A Step Closer To The Alcubierre Drive!

[ThirdHorseman]

You guys still are ignoring my thought experiment. It shows how different observers experience entirely different physical realities when a FTL signal is sent. There is no time travel. Simply that one observer witnesses a bomb explode and the other observer does not. This cannot possibly be, since the two observers are still causally connected to each other- hell, they are only a few hundred meters apart with velocities that differ by only 10 m/s. You guys still have not answered what is WRONG with this simple thought experiment. Instead, you start talking of curved space time, closed time-like curves etc... when that is not the issue at all.

The situation you describe does not violate causality. At what point for any observer does the effect precede the cause? That is a causality violation, and causality violations are what can cause a paradox.

In your example, yes the two observers experience different physical realities but that is not a problem. In the example I used above, when observers O and O' meet, O insists that event * happened already...he might even have video evidence. O' insists that it has not happened yet. Both of them are correct!! That might not make logical sense, but it is not a causality violation and cannot create a paradox. Only when you allow FTL signals and travel do you open the door for events in one frame of reference to affect observers in another.

I'll use again the example of time dilation when travelling close to c. One observer insists they've been gone one year. Another insists he has been gone 10. They are BOTH RIGHT and there is nothing wrong with that.

Close timelike curves are exactly the issue, because that is when you have causality violations and paradoxes. And since it seems that time travel and closed timelike curves ARE mathematically possible, there must be some other system to prevent paradoxes from occurring. That system might be physical manifestations that prevent FTL from being used at all (fatal buildup of energy, etc) or prevent paradoxes from occurring when the systems are used (self consistency principles).

[-Velocity-]

The situation you describe does not violate causality. At what point for any observer does the effect precede the cause? That is a causality violation, and causality violations are what can cause a paradox.

In your example, yes the two observers experience different physical realities but that is not a problem. In the example I used above, when observers O and O' meet, O insists that event * happened already...he might even have video evidence. O' insists that it has not happened yet. Both of them are correct!! That might not make logical sense, but it is not a causality violation and cannot create a paradox. Only when you allow FTL signals and travel do you open the door for events in one frame of reference to affect observers in another.

I'll use again the example of time dilation when travelling close to c. One observer insists they've been gone one year. Another insists he has been gone 10. They are BOTH RIGHT and there is nothing wrong with that.

Close timelike curves are exactly the issue, because that is when you have causality violations and paradoxes. And since it seems that time travel and closed timelike curves ARE mathematically possible, there must be some other system to prevent paradoxes from occurring. That system might be physical manifestations that prevent FTL from being used at all (fatal buildup of energy, etc) or prevent paradoxes from occurring when the systems are used (self consistency principles).

Again, you do not try to refute my example, again, you ignore the problem, and again, you are wrong. Causality is not just about making sure the effect comes after the cause; it is also about requiring that the effect has a cause to begin with at all!

As an example, consider the thought experiment that I made, which I posted once and linked twice to already in this thread, that you apparently still haven't considered so maybe I'm just wasting my breath, but I'll pretend like you might actually read it this time and respond to it this time. Consider the train and the bomb again. As I said a few posts ago, the bomb is not the real problem, the bomb just amplifies the mis-match between physical realities that the use of FTL causes. So don't get too fixed up on the bomb. But... consider that experimental set up anyway, because it makes a more graphic example.

Pretend you are the observer on the train. You don't get blown up by the bomb. But the observer on the ground sees you get blown up by the bomb. So now you stop the train with the emergency brake. The observer on the ground sees an invisible, noncausal force pull the emergency brake handle, while your splattered remains continue to drip off the flatbed car. You walk up to the observer on the ground, who still does not see you. You punch him in the face. The observer on the ground is punched in the face by an invisible, inexplicable force.

Of course the fact that you CAN punch the observer on the ground in the face implies that the atoms in your hand still interact with the atoms in the observer on the ground's face. Which means you still interact through the electromagnetic force, at least, with the observer on the ground. Which means he should see you. But how can he see you when he saw you get blown to tiny bits?

This goes on and on. It is simply impossible.

This is why all observers MUST agree on the same events taking place, otherwise, the universe evolves into different physical realities for each frame of reference, and yet, the frames of reference still interact with each other...

