On "possibility" and "impossibility", also FTL.

[adam_grif]

(I've been lurking 'round these parts for a while now, and I finally signed up. I apologize in advance if I can't meet the same standard of discussion that the regulars can. I'm just a computing/psychology undergrad with no university level physics under my belt, so mistakes are bound to creep in all over the place. Please correct me as harshly as possible, it's the only way I'll learn.)

I had a fairly heated discussion (as they always are) on the subject of FTL recently with some folks on an IRC channel. Naturally, it started with them making all sorts of claims in defense of FTL being plausible, then eventually they retreated back to the old standby, "you can't prove it's impossible".

What is the standard by which we should judge something to be "possible" or "impossible"? Obviously, things that we have already done are possible, and there are a huge range of things that we know we can do but don't for various reasons (i.e. they're not useful, or they're too dangerous, or too expensive), but that we know we can do based on the underlying principles of what is to be done. If something is "possible" in so far as we know we can do it, something being impossible seems to be itself impossible to demonstrate given sufficient wiggling room for the definition of what something is.

Aside from things that are impossible to do by definition, how can we demonstrate the impossibility of something, if at all? Physics seems to be reliant on there being only a very limited number of things that are possible, then complex combinations of these things yielding the world we see around us. It stands to reason that the majority of all things we can express in language will be "impossible", but by the same token I can't see any obvious ways to demonstrate which ones are.

At the extreme, we run into things like Solipsism, but for the sake of discussion we should assume that we are really viewing the universe without any kind of perceptual sorcery going on (if there is, we don't really have any choice but to act as though the universe is real and we're seeing it as it is). At the other extreme, we get the "anything's possible" malarkey, which strikes me as both infuriating and intellectually dishonest (if anything is possible, then impossibility is impossible).

Painting with broad strokes, I'd venture to say that we can reasonable assume that violations of thermodynamics are impossible. Seems to me that most of what we call possible or impossible doesn't reflect what is physically possible or impossible, but is a representation of our knowledge of what is physically possible or impossible. What do you all think?

In addition, without actually delving into discussions on the matter, what is the general consensus of the community on FTL amongst the sd.net community (where FTL is defined as "getting information to propagate at a speed greater than C")

[The Spartan]

As for whether something is possible, if they are making the claim that it can be done then the burden of proof is on them. "We don't know that it can't be done, so we should assume it's possible," is a poor logical construction.

As to whether FTL is possible, as far as I know, it is not, unless and until someone finds a way around the speed limit of C. Kuroneko could explain in more detail though, he's our resident expert on advanced physics. Even the incomprehensible kind.

[adam_grif]

As for whether something is possible, if they are making the claim that it can be done then the burden of proof is on them. "We don't know that it can't be done, so we should assume it's possible," is a poor logical construction.

As to whether FTL is possible, as far as I know, it is not, unless and until someone finds a way around the speed limit of C. Kuroneko could explain in more detail though, he's our resident expert on advanced physics. Even the incomprehensible kind.

The general argument goes:

"If it's not impossible, then it's possible. Since you can't prove that it's impossible, then it must be possible."

Looking at it like that now, I see the obvious problem in that it's confusing the two types of possible and impossible - i.e. I can't demonstrate that our knowledge is sufficient to exclude it as a possibility. This means it's epistemologically possible, in so much as that our knowledge is imperfect and thus we can't rule it out. However they've taken the step to conclude that since it's not impossible in that sense, that it's possible in the physical sense of the laws of the universe permitting it to happen.

[D2F]

The general argument goes:

"If it's not impossible, then it's possible. Since you can't prove that it's impossible, then it must be possible."

As the Spartan pointed out correctly, the party with the claim bears the burden of proof. In this case your friends that claim travelling at velocities FTL were possible.
If they cannot find a rational argument on which to base said hypothesis, then they cannot claim validity.

Fact is: physical movement of any mass at a speed greater than the speed of light is both mathematically as well as physically impossible. If we wish to entertain the thought of "FTL" travel, we need to use tricks. Excemples for such include tunneling, interdimensional travel and spacetime distortion.

