exoplanet - Could we detect an earth-like planet around another star?

The short answer is no; we cannot quite detect earth-like planets around Sun-like stars with orbital periods of 1 year.

The two main planetary detection techniques are transit photometry and the radial velocity variation technique. Direct imaging of earth-like planets at 1 au from the host star is utterly impossible with current technology - the problem is not the sensitivity, it is the contrast achievable at small angular separations.

The first demands high precision photometry (a transit by an "earth" across a "sun" produces a lightcurve dip of about 0.01%). This kind of precision has been achieved (by space-based observatories), but they have not observed stars for sufficiently long to build up the requisite number of transits (you need at least a few) to confirm a detection at periods of 365 days The Kepler primary mission ceased after about 4 years, meaning it will be tricky to dredge out convincing Earth-like transit signals at periods of 1 year (but not impossible) - and even then you need to perform some sort of follow up to prove it is a planetary mass object, rather than some false positive, and actually estimate the mass to show that it is a rocky planet.

Which brings us to the doppler radial velocity technique. The motion of the Earth-Sun system results in the Sun executing a 1-year orbit around the common centre-of-mass, with an amplitude of about 9 cm/s. This is about a factor of 5-10 smaller than the best precision that is available at any telescope in the word right now.

So - although none have been confirmed yet (there are candidates in the Kepler data), that does not mean that Earth-like planets are uncommon. Indeed most sensible extrapolations of the frequency of Earth-sized planets found at closer orbital distances suggests that they could be quite common (e.g. $sim 25$% Petigura et al. 2013)

galaxy - Why aren't new stars in Earth's relative proximity constantly discovered?

To the naked eye, the answer is almost certainly no because of the enormously slow movement of stars across the sky and because 5,000 stars may be a lot but only a tiny percentage of the sky is covered by visible stars.

To Hubble, which can see perhaps tens of millions of stars, maybe more, the link here, has a picture of two stars that are approaching crossing each other's path from our point of view. With a big enough telescope it probably happens from time to time, though I wouldn't want to try to calculate how often, but to the naked eye, I'm comfortable saying no, in fact, it was often assumed that stars didn't move and were fixed in the sky (contrary to what Macrobius said). That was the popular point of view prior to Halley's observation.

There was also Tycho Brahe's "De Nova Stella" or "new star" which we now know to be a super-nova, and that was quite the surprise at the time. Nobody thought a new star could appear because they thought the stars were fixed and permanent, but that appearance wasn't by the method you suggest.

Consider how small stars are from our point of view. Alpha Centauri A, the larger one, it's about 1.7 million KM across and it's about 4.3 light years away, or, 41 trillion KM. It's diameter is 23 million times smaller than it's distance from us. That's the equivalent of looking at a golf ball from nearly 200 miles away. Now if you scatter 5000 golf balls each 200 miles away across the sky and you let them move around very very slowly, how often do you think one golf ball passes in-front of another? Not very often. Granted, that's not quite right as the atmosphere spreads stars out a bit so each golf ball is smudged to maybe the size of a basketball, but they almost never pass infront of one another, at least, not if we only take into account 5,000 visible stars.

Now, binary stars, it happens more often if they are lined up right, then they can pass infront of each other and this has certainly been observed by telescope but not to the Naked Eye, we can't visibly tell that Alpha Centauri is 2 stars (3 with the more distant Proxima but that can't be seen by the eye). They are on average about a billion miles apart but that can't be seen by the naked eye. It was observed by telescope in 1689.

There simply aren't enough visible stars (and taking HDE's point that most of the 5,000 visible stars weren't cataloged until recently), there's essentially zero chance that it was ever observed that a star appeared "new" by passing from behind another star.

Using Hubble, it can happen, but not to human sight.

geocentrism - How can we tell that the sun is moving with theories such as the theory of relativity?

There are some simple answers to your questions, and some (historic) controversy. I'll answer the simple elements first (but backwards by your ordering of the questions), and then describe the nature of the controversy.

