Specific FTL Questions

[McC]

This thread got me thinking about various ways of FTL travel that don't violate SR, GR, or causality. I have some specific questions, to that end.

1) Does a wormhole that undergoes no acceleration at either end result in causality paradoxes?

2) Does 'apparent' FTL have the same causality problems that 'actual' FTL does? That is to say, if you are in one spot and then are instantaneously in another, have you actually traveled FTL, or what? This question rather obviously relates to #1.

3) Does something like an Alcubierre drive suffer from causality effects as other FTL methods, despite the objects within the 'bubble' undergoing no acceleration?

Much like Red, I have an exceedingly hard time wrapping my head around SR's notion of simultineity (or lack thereof), but I want to try to adhere to existing physics as best I can when writing stuff. Technologically impossible devices don't bother me so much as physically impossible ones do.

[GrandMasterTerwynn]

This thread got me thinking about various ways of FTL travel that don't violate SR, GR, or causality. I have some specific questions, to that end.

1) Does a wormhole that undergoes no acceleration at either end result in causality paradoxes?

If you have Captain Alice on one end of the wormhole and Captain Bob at the other, Alice can see Bob enter the wormhole, and observe him travelling to her. However, Captain Paul from some arbitrary point not in direct line-of-sight of the wormhole will observe Bob arriving at Alice's end of the wormhole before he observes Bob entering the wormhole, without being able to observe the transit through the wormhole. So, to Paul, Bob reappears some time before he disappears. So, to Paul, Bob has just engaged in time travel, as he comes from what Paul will percieve as the future.

2) Does 'apparent' FTL have the same causality problems that 'actual' FTL does? That is to say, if you are in one spot and then are instantaneously in another, have you actually traveled FTL, or what? This question rather obviously relates to #1.

Captain Paul, our spoilsport observer, will, again, percieve that Bob has engaged in time-travel, as he will see Bob's departure some arbitrary amount of time after his arrival. Thus, Bob came from the future.

3) Does something like an Alcubierre drive suffer from causality effects as other FTL methods, despite the objects within the 'bubble' undergoing no acceleration?

Yes. Again, Paul just has to be in the right place to witness Bob's arrival, but not his trip to that point. Thus, the next thing he will see is Bob departing from some arbitrarily distant location at some arbitrary point in the future.

The general point is that, regardless of what method you use, there will always be a frame of reference for which FTL travel will appear to be time-travel.

[McC]

If you have Captain Alice on one end of the wormhole and Captain Bob at the other, Alice can see Bob enter the wormhole, and observe him travelling to her. However, Captain Paul from some arbitrary point not in direct line-of-sight of the wormhole will observe Bob arriving at Alice's end of the wormhole before he observes Bob entering the wormhole, without being able to observe the transit through the wormhole. So, to Paul, Bob reappears some time before he disappears. So, to Paul, Bob has just engaged in time travel, as he comes from what Paul will percieve as the future.

This is the thing that always breaks my brain. Isn't it only true if Paul can perceive at an FTL rate? Otherwise, isn't he just seeing the photons in some funky order? Say Paul is 'behind' Alice, who is 'behind' the wormhole. Bob comes through the wormhole from some other wormhole that is 'behind' the first one. Paul will perceive Bob coming through before he perceives him leaving, for sure, because the departure wormhole is farther away, thus the photons take longer. But why does this mean he has actually time-traveled?

More or less the same brain-breaking question that applies to the rest of the answers, so I won't quote them.

[GrandMasterTerwynn]

If you have Captain Alice on one end of the wormhole and Captain Bob at the other, Alice can see Bob enter the wormhole, and observe him travelling to her. However, Captain Paul from some arbitrary point not in direct line-of-sight of the wormhole will observe Bob arriving at Alice's end of the wormhole before he observes Bob entering the wormhole, without being able to observe the transit through the wormhole. So, to Paul, Bob reappears some time before he disappears. So, to Paul, Bob has just engaged in time travel, as he comes from what Paul will percieve as the future.

This is the thing that always breaks my brain. Isn't it only true if Paul can perceive at an FTL rate? Otherwise, isn't he just seeing the photons in some funky order? Say Paul is 'behind' Alice, who is 'behind' the wormhole. Bob comes through the wormhole from some other wormhole that is 'behind' the first one. Paul will perceive Bob coming through before he perceives him leaving, for sure, because the departure wormhole is farther away, thus the photons take longer. But why does this mean he has actually time-traveled?

