#### KelvinZero

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##### Re: Any resolutions to FTL paradoxes?
« Reply #80 on: 07/25/2017 09:27 am »
FWIW, here's physicist Matthew Buckley's (https://twitter.com/physicsmatt) take on explaining why FTL requires giving up relativity or causality http://www.physicsmatt.com/blog/2016/8/25/why-ftl-implies-time-travel
Hey hop, meberbs, and everyone here with decent respect for relativity.

I have known for a long time how to demonstrate the FTL paradox using an instantaneous communicator and multiple FTL messages using different frames, but someone convinced me recently that you could create a paradox with just one FTL message. (It might well be one of you two).

Failing that, I was sure at least that we couldn't solve the problem just by limiting all FTL travel WRT to a single reference frame.

Im less sure now. I have looked through all the examples and they all seem to use FTL in two reference frames to cause the paradox.

Here is someone who thinks you can solve FTL paradoxes by restricting it to a special reference frame:
http://www.physicsguy.com/ftl/html/FTL_part4.html

And going back to hop's link, I notice the physicist says: "So you see the problem: if we could just say that there was only one frame of reference where we needed to set up cause and effect, then we could have FTL without worrying about causality. However, there is no special frame of reference, there cannot be one if relativity is to be true." .. It is almost like he is saying yes, you could solve it by limiting FTL to a special reference frame, if you could choose one. Also, his paradox example, like mine, talks of using two FTL messages relative to different frames.

Can anyone think of a clear example that FTL with just one message, or failing that, wrt to just one special reference frame (eg the CMB rest frame), will still create a paradox?

Im not worried about how or why such a phenomenon could exist, just if it can be described without a paradox.

#### dustinthewind

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##### Re: Any resolutions to FTL paradoxes?
« Reply #81 on: 07/25/2017 01:40 pm »
...

Also, I have no idea why you bring up the concept of rotating reference frames, that is just an irrelevant complication. As for inertial reference frames, we have Michelson-Morley type experiments that show they are all equivalent.

That's right a rotating reference frame that rotates at a very specific velocity.  And an event horizon's reference frame appears to move at the speed of light.

Some of the paradox is discussed here: http://www.theculture.org/rich/sharpblue/archives/000089.html .  As the observer accelerates their space and time lines converge on the light cone.

Their space now passes through time.  Near the speed of light length contraction occurs because further back in space more time is subtracted from the velocity away.  What is behind the ship represents the past.  What is ahead of the ship represents the future.  The space ahead of the ship is length contracted because time is added to the relative velocity the further away an object is.  Space now represents the past and the future.  You can not travel into the past because if you turn around to travel to the past, the past becomes the future via your velocity and time.

Notice how their ansible is pointed to the past behind the ship.  This is key.

The next ansible is pointed to the future, of the ship at near c.

I have my doubts that by having an ansible, and accelerating one can point it to an object in ones past/future and communicate with the past/future.  I suspect if such a thing exists, it would only communicate with the immediate present where they presently exist.  If this is the case, their communication line into the past/future is erroneous.

Take a quantum entanglement that seems to be instantaneous.  Now send one of the charges away at near light speed.  When its wave form collapses the signal should instantaneously go into the past (which I doubt).   Wait, how do you entangle two charges and have them not exist in the same light cone...
« Last Edit: 07/25/2017 01:56 pm by dustinthewind »

#### meberbs

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##### Re: Any resolutions to FTL paradoxes?
« Reply #82 on: 07/25/2017 02:23 pm »
Can anyone think of a clear example that FTL with just one message, or failing that, wrt to just one special reference frame (eg the CMB rest frame), will still create a paradox?

Im not worried about how or why such a phenomenon could exist, just if it can be described without a paradox.

As for the number of messages needed, I believe it is always 2, when you are talking about FTL between 2 spacelike separated points in spacetime.

If you take some x distance away on a spacetime diagram, and draw a line straight down, you pass though multiple regions:
-in the forward light cone, everything is normal. (relativity at least allows long journeys to feel shorter to those on the ship)
-in the spacelike region, you start creating paradoxes if you have an equivalent device moving at some relative velocity to the first device, with the required relative velocity decreasing as you approach your time axis.
-When you get below the time axis, it is easy to see that such travel would allow paradoxes without a second device moving with relative velocity.
-You keep needing a second FTL transmission to cause a paradox until you et into your past light cone, where you can start causing a paradox with a conventional signal.

As for a consistent way to implement FTL, I have not done the math to fully work this out yet, but here are my thoughts:
I believe it is correct that it can be done by picking one reference frame to be the ultimate arbiter of "forward in time" for the entire universe. Every experiment we have done says that this is not out universe, but restricting it so that no FTL drive can move backwards in time in the preferred frame should prevent paradoxes. This also contradicts the most basic principle in relativity, so I am not sure exactly what else would have to change in physics, probably things like the speed of light would only truly be constant in one frame (or maybe the concept of aether would need to be brought back), also relativistic effects if they still exist at all would probably have to be tied to velocity in the special frame. If you are just writing interstellar hard sci-fi, picking a preferred frame for FTL should be good enough. (If you are going to pick a special frame, the center of the galaxy is the closest object you could tie it to that would seem believable, really it should just be some arbitrary frame that even our galaxy has some velocity relative to.)

#### meberbs

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##### Re: Any resolutions to FTL paradoxes?
« Reply #83 on: 07/25/2017 02:53 pm »
Take a quantum entanglement that seems to be instantaneous.  Now send one of the charges away at near light speed.  When its wave form collapses the signal should instantaneously go into the past (which I doubt).   Wait, how do you entangle two charges and have them not exist in the same light cone...
They will exist within the same light cone as the entanglement event, but if they have been moved apart from each other, their current light cone will no longer include each other.

To picture this, imagine a light cone far down in the last picture in your post to represent the light cone of the entanglement event.

Also the problem with using quantum for this is the no-communication theorem. The measurement of the entangled particle will just look like random noise to someone on either side until they get sent a classical, slower than light message from the person on the other end.

#### Chris Bergin

##### Re: Any resolutions to FTL paradoxes?
« Reply #84 on: 07/25/2017 04:19 pm »
What is it with you clever people feeling you have to throw in the occasion insult?