We can debate how viable these options are, but what we cannot simply assume is that actual velocities of physical objects with mass greater than the speed of light are possible.

[The Spartan]

The general argument goes:

"If it's not impossible, then it's possible. Since you can't prove that it's impossible, then it must be possible."

Oh, I know. I've heard that sort of nonsense before; it's from the "anything's possible, you never know" school of thought. Like I said though, it's a poor logical construction. Especially for something with no physical evidence to suggest that it's possible, to say nothing of evidence showing that the opposite is true. Thus, they must demonstrate that it's possible, and expecting you to demonstrate that it's impossible is fallacious.

[Zixinus]

I recall that a similar argument used to justify God: you can't 100% prove or disprove God's existence.
I recall that this is was called logically nonsense. If you can't prove or disprove anything, why should it exist at all?

The consensus here is pretty straightforward: it can't happen. You'll be running up with a lot of Einstein's relativity. Why exactly, I can't say (something about there being to special point of reference or something). That, or the energies required would often several times more mass/energy than what the universe has.

But people still like FTL in fiction. You gotta have fun sometimes.

[The Spartan]

Looking back through my (very basic) Physics book at the equations of Relativity, there are at least* three problems with reaching (and exceeding) lightspeed. Lorentz contraction (shortening of the your dimension along the direction of travel). Time dilation, the slowing of time from an outside observers standpoint. And increase in mass, as your mass approaches infinity the amount of force necessary to continue accelerating you approaches infinity.

There actually is a special case of particles that exceed the speed of light, Hawking radiation, but I don't know enough to say anymore than, "It's a special case."

*I seem to remember that there are more, from a show on Hawking I think, but I couldn't tell you what they are.

[Zixinus]

I recall from the discussion that Einstein actually states that there are no special cases. Thus Hawking radiation would be another conflict between Relativity and Quantum theory.

Oh, and in general on the question whether that you can't prove something is impossible or not: modern scientific method also focuses on disproving theories, in the sense of the scientific process. So when a scientist has a hypothesis, he focuses on disproving it, rather than proving it. That way, he supposedly gets a better theory than if he tries to prove it.

So if you cannot prove or disprove something, you are essentially saying that it cannot be scientifically proven. Science, according to my limited understanding, the scientific method is a mental tool to understand the objective universe around us. Therefore, if your idea cannot be proven or disproven, it cannot belong to the objective universe.

It might work for God, who is supposedly "higher" than the objective universe as he created it. But for FTL? It means that the idea is nonsense, and that the opponent has committed a copout.

At least, that is the way I understand it. Correct me if I am wrong.

[starslayer]

FTL is practically impossible for one reason and one reason only: the speed of light is the same for all observers. The Lorentz transformations are derived from this fact, which leads to the conclusions of special relativity. Now, I say "practically" because if negative matter exists, you can warp space in such a way as to make you move faster than light according to an outside observer... if you've got more energy than the Sun will ever produce in its lifetime on your hands. The problem is, negative matter almost certainly doesn't exist, and the energy density required is just a tad out of reach.

There actually is a special case of particles that exceed the speed of light, Hawking radiation, but I don't know enough to say anymore than, "It's a special case."

It actually is not. At no point in the Hawking radiation scenario do the virtual particles move faster than light. What happens is that a virtual particle pair is created on or just outside the event horizon; one of the particles heads into the black hole, while the other heads off in the opposite direction, by conservation of momentum. Since it was created outside the event horizon, it does not need to travel at c to escape. Then by conservation of energy the black hole loses mass (it's energy created the particle pair in the first place).

Oh, and your mass does not approach infinity as your velocity approaches c. That was the old view, but given all the other consequences of the postulates of relativity (particularly the velocity addition formula), the modern view holds that we must rethink what we mean by velocity at such high speeds, and that is why reaching c by conventional means requires an infinite amount of energy.

[The Spartan]

See? My knowledge was that of a layman with outdated information at that. I should have quit while I was ahead.