More or less the same brain-breaking question that applies to the rest of the answers, so I won't quote them.

No, it assumes that Paul can only recieve informaton at the speed of light. All information-carriers move at the speed of light, be they photons, gravitational waves, electromagnetic force, etc, etc, etc. Let's assume that Paul sets up a ridiculously sensitive gravitational telescope and compass at his frame of reference, so he can keep tabs of Bob and Alice. Let's say that Paul is 50 lighyears from Earth.

Now let's say he sees Bob rendezvous with Alice in 2005, and he trains his telescopes to Earth. The information his instruments record come from Earth as it was in 1955. Now, let's say that Bob is born in 1955 and Paul sees it. He will get to watch Bob grow up. As he observes Bob, he can see that Bob's movements peturb his gravitational telescope, and Bob's electromagnetic moments wiggle Paul's compass. In 2055, Paul's instruments will finally record Bob building his spaceship, and departing for his rendezvous with Alice. At this time, Bob's space-ship will be exerting a gravitational pull on Paul's gravitational telescope.

If Bob were properly obeying causality, Paul would be able to observe him travelling to Alice to arrive in the year 2055 + T_trip. However, we've already established that Paul observed Bob and Alice rendezvousing back in 2005. Yet, in Paul's frame of reference, he saw Bob leave Earth in 2055. From Paul's frame of reference, Bob had to have travelled 50 years into the past in order to have arrived in Paul's 2005.

While, conceptually, he knows that Bob actually left Earth in 2005, all the natural information about Bob's whereabouts, the gravitational pull he exerts on Paul, the photons coming off him, everything else one can think of that describes Bob's position and velocity, only travels at the speed of light. If Paul had the ability to instantaneously send himself and a loaded pistol to the Earth he's observing through his telescopes, then he could concievably arrive before Bob leaves to rendezvous with Alice, and empty the pistol into Bob's brain . . . creating a grandfather paradox. It's all rather better-explained in the other thread, I think, though it is a bit of a dry read.

[McC]

If Paul had the ability to instantaneously send himself and a loaded pistol to the Earth he's observing through his telescopes, then he could concievably arrive before Bob leaves to rendezvous with Alice, and empty the pistol into Bob's brain . . . creating a grandfather paradox.

Yeah, but the Earth he's observing through the telescope is an 'illusion.' It already happened. Thus, if he instantaneously transported, wouldn't he arrive 50 years "after" what he's seeing? What you said is obviously time travel, but I'm at a loss as to why that would actually happen, rather than Paul simply observing old data that is no longer 'current.'

[Kuroneko]

1) Does a wormhole that undergoes no acceleration at either end result in causality paradoxes?

Stable wormholes of overly idealized conditions, no. By a reasonable standard, yes.

2) Does 'apparent' FTL have the same causality problems that 'actual' FTL does? That is to say, if you are in one spot and then are instantaneously in another, have you actually traveled FTL, or what? This question rather obviously relates to #1.

That depends critically on the particulars.

3) Does something like an Alcubierre drive suffer from causality effects as other FTL methods, despite the objects within the 'bubble' undergoing no acceleration?

IIRC, the Alcubierre metric is globally hyperbolic, then it admits a foliation by Cauchy surfaces. Every causal line intersected these surfaces exactly once, so no time travel is possible. This is, in fact, the strongest criterion for causality in general relativity. Unfortunately, the Alcubierre metric also fails to meet the weakest (null) energy condition. In its defense, however, so do stable wormholes, so it is an improvement.

Yes. Again, Paul just has to be in the right place to witness Bob's arrival, but not his trip to that point. Thus, the next thing he will see is Bob departing from some arbitrarily distant location at some arbitrary point in the future. The general point is that, regardless of what method you use, there will always be a frame of reference for which FTL travel will appear to be time-travel.

Only in the sense that if Paul interprets his observations using a flat spacetime model, he will conclude that there were violations of causality. If Paul is simply trying to make sense of his observations, he would inevitably have to give up something of traditional GTR--if not causality, then some energy conditions. But it doesn't have to be causality.

[McC]

Kuroneko, it scares and awes me that you can toss around phrases that I don't even recognize.