It's amazing to see, but running a site with a forum this size, you really can say it's "mainly" the cleverer the member, the more likely they are to act like they are on some sort of throne of intelligence and us mere fools need to peer review our responses before daring to bother the King.

Stop it. This forum has rules for everyone, regardless of how many degrees you may have.

Now where's my warp speed?
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#### WarpTech

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##### Re: Any resolutions to FTL paradoxes?
« Reply #85 on: 07/25/2017 04:29 pm »
That's not even symmetrical! If a rocket of any kind were "accelerated" to reach such a speed, you must realize that the Earth was not accelerated! One accelerated, physical work was done to it, it's energy content changed. The other did not. That's my point! What you call symmetrical is not symmetrical.
After the rocket has finished accelerating, there is no way anyone on the rocket, on the Earth, or in any other inertial reference frame would be able to tell that it hadn't always been moving at that speed. The acceleration could have been to ship 1 instead, or half way to both. It doesn't matter.

And don't bring up the so-called "twin paradox." That is a case where people who arrive at a paradox fail to account for the effect of the acceleration on the time experienced by the twin who is accelerating. In this case, the paradox does not care if the people on the ship their trip as lasting 1 million years, or 1 second. All that matters is that a drive exists that can move between 2 space-like separated points.

Apparently we have different assumptions (realistic vs false) regarding the setup of this problem. Which is why you insist there is a paradox. You are wrong in that I do see why there is a paradox AND how to resolve it. You see only a symmetrical problem, which is like it or not, "identical" to the Twin paradox. What I'm saying that the interpretation you have is wrong. The past does not exist for anyone to travel backwards in time. Causality only requires that there be a finite coordinate speed of light, GR says that the coordinate speed of light is not constant, it's a variable around massive objects. The speed of light in high orbit is "faster" than it is on the surface of the Earth. No causality is broken by this, yet relative to a light signal in vacuum on Earth, the same signal in space far from matter travels a little faster.
"which is like it or not, "identical" to the Twin paradox."
This statement disproves your claim that you see why there is a paradox.
The twin paradox is not a paradox, it is people misusing special relativity, and not recognizing that there are 3 relevant inertial frames that need to be considered. This situation only involves 2 relevant inertial frames, and really is a paradox if you allow FTL travel.

No, it involves 3 relevant frames as soon as Ship 2 heads back toward Earth to cause the paradox. The paradox occurs for the same reason, "misusing special relativity, and not recognizing that there are 3 relevant inertial frames..." You're only considering 2 frames, and assuming the situation is symmetrical. That is the same thing as the twin paradox. The twin paradox teaches us that the problem is NOT symmetrical, that one clock is running slow and the other is not, and what they "see" out the window is an optical illusion. Which is verified when the traveling twin returns home to find his twin older than he is.

In formulating this problem, Ship 1 and Ship 2 are "identical" and both originate from Earth.
Both originating from Earth is both optional and irrelevant.

In accelerating Ship 2 to 0.6c, it's relative mass/energy has increased to 125% of that of Ship 1, it's clock has slowed down and it's length has contracted. Nothing changed on Ship 1, it's still in the hanger on Earth. This is not a symmetrical problem.
In ship 2's frame, everything you said about ship 2 is true about ship 1, except the hangar on Earth part. If they started in deep space with no nearby reference points, and the crews of each ship were unconscious during the acceleration, no measurement they could do onboard the ship, or by observing the other ship could tell them which one had accelerated. (They could look at far away stars and see the redshift of course, but those were all moving at different velocities to start with as well, and in no way affect the problem. )

I already said this, but I will keep repeating it until you read it, because you did not actually addres this statement:
Quote
After the rocket has finished accelerating, there is no way anyone on the rocket, on the Earth, or in any other inertial reference frame would be able to tell that it hadn't always been moving at that speed. The acceleration could have been to ship 1 instead, or half way to both. It doesn't matter.

It does matter if you want to resolve the paradox. It doesn't matter if you want to continue believing that there is a paradox and time-travel is feasible. True, there is no way to tell while the two ships are moving away from each other, but if Ship 2 returns to Earth, FTL or otherwise, it requires that 3rd inertial reference frame. It still finds the clock on Earth has elapsed more time than theirs and their perception of symmetry was WRONG. The vacuum around the Earth is our baseline. Motion relative to this background causes time dilation and length contraction, relative to Earth. The center of the galaxy is another baseline. Choose your baseline to be anywhere you like, but once you do, you must keep the same baseline when discussing the motion of Ship 1 and Ship 2. You can't assume it is symmetrical, that's the same as changing the baseline you started with. (resetting your zero to be something else)

there is no difference between gravitational time dilation and SR time dilation.
General relativity is just the full version of special relativity, of course time dilation is the same thing in both. You treating this statement like it is some kind of revelation or thinking that it changes anything I have already said is just further evidence that you don't understand the relevant topics.

It specifically contradicts your belief that there is symmetry in this problem, because in GR, if Ship 2 is in a gravity well and it's clock runs slow, it does not look up at Ship 1 and see it's clock there running slow. It runs fast. Which is identical to the temporal relationship between Ship 1 and Ship 2 when Ship 2 was accelerated to 0.6c.
Except there is no gravity well in this problem. In this problem as stated, ship 2 does see ship 1's clock running slow. As I said before go setup this problem by sending both ships off in opposite directions at c/3 (to get 0.6 relative). They are all equivalent, and once the acceleration is done, there is no way to tell it ever happened.

The space-time diagrams that I provided last night shows the trip of Ship 1 and Ship 2, at the speed "c". If these paths are slightly faster than c, Ship 2 may get to Earth at year 7 on Earth's clock instead of year 8 but, it does not cause a paradox. The paradox only occurs when you "assume" the problem is symmetrical in both frames, when in reality, it is not.
Your so called "solutions" are just to not act out the problem. You have suggested adding a gravity well when there is none. You have also just turned down the effectiveness of the FTL drives to almost nothing, without having the ships actually have enough relative velocity for the given amount of FTL to illustrate the paradox.

Not true. If Ship 2 returns instantaneously to Earth, it would get there in year 5, not year 4 in Earth's frame. The ship's clock is slow, Earth's clock is not, the situation is not symmetrical.