But you think the above scenario is possible... why?!

Edited October 15, 2013 by |Velocity|

[K^2]

I'm not sure if time travel is possible or not, but I tend to say no, as from what I've heard, every time they come up with some kind of time travel mechanism, someone figures out a way in which it would not be usable in the real universe.

It's not really up to whether you think it's possible or not. Under General Relativity, it is possible and closed time loops already exist. So field theory that governs matter already accounts for time travel as a possibility.

There is no question about it. It's as certain as gravity. Even if we learn of some corrections to the field theories in place, they are not of the magnitude sufficient to make time travel impossible. It's a fact of this universe, and everyone will just have to figure out how to live with it.

Anyway, I relinked the post for you yesterday, after you requested it. You must have missed the link. Here is is re-relinked: http://forum.kerbalspaceprogram.com/threads/47034-A-Step-Closer-To-The-Alcubierre-Drive%21?p=688102&viewfull=1#post688102

Thank you, and sorry for missing it last time.

So lets start with what you got right. Instantaneous communication is impossible in classical theory. And this is actually a very neat example of why. I hope you don't mind that I borrow it at some point.

Now to the meat of the matter. Let us first start with classical relativistic mechanics. Instantaneous communication just cannot happen, but what about very rapid, FTL, yet finite speed communication. Say, 10c. After all, that's all that Alcubierre Drive promises - travel at some multiple of speed of light.

Let us say that bomb is located some distance d from each receiver. Beam of light is sent at the speed c, and reaches each of the detectors in time d/c as seen by observer on the train. The return signal is sent at 10c, and so the total round time is 1.1d/c for both signals as seen by observer on the train.

Now, let us suppose that the train is traveling at some velocity v, and we consider the whole scenario from perspective of the observer who is standing nearby, braced against the immense shock wave generated by a train traveling at a fraction of c. Let us say that the observer was located right next to the train, so close that we can ignore any transverse separation and treat it as a 1D problem. And for simplicity, lets say that the observer was right next to the bomb when the original light signals were sent. This simplifies things, letting us place the event of sending light signals at x=0 and t=0 for both observers.

First and foremost, stationary observer, as the blazes of plasma engulf him, manages to nonetheless spot that the two receivers are a distance d√(1-v²/c²) = d' away from the bomb. They nevertheless, still move at the speed of v, and light moves at the speed c. Therefore, from perspective of the observer, the light beams reach the detectors in time d'/(c-v) and d'/(c+v) for the forward and rear detectors respectively. Now the detectors send their faster than light signal. And here is where things get really interesting.

From perspective of observer, the FTL signals return at speeds of 10c. But this isn't speed of light. This speed is not the same in all coordinate systems. And neither is it 10c+v and 10c-v, because velocities just don't add up this way. Fortunately, we have the formula for adding relativistic velocities. And most fortunately of all, this formula works for FTL speeds.

The singal from the front of the train has velocity of the train subtracted from the signal propagation speed giving us v_f = (10c - v)/(1-10v/c). The signal catching up from the back, however, has the velocity added. v_r = (10c + v)/(1+10v/c). Note that if I had c instead of 10c, both of these simplify to just c. That's what you expect - speed of light is the same in all frames, but speed of object traveling FTL is frame-dependent same as that of object traveling slower than light.

Naturally, each of these still needs to cover the distance of d' while the train is moving along at v. So the times are d'/((10c - v)/(1-10v/c) + v) and d'/((10c + v)/(1+10v/c) - v)

So now we look at the total. t_± = d'/(c∓v)+d'/((10c ∓ v)/(1 ∓ 10v/c) ± v). The - in ∓ goes with the + in the ±, and vice versa. Let us collect these fractions.

t_± = d'/(c∓v)+d'(1 ∓ 10v/c)/((10c ∓ v) ± v(1 ∓ 10v/c))

t_± = d'[(10c ∓ v) ± v(1 ∓ 10v/c) + (c∓v)(1 ∓ 10v/c)]/[(c∓v)((10c ∓ v) ± v(1 ∓ 10v/c))]

t_± = d'[10c ∓ v ± v - 10v²/c + c + 10v²/c ∓ v ∓ 10v]/[10c² ∓ vc ± vc - 10v ∓ 10vc + v² - v² + 10v²/c]