IIRC, the Alcubierre metric is globally hyperbolic, then it admits a foliation by Cauchy surfaces. Every causal line intersected these surfaces exactly once, so no time travel is possible. This is, in fact, the strongest criterion for causality in general relativity. Unfortunately, the Alcubierre metric also fails to meet the weakest (null) energy condition. In its defense, however, so do stable wormholes, so it is an improvement.

This is the part where it requires negative energy densities on either side of the warp bubble, right?

Only in the sense that if Paul interprets his observations using a flat spacetime model, he will conclude that there were violations of causality. If Paul is simply trying to make sense of his observations, he would inevitably have to give up something of traditional GTR--if not causality, then some energy conditions. But it doesn't have to be causality.

See, this is the part I have never been able to grasp. How is it that Paul will end up in the past? If Paul observes something from 50 LY away, he's seeing what happened 50 years ago. Even if he instantly teleports to the location he's viewing, the events that he witnessed from his telescope already happened 50 years ago, so how could he possibly intervene? He'll arrive 50 years after the events he saw, won't he?

[Kuroneko]

This is the part where it requires negative energy densities on either side of the warp bubble, right?

Right. Wormholes require this also in order to be stable.

See, this is the part I have never been able to grasp. How is it that Paul will end up in the past? If Paul observes something from 50 LY away, he's seeing what happened 50 years ago. Even if he instantly teleports to the location he's viewing, the events that he witnessed from his telescope already happened 50 years ago, so how could he possibly intervene? He'll arrive 50 years after the events he saw, won't he?

[img=left]http://i4.photobucket.com/albums/y121/v ... ef81de.png[/img] The key thing to realize is that what observers reckon as their present depends on their state of motion.

In flat spacetime (special relativity), if Paul has the capability to move instantaneously, he can't actually travel to the moment he is observing through his telescope--but he can, in principle, travel arbitrarily close to that moment, which is for all practical purposes just as good. Let's say Paul's sense of "now" cuts some slice of spacetime--as he reckons it, events along on this slice are in his present; some other events may be in his future or past. By giving himself a large Lorentz boost (i.e., accelerating to an extreme velocity), Paul's sense of "now" can be rotated in spacetime to an entirely different. If Paul makes his teleport while in this state,

Let me revisit a diagrame made in the previous state.

Suppose that Paul is at B while the location he is observing is along the t-axis (line AC), separated by fifty light-years (AB = 50). If Paul and his observee are at rest relative to each other, Paul's "now" is along the line AB. Paul's teleport will indeed take him fifty years too late. However, if he suddenly gains a large velocity, his "now" will be along the line BC. Note that he arrives before the point he otherwise would have if he had not accelerated. If he is very close to the speed of light, his line of "now" will very nearly coincide with the path of light, and so he could travel as close to the event as he wishes if he has the capability of making his relative velocity arbitrarily large.

Note that after such a teleport (say, to C), Paul could decelerate to zero relative velocity, and jump back to his old spatial location--but since his sense of "now" will be parallel to line AB, he travels into his own past.

[Ariphaos]

IIRC, the Alcubierre metric is globally hyperbolic, then it admits a foliation by Cauchy surfaces. Every causal line intersected these surfaces exactly once, so no time travel is possible. This is, in fact, the strongest criterion for causality in general relativity.

How could this work, and how does it being hyperbolic change things as opposed to elliptical or euclidean? To quote your rebuttal of my last point in the previous thread:

There is no superluminal motion for any physical medium. If that's not your point, than I'm afraid I don't see the reason for your preoccupation with wave motion, as it simply does not matter how the relative motion is obtained--the reversal of causality is present in all attemps at totally ordering events regardless of how it is obtained.

Given what you say, I take it that any interference by a single object on two spacelike events could violate causality, no matter what. Unless you were simply referring to my hypothesis not allowing for FTL travel on its own anyway?

[Kuroneko]

How could this work, and how does it being hyperbolic change things as opposed to elliptical or euclidean? ...

This term does not refer to the elliptical/parabolic(Euclidean)/hyperbolic geometries, but to a type of differential equation--a type under which the wave equation and the field equations happen to fall. The point of having a Cauchy surface is that knowing the configuration on the surface enables one to, in principle, calculate the configuration of the entire universe at any time in the past or future. Actually, the term 'globally hyperbolic' is defined in terms of the strong causality condition and some other assumption, but there is a theorem that states that a spacetime is globally hyperbolic iff it admits a Cauchy surface. The full details of this are too involved to be repeated here; besides, you don't seem to be too familiar with PDEs and topology, so I doubt it would be fruitful anyway. If anyone here has familiarity with these topic, see, for example, Hawking and Ellis, the large-scale structure of spacetime, esp. p.192 and Sec. 6.6.