#### meberbs

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##### Re: Any resolutions to FTL paradoxes?
« Reply #86 on: 07/25/2017 04:46 pm »
No, it involves 3 relevant frames as soon as Ship 2 heads back toward Earth to cause the paradox.
What is the third frame? What velocity is it moving at relative to any other given frame?

The paradox does not care what length of time is experienced by ship 2, only that in its initial frame, which is no more or less special than the frame ship 1 started in, it travels at a sufficient FTL velocity.

I am running out of ways to state that there is nothing special about the ship 1 initial frame or the ship 2 initial frame. You have repeatedly ignored my suggestion to consider the problem from the perspective of both ships having initially been accelerated from a central point.

Another question you either missed or ignored is: What is different about ship 2's frame? What experiment can they run that tells them that they have been accelerated at some point in the past? Why would their FTL drive run much slower than ship 1's?

Not true. If Ship 2 returns instantaneously to Earth, it would get there in year 5, not year 4 in Earth's frame. The ship's clock is slow, Earth's clock is not, the situation is not symmetrical.
You are defining the Earth's frame as the only correct reference frame in the universe, this is simply contradictory to all of relativity.
« Last Edit: 07/25/2017 04:50 pm by meberbs »

#### WarpTech

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##### Re: Any resolutions to FTL paradoxes?
« Reply #87 on: 07/25/2017 06:30 pm »
No, it involves 3 relevant frames as soon as Ship 2 heads back toward Earth to cause the paradox.
What is the third frame? What velocity is it moving at relative to any other given frame?
The 3rd frame is the frame in which Ship 2 is now moving "toward" the Earth, not away from it. The velocity can be anything. It can be instantaneous travel taking 0 time, the Earth's clock will still have elapsed more time than Ship 2, which "was" accelerated to 0.6c moving away from Earth.

The paradox does not care what length of time is experienced by ship 2, only that in its initial frame, which is no more or less special than the frame ship 1 started in, it travels at a sufficient FTL velocity.

I am running out of ways to state that there is nothing special about the ship 1 initial frame or the ship 2 initial frame. You have repeatedly ignored my suggestion to consider the problem from the perspective of both ships having initially been accelerated from a central point.

Another question you either missed or ignored is: What is different about ship 2's frame? What experiment can they run that tells them that they have been accelerated at some point in the past? Why would their FTL drive run much slower than ship 1's?

I didn't ignore it. I said that Ship 2 started on Earth and was accelerated to 0.6c moving away from Earth. This "work" that was done to Ship 2 puts it in a higher-energy relative to Earth, in which it's clock runs show. That is what is different about ship 2's frame.

What experiment can they run? I said, they can return to Earth and find that the twin left behind has aged more. That proves the situation is not symmetrical. It can't be done remotely, they have to bring the two clocks back together to ompare them "accurately".

Why would their FTL drive be slower than ship 1's? Because ship 2 was accelerated and has a higher relative mass/energy content than ship 1. Therefore, it takes more Work to accelerate it back toward the Earth, than it does for Ship 1 to leave Earth.

Not true. If Ship 2 returns instantaneously to Earth, it would get there in year 5, not year 4 in Earth's frame. The ship's clock is slow, Earth's clock is not, the situation is not symmetrical.
You are defining the Earth's frame as the only correct reference frame in the universe, this is simply contradictory to all of relativity.

No, that's your assumption. I'm explaining that if you start from rest within our galaxy, you are not moving very fast relative to Earth, v << c to begin with. If you start from rest near "Sagittarius A", that would be your correct reference frame. If you start at rest on Proxima Centauri, then that is your correct reference frame. It's all relative, but they are not all the same! Basically what I'm saying is that you can have inertial reference frames, with different vacuum spectral energy densities, different scaling of rulers, clocks, matter and energy. All inertial frames are NOT created equally.

#### gargoyle99

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##### Re: Any resolutions to FTL paradoxes?
« Reply #88 on: 07/25/2017 07:21 pm »
If Ship 2 returns instantaneously to Earth

That word, instantaneous...that's tricky. By instantaneous, I think you mean simultaneously in 2 different places. However, what is simultaneous in one reference frame will not in general be simultaneous in other reference frames. So, when you say instantaneously, you're already choosing a specific reference frame, and that isn't how special relativity works because it says that all inertial reference frames are equally valid. What's instantaneous in one reference frame (say Earth's) happens in a different order in different reference frames. In one, your space ship shows up at Earth before it left, and in another, it shows up after it left. So, you only need a single FTL teleportation event to cause a paradox, that is, arriving before you left (and physically existing twice in the same time line in a valid reference frame).

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

The Wikipedia page on the Twin Paradox goes into a lot of detail about the symmetry and asymmetry of the traveling twins, and might help one understand the subtleties of the problem. In summary, the system IS symmetric at all times except when the spaceship either accelerates or decelerates or otherwise changes reference frames, but that's what makes the difference when the spaceship returns. When the spaceship is just coasting along at 0.7c, time is going slower on the spaceship compared to Earth AND ALSO time is going slower on Earth compared to the spaceship. Yeah, physics is cool like that.

It seems to me the easiest way around FTL paradoxes is to say that Einstein was wrong and special relativity is incomplete (see E.E. Doc Smith and many others since) in whatever way is most convenient for the plot. Another option is to live with special relativity and note that the limit of the speed of light doesn't actually limit how far you can hypothetically travel in a year of your local time. A space ship's "effective speed" through the Galaxy is only limited by energy and the Gs you can pull, since at relativistic speeds distance is compressed. See Forever War or similar works. Just be prepared to outlive your twin.

#### meberbs

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##### Re: Any resolutions to FTL paradoxes?
« Reply #89 on: 07/25/2017 07:22 pm »
No, it involves 3 relevant frames as soon as Ship 2 heads back toward Earth to cause the paradox.
What is the third frame? What velocity is it moving at relative to any other given frame?
The 3rd frame is the frame in which Ship 2 is now moving "toward" the Earth, not away from it. The velocity can be anything. It can be instantaneous travel taking 0 time, the Earth's clock will still have elapsed more time than Ship 2, which "was" accelerated to 0.6c moving away from Earth.
Lets assume it is instantaneous for simplicity. What frame is it instantaneous in though? The only sensible answer is the ship 2 frame, but in this frame ship 1 hasn't left yet, so it produces the paradox.