Terms like ∓ v cancel terms like ± v regardless of the sign.

t_± = d'[11c ∓ 11v]/[10c² - 10v ∓ 10vc ± 10v²/c]

t_± = d'[11(c ∓ v)]/[(10c - 10v/c)(c ∓ v)]

Hey, I got a common factor of (c ∓ v), which is never zero, so I can divide through by.

t_± = 11d'/(10c - 10v/c)

And the magic has happened. t₊ = t_-. So the round trip for the two signals is exactly the same from perspective of observer, despite return signal traveling FTL. The observer standing on the ground, who must be a Kerbal for being able to survive the passing of super-relativistic train and moreover take notes, makes an observation that both signals reached the bomb at the same time. No explosion!

So relativity wins, once again. I could derive this whole thing with an arbitrary velocity for signals going away and towards the bomb, and so long as the speeds are the same for the forward and rear signals, it will always work out that round trip time is the same, even if one or either of these speeds is FTL. It's all in how relativistic speeds add up.

And this resolves your paradox. Agreed? I'll give you some time to check all the math, and feel free to ask questions if I didn't make some of the steps clear, but this is how it works.

-------------------------------------------------------------------------------------------------

Now for the elephant in the room. Time travel. I already said that if the communication is instant, bad stuff happens. And I already said that time travel is possible. And it is obvious that using time travel you can make faux instant communication by simply sending the signal with enough lead time. So what's up? Did I just dig myself into a hole? Well, not exactly. Here is how we can make the detectors at either end send "instant" signal to the bomb.

Imagine, if you will, that an ancient alien civilization being able of many technological wonders, living in relative proximity to a rotating black hole, and trying to win a bet with their neighbors have built an automated station that accepts radio messages and fires them into the black hole's ergosphere juuust right. And it receives these messages hundreds of thousands of years before sending them, and bounces them back towards whoever sent them. You, having decoded in cosmic background a hidden message with instructions and the activation codes required to make this station do your bidding realize that ability to end the universe is finally within your grasp. So you build the train bomb, arm the transmitters, and time everything so that the signal to detonate the bomb is sent by receivers "instantly". Of course, what really happens is that transmitters receive the beam from the bomb, send message to the ancient station thousands of light years away, the message is sent thousands of years back, relayed back to your detectors, and arrives with enough lead time for you to send the message to the bomb to arrive at the exact instance that the signal is received by transmitters.

Devious.

Yet, there is a problem. Simultaneity is in the eyes of the beholder. Two events happening at the same exact time in one coordinate system happen at different times from the other. From perspective of you, riding on the train of doom, the signal is sent instantly from receivers to the bomb. From perspective of the lone kerbal scientist on the tracks, the two receivers got triggered at different times, but they also did not send the signal instantly. In fact, one fires it too early, and the other fires it too late, which results in the bomb still getting the two signals at the same exact time!

Curses!

And yet, the day is once again saved by the relativity.

[Nibb31]

I have another example where FTL breaks causality. Imagine two space warships: "Argonaut A" is equipped with lasers and a cloaking device, but when the lasers are fired, its position is revealed. "Battlestar B" is equipped with FTL torpedoes but can't see "Argonaut A" as it approaches.

Now, "Argonaut A" detects "Battlestar B" and fires its lasers at it. Lasers travel at light speed and inflict some minor damage to "Battlestar B". Some crew members are killed. "Battlestar B" immediately retaliates by firing its FTL torpedoes at the source of the laser fire. Because they go faster than light, the torpedoes can actually hit and destroy "Argonaut A" before it fired its lasers or even detected "Battlestar B".

The consequence of this is that we have a causality paradox: "Argonaut A" is preemptively destroyed by "Battlestar B"'s torpedoes, while at the same time "Battlestar B" was never even aware of the threat and still has its torpedoes on board.

Any civilization that can manage FTL can also manage this level of time travel, because going back in time is a corollary of going faster than light. Once this happens, all sorts of paradoxes are created with causality, which is why I think FTL is impossible and even undesirable. It becomes the ultimate weapon where any threat can be annihilated before it even exists and the result would be that you wouldn't even be aware that such a threat ever existed.