Oh well, it happens. Thanks for the info Starslayer.

[Kuroneko]

What is the standard by which we should judge something to be "possible" or "impossible"?

There is no fixed, context-independent standard. The specifics of what is meant by 'possible' is either implicit in a given discussion or should be agreed upon beforehand. The loosest sense of possibility is that of logical possibility, under which only the logically incoherent is impossible.

That FTL (or almost whatever else) is logically possible completely true, but the category is so broad as to be "too true to be good." The phenomenon under discussion is a physical one, and thus should be informed by physical evidence and theory. Saying it is possible in the logical sense, while correct, is disingeneous and uninteresting. It's a kind of vacuous conclusion that (in asmuch as logic is presupposed anyway) carries no information whatsoever.

If the particular interpretation of an unqualified 'possible' is not disputed, it's simply best to specify explicitly what is meant.

Painting with broad strokes, I'd venture to say that we can reasonable assume that violations of thermodynamics are impossible. Seems to me that most of what we call possible or impossible doesn't reflect what is physically possible or impossible, but is a representation of our knowledge of what is physically possible or impossible.

If you want to go there, then one further split the discussion:
(1) what our current knowledge, empirical and theoretical, of the physical world implies about FTL, and
(2) the confidence or certainty of the above knowledge--it's true but useless to simply say "it could be wrong" in any absolute (logical) sense, so how likely is it wrong (and sufficiently wrong as to allow FTL).
There are again really two slightly different senses of possibility; the latter is analogous to the very common usage of 'impossible' as 'so unlikely that is unreasonable to consider the possibility'. Relevant to it is that we're not observing FTL propagation of information, and quantum mechanics follows the so-called totalitarian principle: everything not forbidden is compulsory. This is independent of the quantitative particulars of the quantum theory.

In addition, without actually delving into discussions on the matter, what is the general consensus of the community on FTL amongst the sd.net community (where FTL is defined as "getting information to propagate at a speed greater than C")

If that means locally, then FTL is physically impossible.

Looking at it like that now, I see the obvious problem in that it's confusing the two types of possible and impossible - i.e. I can't demonstrate that our knowledge is sufficient to exclude it as a possibility. This means it's epistemologically possible, in so much as that our knowledge is imperfect and thus we can't rule it out.

In such cases, pretty much the only things you can do is to be very specific as to what sense of 'possible' you're using, demand the same from your interlocutor, and point out that if their entire position rests entirely on logical possibility rather than likelihood or other factor (i.e., merely that it is logically possible for the actual laws to provide loopholes not present in the known physics), then their entire analysis is basically of the same caliber as verifying that "bachelors are unmarried" is true: correct but completely content-free and generally waste of time.

I recall from the discussion that Einstein actually states that there are no special cases. Thus Hawking radiation would be another conflict between Relativity and Quantum theory.

It's not in conflict. It is, however, incomplete and rather confusing. To an freefalling particle, the spacetime around the black hole is not special, and there is no Hawking radiation, but to an external stationary observer, the horizon has positive temperature, so (due to gravitational redshift) the particle encounters thermal radiation of temperature that diverges to infinity as it gets closer to the horizon.

But despite initial appearances, this is not a contradiction, which can be seen be thinking operationally: if a particle has a sensor and sends out a signal to the observer whenever it encounters thermal radiation, what does its report say? The closer the sensor is to the horizon, the quicker it must act on detecting and sending the signal (since once it crosses the horizon, it can no longer communicate with the observer), and thus be more energetic (by the the Heisenberg uncertainty principle). But the more energetic it is, the higher the probability of the sensor going off is, even in free space. So there is no disagreement as to whether the sensor detects anything prior to the horizon--only the interpretation of what caused the detection event is different.

[adam_grif]

Fact is: physical movement of any mass at a speed greater than the speed of light is both mathematically as well as physically impossible. If we wish to entertain the thought of "FTL" travel, we need to use tricks. Excemples for such include tunneling, interdimensional travel and spacetime distortion.