Also, despite your claim to the contrary, you still are ignoring considering the problem from any case other than "ship 2 was accelerated." All of the cases have the same result of time travel.

The paradox does not care what length of time is experienced by ship 2, only that in its initial frame, which is no more or less special than the frame ship 1 started in, it travels at a sufficient FTL velocity.

I am running out of ways to state that there is nothing special about the ship 1 initial frame or the ship 2 initial frame. You have repeatedly ignored my suggestion to consider the problem from the perspective of both ships having initially been accelerated from a central point.

Another question you either missed or ignored is: What is different about ship 2's frame? What experiment can they run that tells them that they have been accelerated at some point in the past? Why would their FTL drive run much slower than ship 1's?

I didn't ignore it. I said that Ship 2 started on Earth and was accelerated to 0.6c moving away from Earth. This "work" that was done to Ship 2 puts it in a higher-energy relative to Earth, in which it's clock runs show. That is what is different about ship 2's frame.
Ship 2 is at rest in the ship 2 frame, and ship 1 has the higher energy, and nothing is special about Earth.

What experiment can they run? I said, they can return to Earth and find that the twin left behind has aged more. That proves the situation is not symmetrical. It can't be done remotely, they have to bring the two clocks back together to ompare them "accurately".
All that experiment would tell them is that after they woke up, they accelerated towards Earth.

Ship 1 could run the same experiment and accelerate the same amount to "catch up" to ship 2 and they would find that ship 1 had had the slow clock.

Why would their FTL drive be slower than ship 1's? Because ship 2 was accelerated and has a higher relative mass/energy content than ship 1. Therefore, it takes more Work to accelerate it back toward the Earth, than it does for Ship 1 to leave Earth.
No it would take the same amount of work.

No, that's your assumption. I'm explaining that if you start from rest within our galaxy, you are not moving very fast relative to Earth, v << c to begin with. If you start from rest near "Sagittarius A", that would be your correct reference frame. If you start at rest on Proxima Centauri, then that is your correct reference frame. It's all relative, but they are not all the same! Basically what I'm saying is that you can have inertial reference frames, with different vacuum spectral energy densities, different scaling of rulers, clocks, matter and energy. All inertial frames are NOT created equally.
Except the very principle of relativity is that ALL frames are created equally. You cannot claim that Earth and Sagittarius A are both correct and then say that not all are equal.

You have put no restriction on how fast your FTL can go, explicitly referencing instantaneous travel. Even the slightest difference in speed will lead to a paradox as you approach instantaneous travel. Try it with the Earth orbital speed (30 km/s) and effectively instantaneous travel between here and some point, say 10 light years away.

#### WarpTech

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##### Re: Any resolutions to FTL paradoxes?
« Reply #90 on: 07/25/2017 07:56 pm »
No, it involves 3 relevant frames as soon as Ship 2 heads back toward Earth to cause the paradox.
What is the third frame? What velocity is it moving at relative to any other given frame?
The 3rd frame is the frame in which Ship 2 is now moving "toward" the Earth, not away from it. The velocity can be anything. It can be instantaneous travel taking 0 time, the Earth's clock will still have elapsed more time than Ship 2, which "was" accelerated to 0.6c moving away from Earth.
Lets assume it is instantaneous for simplicity. What frame is it instantaneous in though? The only sensible answer is the ship 2 frame, but in this frame ship 1 hasn't left yet, so it produces the paradox.

Also, despite your claim to the contrary, you still are ignoring considering the problem from any case other than "ship 2 was accelerated." All of the cases have the same result of time travel.

The paradox does not care what length of time is experienced by ship 2, only that in its initial frame, which is no more or less special than the frame ship 1 started in, it travels at a sufficient FTL velocity.

I am running out of ways to state that there is nothing special about the ship 1 initial frame or the ship 2 initial frame. You have repeatedly ignored my suggestion to consider the problem from the perspective of both ships having initially been accelerated from a central point.

Another question you either missed or ignored is: What is different about ship 2's frame? What experiment can they run that tells them that they have been accelerated at some point in the past? Why would their FTL drive run much slower than ship 1's?

I didn't ignore it. I said that Ship 2 started on Earth and was accelerated to 0.6c moving away from Earth. This "work" that was done to Ship 2 puts it in a higher-energy relative to Earth, in which it's clock runs show. That is what is different about ship 2's frame.
Ship 2 is at rest in the ship 2 frame, and ship 1 has the higher energy, and nothing is special about Earth.

What experiment can they run? I said, they can return to Earth and find that the twin left behind has aged more. That proves the situation is not symmetrical. It can't be done remotely, they have to bring the two clocks back together to ompare them "accurately".
All that experiment would tell them is that after they woke up, they accelerated towards Earth.

Ship 1 could run the same experiment and accelerate the same amount to "catch up" to ship 2 and they would find that ship 1 had had the slow clock.

Why would their FTL drive be slower than ship 1's? Because ship 2 was accelerated and has a higher relative mass/energy content than ship 1. Therefore, it takes more Work to accelerate it back toward the Earth, than it does for Ship 1 to leave Earth.
No it would take the same amount of work.

No, that's your assumption. I'm explaining that if you start from rest within our galaxy, you are not moving very fast relative to Earth, v << c to begin with. If you start from rest near "Sagittarius A", that would be your correct reference frame. If you start at rest on Proxima Centauri, then that is your correct reference frame. It's all relative, but they are not all the same! Basically what I'm saying is that you can have inertial reference frames, with different vacuum spectral energy densities, different scaling of rulers, clocks, matter and energy. All inertial frames are NOT created equally.
Except the very principle of relativity is that ALL frames are created equally. You cannot claim that Earth and Sagittarius A are both correct and then say that not all are equal.

You have put no restriction on how fast your FTL can go, explicitly referencing instantaneous travel. Even the slightest difference in speed will lead to a paradox as you approach instantaneous travel. Try it with the Earth orbital speed (30 km/s) and effectively instantaneous travel between here and some point, say 10 light years away.