3. What is absolute motion?

Absolute motion is motion that is referenced (compared to) a feature that you can say is standing still. For example, how do you know the speed of a car? You compare it to something that is standing still.

2. What is relative motion?

Relative motion is motion that is referenced (compared to) something that may be moving. For example, when driving, you may find that the car next to you is edging ahead of you. You can say that it is moving 5 miles per hour faster than you - that is its relative speed. (Note, it also has an "absolute" speed, say 65 miles per hour, while you have an "absolute" speed of 60 miles per hour. Here I use "absolute" in the sense of comparing speed to the surface of the Earth, not a universal absolute.)

This brings us to the definition of a reference frame, which is critical for understanding the later arguments. A reference frame is a perspective from which one can begin to measuring things. It is a defined zero point from which you can measure distance, speed etc. So, in the example above, you have a reference point, yourself in the car, and you see the other car moving ahead of you at 5 miles an hour, and you also see the ground moving past you at 60 miles an hour. The driver of the car also has a reference point, himself, and sees you as moving backwards at 5 miles an hour, and the ground moving past at 65 miles an hour. Someone sitting on the ground also has a reference point, seeing two cars moving away at 60 and 65 miles an hour respectively.

1. How do we know that indeed the earth moves?

We compare the Earth to other things. We can compare it to the sun, and therefore know that it is both moving around itself (rotating) and around the sun (revolving). We compare the sun to the milky way, noting that the entire solar system is orbiting around the center of our galaxy. We compare the galaxy to other galaxies, and note that our galaxy is drifting towards our local great attractor. And (this is where the controversy of the other answers comes into play) we can compare our speed to the equivalent motion of an object at rest with the Cosmic Microwave Background Radiation (called CMBR for short), and can even deduce how fast the local great attractor is moving compared to that.

So what is the controversy? The controversy is around the question, "Is there a universal reference frame?" In other words, is there such thing as a point in the universe that we can say is the zero point that we measure all positions and velocities from?

Historically, this was fought out between Einstein and Lorentz. Before the Michelson-Morley experiments, it was thought that light traveled through a ghostly material called an "aether" that wasn't moving, which could be considered the universal reference frame. The Michelson-Morley experiments were set up to determine the Earth's relative motion through the aether, but it didn't find any. Lorentz created a mathematical method that could account for this, but it was missing a physical basis. Then along came Einstein, who replaced the assumption of an aether with the assumption that light travels at a constant speed. From this he developed the now famous Special Theory of Relativity (although, that is the name it has subsequently come to be called). This was a little too far for Lorentz, and he developed a counter theory, which slowly transformed into a very similar theory to Einstein's, with one exception - Lorentz believed that there was an, as yet undetectable, zero reference frame for the universe. Here is what he said in 1910

Provided that there is an aether, then under all systems x, y, z, t, one is preferred by the fact, that the coordinate axes as well as the clocks are resting in the aether. If one connects with this the idea (which I would abandon only reluctantly) that space and time are completely different things, and that there is a "true time" (simultaneity thus would be independent of the location, in agreement with the circumstance that we can have the idea of infinitely great velocities), then it can be easily seen that this true time should be indicated by clocks at rest in the aether. However, if the relativity principle had general validity in nature, one wouldn't be in the position to determine, whether the reference system just used is the preferred one. Then one comes to the same results, as if one (following Einstein and Minkowski) deny the existence of the aether and of true time, and to see all reference systems as equally valid. Which of these two ways of thinking one is following, can surely be left to the individual.

Einstein maintained that not only was a universal reference frame undetected, it was unnecessary, and Occam's razor should rule (i.e. that if something is unnecessary for the theory to work, then it shouldn't be included in the theory). It is interesting that both theories actually predict the same things, but in the end, Einstein won. Most physicists these days would state that a universal reference frame does not exist.

