Author Topic: Any resolutions to FTL paradoxes?  (Read 59185 times)

Offline meberbs

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Re: Any resolutions to FTL paradoxes?
« Reply #420 on: 01/04/2018 07:39 AM »
Quote from: Einstein’s 1917 Static Model of the Universe: A Centennial Review
approximate assumption
As 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 Review
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.

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). 
No, if you read the paper you certainly did not comprehend it. the assumptions Einstein used were wrong and the paper explained why. The cosmological constant is necessary to have general relativity allow the solutions Einstein came up with, but later Einstein denounced the cosmological constant because it was found that the solution of a static universe does not describe our universe, and his assumptions were wrong. It was only determined to be necessary for opposite reasons (accelerating expansion measured) after his death.

Your statement here does not even address the points that I made in my post.

expansion of space sounds a lot like expansion of a metric.
This is a tautology, a metric is how you describe the shape of spacetime.

It also seems to suggest the matter generates the metric.
This is part of one of the most basic explanations of general relativity. The distribution of matter determines the curvature of spacetime. However, Einstein's statement "In my opinion, the general theory of relativity is a satisfying system only if ..." seems to be what you are basing this on, even though this quote is from a criticism he made of someone else's solution to the GR equations, when his criticism was actually what was wrong.

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. 

Every sentence in this quote is wrong. There is nothing special about the frame of those stars other than the math being easier, but this is inapplicable to the universe we live in anyway. Your description that clock rates all must be relative to this frame is the exact opposite of the principle of relativity, and therefore contradictory. Your final statement simply confuses things because you are then seem to be talking about spacetime diagrams in special relativity, and neither frame has a distorted metric in that case. In fact they have the exact same metric. Also, neither is the "one" that has its axes tilted, because you can validly and symmetrically draw either frame as the one with the straight axes.

With that said, I reiterate the idea that an ftl jump, when one is moving,
The phrase "when one is moving" makes your entire statement wrong. There simply is no special frame in reality to measure motion relative to, and that is the basis of relativity. (We have already covered in this thread that if you define some special frame that a magic FTL drive must move forward in time in then paradoxes are avoided)

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. 
There didn't seem to be any citations on the first paper you posted. There are multiple things indicating that they fall somewhere on the crackpot spectrum:
-discussing a situation clearly described by GR and only mentioning GR once in passing, never comparing their results to GR.
-They refer to c^4/G as the "Kostro constant" a term only they seem to use. (The constant itself shows up in the Einstein field equations, but doesn't need a name)
-9 citations for that new paper is not exactly a stunning endorsement (some were from themselves).

Offline dustinthewind

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Re: Any resolutions to FTL paradoxes?
« Reply #421 on: 01/12/2018 01:51 AM »
What then do you think about Minkowski space or metric. 

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.

A further elaboration

Four-dimensional Euclidean spacetime[edit]
See also: Four-dimensional space
In 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.

So then coordinate time defines time when stationary relative to the local metric it would appear while proper time is time experienced which distorts ones view of the metric. 

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.

Going back to a vertical ict vector with respect to the horizontal local metric and simplifying for a 2d space with time as the 3rd axis (giving layers of space in time?).  It looks as if when one is moving, one then has a tilt in angle of the ict vector with respect to the plane of the local horizontal metric which has a coordinate time used to get the proper time of events for a moving observer. 

It seems the idea of general relativity can be extended to this metric by creating a dip or well in the metric.  Any object not moving in the metric still has a vertical ict vector, but in the gravity well it is now at an angle with the local metric.  It seems this angle of the ict vector with respect to the local metric either simulates having velocity with respect to the metric, slowing time, or just having an angle w.r.t. it slowing time. 

So then being at rest on a gravitational object at rest, one having a vertical ict vector with respect to the tilted metric then has slow time where as an object freely falling into the the gravity well speeding up has a faster clock?  Not sure this makes complete sense as this gives some strange effects for living on a highly relativistic gravity well it would seem. (i.e. having a tilted ict vector with respect to a gravity well. -effects on magnetic fields measured on earth perhaps? - their experiment measuring an electric field from a magnetic field in the lab frame?)

Orbiting clocks have a dual time slowing effect.  Their tilted ict vector or velocity with respect to the local metric radially and their angular velocity causing further ict angle tilt.

Some of the concepts seem very close to suggesting having actual velocity with coordinate time and space or is this just my misinterpretation? 

The description of The twin "paradox" "So being "at rest" in a special relativity coordinate system means that proper time and coordinate time are the same." I mean where they suggest experimental measurements can determine proper time to derive the coordinate time seems quite suggestive. 
« Last Edit: 01/12/2018 08:34 PM by dustinthewind »