There is no superluminal motion for any physical medium. If that's not your point, than I'm afraid I don't see the reason for your preoccupation with wave motion, as it simply does not matter how the relative motion is obtained--the reversal of causality is present in all attemps at totally ordering events regardless of how it is obtained.

Given what you say, I take it that any interference by a single object on two spacelike events could violate causality, no matter what. Unless you were simply referring to my hypothesis not allowing for FTL travel on its own anyway?

Please don't take my statements so far out of context. That entire thread implicitly assumed a Minkowski spacetime, and it was assumed by me explicitly. In curved spacetimes, there it is quite possible for a timelike curve (locally subluminal) to be globally superluminal. The most straightforward example of this is having a positive cosmological constant in an infinite universe, which causes superluminal separation between points sufficiently far enough away from each other. There is no violation of causality because every object stays within its own light cone--it is space itself that is expanding. Another expample an object falling into a black hole, which gains superluminal velocity relative to external observers when crossing the event horizon. The event horizon protects the external observers from this fact, but what Alcubierre discovered was that instead of breaking causality or having such a horizon, one could have superluminal motion by breaking the energy conditions instead. The ship is still within its own light cone, and hence does not have a spacelike path--again, the key concept is being locally subluminal.

[Ariphaos]

This term does not refer to the elliptical/parabolic(Euclidean)/hyperbolic geometries, but to a type of differential equation--a type under which the wave equation and the field equations happen to fall. The point of having a Cauchy surface is that knowing the configuration on the surface enables one to, in principle, calculate the configuration of the entire universe at any time in the past or future. Actually, the term 'globally hyperbolic' is defined in terms of the strong causality condition and some other assumption, but there is a theorem that states that a spacetime is globally hyperbolic iff it admits a Cauchy surface. The full details of this are too involved to be repeated here; besides, you don't seem to be too familiar with PDEs and topology, so I doubt it would be fruitful anyway. If anyone here has familiarity with these topic, see, for example, Hawking and Ellis, the large-scale structure of spacetime, esp. p.192 and Sec. 6.6.

I got such a thrashing in normal DiffEq I had no will to try and go further, true :-p The most intensive math I've done is a freaking spring equation, and no way I could repeat that without the book now. I suppose I'd have been more interested if I'd known it could lead to stuff like this.

Is it accurate to describe the hyberbolicness as one where all spacetime lines diverge, then?

Please don't take my statements so far out of context. That entire thread implicitly assumed a Minkowski spacetime, and it was assumed by me explicitly. In curved spacetimes, there it is quite possible for a timelike curve (locally subluminal) to be globally superluminal. The most straightforward example of this is having a positive cosmological constant in an infinite universe, which causes superluminal separation between points sufficiently far enough away from each other.

Sorry, I was used to your comments as being rather explicit and that Minkowski Spacetime was it, so to speak.

Anyway, the set expansion of space, or matter falling into a black hole (or that the two may be related) is extremely straightforward in comparison to something going from point A to B and back to A again.

There is no violation of causality because every object stays within its own light cone--it is space itself that is expanding. Another expample an object falling into a black hole, which gains superluminal velocity relative to external observers when crossing the event horizon. The event horizon protects the external observers from this fact, but what Alcubierre discovered was that instead of breaking causality or having such a horizon, one could have superluminal motion by breaking the energy conditions instead. The ship is still within its own light cone, and hence does not have a spacelike path--again, the key concept is being locally subluminal.

I suppose that main problem I generally have regarding the 'Warp Drive' is that, if gravity propogates at c, it's going to be a humdinger to actually create a meaningful warp effect, aside from building gates between stars as you go to them or something similar.

Also, I thought that an outside observer wouldn't actually witness an event horizon crossing to occur very rapidly, if at all?

[Kuroneko]

I suppose that main problem I generally have regarding the 'Warp Drive' is that, if gravity propogates at c, it's going to be a humdinger to actually create a meaningful warp effect, aside from building gates between stars as you go to them or something similar.