In the problem formulated my way and not all the other ways you're trying to drag us into; the clock on Ship 2 runs slow. The clock on Earth/Ship 1 does not. (Again, assuming my FTL warp drive in my JBIS paper where, when FTL is engaged, the rate of the clock on the ship does not change rate relative to it's rate before FTL was engaged.)

At the time Ship 1 reaches Ship 2, what I mean by "instantaneous" is, that if the FTL trip took 0 time for Ship 1, it would leave Earth at Year 5 and arrive at Ship 2's location, when Ship 2's clock is at Year 4. Likewise, when Ship 2 sees Ship 1 arrive, they instantaneously travel back to Earth. The clock on Earth is at Year 5, the clock on Ship 2 is still Year 4. Neither Ship 1 nor Ship 2 took any time to travel the 3 light years between them, but the clocks do not agree. There is no paradox, we can't go any faster than "instantaneous", and we can never go backwards in time in either frame.

IMO, this model makes perfect sense, there are no paradoxes and it is consistent with General Relativity. Symmetry is not required, it's the "special" case, and because of its specialness, SR leads to paradoxes. The principle that all inertial frames are equal is an "assumption" of the the theory of SR. It is what makes SR Special, but it's not realistic.

« Last Edit: 07/25/2017 10:21 pm by WarpTech »

#### ppnl

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##### Re: Any resolutions to FTL paradoxes?
« Reply #91 on: 07/25/2017 08:36 pm »
KelvinZero,

Clearly what you need is a way to visualize spacetime geometry so that you can answer these questions for yourself.

Let's start with Newtonian space and the Galilean transform. Imagine a vast frozen lake and ice skaters on it. The skate blades can bite into the ice allowing the skaters to push against it and change their direction of travel. But imagine the ice was infinitely hard and had zero friction. The only way the skaters can change directions is to collide with each other and push off each other. Energy and momentum is conserved and velocity only exists relative to some point of view. It's like the ice is an illusion. Now imagine that in three dimensions with space.

For the geometry of relativity I like Brian Green's idea of a loaf of bread and now slices. Let's reduce space dimensions to two again and use the third dimension for time. That way we can imagine the present as a slice of bread. Let's make it raisin bread so that events can be marked with raisins. There are many slices of bread that contain past events and many slices of bread containing future events. This loaf of bread is a model of spacetime containing all the events that happen in the entire universe past, present and future. The now slice is the slice of all events that are happening now. These are all the events that you could visit if you could travel instantaneously. All the others are in the past and out of reach or in the future and you will have to wait till they happen in the now.

Now relativity does a strange thing to the now slice. Motion causes a rotation of the space-time axis.If we are traveling with respect to each other then our now slices are tilted with respect to each other. My now slice contains events both in your future and in your past. That means that with instantaneous travel I could visit both your future and your past. I could then deliver a message from your future to your past thus causing a paradox.

Now can a single instantaneous message or trip cause a paradox? No because the only points available for you to go to are the points in your now slice. In order to time travel you have to accelerate to some velocity with respect to that now slice. Then your now slice has a tilt with respect to the original now slice. This will allow you to travel to your own past. Paradox.

Can you prevent time travel by limiting your FTL to with respect to a single frame of reference? Well yes but that's like having a time traveling machine in the room and just deciding not to use it. It will not for example prevent aliens from using time travel to screw with our past. FTL travel makes time travel possible under relativity. Choosing not to use it does not change anything. Paradoxes are but a decision away.

Can we avoid paradoxes if the physics of the universe established a universal frame of reference? Well yes but then it makes no sense to worry about what relativity has to say about it since relativity is wrong. Also just about all of modern physics would be horribly wrong. Could you do it while reproducing all the correct predictions of our current wrong physics? Maybe but it would be horribly complex and very very difficult to do. I wouldn't even know where to begin.

#### KelvinZero

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##### Re: Any resolutions to FTL paradoxes?
« Reply #92 on: 07/25/2017 10:53 pm »
KelvinZero,

Clearly what you need is a way to visualize spacetime geometry so that you can answer these questions for yourself.

...

Now can a single instantaneous message or trip cause a paradox? No because the only points available for you to go to are the points in your now slice. In order to time travel you have to accelerate to some velocity with respect to that now slice. Then your now slice has a tilt with respect to the original now slice. This will allow you to travel to your own past. Paradox.

Can you prevent time travel by limiting your FTL to with respect to a single frame of reference? Well yes but that's like having a time traveling machine in the room and just deciding not to use it. It will not for example prevent aliens from using time travel to screw with our past. FTL travel makes time travel possible under relativity. Choosing not to use it does not change anything. Paradoxes are but a decision away.

Can we avoid paradoxes if the physics of the universe established a universal frame of reference? Well yes but then it makes no sense to worry about what relativity has to say about it since relativity is wrong. Also just about all of modern physics would be horribly wrong. Could you do it while reproducing all the correct predictions of our current wrong physics? Maybe but it would be horribly complex and very very difficult to do. I wouldn't even know where to begin.

Hi ppnl,
I have the basic understanding that allows me to demonstrate these paradoxes using two 'instantaneous' messages using different frames. Normally I use a synchronizing pulse sent out from exactly halfway between to points to define 'instantaneous' and then I explore what that looks like in different frames of reference, using "the speed of light is the same for all observers".

Someone had convinced me recently that you could cause a paradox with a single ftl message. After all, a spaceship a mere kilometer long rushing past you at near the speed of light could have its front end a thousand years lagged in time compared to it's back end. When I recently tried to draw it out on paper, although yes, I was clearly sending messages back in time, it seemed impossible to exploit this by a lightspeed message between the two end points. The same geometry that says the front of the ship is lagged in time also explains why any message would take more than a thousand years to catch up to it.

I think we are on about the same page there.

I think I misexplained myself when I said "Im not worried about how or why such a phenomenon could exist, just if it can be described without a paradox."

I don't mean "I am ok with any hypothetical universe, so long as it is self consistent". It absolutely must not contradict what we already observe about the real world, ie relativity.

Given that, Im prepared to entertain all sorts of arbitrary rules to prevent paradoxes, such as impenetrable walls suddenly appearing, preventing relativistic travel in a defined region/period. Postulating a wall is not the same as pretending relativity is no longer a thing.

