Strange

That is probably why you are getting so confused. It is more productive to just stick to what the theory really says. Unfortunately, your imagination is giving you the wrong answer. And if that is so, then the two of you will have experienced a different time between the pulses.

You don't need to do both GR and SR. They are not two different theories. You do the GR calculations. That includes any effects that would be covered by SR. If you don't need to worry about gravity, then you can get away with the simpler SR calculations.

If it was just the relative velocity, you could approximate it with SR. But it isn't.

You do have a right to know. But if you are not capable of understanding, I'm not sure what you expect us to do. "Path of desire" is an analogy for what is colloquially called the "path of least resistance" or more accurately, the path of least action. This is the "natural" path for something to take. It can be the physical path (of walkers across a lawn or water down a hill) or, as in this case, a path through a virtual state space. Quantum theory does not disregard mass. As noted, mass is critical. However it does disregard gravity for two reasons: the effect of gravity with masses of these scales is largely irrelevant; we don't (yet) have a theory that explains gravity at these scales. It is not just speculation, it is just plain wrong. The muon is a fundamental particle. It is an objective physical science based on experiment and measurement. I can't imagine why you would think otherwise. The article that started this thread is a great example of people using advanced experimental techniques to test the theory.

You are hilarious.

Each satellite will be moving at a different speed relative to the receiver. The receiver itself may be moving. The receiver's altitude may vary. And so on...

It is already done. Isn't it? I think you are confusing chess and tic-tac-toe (where whoever moves first wins).

The problem that Doppler causes is the need to scan a wide range of radio frequencies to find each satellite at start up. It doesn't have (as far as I remember) any effect on the triangulation process. GR has to be used when doing the triangulation otherwise the times and distances used would be wrong. Remember this is the theory of relativity, i.e. the receiver needs to calculate the difference between its frame of reference and the satellite's. This is, potentially, different for every satellite.

It is correct, but incomplete. That is only about sending corrections to the satellites. There are also corrections made in the receiver which need to take into account the differences between the receiver and each satellite (based on its relative velocity, etc.) No, because that Earth time would need to be translated to the reference frame of each satellite, which requires GR.

The GPS receiver has to correct for GR effects in both timing and distance in order to correctly triangulate positions. Without this it would only be accurate to 10s of meters (or maybe worse, it is a long time since I worked on them). (I don't know what you mean by "GR time")

Ah, well. Good in its day, perhaps. It varies. I imagine the case is made of thermosetting plastic which wouldn't really melt. Just catch fire if it gets hot enough. I have always used them continuously, including for very compute intensive tasks. It will have gone through a very thorough thermal design process, modelling heat conduction, air flows, etc. The processor will turn fans on and/or change clock speed/supply voltage as necessary to keep it in a safe working temperature.

I suppose that if you set fire to it, it might create some fairly toxic fumes. And you probably shouldn't eat it. I'm not aware of any other way the plastic can become toxic. The laptop is designed to withstand the levels of heat it generates so I would not expect the plastic to melt or catch fire. So I can't see any danger from it. There should not be any lead or mercury in a modern device so the only toxic materials might be the metals in the battery (if they were dissolved in your drinking water). Good laptop, though.

That is within my error bounds for "*roughly* 90 degrees" I really had no idea. I did try looking it up but couldn't find anything, so thanks for that.

You were all in the same frame of reference, that is why. However, if some of those people lived high in the Andes or Himalayas (or even up a small hill) they would disagree very slightly about how much time had elapsed since you were all in the same room together a year before. Quite the contrary. The Mars probe is moving and n a different gravitational potential to us. Therefore it is experiencing a very slightly different time. This is probably small compared to the Doppler effect but it would probably be possible to measure the difference in the frwquency of its radio signals sent and received, due to relativistic effects. That is only true in special relativity. That symmetry breaks down when you take gravity into account. And that is exactly why there is no universal or absolute time. Then why are you contradicting them? 1. Time runs at a different rate on the moon. 2. If the moon exploded you would have to wait 1.2 seconds to find out. Just plain wrong.

That doesn't sound right. The entropy of a black hole is porportional to its surface area: http://en.wikipedia.org/wiki/Black_hole_thermodynamics#Black_hole

The phrase "artificial atom" appears in the news article (see links in post 2). This, again, is an analogy. I have no idea what that means. "Einsteinium is a synthetic element with the symbol Es and atomic number 99. It is the seventh transuranic element, and an actinide." (Wikipedia) In the same way energy defines the wavelength of a photon: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/debrog2.html I have no idea. You haven't mentioned it before. But the Compton wavelength is related to mass, as well. Sorry. No idea what that means, either. No, he just means that the paper was written for other scientists. That is what scientists do most of the time. The "paths of desire" article was written for non-scientists. But, as it is trying to describe something very complex that cannot be understood without knowing the relevant science, it used simplifications, analogies and metaphors. This means you cannot tell what the science really is. You seem to think there is some sort of deliberate effort to keep information away from "ordinary people". There isn't. It is just very, very complicated. There is no reason a plumber should be able to do brain surgery.

