It was something that stuck in my mind from an explanation from a colleague, (Ph.D in film studies) so I'm not sure of a good citation. The best I can find with a quick Google is an appeal to QI (http://www.comedy.co.uk/guide/tv/qi/episodes/8/12/)
Well, it was the fashion of the time. Now gimme five bees for a quarter.
The reason that this became a widespread thing is that it was typically used in physical comedy in the early cinema era. Banana skins actually were substituted for horse dung, which is slippery to step in, and this was a much more common occurrence back before cars became ubiquitous. It was considered unseemly to show someone slipping in horse droppings, and would be stopped by the overzealous censors (not to mention offend the sensibilities of the time). The discarded banana skin took on the role as an inoffensive placeholder.
Well, there are a few things that would have to happen for them to compare clocks, and a key thing you're overlooking in your analysis:
1) For circular motion, the two ships would not have constant velocity in their _own_ reference frames - they're both accelerating towards the center (I'm assuming a flat space-time here for simplicity, but in GR things don't change much). Acceleration causes time dilation too!
2) For the ships to come together, they would have to maneouver. This will require further accelerations. Its during these that the other ship's clock will always appear to be moving faster.
What you've really got here is a reworking of the classical twin paradox - if one twin goes to Alpha Centauri (AC) and back, and the other stays on Earth, from _each_ perspective, the other one moves away then comes back. Yet the one who went to AC and back comes back younger - why? Well, what you're missing is that _at_ AC you have to slow down and then accelerate back towards Earth. This is the missing segment of the space-time picture, as the surfaces of simultaneity change during this acceleration.
I hope that clarifies things a bit.
We're in the EU, we're not dead. Are you confused, perhaps about the Euro?
That's no planet...
A big part of the problem is that there are few negative results in scientific literature. Ever found a paper with a clear negative outcome? I didn't.
Perhaps you should publish this finding.
The answer is that it's not much more difficult, but a lot more time consuming (gleaned from going to talks on the subject, not my area of expertise).
There are two basic ways that these planets are observed: They make the stars they orbit wobble (the basic 2 body problem - each body orbits the center of mass of the pair) and they dim the light from the star when they pass in front (like an eclipse).
The time problem comes from the fact that orbits are longer for objects more distant from the star. If we make the simplification that the orbit of the planet is basically circular, the time period for an orbit increases as radius^(3/2). (Insert semi-major axis for radius for non-circular). The standard is about three events separated by equal times to count as an observation - you have to wait to see an event at least twice to know the time period and so infer the radius of orbit, and once again to remove some flukes. Hence you're having to wait a long time looking at a star to see this happen.
Now, on top of that you've got the possibility that there's more than one planet, that the earth-like planet isn't the dominant mass, etc etc. This can all be cleverly dealt with (multiple wobbles, multiple eclipses) but it adds time to the confirmation process.
To give an example: Suppose you were somewhere near Proxima Centauri, and making the relevant observation looking for Earth. It would take at least three years to detect Earth, even if your telescope was amazing. Dynamics of the system would pick up the effect of Jupiter on the sun first, for the wobble detection (you wouldn't get much eclipse given the angle between the plane of the solar system and the position of PC) and it might take quite some analysis to pick up Earth at all given the effects of all the other planets.
Anyway, I'm sure some astro people can give a much better version of all this. Suffice to say that we aren't looking for Earth like planets at Earth like radii yet, but I imagine over the next ten to twenty years there will be a lot of poor graduate students analyzing data desperately looking for Gallifrey.
I can't do you a car analogy, but here's the very basic idea (massively watered down, physics friends - I know, I know, but let's try to keep this simple enough):
Consider a ball rolling on a set of hills and valleys. For our purposes, let's make it simple and 2-dimensional, but you can generalize quite easily. A 'vacuum' for this system equates to being at the bottom of a valley, as this is a point of lowest energy, and things tend to roll down and end up in the bottoms of valleys. The shape of the hill (called a potential which relates strongly to potential energy you might recall from high-school/college intro physics) determines the physical properties of the particle like its mass.
However, the valley you're at the bottom of might not be the lowest point overall in the system, it might just be a local minimum. This is what we call a 'false vacuum' in particle physics: A point in the system which looks to all intents and purposes to be a minimum in a small locale. However there could be a lower point.
Now, when you're just dealing with classical systems (like a ball rolling on a hill) this is all well and good. However in a quantum theory the wavefunction describing the particle can happily have non-zero values anywhere and (again very roughly speaking) this means that you can 'tunnel' from one minimum to another with some probability - breaking your false vacuum and moving you to another one. This tends to be in a downward motion - you go to a vacuum lower than the one you're in. This means that the mass of the particle will appear to change, and so all the physics you observe will be completely different.
These effects can related to all kinds of cool physics - the ones often talked in about popular-ish media are inflation/cosmological constant type things - if there is some energy associated with a particle being in a certain state, this can look a lot like a cosmological constant and produce and accelerating universe. However, if this isn't the global minimum there is a probability at all times that the tunneling effect mentioned above can happen, turning off the acceleration.
Anyway, hope that helps. Sorry I couldn't give you a car analogy, but here's an effort at one:
You (the particle) get a Mustang for your 17th birthday (lucky you!) and all your friends are jealous. You then start to think that since all the cars you see around you are worse than yours that you have the best car ever, and act accordingly. However, there is a chance that one day you'll catch glimpse of something sublime - an E-type. And your world view will change - there's a better car out there! Yours is only a false "best car ever", and now you have to act according to your new knowledge, which changes your behavior. Eventually you save up and buy yourself an E-type, moving to the 'true vacuum' / best car ever, and all your interactions with your friends are now based on this new car.
OK, that was godawful. But I tried.