Let's take this a little further. Imagine that we have FTL travel and we stumble upon a belligerant species on the other side of the galaxy that wants to destroy us. We could just send some sort of bacteriological weapon or virus on an FTL probe that wipes out life on their home planet millions of years before they even evolve into becoming sentient organisms. The result would be that we would never encounter them in the first place or even be aware of their existence. Rinse and repeat this a couple of times, and what would the universe look like to us? We would probably be scrutinizing the galaxy and wondering why we can't find any evidence of other forms of life... Sounds familiar?

[K^2]

Now, "Argonaut A" detects "Battlestar B" and fires its lasers at it. Lasers travel at light speed and inflict some minor damage to "Battlestar B". Some crew members are killed. "Battlestar B" immediately retaliates by firing its FTL torpedoes at the source of the laser fire. Because they go faster than light, the torpedoes can actually hit and destroy "Argonaut A" before it fired its lasers or even detected "Battlestar B".

You got confused somewhere. Torpedoes from B are fired after it is hit by lasers, which happens after the lasers are fired with a light cone lag. No matter how FTL the torpedoes are, they will still hit A well after the lasers have fired.

What you can have is when viewed from alternative coordinate system, torpedoes may hit A before they are fired from B. But still after the lasers on A have been used.

[drakesdoom]

Let them build their machine either it works or it doesn't. If it works it will most likely reveal a closer step to a unified field theory. If it doesn't how many people could that possibly kill?

[Tommygun]

Let them build their machine either it works or it doesn't. If it works it will most likely reveal a closer step to a unified field theory. If it doesn't how many people could that possibly kill?

I've seen that movie, it doesn't end well.

Lots of hallucinating and self mutilations.

[UltraVires]

I've seen that movie, it doesn't end well.

Lots of hallucinating and self mutilations.

You've seen "Event Horizon" one too many times Tommygun....

Personally I can't wait for real Warp Drive... That's one of the things I think has held us back as a species... We have always been explorers, always going over the next hill, across the next ocean... Maybe for money, maybe just for the hell of it! But the Ocean of stars is very hard to sail through...

I think of myself now, like someone watching Columbus's ships get built. Standing on the edge of the Known world, watching a new era of human history just beginning...

Edited October 17, 2013 by UltraVires

[-Velocity-]

...

Thank you for responding to my thought experiment! I'm going to check it out and run through the numbers myself when I get the chance, but it's not going to be today, as I'm rather busy. Maybe tomorrow or the next day.

Anyway, if I understand you correctly, relative velocities add by the following formula:

Vr = (v1 - v2)/(1 - v1*v2/c^2)?

Say v2 = 0. In the limit of v1 getting extremely high, this goes negative.... isn't that a problem?! Or is the bottom sign wrong? If so, then didn't you get your relative velocities wrong?

If the above formula is not correct, why is it not possible for FTL speeds to get so high that they are effectively infinitely fast- i.e., instantaneous communication? Basically, if FTL speeds are possible, how does that not imply instantaneous communication is possible, because instantaneous communication is just the limit as the velocity goes to infinity.

Edited October 17, 2013 by |Velocity|

[NASAFanboy]

Hopefully will come on time for 2063!

[-Velocity-]

You've seen "Event Horizon" one too many times Tommygun....

Personally I can't wait for real Warp Drive... That's one of the things I think has held us back as a species... We have always been explorers, always going over the next hill, across the next ocean... Maybe for money, maybe just for the hell of it! But the Ocean of stars is very hard to sail through...

I think of myself now, like someone watching Columbus's ships get built. Standing on the edge of the Known world, watching a new era of human history just beginning...

Yes, the wonderful new era where tens of millions of Native Americans get enslaved, murdered, and subjugated, a new world that brings with it wonderful things like free smallpox-infected-blanket handouts, and the African slave trade.

No, I do not believe that warp drives are possible, and I'll actually be happy about that if I'm right. We would have been the Native Americans.

Edited October 17, 2013 by |Velocity|

[Galacticruler]

if it happens, I'll be safe to claim the position of 1000th tester, if all the bugs are worked out.(I don't much prefer vanishing or being a pile of sentient goo.)

[NASAFanboy]

Yes, the wonderful new era where tens of millions of Native Americans get enslaved, murdered, and subjugated, a new world that brings with it wonderful things like free smallpox-infected-blanket handouts, and the African slave trade.