The problem with taking statements like "gravity propagates at c" as a principle is that it is not at all clear what is meant. If the intended meaning is that if one wiggles a mass a bit, the detectability of this action by the gravitational effects at some distance will be limited by the speed of light, then yes, gravity propagates at c. On the other hand, if what is meant is that spacetime movement is limited to the speed of light, then the statement is just plain false. Again, the scenarios mentioned above are counterexamples--spacetime superluminally flows into a black hole singularity, which is responsible for the particle's superluminal descent past the event horizon.

Sorry, I was used to your comments as being rather explicit and that Minkowski Spacetime was it, so to speak.

Alright. The context was specified to be special relativity several times in that thread prior to that comment, so it did not occur to me to repeat it.

Anyway, the set expansion of space, or matter falling into a black hole (or that the two may be related) is extremely straightforward in comparison to something going from point A to B and back to A again.

That's true, but it demonstrates that spacetime itself is not subject to the speed of light limit. Alcubierre simply exploited this in a fair novel way, although by breaking something else.

Also, I thought that an outside observer wouldn't actually witness an event horizon crossing to occur very rapidly, if at all?

Right--the event horizon shields this. Nevertheless, if one takes a stationary observer at some distance ε>0 above the event horizon to measure the velocity v of the infalling object as it flies past, then v→c as as ε→0, which is obvious if one recalls that the escape velocity at the horizon is the speed of light (and that infalling trajectories are just time-reversals of escape trajectories), so it is quite correct to say that the object reaches the speed of light at the horizon relative to stationary external observers. It grows worse from there, but the event horizon hides it.

[Kuroneko]

I forgot to answer this...

Is it accurate to describe the hyberbolicness as one where all spacetime lines diverge, then?

No. But it does relate to your attempt at creating a total order out the events in the previous thread, a kind of unique "universal time." Note that this does not mean that the order will be physically meaningful, in the sense that there can be observers for which the order is reversed (the crux of my objection previously), but it does mean that the spacetime has a stable causality. The details follow.

A set is achronal if it contains no two points that have timelike separation. A Cauchy surface is an achronal closed set for which every timelike curve with no endpoints intersects the surface exactly once--no things such as looping back to it, etc., but also covers every one of them. A spacetime is globally hyperbolic iff can be foliated by Cauchy surfaces [*]. This partitions the spacetime into such surfaces, which is probably the best intuitive way to think of it (neglecting some criteria--a foliation isn't "just" a partition). Things aren't really defined that way, but this is a theorem that comes out which is a lot easier to explain to someone who has little topological knowledge ('easier' is still relative).

[*] To be more precise: a spacetime is globally hyperbolic iff it has the same topological structure as R×Σ for real number line R and some three-dimensional manifold Σ, and for each t in R {t}×Σ is a Cauchy surface.

[Ariphaos]

The problem with taking statements like "gravity propagates at c" as a principle is that it is not at all clear what is meant. If the intended meaning is that if one wiggles a mass a bit, the detectability of this action by the gravitational effects at some distance will be limited by the speed of light, then yes, gravity propagates at c. On the other hand, if what is meant is that spacetime movement is limited to the speed of light, then the statement is just plain false. Again, the scenarios mentioned above are counterexamples--spacetime superluminally flows into a black hole singularity, which is responsible for the particle's superluminal descent past the event horizon.

I was referring to said 'gravity waves' usually being the explanation for such drives, and that unless physics turns up something truly astounding it would seem we're stuck (large scale negative energies or something else completely new).

On that topic, is it actually considered feasible that we might get a particle to plank energy (nearly two gigajoules?) some day? And if so, is it expected that something weird might happen at that point? Or is it a bit much to guess that hyperinflation and 'exceeding plank temperature' might be related?

Alright. The context was specified to be special relativity several times in that thread prior to that comment, so it did not occur to me to repeat it.

I was being hasty in that thread as I'd stumped a lot of other people before, especially as there are still a lot of poor examples out there.

snip black hole stuff

I hate to take multiple tangents in the same thread, but:

A black hole, is constantly drawing spacetime into it at c.

We have our Universe, the edges of which are observed as expanding at (near enough to) c and we can calculate the age of the Universe by analysing this expansion and extrapolating, amongst other means.

A black hole's central singularity would appear to be receiving collisions from objects travelling in excess of c.

We have our Big Bang, which involves energies at scales which are easier to think of as being on the order of infinite.