If you look at this image, for example, the red band across the middle is the emissions from our galaxy. Earth's axis is not aligned with the galaxy's axis. I think it is *roughly* 90 degrees away. http://commons.wikimedia.org/wiki/File:WMAP_2008_41GHz.png

She experience less time. (Which is why, on average, she must see the ticks from the pulsar happen more quickly.) Actually, this can all be described with special relativity (which is good as the mathematics is pretty simple). The pulsar is (I assume) in the same frame of reference as the twin on Earth (i.e. not moving significantly relative to Earth). Therefore an observer on the pulsar will see the same as the observer on Earth. (Otherwise you are introducing a third frame of reference which just makes the whole thing needlessly complicated.) There is no "just one time". This is equivalent to the travelling twin heading towards the pulsar then turning round and heading away from it. This is all explained in great detail on the Wikipedia page for the twin paradox. I honestly don't think I can do it better or simpler. (The twins will, of course, disagree about when the halfway point occurs.)

I wouldn't call myself an expert ... And now I have to attempt an answer! I will give a quick answer now, as I don't have much time, and then add more detail later. All of these questions revolve around understanding the concept of "expanding space". An important point here is that this is due to everything (on sufficiently large scales) moving away from everything else. As a result, wherever you are in the universe, you will see the same thing: everything moving away from you. So we are are in the center of our "observable universe". But so is every other point in space. But the universe as a whole doesn't have a centre. One way of thinking about this is to "wind the clock back" and imagine the universe shrinking instead of expanding. All the gaklaxies in the universe will get closer and closer ... until they are all compressed into the same tiny space. So everywhere is where the big bang started. Everywhere is the "centre". I don't really follow this. The most distant galaxies we can see were already a few billion light years away when the light we see now was emitted. They are now about 45 billion light years away (I think). Note that this is not the accelerating expansion. This is just expansion. It is a simple consequence of geometry. Consider a number of galaxies separated by the same distance (far enough apart that the expansion of space is significant and is the same between all of them). At time 0, they are 1 unit apart: A.B.C.D.E.F After some time they are 2 units apart: A..B..C..D..E..F After the same time again, they are 3 units apart: A...B...C...D...E...F And so on: A....B....C....D....E....F Now, if we look at the distance between B and C, for example, it increases by 1 at every time step. But the distance between B and D increases by 2 at every step. So the distance between B and D is increasing twice as fast as the distance between B and C; i.e. the speed of separation is twice as great. Choose any pairs of galaxies and you will see that apparent the speed of separation is proportional to the distance between them. Take two objects far enough apart and the speed of separation will be greater than the sped of light. (But that is OK, because the speed of light limit is a local thing, whereas these objects are in different frames of reference - see below.) Now, more detailed observation and analysis showed that at some point in the past, this rate of expansion increased and so the speed of separation at any given distance increased. This is an important, but quite subtle, point. Firstly, note that the "speed limit" comes from Special Relativity which is an approximation that only applies locally. So something nearby cannot move through space faster than the speed of light. However, the expansion of space is described by (and is an inevitable consequence of) General Relativity. In this case, the expansion of space between two points is not limited. As we can see from the description above you can always choose two points which are sufficiently far apart that the total amount of space between them will cause them to appear to be separating faster than light. This has always been true. There are now, and always have been, galaxies we can see which are moving away at greater than light speed. Hope that helps a bit. It is quite a confusing subject! More answers and detail here: http://www.astro.ucla.edu/~wright/cosmology_faq.html

Sorry, that's all I know. As I say, I have heard of the concept but never encountered or even seen any details of one. A couple of very old reports: http://www.analogmuseum.org/library/simstar_brochure.pdf http://deepblue.lib.umich.edu/bitstream/handle/2027.42/68553/10.1177_003754976600600408.pdf?sequence=2 http://www.computer.org/csdl/proceedings/afips/1961/5058/00/50580299.pdf

Ah, not completely wasted then.

One piece of advice I was given when doing this (for an industrial research proposal) was to make sure you structure the proposal so you have an effective "story" going from "what the problem is", what other approaches have been tried, what you (and partners, if relevant) will do (and why), why you think this will succeed (and why it may not - the risks) through to what the results will be why you think they will be useful/valuable. I think the idea is to make it more engaging and easier for the reviewers to follow, rather than a dry summary of the facts. It seems to have worked...

You mean my two-word reply was wasted!

Hybrid computers combine digital computing and analog computing. I have designed and worked with many different types of computers for more than 40 years and have never come across one. If they are used, I assume they are in very specialised fields.

What the ... !!