We can debate how viable these options are, but what we cannot simply assume is that actual velocities of physical objects with mass greater than the speed of light are possible.

Nobody ever disputed that you can't just accelerate up to C+1 meters per second, the dispute was (not in so many words, but) whether or not you could have a photon leave point A, traveling through a perfect vacuum and arriving at point B could be beaten there by something leaving after it did.

As part of my "can't be done" routine, I direct people to the Tachyon Pistol Duel thought experiment, as well as retorts for popular proposed methods ("Alcubierre drive needs a ring of negative energy that can be turned off and on at will", "there are no methods by which one may create a wormhole" and so on). Tachyon Pistol Duel is typically the heavy hitter though, with the ever useful "FTL by any method = time paradox" result you get from it. At one particularly amusing point, somebody went "well all your saying is that time paradoxes are scary and thus it can't happen! Prove it!"


@Kuroneko:

Thanks for the detailed reply.

Relevant to it is that we're not observing FTL propagation of information, and quantum mechanics follows the so-called totalitarian principle: everything not forbidden is compulsory. This is independent of the quantitative particulars of the quantum theory.

That seems mighty strange. But that's not exactly unusual for QM.


In my limited understanding, although there are many things in QM that are FTL, none of the ones that are can be used to transmit information. Hence the framing of the argument as "information propagating faster than C". According to info I've read about theoretical particles like tachyons, even if they did exist they still would be useless for transmissions and travel, because they can't be used to propel, and detecting Tachyons is directly equivelant to generating them. The No-communication theorem, no-teleportation theorem and no-cloning theorem put a bullet through the brains of the "quantum entanglement = ftl communications" meme.

I don't think I've ever read that there is an explicit law in QM forbidding information transfer, but so far none of the phenomena discovered have allowed for it. Given that relativity, despite not being directly compatible with QM, seems to agree with it on the "can't do FTL" thing, that a rather strong inductive case can be made for the impossibility of FTL in future theories. Even if QM and Relativity are trashed by something tomorrow, it's very likely that those elements of it will stay firmly in place.

[Kuroneko]

Tachyon Pistol Duel is typically the heavy hitter though, with the ever useful "FTL by any method = time paradox" result you get from it.

That's not strictly true--wormholes, Alcubierre drives, and Krasnikov tubes can be causal. Although it would appear that if one can construct them, then one can construct a time machine as well, they don't automatically perform as such (as tachyons would), and there are factors that suggest that trying to build a time machine creates a loop of vacuum fluctuation that destroys the time machine before it can be used.

That seems mighty strange. But that's not exactly unusual for QM.

It's not so strange if you remember that QM is probabilistic on the observational level. If it's something that's allowed to happen, then it has a positive probability of happening, and thus does happen with some regularity, however large or small.

I don't think I've ever read that there is an explicit law in QM forbidding information transfer, but so far none of the phenomena discovered have allowed for it.

There is: Lorentz invariance. In QFT, operators of observables commute when they have spacelike separation; their order is irrelevant and they do not interfere with one another--this is analogous to the STR-mechanical tachyonic ambiguity between transmitter and receiver.

Given that relativity, despite not being directly compatible with QM, seems to agree with it on the "can't do FTL" thing, that a rather strong inductive case can be made for the impossibility of FTL in future theories.

Quantum electrodynamics passes empirical tests to a stupendously high precision, and it presupposes Lorentz invariance.

In case this is not clear, Lorentz invariance forbids locally superluminal transfer of information: i.e., for any small region of spacetime, light is the fastest signal. The aforementioned methods of wormholes, etc., try to do this in a non-local manner, such as by constructing shortcuts. They are also impossible (for reasonable standards of possibility), but for other, less direct reasons.

[adam_grif]

It's "adam_grif" not "adom_grif"

That's not strictly true--wormholes, Alcubierre drives, and Krasnikov tubes can be causal. Although it would appear that if one can construct them, then one can construct a time machine as well, they don't automatically perform as such (as tachyons would), and there are factors that suggest that trying to build a time machine creates a loop of vacuum fluctuation that destroys the time machine before it can be used.

