Any resolutions to FTL paradoxes?

[meberbs]

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:

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).

[dustinthewind]

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 https://en.wikipedia.org/wiki/Proper_time 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. 

[BSu]

Has there been any progress toward even possibly sending an FTL signal regardless of paradoxes or causality?

[meberbs]

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.

[dustinthewind]

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.

Thanks meberbs.  I guess when I was suggesting a metric I was thinking of an actual structure to the vacuum.  Something like quantum loop gravity where the structure of the vacuum has a quantized volume as do solid objects. 

https://en.wikipedia.org/wiki/Loop_quantum_gravity

[kamill85]

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.

[tchernik]

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.

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.

[meberbs]

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.

Simple, there are 3 possibilities, which have already been discussed in this thread, and which one would be evident from the experimental data:

1. Time travel is possible
2. There exists a fixed universal reference frame that all FTL travel is relative to. (causality holds because you can't do an FTL jump backwards in time in this frame.)
3. It has been suggested that wormhole type FTL could have a condition where any configuration of wormholes with a potential time loop would cause the wormholes to collapse. It is not obvious if this is actually a looser condition than #2, (it is at worst equivalent) since it is complicated to work out for the arbitrary number of wormholes case, and I suspect you could create a time travelling communication method by opening a small wormhole and seeing if it collapses.

Just about anything else wouldn't work because it would directly contradict experimental data that already exists in the real world.

[KelvinZero]

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.

Hi kamill85, look at the first post. I have edited a sort of index of later quotes into there. I can't remember if I included the wormhole idea though.

(edit: apparently not, but it is in the second post)

[ChrisWilson68]

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.

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.

That's like people in the 15th century admitting they don't know about math and physics but saying they don't believe the Earth goes round the sun.

The conclusions you come to just thinking about it without understanding what others have learned are not valid conclusions.

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

That's not a valid conclusion.

Just because we haven't seen something doesn't mean we can't make conclusions about it, if we have a theory that fits a large body of evidence and that evidence can predict what would happen.  That's how we knew what would happen when we set off an atomic bomb before we had ever seen one.

[colbourne]

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.

[KelvinZero]

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.

There was some discussion of that possibility in this thread somewhere.

It never seemed satisfactory because the result seemed to be a universe where the people who enter FTL and the people who exit it have no clear relationship to each other. Sometimes they just vanish. Sometimes people appear who have no history... and EVERY combination in between.

It could be an interesting SF scenario.. a universe where FTL changes other people but never yourself.. but it could not be defined well enough to include as a solution IMO

[dustinthewind]

I found this research paper

https://scholar.google.com/scholar?cluster=3548262082901723021&hl=en&as_sdt=0,14

Dynamical 3-Space: neo-Lorentz Relativity
Reginald T Cahill (Flinders University)
(Submitted on 5 Jul 2012)

There are some newer papers but not a lot of citations.  However It seems to hit to spot for me in regards to what I was thinking about the structure of space time and the vacuum having a local velocity. 

They mention the solution to the twin paradox, absolute clock slowing, velocity with respect to the CMB is indirectly referenced as having velocity at ~ 500km/s.  Some other stuff mentioned.  I haven't read all the newer stuff. 

This goes along with my claim that I thought it was likely that a jump backward at near light speed wouldn't make one jump backward in time but that rather jumps were w.r.t. absolute space - Circumnavigating time paradoxes.  That clocks might tick faster if sent to be at rest with respect to the CMB.  That Lorentz contraction had something to do with motion w.r.t. the vacuum ect.  Motion w.r.t. the CMB.  That it fixes the twin paradox ect. 

I think it also suggests the clock of an object flying toward a gravitational object should speed up and the clock of an object should slow down when flying away from a gravitational object.  Also predicts for lens thiring effect (or frame dragging) where the speed of light is faster around in one direction than the other for large rotating objects.  Or going around in one direction speeds up the clock more than going the other direction.

I.e. gravity and gravito magnetism via curvature induces an effective relative velocity on the vacuum or space time. 

The gamma factor of special relativity can also be thought to be a geometric description of local velocity with respect to space time.  Also why satellites clocks are slowed down not only by the gravitational potential they exist in but also their angular velocity which have separate velocity components which are perpendicular to each other.