It just has to be describable in this universe without having paradoxes that mean you haven't really described anything.

#### meberbs

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##### Re: Any resolutions to FTL paradoxes?
« Reply #93 on: 07/25/2017 11:09 pm »
Can we avoid paradoxes if the physics of the universe established a universal frame of reference? Well yes but then it makes no sense to worry about what relativity has to say about it since relativity is wrong. Also just about all of modern physics would be horribly wrong. Could you do it while reproducing all the correct predictions of our current wrong physics? Maybe but it would be horribly complex and very very difficult to do. I wouldn't even know where to begin.
Rather than attempting to match everything I would be curious if there is some minimal set of experiments to throw out that would again allow a consistent description that isn't overly complex. This might not be reasonable to do either, since so many parts of physics are intertwined (Electrodynamics is inherently relativistic for example).

I don't mean "I am ok with any hypothetical universe, so long as it is self consistent". It absolutely must not contradict what we already observe about the real world, ie relativity.

Given that, Im prepared to entertain all sorts of arbitrary rules to prevent paradoxes, such as impenetrable walls suddenly appearing, preventing relativistic travel in a defined region/period. Postulating a wall is not the same as pretending relativity is no longer a thing.

It just has to be describable in this universe without having paradoxes that mean you haven't really described anything.
I have some had some ideas on where to start with that (how far apart do you keep your wormholes, what relative velocity, etc.), but it will take some time before I can flesh it out, and it may get incredibly complex for more than 2 wormholes, so I might not be able to do it in general.

Note: I say wormholes for FTL, because for any given FTL travel, I think it can be treated as a wormhole between 2 events in space-time for the purpose of determining causality.

#### meberbs

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##### Re: Any resolutions to FTL paradoxes?
« Reply #94 on: 07/25/2017 11:29 pm »
In the problem formulated my way and not all the other ways you're trying to drag us into;

You are the one who "changed" the problem by insisting that ship 2 start at Earth and accelerate before the problem begins. (There is actually no difference to the problem either way, but by starting ship 2 at Earth you are hand-waving that Earth is the preferred reference frame for the universe, which you then deny before repeating that the Earth frame is special.)

the clock on Ship 2 runs slow. The clock on Earth/Ship 1 does not. (Again, assuming my FTL warp drive in my JBIS paper where, when FTL is engaged, the rate of the clock on the ship does not change rate relative to it's rate before FTL was engaged.)
I will try repeating this again:

The paradox does not care how much time passes for the people on the ship.

All that matters are how events transpire in the initial frame of ship 1 and the initial frame of ship 2. If you need to, just imagine someone co-travelling with these ships who is left behind by an FTL jump.

All statements related to the amount of time passing on the ship during FTL are irrelevant.

If you mention the amount of time passing on the ship during FTL again, other than to acknowledge these statements, I will just repeat this, because if you do not get this, you haven't understood anything I have said.

At the time Ship 1 reaches Ship 2, what I mean by "instantaneous" is, that if the FTL trip took 0 time for Ship 1, it would leave Earth at Year 5 and arrive at Ship 2's location, when Ship 2's clock is at Year 4. Likewise, when Ship 2 sees Ship 1 arrive, they instantaneously travel back to Earth. The clock on Earth is at Year 5, the clock on Ship 2 is still Year 4. Neither Ship 1 nor Ship 2 took any time to travel the 3 light years between them, but the clocks do not agree. There is no paradox, we can't go any faster than "instantaneous", and we can never go backwards in time in either frame.
You are defining instantaneous differently for the 2 ships. In the ship 2 frame, the Earth clock is at Year 3.2, when the ship 2 is at Year 4.

IMO, this model makes perfect sense, there are no paradoxes and it is consistent with General Relativity. Symmetry is not required, it's the "special" case, and because of it's specialness, SR leads to paradoxes. The principle that all inertial frames are equal is an "assumption" of the the theory of SR. It is what makes SR Special, but it's not realistic.
General relativity introduces more ways to get paradoxes, and reduces to special relativity in the relevant cases we are discussing (The GR paradoxes are all currently excluded from implementation by things like event horizons and the need for exotic (negative mass) matter). The assumption that all inertial reference frames are equal is also part of general relativity. It is a very realistic assumption because it has been experimentally observed to be true.

#### KelvinZero

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##### Re: Any resolutions to FTL paradoxes?
« Reply #95 on: 07/25/2017 11:30 pm »
As for a consistent way to implement FTL, I have not done the math to fully work this out yet, but here are my thoughts:
I believe it is correct that it can be done by picking one reference frame to be the ultimate arbiter of "forward in time" for the entire universe. Every experiment we have done says that this is not out universe, but restricting it so that no FTL drive can move backwards in time in the preferred frame should prevent paradoxes. This also contradicts the most basic principle in relativity, so I am not sure exactly what else would have to change in physics, probably things like the speed of light would only truly be constant in one frame (or maybe the concept of aether would need to be brought back), also relativistic effects if they still exist at all would probably have to be tied to velocity in the special frame. If you are just writing interstellar hard sci-fi, picking a preferred frame for FTL should be good enough. (If you are going to pick a special frame, the center of the galaxy is the closest object you could tie it to that would seem believable, really it should just be some arbitrary frame that even our galaxy has some velocity relative to.)

If we can demonstrate that it requires messing with the speed of light universally, then we have killed it. We will have to keep thinking about that.

Though in science fiction, that could be one solution:
SCIENTIST: I have just created AI!
AI: Urp.
AI: FTL is possible.
SCIENTIST: No it is n...
AI: Hehehe.
SCIENTIST: Did you just consume the solar system, build a matrioshka brain, and then emulate me in some sort of.. of video game??
AI: No.
AI: Would I lie to you?