No, I do not believe that warp drives are possible, and I'll actually be happy about that if I'm right. We would have been the Native Americans.

As in what? We would most likely receive a much, much better bargaining position and much more respect for our culture and race if we met the aliens on a FTL-capable ship in orbit over a planet light years from Earth.

Had those native Americans decided to build ships to explore that "big endless lake", we would be having Mayan spacestations and stuff like that going on, instead of their culture being slagthered like mere animals. Be if we where FTL-capable and met another FTL-capable race, they would most likely treat us much, much better, as if the Spanish would've done if the Aztecs met them with giant ships in the Canary Islands.

I fully believe in the possibility of this drive, and hope for it to work. If it suddenly is invented today, we'll probably have interstellar colonies by 2015, and good stuff.

And yes, while the natives got massacred, it breathed life into a new country, that, utilizing the resources of the new world, would go on and pave the way for most of the 20th century industry and pave the way for massive scientific and technological advancements.

Edited October 18, 2013 by NASAFanboy

[-Velocity-]

As in what?

As in, if warp drive capable ships were possible, there's a very good chance we would have been colonized millions or billions of years ago. There's a good chance we wouldn't be here. We (Earth life) would have been the Native Americans.

I'm not saying that's necessarily likely, I just said a "good chance". There's a lot of variables we don't know. My point is, the difficulty of interstellar travel helps keep one invasive set of lifeforms from taking over the galaxy. Just as the oceans help isolate groups of plants and animals into separate populations, increasing speciation and the diversity of life, so does the gulf between the stars give planetary systems a chance to grow their own civilizations without outside interference.

Edited October 18, 2013 by |Velocity|

[m4v]

if warp drivers were possible and if we could build them, it would be just another weapon of mass destruction for our arsenal.

Exploration? don't be naïve.

[xxfallacyxx]

if it happens, I'll be safe to claim the position of 1000th tester, if all the bugs are worked out.(I don't much prefer vanishing or being a pile of sentient goo.)

But what else would we fill our Mystery Goo Containment Units with?

[Awaras]

As in, if warp drive capable ships were possible, there's a very good chance we would have been colonized millions or billions of years ago.

What if we WERE colonized about 3.5 billion years ago?

Maybe we all are 'colonists'...

[Bacterius]

What if we WERE colonized about 3.5 billion years ago?

Maybe we all are 'colonists'...

Our forefathers must've been pretty smart, they managed to FTL without knowing how to read, write, count, or even make fire (unless some aliens decided to picnic on our still-forming planet and left behind some biological stuff which became us... I could believe that, maybe)

Honestly I don't understand the argument, and I DO believe we will discover a "miraculous" way to travel faster than light in the future. But to say that the existence of such a device would imply that aliens are everywhere is ludicrous. Though realistically it is likely there are civilizations out there that are millions of years old, we're talking about huge distances here. Maybe there is a fundamental speed limit which makes interstellar travel possible, but not intergalactic (for instance) so that civilizations don't have to be annihilated by the first one to discover the warp drive...

Edited October 18, 2013 by Bacterius

[Awaras]

Our forefathers must've been pretty smart, they managed to FTL without knowing how to read, write, count, or even make fire

I mean the whole panspermia theory thing...

Edited October 18, 2013 by Awaras

[K^2]

Anyway, if I understand you correctly, relative velocities add by the following formula:

Vr = (v1 - v2)/(1 - v1*v2/c^2)?

Say v2 = 0. In the limit of v1 getting extremely high, this goes negative.... isn't that a problem?! Or is the bottom sign wrong? If so, then didn't you get your relative velocities wrong?

The signs are right. Say v1 is c and you look at it from a coordinate system moving at v2=v. (c-v)/(1-v/c) = c(c-v)/(c-v) = c. Speed of light is the same in all frames. This would not work with a + sign.

The sign changing for v1*v2 > c² and v1 < v2 is simply an indication of event order changes when you go FTL. That's what we've been talking about all along.

And these formulae are correct, or the whole thing would break down even with both velocities being subluminal, and then you could recreate your paradox by simply having detectors at either end of the train fire a gun into the targets on the bomb. The train wouldn't even have to move that fast for this to be measurable.

