timo

Strictly speaking, the article does not say "above" infinity, it says "hotter" than infinity. If you interpret "infinity" as "any/every positive temperature" and "hotter" as "higher energy" then what the article states is -at least in this respect- correct.

"The laws of physics are the same in all fields frames of reference" (or similar) indeed is a key phrase in relativity. But that is not the same as "the laws of physics are the same everywhere". The latter talks about the physics at locations/areas, the former about how physics laws should be formulated in order to be robust under the rather different ways to describe a location/area in relativity.

(EDIT: The following is in reply to your original post, not the 2nd one where you asked further questions) I don't really think that "the laws of physics are the same everywhere" is particularly tied to relativity. "Astrophysics" and "cosmology" may be more adequate characterizations of the fields where this assumption is important. And in e.g. astrophysics, the laws of relativity being the same is pretty much equally important as the law of chemical elements' spectral lines being the same. I also disagree with the notion that the assumption was fundamental for relativity. It's merely important for some of its applications (as mentioned).

Until I read the hype today I was under the impression that a population inversion of states was important for certain types of lasers to work. So it's a bit strange that what I considered decade-old technology is suddenly sold as the scientific breakthrough of the century.

Despite proximity1's repeated claims that the OP had been ignored, I disagree. As I said in post #3, Airbrush's conceptual problem is due to incorrect premises - owing to leaving out or over-reading the important word "visible" (which may not the fault of Airbrush but possibly of his source). Hinting to this important point completely answers the original question. For the related question how a finite expansion rate can lead to something infinite arising from something of size zero, see this thread: http://www.scienceforums.net/topic/69359-infinity/ However, while this may seem a similar question, it is in fact something completely different: No one would claims that a finite expansion rate can result into an object the size of a proton expanding to infinite size in finite time. For the record: Even though good manners would dictate it, I did not read all of the posts here (in fact I ignored most). I did not feel they really added to this rather simple issue. So sorry if I missed the point (but I did read the OP, at least )

It's remarkable that in public understanding having had an idea seems to be considered the striking feature characterizing Albert Einstein.

My guess would be that the source you got the size of a proton from actually said "size of the visible universe" (which actually is considered finite). Otherwise, the source would make quite an extraordinary claim (or be a confused newspaper editor).

That does indeed seem to be the case. Which of course begs for the question why matter and space should not be something different. I've seen people treating iron and glass as being something different, and on first glance they seem to have more in common than matter and space.

I was referring the other one of the two sentences in post #2. Possibly should have made that more clear . EOD for me.

See post #2.

It's not so complicated, actually. But to be clear: 1) "Coordinate system" is much more general than the special-relativistic "frame of reference". Too general to be of use here, even though I usually prefer it. In the context of this thread (and pretty much any Relativity thread on sfn) you can probably assume the two terms to mean the same. 2) In the frame of reference of a source emitting two beams of light to positive x-direction and negative x-direction, respectively, the difference between the light beams velocity is [math]\Delta \vec v = (c,0,0) - (-c,0,0) = (2c,0,0)[/math] (or its negative). The magnitude of the velocity difference is [math] |\Delta \vec v| = 2c[/math]. 3) In the frame of reference of a source emitting two beams of light into opposite but otherwise arbitrary directions, the magnitude of the velocity difference is again 2c. 4) In any frame of reference, in which the two beams move in opposite directions, their relative velocity is 2c. Irrespective of whether this is the frame of the source or not. 5) If the two beams do not move in exactly opposite directions, the magnitude of the relative velocity is not equal to 2c. 6) Generally, the relative velocity between the beams of light is [math] c (1-\cos x) [/math], where x is the angle between the two velocities. This follows from basic geometry. 7) If there exists a frame of reference in which the relative velocity of the two beams is 2c, then there exists another frame of reference in which their relative velocity is smaller than 2c. In the case of case (2), such a "<2c"-System would be one moving in y-direction relative to the light source. 8) There is no frame of reference in which either beam of light does not have a velocity with [math]|\vec v| = c [/math] - as pretty much everyone in this thread felt the urge to repeat. In all of the statements above, there is pretty much no change with respect to non-relativistic physics. The big change that Relativity introduces is, in this context, the definition of how velocities transform between different frames of reference (namely not by simply adding the velocity of the new frame to the velocities of the light beams). But within a frame of reference, no one stops you from defining "relative velocity" as the difference of the velocity vectors (whatever that definition may be good for). There is, of course, much more to special relativity than just the transformation rules of velocities upon a change of frame of reference. But I don't believe that any of it matters here.

Unless there is a reason to believe that an expansion of space-time contradicts with motion within this space-time I think you are correct: The expansion of space does indeed not prove that matter doesn't actually move. Btw.: It's rather interesting to see capitalization ignorance the other way round.

I would be very surprised if plant growth in weightlessness hadn't been tried out on MIR, ISS, or similar conditions. Such research is one of the first things that comes to my mind for justifying huge amounts of money being put into space stations in particular or space research in general.

