Most insidiously, of course, you can get the physics just wrong, but right enough to mimic the data within the limits of the fit's accuracy.

Oh, and lastly, do you know of any chart or list anywhere that details the known possible decay paths of bosons and fermions?

You could try the PDG's summary tables.