As others have suggested, co-op games are certainly the way to make things interesting and fun, especially when there's going to be an obvious skill imbalance. Also try to pick things with a very shallow learning curve - if she hasn't played games before, just getting the coordination with a controller or mouse can be frustrating enough.
Games that have a low punishment for failure are going to be key when someone is first starting. This isn't quite the same as a shallow curve, but you want a game that is forgiving of your errors whilst you learn to play. Similarly something that isn't high pressure is probably good for early games. Left 4 dead, despite its excellence, probably isn't the best way to get into things (but will make an incredible game later if she gets into it!)
There are a couple of games I've found that can be really great fun in this way, and depending on
First there's Trine (and its sequel). You can pick this up quite cheaply, and it's a lovely fairytale of a game, beautifully drawn, gently but excellently narrated. It's a 1-3 player co-op platformer/puzzler (I played it with my partner who loved it) and having more people massively increases the fun. It also doesn't do the usual gendered thing with games of having "chick-armor" or "all people are male" - the female character (one of the three players) is very nicely done. Set on an easy mode it's simple to learn, works excellently with controllers and doesn't require too much coordination for a newcomer. If you pick your timing right, you can get it for about five dollars on Steam.
Another great coop game is Civilization V. I know it's not the most hardcore in terms of strategy of the series, (and I'm presuming as a gamer you know the series) but its very easy to learn and playing as a team, either hot-seat or with two computers, is very satisfying. A more experienced player can provide cover the learner in terms of military protection etc, or just set the game on sufficiently easy mode whilst she learns the basics. In coop mode you can learn a section of the game at a time whilst your partner takes care of the rest, so she can focus on military strategy and world domination whilst you build the empire to fund it, or she can learn to manage cities to produce culture and science whilst you cover her borders. The turn based nature of the game makes it easy for teaching someone how to play, and it offers a ton of depth and replayability.
On the RPG front, Torchlight is marvelous, with its sequel being a great 2-player game. It's diablo-esque, but maintains the joys of D2. It can get a bit hectic on occasion, which is very frustrating, but with a co-op game again you can cover her.
On the FPS/strategy, Orcs Must Die (2) is a nice one, but does suffer horrendously from a couple of things - it has a nice learning curve, but can get overwhelming fast which leads to frustration. Also it has tongue-in-cheek cliched characters which at first will look rather like the female is supposed to be the stuff of adolescent fantasy. It's not as bad as many out there, but let's just say that her armor is less than optimal in some regions.
Hopefully that should be something to get you going. Ignore the people who say "Don't do it" - of course you should try out new hobbies together, and you may find an excellent way to have fun together. My partner and I game together often, and sometimes at long distance is a great way to spend time "together" when you're apart.
It's a good question. I think you've gotten things a little backwards, though, with regars to the problem of propagation - inflation is a proposed explanation for propagation in the sense that it allows otherwise separate regions of the sky to have been in causal contact in the past. But this certainly does have impact upon the current inflationary paradigm in the following sense:
If there were large structures or large inhomogeneities in the early universe (before inflation) then it would be hard to get inflation going. The basic models of inflation contain a field whose energy can be decomposed (and I'm playing very fast and loose here) into three parts: Potential, Kinetic and fluctuations. From these parts, we say that if the potential is large enough, the inflaton undergoes a "slow roll" down the potential during which our regular inflation happens. Fluctuations are treated as perturbations on this background, and it's from these that we expect to see the everyday structure in the universe. A warning though: We don't know the physics that causes these fluctuations to stop being quantum fluctuations and become classical perturbations in matter on this background.
Now, if the fluctuations are too big, this model breaks down - the inflaton can't be high enough up its potential, and so slow roll can't happen. Hence before inflation we have to assume that the universe is largely homogeneous and isotropic, and fluctuations begin very small (technically in the "Bunch-Davies vacuum state).
A big inhomogeneity AFTER inflation isn't too bad - it could well be that this is just the result of one of the longer wavelength fluctuations. Of course, one would then have to explain
Now, if we had been dealing with a serious overdensity (tons of quasars in the same spot) rather than a large strung-out structure, we would certainly have a problem with inflation, but so far as I know this isn't too big of an issue.
Disclaimer: I work on the mathematical structure end of things, not the computation or observation, so there are certainly people more qualified than I, to whom I would happily defer if they want to post!
Sadly, it's actually the most visited online news site: http://www.bbc.co.uk/news/magazine-16746785
It's not surprising it gets a lot of press - a lot of people "read" it.
I write my CV in LaTeX. It's incredibly easy and spits out a good looking PDF. I'd wager I'm far from unique amongst people in my field (physics) in doing this - we write all our papers that way, most presentations too, so it seems a logical step.
A figure-8 is quite hard to find, since the symmetries involved would require almost perfectly equal masses between the stars and perfectly circular orbits of the stars. (This is from memory running simulations a long while back). However it is certainly possible to have a planet be orbiting one star for a few loops and then be captured by the other, orbit it a few times and keep getting passed back and forth.
The basic condition you need for this is for the planet to have enough energy to get over the maximum between the two gravity wells of the stars. If you think of kinetic and potential energy being like those of a ball rolling on a set of hills, you'd say that the ball is either trapped between two peaks or not. However with this case it would appear that the hills themselves are moving, so the "hump" between them will grow and shrink with time, sometimes letting the ball pass between valleys, sometimes trapping it in a single valley for a few cycles.
What's really remarkable is that this is all do-able without too much technical knowledge. You'd need:
About a second year undergrad level of physics - You could do it with Newtonian mechanics, but Lagrangians make it a LOT easier);
A bit of programming technique (two days or so with MATLAB and you'll get the basics of ODE solvers).
A LOT of patience
As an aside, you could just grab the game "Osmos" which has a lovely set of orbital levels that basically implement this