It's true in all reference frames in which the two packets of light move in opposite directions, since only then and only then the difference between the two (3-)velocity vectors with a magnitude of c has a magnitude of 2c. That does include the frame of the light source in this case, because leveni defined the light source to emit in opposite directions.

There is some argument/proof that the Carnot efficiency is the best you can get. So I believe what the engineers have in mind is an effective device, not necessarily a reversible one.

I must have overlooked that picture in your earlier posts - not to mention that I still don't see a definition of h or how your claim follows from the term. I'm not even convinced that your "gravitational interaction" term actually has units of energy as you claim - but that's just silly nitpicking and doesn't really add something. I'm not convinced that your knowledge extends beyond having seen images of equations in a book of Feynman, and you probably believe I don't even know that much. Given that we already left the part where it's about the other's opinion, I don't wish to continue this discussion.

"The gravitational interaction is given by <some unspecified physical quantity with units of energy>" isn't exactly more helpful to me than "the gravitational interaction is given by <some number>". I doubt it. Sure. In the very same sense, the effect of classical gravity on a free-falling object depends on that object's mass (except that in non-relativistic physics the comparison of momenta at different locations is properly defined).

I don't know what "the gravitational interaction is <some number>" is supposed to mean. And I don't know what "h" is, either. I certainly didn't doubt that you can write down expressions involving the energy-momentum tensor. In physics, math and computer science (and presumably other sciences, too) "or" usually means an inclusive or, not an exclusive or (xor). That's the sense I meant here, not least since momentum usually implies kinetic energy, anyways. It's kind of interesting that I had chosen the very same example to claim that the effect of gravity does not depend on energy and momentum of the light pulse.

Actually, the Higgs Boson doesn't give mass to anything. The interaction with some of the non-Higgs-Boson part of the Higgs-Field results in mass. But that's the mass of the known elementary particles, only. The origin of e.g. the mass of protons is the strong interaction. And the existence of (sane) people calling the Higgs boson "God particle" is an urban myth.

I assume with "nonzero energy-momentum" you mean "anything with either non-zero momentum or non-zero energy". While you run into technical issues with the p->0 limit for light (which apart from a possible potential energy implies E->0), the effect of gravity on a light pulse is independent on its momentum (in the sense that the equation of motion can be sensibly written down as the 4-acceleration being a function of the 4-position and the 4-velocity and not including the 4-momentum). In that respect, I tend to disagree with your statement. I do agree with the statement that "gravity is a force between objects with mass" is only the everyday-world simplification of a conceptually greater principle, though. @Arjun: I haven't gone through the calculation, so I am slightly hypothesizing here: Certain aspects of gravity that you learn in non-relativistic gravity are simply not true in relativistic gravity. You mentioned that all objects get accelerated equally, irrespective of their mass. The statement implies an even more astonishing assumption that is so fundamental to much of non-relativistic physics that people tend to not even recognize it as a strong assumption: The assumption that the acceleration due to gravity is independent of the current velocity [*]. Now, if you actually look at the equation of motion in relativistic gravity (you should readily find it as "geodesic equation" on Google or Wikipedia) you will find that the acceleration of an object does depend on its velocity [**]. As the velocity of a massless object strikingly differs from that of a massive one, so can its acceleration. [*] In some sense it is rather remarkable that people take this as granted, given that friction is a well-know everyday-phenomenon no satisfying this assumption. [**] There is the possibility that due to extra constraints the velocity as you know it may actually cancel out. This is exactly the part where I am hypothesizing in assuming it not to always cancel.

I vaguely remember a "better people" program having been tried, already. They lost the war, and the whole concept doesn't have a very good reputation amongst civilized people since then.

What do you believe the or even an "equation for momentum of gases" to be? EDIT: Whatever: The average translational energy of a gas molecule is given by E = 3/2 kT, with k being the Boltzmann constant and T being the temperature. You directly get an average square of the momentum of such a gas molecule from that. That's probably towards what you think you meant.

The two things are quite closely related, but I am not sure if there is "the" definition of either. Already the very common term "vector" has different default meanings for a mathematician (element of a vector space), a physicist working with relativity (object that has a certain behavior under coordinate transformations) and an engineer or computer scientist (combination of values (x,y,z)) that are related but not identical. Generally, in the framework that I know the term tensor from, a vector could be considered be a special case of a tensor (a rank-1 tensor). In fact, something along the lines of "a tensor is a generalization of a vector" may be the explanation you may hear most often. A definition of "tensor" that I like is that it is a function that maps a number of vectors on a value [and that is linear in each of its arguments].

It's whatever you want it to be, from an escalator to the most powerful weapon in the Star Trek universe. Most people on Internet forums would probably argue that true anti-gravity has to be related to magnetism (that they don't understand, either - so the two things just have to be related, somehow).

Imho the biggest failure of such endeavors is the implicit assumption that people having undergone scientific training prefer putting energy into the next-best stranger's ideas over simply working on their own ones. Or in other words: Scientists do not lack ideas. What we are usually short of are time, manpower and funding to work on all the ideas we have.