Quote from: meberbs on 01/02/2018 09:56 pmQuote from: dustinthewind on 01/01/2018 05:35 amQuote from: Einstein’s 1917 Static Model of the Universe: A Centennial ReviewQuoteapproximate assumptionAs Einstein stated, it was an approximate assumption made while deriving a specific solution to his equations. It allows for picking a frame that makes the math easier, but it does not make that frame "special" as you are presenting it. Also if you actually bothered to read the paper you referenced, you would see that his assumptions were incorrect for our universe, since the universe is expanding. In fact the last sentence you quoted was immediately preceded by:Quote from: Einstein’s 1917 Static Model of the Universe: A Centennial ReviewIndeed, many years were to elapse before the discovery of a linear relation between the recession of the distant galaxies and their distance (Hubble 1929), the first evidence for a non-static universe.The entire paragraph it was a part of was explaining that our modern knowledge that his assumptions do not describe our universe was not available to Einstein, so his assumptions were reasonable from his perspective. By pulling that sentence out of context you completely changed its meaning.If you read the paper then you know that solution was only lacking the cosmological constant which he adds later. This doesn't change the frame work in which he lays out his conditions (density, stars with low velocity that define a metric, closed universe, 𝜆).

Quote from: dustinthewind on 01/01/2018 05:35 amQuote from: Einstein’s 1917 Static Model of the Universe: A Centennial ReviewQuoteapproximate assumptionAs Einstein stated, it was an approximate assumption made while deriving a specific solution to his equations. It allows for picking a frame that makes the math easier, but it does not make that frame "special" as you are presenting it. Also if you actually bothered to read the paper you referenced, you would see that his assumptions were incorrect for our universe, since the universe is expanding. In fact the last sentence you quoted was immediately preceded by:Quote from: Einstein’s 1917 Static Model of the Universe: A Centennial ReviewIndeed, many years were to elapse before the discovery of a linear relation between the recession of the distant galaxies and their distance (Hubble 1929), the first evidence for a non-static universe.The entire paragraph it was a part of was explaining that our modern knowledge that his assumptions do not describe our universe was not available to Einstein, so his assumptions were reasonable from his perspective. By pulling that sentence out of context you completely changed its meaning.

Quote from: Einstein’s 1917 Static Model of the Universe: A Centennial ReviewQuoteapproximate assumption

Quoteapproximate assumption

approximate assumption

Indeed, many years were to elapse before the discovery of a linear relation between the recession of the distant galaxies and their distance (Hubble 1929), the first evidence for a non-static universe.

expansion of space sounds a lot like expansion of a metric.

It also seems to suggest the matter generates the metric.

All I am suggesting is that this proper metric generated by the low velocity stars gives a metric of fastest time progression. Moving relative to is distorts your time so that your time passes slower and gives the illusion of a distorted metric via your distorted clock. You will notice in the graphics of the moving ship that its the non-distorted metric where time passes faster.

With that said, I reiterate the idea that an ftl jump, when one is moving,

I wouldn't be so quick to just dismiss them as crackpots. It is relevant with respect to possible detection of motion through some form of a metric....Several citations on their work it appears.

In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zürich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the definition of a spacetime interval that combines distance and time. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded.Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed how mass and energy curve this flat spacetime to a Pseudo Riemannian manifold.

Four-dimensional Euclidean spacetime[edit]See also: Four-dimensional spaceIn 1905–06 Henri Poincaré showed[4] that by taking time to be an imaginary fourth spacetime coordinate ict, where c is the speed of light and i is the imaginary unit, a Lorentz transformation can formally be regarded as a rotation of coordinates in a four-dimensional space with three real coordinates representing space, and one imaginary coordinate representing time, as the fourth dimension. ...Minkowski's principal tool is the Minkowski diagram, and he uses it to define concepts and demonstrate properties of Lorentz transformations (e.g. proper time and length contraction) and to provide geometrical interpretation to the generalization of Newtonian mechanics to relativistic mechanics.

The formal definition of proper time involves describing the path through spacetime that represents a clock, observer, or test particle, and the metric structure of that spacetime. Proper time is the pseudo-Riemannian arc length of world lines in four-dimensional spacetime. From the mathematical point of view, coordinate time is assumed to be predefined and we require an expression for proper time as a function of coordinate time. From the experimental point of view, proper time is what is measured experimentally and then coordinate time is calculated from the proper time of some inertial clocks.

For a twin "paradox" scenario, let there be an observer A who moves between the A-coordinates (0,0,0,0) and (10 years, 0, 0, 0) inertially. This means that A stays at {\displaystyle x=y=z=0} x=y=z=0 for 10 years of A-coordinate time. The proper time interval for A between the two events is then...So being "at rest" in a special relativity coordinate system means that proper time and coordinate time are the same.

BSu, it has been stated in the other thread you started, and discussion can continue there if you want, but for the record in this thread: No. There are no FTL technologies of any sort compatible with known physics. Any hypothetical things you hear about FTL involve things that to the best of our knowledge don't exist and there is no way to create.Dustinthewind, I meant to write a thorough response, but never got the time, so here is a "short" one:You seem to be confused between a metric and a representation of a metric. The metric itself in relativity does not depend on what frame you are viewing it from. To write down a metric in notation that you can do calculations with, you need to pick what coordinates to write it down in. An equivalent concept is vectors. You can do various math with vectors (say vectors that represent points on your computer screen) You can write down the differences between the locations of various points, or calculate the derivative of a moving point to get its velocity vector. To get the results in a numeric representation though, you need to pick a point on the screen to be the origin, and choose which direction is "x" and which direction is "y." The need to pick a coordinate system for final calculations does not mean that your choice is "special" in any way. Any choice works as long as you are consistent.

meberbs, here is a mental challenge for you:Lets imagine that FTL travel has been proven to be possible, with 100% solid experimental results. We can do FTL jumps to any XYZ coordinates in the Universe. They are instantaneous, preserve our momentum (+/frame of reference) and do not produce time-travel paradoxes.Scientists around the world are trying to figure the math behind it, namely, what they got wrong before, thinking there would be time-paradoxes. You are one of them, lets hear how you would fix the math.

Scientists around the world are trying to figure the math behind it, namely, what they got wrong before, thinking there would be time-paradoxes. You are one of them, lets hear how you would fix the math.

Quote from: kamill85 on 08/29/2018 03:06 pmmeberbs, here is a mental challenge for you:Lets imagine that FTL travel has been proven to be possible, with 100% solid experimental results. We can do FTL jumps to any XYZ coordinates in the Universe. They are instantaneous, preserve our momentum (+/frame of reference) and do not produce time-travel paradoxes.Scientists around the world are trying to figure the math behind it, namely, what they got wrong before, thinking there would be time-paradoxes. You are one of them, lets hear how you would fix the math.Personally, I'm not a strong believer in the weirder interpretations of superluminal phenomena. Yeah, I'm just an ignorant person on the Internet that knows nothing of relativity and physics.But nevertheless, inferring that going FTL would take us to the past strikes me as an example of taking math too far.If such a thing proves possible, we will probably learn that our models break at some point and new realities emerge.

We simply don't have enough examples (zero, probably) as of today for telling what would happen.

I thought the current thinking was that there are no FTL paradoxes, as new parallel universes are created. You may be able to go back in time and think you have killed your grandfather, but it will only be in your universe. Your original grandfather will be untouched.