Without delving too deep into the physics, is it possible to get an explanation as to why? I thought that with the pistol duel, if you replace "instantaneous FTL" with "shot through a wormhole" or "fired an alcubierre missile at him" that you get exactly the same result, since the relativity of simultaneity means that beating the light there in a race by any method what-so-ever is what creates the grandfather paradox involved?

The version of the experiment I read is:

http://sheol.org/throopw/tachyon-pistols.html

They idealize the tachyon pistols as instantaneously hitting for simplification, although unless I'm missing something obvious, it should hold for other methods.

[Kuroneko]

It's "adam_grif" not "adom_grif" ;)

Sorry. I think it's a subconscious slip from fiddling with this game just now.

Without delving too deep into the physics, is it possible to get an explanation as to why? I thought that with the pistol duel, if you replace "instantaneous FTL" with "shot through a wormhole" or "fired an alcubierre missile at him" that you get exactly the same result, since the relativity of simultaneity means that beating the light there in a race by any method what-so-ever is what creates the grandfather paradox involved?

There are several relevant differences. First, notice that the tachyon pistol scenario implicitly uses inertial frames to cover the entire exchange--with the quantitative details filled in, it even assumes that a Lorentz transformation is globally valid between said frames. Second, the tachyon scenario illustrates the impossibility that a signal travels along a spacelike path--being locally superluminal is not allowed (as any small enough region of spacetime looks flat, similar to how the Earth looks flat if one doesn't venture or look far). That's still true for curved spacetimes, but here we have the possibility of there being two different non-spacelike paths in spacetime that just happen to eventually meet.

Let's try an analogy. If I have a sufficiently large contraption of mirrors such that an incident light beam on the first mirror at A eventually comes out of the last mirror at B a significant time delay later (maybe I'll bounce a laser beam off the Moon, or whatnot), then it is absolutely nothing special that I'm able to travel between A and B before the beam does. We're just taking different paths in space. I can beat a light beam in this trivial sense rather easily. But if I look at the light's trajectory over a small enough region rather than the entire mirror construction, I find that I just can't catch up to it. That's roughly what's meant by 'local'.

What GTR's superluminal devices do is pretty much the same thing, although it may be less obvious because we're explicitly dealing with spacetime instead of just paths in space. All of them have the same idea: somehow create or take advantage of an alternative path that's shorter. However, it is true that if arbitrary creation and manipulation of these devices are allowed, then getting a time machine would be easy. But it remains the case that they don't automatically break causality.

They idealize the tachyon pistols as instantaneously hitting for simplification, although unless I'm missing something obvious, it should hold for other methods.

The first part's fine--if a signal is spacelike (locally superluminal) in one inertial reference frame, then it is instantaneous in some other.

[adam_grif]

I follow how shortcut drives work in theory, but I don't follow how they prevent the grandfather paradoxes.

I'll try to explain, but it will probably end up incomprehensible, so I apologize:

- Even not traveling in a straight line through space, if Observer A from the tachyon scenario at second 0 fired a regular gun through a wormhole that flies out next to observer B and strike him, won't it still come out at second 4 from his perspective? Or does the wormhole being very close somehow invalidate the time dilation stuff?

[Kuroneko]

- Even not traveling in a straight line through space, if Observer A from the tachyon scenario at second 0 fired a regular gun through a wormhole that flies out next to observer B and strike him, won't it still come out at second 4 from his perspective?

It's possible for that to be the case, but without bidirectional traversibility, we have no possibility of forming a closed timelike curve (note that the simplest Schwarzschild-type wormhole is unidirectional, as is the Kransnikov tube).

Another possibility is a bidirectional wormhole with mouths stationary relative to one another that refuse to be accelerated and a throat of zero length. In that kind of degenerate case, the intervening line of simultaneity of the diagram is effectively always horizontal across the mouths (which means for an observer at a high relative velocity, it would not be straight: it would look like a piecewise linear slanted-horizontal-slanted on the diagram). Because of the sudden 'change in direction' in the line of simultaneity when traveling through the wormhole [1], you don't get the conclusion that B's returning shot arrives earlier than the A's.