Since that time, two key things have happened that impact this. First is the discovery of the expansion of the universe. This means that, even if we were to make an arbitrary universal zero position and time, other reference frames that start out at stationary compared to this reference frame will start to move away, even though any object there has undergone no acceleration. This greatly complicates any attempt to set a universal reference frame, an makes it much easier to consider that none exist. Tick one for Einstein.

The second thing was the discovery of the CMBR. This is the relic of a change in the entire universe at around 380,000 years after the big bang. At that point, the universe went from opaque (where light couldn't travel very far without encountering some matter to interact) to transparent (where some light could travel consistently without interruption until someone like you measures it). Two interesting (and relevant) features were found about this CMBR - it comes from every direction (consequently it is universal, i.e. can be seen from anywhere), and it is very consistent in intensity from every direction (termed isotropic). This means that anyone, anywhere, can measure their speed relative to the local knowledge of the universe. Furthermore, this effective reference frame can be used to measure velocity irrespective of the expansion of the universe, if one considers certain interpretations about comoving reference frames. Although this is very different to a universal reference frame of an aether, it is certainly, in one sense, a universal reference frame. Tick one to Lorentz.

So what does this mean? Does it mean that Einstein was wrong? No. Einstein was concerned with the physics of light and electrodynamics, of the relationship between time and position and velocity. The basis of Einstein's argument was that, no matter how fast you go relative to any other object, the physics of what you measure locally will be the same. The original concept of a universal frame implied otherwise, and Einstein has been proven experimentally correct over that original concept.

However, the concept of using the CMBR to define a universal reference frame is a slightly different idea than the original concept (and more in line with Lorentz's final theory). It does not imply any change in the local physics due to relative speed. But it is, as suggested by Rob Jeffries above, a useful reference frame. I would argue it is a special reference frame, in a manner that science has created special zero points throughout history (e.g. sea level, 0 degrees latitude, binding energy etc). None of these zero points change the physics of what is measured locally, but they make it much easier to compare measurements at different locations etc. In the same way, the CMBR reference frame makes it easier to answer a range of questions about non-local physics. For example, what is the age of the universe? (The age is maximum at the CMBR reference frame.)

So, in conclusion, when we see some arguments between physicists about whether the CMBR is an absolute or universal reference frame, it is usually because one side or the other is interpreting the term in the same manner as the original concept, with all its incorrect implications, rather than the lesser concept of a natural definer of the local speed to a universal feature of the universe.

gravity - Wouldn't the rings of Saturn experience tidal effect?

Most of the 60 moons in the Saturn system are far away from the rings and very small, so their effect on the rings is negligible. But larger ones that are closer in (Enceladus) do have a rather significant effect on the rings, but as the gravitational pull of these moons is radially outward, it is hardly visible. On the other hand, small moons inside the rings that are a few kilometers in diameter cause significant changes in the ring system.

The orbits of those giant rocks are slightly inclined relative to the rings, which causes the rings to create a bulge in the direction of the small moon as seen in the picture. And these effects are fairly significant as the rings are mostly just a few hundred meters thick or less without a moon present, but with one, they are possibly hundreds of kilometers spread out.

Why can we detect gravitational waves?

The short answer is that waves that are "in the apparatus" are indeed stretched. However the "fresh waves" being produced by the laser are not. So long as the "new" waves spend much less time in the interferometer than it takes to expand them (which takes roughly 1/gravitational wave frequency), then the effect you are talking about can be neglected.

Details:

There is an apparent paradox: you can think about the detection in two ways. On the one hand you can imagine that the lengths of the detector arms change and that the round-trip travel time of a light beam is subsequently changed and so the difference in the time-of-arrival of wavecrests translates into a phase difference that is detected in the interferometer. On the other hand you have the analogy to the expansion of the universe - if the arm length is changed, then isn't the wavelength of the light changed by exactly the same factor and so there can be no change in the phase difference? I guess this latter is your question.

Well clearly, the detector works so there must be a problem with the second interpretation. There is an excellent discussion of this by Saulson 1997, from which I give a summary.