Rather than the center of the galaxy, how about the CMB reference frame?
https://en.wikipedia.org/wiki/Cosmic_microwave_background#CMBR_dipole_anisotropy
"From the CMB data it is seen that the Local Group (the galaxy group that includes the Milky Way galaxy) appears to be moving at 627±22 km/s relative to the reference frame of the CMB (also called the CMB rest frame, or the frame of reference in which there is no motion through the CMB)"
« Last Edit: 07/25/2017 11:31 pm by KelvinZero »

#### WarpTech

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##### Re: Any resolutions to FTL paradoxes?
« Reply #96 on: 07/26/2017 01:54 am »
At the time Ship 1 reaches Ship 2, what I mean by "instantaneous" is, that if the FTL trip took 0 time for Ship 1, it would leave Earth at Year 5 and arrive at Ship 2's location, when Ship 2's clock is at Year 4. Likewise, when Ship 2 sees Ship 1 arrive, they instantaneously travel back to Earth. The clock on Earth is at Year 5, the clock on Ship 2 is still Year 4. Neither Ship 1 nor Ship 2 took any time to travel the 3 light years between them, but the clocks do not agree. There is no paradox, we can't go any faster than "instantaneous", and we can never go backwards in time in either frame.
You are defining instantaneous differently for the 2 ships.
Yes, that is correct, because the situation is not symmetrical.

In the ship 2 frame, the Earth clock is at Year 3.2, when the ship 2 is at Year 4.

... and that observation is incorrect, it is an illusion.

Can we agree that the symmetry is the cause of the paradox please?

I put forward that the paradox cannot happen, because the symmetrical scenario which results in a paradox is not physically possible within the confines of our galaxy, or local cluster.

I repeat...
IMO, this model makes perfect sense, there are no paradoxes and it is consistent with General Relativity. Symmetry is not required, it's the "special" case, and because of it's specialness, SR leads to paradoxes. The principle that all inertial frames are equal is an "assumption" of the the theory of SR. It is what makes SR Special, but it's not realistic.
General relativity introduces more ways to get paradoxes, and reduces to special relativity in the relevant cases we are discussing (The GR paradoxes are all currently excluded from implementation by things like event horizons and the need for exotic (negative mass) matter). The assumption that all inertial reference frames are equal is also part of general relativity. It is a very realistic assumption because it has been experimentally observed to be true.

GR is perfectly consistent with inertial reference frames having different rates of time passage. By insisting on having symmetry, what you are saying is that when Ship 2 accelerates away from earth, (not FTL) to 0.6c, it's clock rate is unaffected. It is still the same as it was on Earth. As such, you expect the situation to be symmetrical and therefore you end up with a paradox. I'm saying, the clock on the ship really is slower than the clock on Earth, not vis-versa. It is not symmetrical, and it can't be symmetrical within our galaxy.

Anyone: Please give a "realistic" example of how Ship 2 came to be moving at 0.6c relative to the Earth where, it did not previously accelerate to that speed. Given that there have been no observations of stars or planets in our galaxy that are moving more than a little over 100 km/s. Nowhere near 0.6c, and there are no worlds orbiting stars or BH's at 0.6c either. The fastest stable orbit around a BH is .5c and it oscillates relative to Earth. So the situation in which Ship 2 has always been moving 0.6c relative to the Earth is unrealistic (if not impossible). Therefore, the symmetry required to cause a paradox, does not exist.

#### dustinthewind

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##### Re: Any resolutions to FTL paradoxes?
« Reply #97 on: 07/26/2017 03:45 am »
At the time Ship 1 reaches Ship 2, what I mean by "instantaneous" is, that if the FTL trip took 0 time for Ship 1, it would leave Earth at Year 5 and arrive at Ship 2's location, when Ship 2's clock is at Year 4. Likewise, when Ship 2 sees Ship 1 arrive, they instantaneously travel back to Earth. The clock on Earth is at Year 5, the clock on Ship 2 is still Year 4. Neither Ship 1 nor Ship 2 took any time to travel the 3 light years between them, but the clocks do not agree. There is no paradox, we can't go any faster than "instantaneous", and we can never go backwards in time in either frame.
You are defining instantaneous differently for the 2 ships.
Yes, that is correct, because the situation is not symmetrical.

In the ship 2 frame, the Earth clock is at Year 3.2, when the ship 2 is at Year 4.

... and that observation is incorrect, it is an illusion.

Can we agree that the symmetry is the cause of the paradox please?

I put forward that the paradox cannot happen, because the symmetrical scenario which results in a paradox is not physically possible within the confines of our galaxy, or local cluster.

I repeat...
IMO, this model makes perfect sense, there are no paradoxes and it is consistent with General Relativity. Symmetry is not required, it's the "special" case, and because of it's specialness, SR leads to paradoxes. The principle that all inertial frames are equal is an "assumption" of the the theory of SR. It is what makes SR Special, but it's not realistic.
General relativity introduces more ways to get paradoxes, and reduces to special relativity in the relevant cases we are discussing (The GR paradoxes are all currently excluded from implementation by things like event horizons and the need for exotic (negative mass) matter). The assumption that all inertial reference frames are equal is also part of general relativity. It is a very realistic assumption because it has been experimentally observed to be true.

GR is perfectly consistent with inertial reference frames having different rates of time passage. By insisting on having symmetry, what you are saying is that when Ship 2 accelerates away from earth, (not FTL) to 0.6c, it's clock rate is unaffected. It is still the same as it was on Earth. As such, you expect the situation to be symmetrical and therefore you end up with a paradox. I'm saying, the clock on the ship really is slower than the clock on Earth, not vis-versa. It is not symmetrical, and it can't be symmetrical within our galaxy.

Anyone: Please give a "realistic" example of how Ship 2 came to be moving at 0.6c relative to the Earth where, it did not previously accelerate to that speed. Given that there have been no observations of stars or planets in our galaxy that are moving more than a little over 100 km/s. Nowhere near 0.6c, and there are no worlds orbiting stars or BH's at 0.6c either. The fastest stable orbit around a BH is .5c and it oscillates relative to Earth. So the situation in which Ship 2 has always been moving 0.6c relative to the Earth is unrealistic (if not impossible). Therefore, the symmetry required to cause a paradox, does not exist.

About the twin paradox and time moving slow along with length contraction via acceleration (velocity + time travel) velocity coming with acceleration.

When I was in class they had this old macintosh program where you could switch between two relative frames.  The earth and a space ship.  It had multiple clocks running so you could see synchronous/non-synch clocks.  The earth frame saw the ship as length contracted and de-synched its clocks.  This would be due to time travel.  The tip of the space ship has time subtracted from it with its forward velocity while the back of the ship has less time subtracted from it.  Essentially the earth observer sees the ship as traveling into the past which makes sense because the ship person will have less time pass.