So again, relativity works. You can't use contraction/dilation formulae from Special Relativity under v > c, because space-time has to be curved for you to get FTL, and these formulae are for flat space-time. But velocity addition formulae can be used so long as space-time outside of the warp bubble is flat.

[DJEN]

I'll watch the progress.

Edited October 18, 2013 by DJEN

[DJEN]

As in, if warp drive capable ships were possible, there's a very good chance we would have been colonized millions or billions of years ago. There's a good chance we wouldn't be here. We (Earth life) would have been the Native Americans.

I'm not saying that's necessarily likely, I just said a "good chance". There's a lot of variables we don't know. My point is, the difficulty of interstellar travel helps keep one invasive set of lifeforms from taking over the galaxy. Just as the oceans help isolate groups of plants and animals into separate populations, increasing speciation and the diversity of life, so does the gulf between the stars give planetary systems a chance to grow their own civilizations without outside interference.

Ah, yes. Yes indeed.

We humans like to say that we're changing, but many are ignorant of the evidence.

What we should do is to muck around the solar system and perish for the rest of the universe.

Of course, we won't do that. We're too stupid for that.

Whatever it takes, humanity will point its middle finger to Earth and flee to the stars.

Ad Astra Per Aspra, we will do anything.

[NASAFanboy]

Our forefathers must've been pretty smart, they managed to FTL without knowing how to read, write, count, or even make fire (unless some aliens decided to picnic on our still-forming planet and left behind some biological stuff which became us... I could believe that, maybe)

Honestly I don't understand the argument, and I DO believe we will discover a "miraculous" way to travel faster than light in the future. But to say that the existence of such a device would imply that aliens are everywhere is ludicrous. Though realistically it is likely there are civilizations out there that are millions of years old, we're talking about huge distances here. Maybe there is a fundamental speed limit which makes interstellar travel possible, but not intergalactic (for instance) so that civilizations don't have to be annihilated by the first one to discover the warp drive...

I believe that the acclubbierre drive does not go that fast past the speed of light for aliens to be everywhere. After all the space agency still says that the drive they're working on is supposed to go at 10c.

That's not that fast.

And who knows? Maybe we could be one of the first intelligent races, or almost all spices wipe each other out when im they discover e=mc2

[K^2]

... at 10c.

That's not that fast.

It's fast enough. At 10c, we can cross interstellar space easy enough. That means we can plant colonies on multiple stars and gradually expand outward. With a 10c drive, there is no single or any plausible chain of disasters that can wipe out our entire civilization short of encountering a more advanced civilization. From there on, even if the actual frontier expands at merely .1c, entire MW galaxy is going to be colonized in under a million years. That might sound like a really long time, but it really is not. Humans were less evolved a million years ago, but out of 3-something billion years that life has been evolving on this planet, a million years faster or slower to reach a certain stage in evolution is not much. And there are planets in MW that would have had a head start by billions of years simply based on how their star systems have formed.

So how hard is it to build a 10c warp drive? Hard enough so that no civilization in MW galaxy has managed it until less than a million years ago, which on the scale of the age of the galaxy is equivalent to saying that nobody has built one yet.

Same argument can be implied to seeders, Von Neuman probes, etc., however, which suggests that advanced civilizations are pretty rare in our parts of the universe, and that they manage to stagnate or wipe themselves out before reaching that point. Given that we are pretty close, we are either managing to do better than everyone else, or we are at a brink of a very serious, persistent cataclysm.

Personally, I think our best bet is to aim for singularity, because past that point, there seems to be no way for civilization to simply end. Humans will probably go extinct, but civilization will go on.

[Seret]

So how hard is it to build a 10c warp drive? Hard enough so that no civilization in MW galaxy has managed it until less than a million years ago, which on the scale of the age of the galaxy is equivalent to saying that nobody has built one yet.

Same argument can be implied to seeders, Von Neuman probes, etc., however, which suggests that advanced civilizations are pretty rare in our parts of the universe, and that they manage to stagnate or wipe themselves out before reaching that point.

I'm inclined to agree. It's the answer to the Fermi Paradox we least want to hear, but the most plausible one IMO. Space is just too big for interstellar flight to be commonplace.