----

Combined with the Schwarzschild radius of the observable Universe being, at a minimum, on the same scale as our Universe, is there anything to suggest that our Universe is not the singularity of a black hole?

[Ariphaos]

No. But it does relate to your attempt at creating a total order out the events in the previous thread, a kind of unique "universal time." Note that this does not mean that the order will be physically meaningful, in the sense that there can be observers for which the order is reversed (the crux of my objection previously), but it does mean that the spacetime has a stable causality. The details follow.

Ahh, thanks again.

The furthest I got with that idea was that a kind of relativity still seemed to apply to 'universal' frames like that because you still could only analyze a finite region of spacetime. I just found that strangely fitting.

But I'm guilty, my math is weak. Maybe I should go back for more someday.

[His Divine Shadow]

If you have Captain Alice on one end of the wormhole and Captain Bob at the other, Alice can see Bob enter the wormhole, and observe him travelling to her. However, Captain Paul from some arbitrary point not in direct line-of-sight of the wormhole will observe Bob arriving at Alice's end of the wormhole before he observes Bob entering the wormhole, without being able to observe the transit through the wormhole. So, to Paul, Bob reappears some time before he disappears. So, to Paul, Bob has just engaged in time travel, as he comes from what Paul will percieve as the future.

You don't even need Paul, just Alice and a telescope powerfull enough.

Say Alice sees Bob stepping through this stargate looking device and coming here, which takes just an instant, they now both go to a telescope and look at Bobs position. Oh look there's Bob now(he only traveled a few light minutes), he's dialing the coordinates, he's stepping through...but Bob has been here for several minutes already.

[McC]

You don't even need Paul, just Alice and a telescope powerfull enough.

Say Alice sees Bob stepping through this stargate looking device and coming here, which takes just an instant, they now both go to a telescope and look at Bobs position. Oh look there's Bob now(he only traveled a few light minutes), he's dialing the coordinates, he's stepping through...but Bob has been here for several minutes already.

Yeah, but that's just Bob's light. It's not Bob's actual presence.

[CoyoteNature]

Would causality even be relevant in say a pocket universe or alternative universe?

Say in a interaction between two universes?

[His Divine Shadow]

Yeah, but that's just Bob's light. It's not Bob's actual presence.

Incorrect, under SR that is actual time travel. Your perception of this as an optical illusion is only valid under a newtonian model of the universe where light is just a particle travelling at 300,000km/s through the universe and time is something that keeps ticking at a constant pace irreevant of our positions and speeds.

There is a simple explanation for this I am sure of it, I just don't have it.

[Ariphaos]

Incorrect, under SR that is actual time travel. Your perception of this as an optical illusion is only valid under a newtonian model of the universe where light is just a particle travelling at 300,000km/s through the universe and time is something that keeps ticking at a constant pace irreevant of our positions and speeds.

There is a simple explanation for this I am sure of it, I just don't have it.

If we see a gun an Alpha Centauri fire a projectile at Antartica at say, 99% of the speed of light, from the moment we see the projectile being fired, it looks as if it is arriving here within a couple weeks, and doing the math based on that 'illusory' superluminal velocity, you will accurately calculate the projectiles impact energy.

[Ariphaos]

Would causality even be relevant in say a pocket universe or alternative universe?

Say in a interaction between two universes?

If two "Universes" are capable of interacting with eachother, they are technically a part of the same Universe. So yes.

[Kuroneko]

I was referring to said 'gravity waves' usually being the explanation for such drives, and that unless physics turns up something truly astounding it would seem we're stuck (large scale negative energies or something else completely new).

Be careful not to mix concepts here. Gravity waves are transverse, whereas if one insists on interpreting Alcubierre's warp drive as a wave, it would be longitudinal (compression/rarefraction) wave. Reasoning about one does not necessarily carry over to the other unless concrete reasons are provided. (In the language of GTR, gravity waves are carried Weyl curvature, while Alcubierre exploits Ricci curvature.) Besides, Alcubierre was successful only by ignoring conditions most relativists insisted are necessary for the solutions to be physical.

On that topic, is it actually considered feasible that we might get a particle to plank energy (nearly two gigajoules?) some day? And if so, is it expected that something weird might happen at that point? Or is it a bit much to guess that hyperinflation and 'exceeding plank temperature' might be related?