So time in this case did slow for the ship but during acceleration is when the length contraction magic happens which allows time travel via the rotation of the time space axis on a light cone.  The length contraction only happens to the ship and not the universe so the time travel is limited to the ship.

In the ship frame, if I remember correctly, both effects happened as well.  Time slowed down for the universe but during acceleration, length contraction was induced by your change in velocity.  Time being added more the further away means that regardless of the universe time slowing down your forward progression (through time travel - length contraction) advances you more rapidly through the universes future than the effects of slowed time.  I think the reason the clock still passes more slowly for the space outside the ship is because of the constancy of the speed of light.  The same reason for the slow clock for those observing the contracted ship from earth.

It seems to describe their immediate local frame.  Locally this keeps the speed of light constant but non-locally light from the short objects frame does seem to have light moving slowly compared to our space.  Us not directly observing their slow light.  Maybe we only see the translation between frames via slowed osculation in the light, or red-shifting via slowed time + moving away or towards effects.

As space outside contracts time must slow for the speed of light to remain c or dx/dt in the two frames.

This time travel (length contraction) via acceleration being limited to forward velocity limits us to traveling into the future and somewhat clarifies the twin paradox.

The math for the gradient in time over space for a moving observer is in this video at 2:43
Edited: dt=gamma(ti-v*dx/c^2) they forgot c^2 at the end of the equation in the video.

« Last Edit: 08/04/2017 01:28 am by dustinthewind »

#### meberbs

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##### Re: Any resolutions to FTL paradoxes?
« Reply #98 on: 07/26/2017 06:13 am »
At the time Ship 1 reaches Ship 2, what I mean by "instantaneous" is, that if the FTL trip took 0 time for Ship 1, it would leave Earth at Year 5 and arrive at Ship 2's location, when Ship 2's clock is at Year 4. Likewise, when Ship 2 sees Ship 1 arrive, they instantaneously travel back to Earth. The clock on Earth is at Year 5, the clock on Ship 2 is still Year 4. Neither Ship 1 nor Ship 2 took any time to travel the 3 light years between them, but the clocks do not agree. There is no paradox, we can't go any faster than "instantaneous", and we can never go backwards in time in either frame.
You are defining instantaneous differently for the 2 ships.
Yes, that is correct, because the situation is not symmetrical.

In the ship 2 frame, the Earth clock is at Year 3.2, when the ship 2 is at Year 4.

... and that observation is incorrect, it is an illusion.
No, it is not an illusion.

Can we agree that the symmetry is the cause of the paradox please?
Depends, we first would have to agree on the meaning of the word "symmetry."

You keep acting as if a spacecraft travelling at 0.7 c from some distant galaxy that has a high relative velocity to Earth would be fundamentally different from a spaceship that accelerated from Earth to the same speed. You however cannot name a single thing that is physically different between them (hint: there is no difference).

When you stop trying to simultaneously claim "no reference frame is special" and "some reference frames are special" this conversation might start getting somewhere.

I put forward that the paradox cannot happen, because the symmetrical scenario which results in a paradox is not physically possible within the confines of our galaxy, or local cluster.
Go back a couple posts where I asked you to do the math on (nearly) instantaneous travel, and frames separated by Earth's orbital velocity of 30km/s assuming a 10 light year jump.

GR is perfectly consistent with inertial reference frames having different rates of time passage. By insisting on having symmetry, what you are saying is that when Ship 2 accelerates away from earth, (not FTL) to 0.6c, it's clock rate is unaffected.
Where in the world did you get that contradictory idea?
Insisting on symmetry, meaning "all reference frames are equivalent" and therefore "the speed of light is the same in all reference frames" requires that Ship 2's clock rate runs slow as it approaches c. It also means that in the ship 2 inertial frame, it is ship 1's clock that runs slow.

Anyone: Please give a "realistic" example of how Ship 2 came to be moving at 0.6c relative to the Earth where, it did not previously accelerate to that speed.
Again, what is the difference whether it had undergone acceleration in the past? How can you tell that ship 2 didn't come from atoms that had been ejected from a distant galaxy? What is the magical "rest frame" that it originated from? What do you mean by the word always?

The whole point of these questions is for you to recognize the absurdity of your claim that as I said earlier in this post:
You keep acting as if a spacecraft travelling at 0.7 c from some distant galaxy that has a high relative velocity to Earth would be fundamentally different from a spaceship that accelerated from Earth to the same speed.

#### WarpTech

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##### Re: Any resolutions to FTL paradoxes?
« Reply #99 on: 07/26/2017 04:12 pm »
At the time Ship 1 reaches Ship 2, what I mean by "instantaneous" is, that if the FTL trip took 0 time for Ship 1, it would leave Earth at Year 5 and arrive at Ship 2's location, when Ship 2's clock is at Year 4. Likewise, when Ship 2 sees Ship 1 arrive, they instantaneously travel back to Earth. The clock on Earth is at Year 5, the clock on Ship 2 is still Year 4. Neither Ship 1 nor Ship 2 took any time to travel the 3 light years between them, but the clocks do not agree. There is no paradox, we can't go any faster than "instantaneous", and we can never go backwards in time in either frame.
You are defining instantaneous differently for the 2 ships.
Yes, that is correct, because the situation is not symmetrical.

In the ship 2 frame, the Earth clock is at Year 3.2, when the ship 2 is at Year 4.

... and that observation is incorrect, it is an illusion.
No, it is not an illusion.

Okay then, back to the Twin Paradox. The twin on Earth calculates his brother traveling at 0.6c will age 8 years, the traveling twin calculates that his brother at home will age 6.4 years. One is right, the other is wrong. It's not symmetrical, their calculations are not even the same. The one who gets it wrong sees an illusion, because when he gets home he finds that his brother aged 10 years, not 6.4 years. "His" clock rate was slow, his brother's on Earth was not. Again, the rates are not physically symmetrical, so what he measures based on his slow clock is wrong.
« Last Edit: 07/26/2017 04:13 pm by WarpTech »

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