Interpretation 1:

If the two arms are in the $x$ and $y$ directions and the incoming wave the $z$ direction, then the metric due to the wave can be written
$$ds^2 = -c^2 dt^2 + (1+ h(t))dx^2 + (1-h(t))dy^2,$$
where $h(t)$ is the strain of the gravitational wave.

For light travelling on geodesic paths the metric interval $ds^2=0$, this means that (considering only the arm aligned along the x-axis for a moment)
$$c dt = sqrt{(1 + h(t))}dx simeq (1 + frac{1}{2}h(t))dx$$
The time taken to travel the path is therefore increased to
$$tau_+ = int dt = frac{1}{c}int (1 + frac{1}{2}h(t))dx$$

If the original arm is of length $L$ and the perturbed arm length is $L(1+h/2)$, then the time difference for a photon to make the round trip along each arm is
$$ Delta tau = tau_+ - tau_- simeq frac{2L}{c}h(t)$$
leading to a phase difference in the signals of
$$Delta phi = frac{4pi L}{lambda} h(t)$$

Interpretation 2:

In analogy with the expansion of the universe, the gravitational wave does change the wavelength of light in each arm of the experiment. However, only the waves that are in the apparatus as the gravitational wave passes through can be affected.

Suppose that $h(t)$ is a step function so that the arm changes length from $L$ to $L+h(0)/2$ instantaneously. The waves that are just arriving back at the detector will be unaffected by this change, but subsequent wavecrests will have had successively further to travel and so there is a phase lag that builds up gradually to the value defined above in interpretation 1. The time taken for the phase lag to build up will be $2L/c$.

But then what about the waves that enter the apparatus later? For those, the laser frequency is unchanged and as the speed of light is constant, then the wavelength is unchanged. These waves travel in a lengthened arm and therefore experience a phase lag exactly equivalent to interpretation 1.

In practice, the "buildup time" for the phase lag is short compared with the reciprocal of the frequency of the gravitational waves. For example the LIGO path length is about 300 km, so the "build up time" would be 0.002 s compared with the reciprocal of the $sim 100$ Hz signal of 0.01 s and so is relatively unimportant when interpreting the signal.

human biology - What evidence gives clues to the physiological basis for conversion disorder?

Conversion disorder has a set of DSM diagnosis criteria, which, among other things, includes ruling out all neurological disease.

However, as the media has shown us (and one could argue a biased portrayal), many of these young people in Le Roy, NY who were diagnosed with conversion disorder have exhibited tics and starts that are highly reminiscent of Tourette's Syndrome, which is thought to have some basis in pathology of the basal ganglia (and perhaps the thalamus and frontal cortex).

Granted, the issue is being looked into as having an environmental cause, so I can understand how the diagnosis may be reshaped, but I'm more curious about the initial diagnosis of "mass hysteria".

If this syndrome causes real physical symptoms and yet is "psychogenic", through what physiological means is the disease acting? Why would ruling out a neurological basis be a valid criterion?

gravity - Gravitational Propulsion - Astronomy

I am not a physicist, in fact I am just a family doctor, so I beg of you to excuse me of anything I say that you may find outrageous :)

But I came to this forum to see if anyone would be able to validate or offer a perspective on a documentary I watched today. It is an old one to say the least, probably from the 80s, but still has some very interesting information.

Basically, a supposed physicist by the name of Rob Lazar had been working on gravitational propulsion systems at Los Alamos Laboratory, and had been part of a project where they harnessed gravity for travel. Since gravity distorts spacetime, he proposed the idea that a ship in the same way could do this to travel. Furthermore, he said by harnessing gravity and targeting gravitons at points in spacetime, it would create a divet in that location, and thus the ship could move toward it in as little time as possible. Basically, this is not a propulsion system at all, but rather an "attractive" system. He was talking about a stable super-heavy element with 115 protons (element 115) that could create this "amplifying of gravity waves". I am really confused, and do not worry, I will provide a link to this information. Could someone comment on the validity of such a case?

http://www.karinya.com/travel1.htm