I would be very suprised if many scientists are that optimistic. Although, 'some day' is rather open-ended, it's still a bit much. Synchrotron radiation would leech the particle's energy much before anything near this could be obtained. Bulding something this extreme is probably on par with building a Niven ring or worse. As for what would be observered as a result--well, other than general statements of "probling on the Planck scale" (the theoretical limit of observability) and "potentially exploring big bang conditions", I really can't say. I would be very suspicious of anyone who claims anything concrete.

I hate to take multiple tangents in the same thread, but: A black hole, is constantly drawing spacetime into it at c. We have our Universe, the edges of which are observed as expanding at (near enough to) c and we can calculate the age of the Universe by analysing this expansion and extrapolating, amongst other means. A black hole's central singularity would appear to be receiving collisions from objects travelling in excess of c. We have our Big Bang, which involves energies at scales which are easier to think of as being on the order of infinite.

A black hole's singularity is not physically real in the sense that it is not part of the universe. The closest analogy would be that it is a 'hole' in the universe--an absense of spacetime--so it doesn't 'collide' with anything in any physically meaningful sense.

Combined with the Schwarzschild radius of the observable Universe being, at a minimum, on the same scale as our Universe, is there anything to suggest that our Universe is not the singularity of a black hole?

Yes. First of all, a black hole the size of the observed universe should have a lot more matter in it, should have some tidal effects for us to observe, and geodesics within it should converge. Now, it is probably possible to rationalize all of this by saying that the black hole is much larger than the observed universe and tweaking the cosmological constant some, etc., but nevetheless this shows that the hypothesis that the universe is a black hole is a very poorly supported one.

[Kuroneko]

If we see a gun an Alpha Centauri fire a projectile at Antartica at say, 99% of the speed of light, from the moment we see the projectile being fired, it looks as if it is arriving here within a couple weeks, and doing the math based on that 'illusory' superluminal velocity, you will accurately calculate the projectiles impact energy.

Where did this come from?

[Ariphaos]

Where did this come from?

Oi, I was wrong, again, I think.

If you see something fired at you at .86 of c, the projectile appears to approach at (roughly) 6 times c. For some reason I'd thought it was different, and that the apparrent Newtonian value lined up, but that's not the case. I should just keep my fingers still :-/

[Ariphaos]

Be careful not to mix concepts here. Gravity waves are transverse, whereas if one insists on interpreting Alcubierre's warp drive as a wave, it would be longitudinal (compression/rarefraction) wave. Reasoning about one does not necessarily carry over to the other unless concrete reasons are provided. (In the language of GTR, gravity waves are carried Weyl curvature, while Alcubierre exploits Ricci curvature.) Besides, Alcubierre was successful only by ignoring conditions most relativists insisted are necessary for the solutions to be physical.

We can percieve that gravity waves aren't compression waves?

Regarding Ricci and Weyl curvature, I can read the words, get an impression of the math behind them but its beyond me, at least at 4 in the morning (again...).

I would be very suprised if many scientists are that optimistic. Although, 'some day' is rather open-ended, it's still a bit much. Synchrotron radiation would leech the particle's energy much before anything near this could be obtained. Bulding something this extreme is probably on par with building a Niven ring or worse. As for what would be observered as a result--well, other than general statements of "probling on the Planck scale" (the theoretical limit of observability) and "potentially exploring big bang conditions", I really can't say. I would be very suspicious of anyone who claims anything concrete.

I read people talking about Type II civilizations doing this and I have to wonder about the ... optimism involved. Though I would at least think that, at least it doesn't require scrith and magnets with better properties are probably still out there.

Yes. First of all, a black hole the size of the observed universe should have a lot more matter in it, should have some tidal effects for us to observe, and geodesics within it should converge. Now, it is probably possible to rationalize all of this by saying that the black hole is much larger than the observed universe and tweaking the cosmological constant some, etc., but nevetheless this shows that the hypothesis that the universe is a black hole is a very poorly supported one.

Geodesics I get, but why so much matter and tidal effects, if, by this hypothesis, we can't entirely assume the conditions of the 'parent' Universe apply to this one in their entirety? I'm assuming by matter you mean density rather than raw quantity for some reason, and that tidal effects would come from the (almost garaunteed) rotation of the black hole in question?

Didn't the WMAP data at least suggest that the Universe was bigger than what we could observe, since no patterns could be found?