(Actually, it would be more correct to say that there is no 'between' line of simultaneity at all, and it simply jumps horizontally across mouths.) More complicated variations of wormholes are also possible.

Or does the wormhole being very close somehow invalidate the time dilation stuff?

It doesn't invalidate time dilation. It invalidates global inertial reference frames, and it invalidates drawing straight lines on a little spacetime diagram and calling it a day. The causal structure of a spacetime with a wormhole is a lot different than that of an ordinary flat spacetime of STR.

[adam_grif]

I still don't quite follow but I trust you.

Am I correct in assuming that a hyperspace style FTL weapon will be largely the same as the Tachyon one in that scenario?

[Kuroneko]

I still don't quite follow but I trust you.

Notice that the real problem starts when B fires back--the conclusion is that B's shot kills A before A fires. So if the FTL effect is just unidirectional, i.e., B can't fire back, there's no violation of causality. In STR, there's no way to ensure that unidirectionality, but in GTR, that is possible. Note that it does not mean that such constructions are possible in any useful sense; only that they do not have to violate causality.

Second, notice that the lines of simultaneity in the diagram are straight in the diagram. That ensures that B's "now" includes a events before A's firing. But what if we have a situation in which they're not straight, and actually bend in a way that B's "now" upon being hit by the wormhole-bullet never includes an event before A fired it? Again, GTR makes this possible, and the above construction is an explicit example of such.

Is that clearer?

Am I correct in assuming that a hyperspace style FTL weapon will be largely the same as the Tachyon one in that scenario?

That depends on what 'hyperspace' actually does.

---
There's actually a loophole even in a completely flat, special-relativistic spacetime. For example, pick an inertial reference frame, with its time coordinate t. Make a field that propagates instantaneously in that frame (e.g., something mimicking Newtonian gravitation), but whose dynamics are explicitly reference this time coordinate. Then superluminal transfer of information is possible, but the dynamics are causal anyway, because this special t coordinate is increasing in every observer's time direction.

So the problem for FTL is not just the structure of spacetime, but also the principle of relativity--specifically, then non-existence of a preferred frame of reference in any of the the laws of physics. That's exactly what this trick does: it introduces a preferred frame. In terms of tachyon pistols, it means that the bullet is instantaneous only in this frame; if it is so in A's frame, then it will not be in B's frame, which prevents B from striking back before A fires his shot.

[Modax]

How likely is it that a future theory of quantum gravity would rule out the existence of wormholes altogether? For instance, do current incarnations of string theory predict wormholes? I'm thinking of other obsolete predictions of physics, like the luminiferous aether.

[adam_grif]

I don't think you could really put realistic odds on that. Too many unknowns. But given GR and QM's general eagerness to prevent information transfer at FTL speeds, I'd probably say it's likely that a GUT would close off the loopholes that exist today, either theoretically or put a spanner in the works of the technical implementations of them (provide unexpected engineering concerns that can't be overcome).

[Kuroneko]

How likely is it that a future theory of quantum gravity would rule out the existence of wormholes altogether? For instance, do current incarnations of string theory predict wormholes?

In string theory, there is an extra scalar field, the dilaton, that controls the strength of string coupling. which may violate the usual energy conditions, and thus act like the requisite exotic matter for the wormhole. It's not at all clear (to me) that it could actually be adjustable in the necessary manner, but it doesn't seem to close off any loopholes and maybe introduces another. In M-theory, the dilaton field is absorbed into the metric component of the extra (eleventh) dimension. However, QFT does place rather restrictive limits on its sources of negative energy, with the conclusion that any macroscopic wormholes must involve vast quantities of negative energy compacted into extremely thin shells.

[Feil]

To step away from physics for a bit, the (bad) argument you're looking at boils down to the following form (where P(X=x) is the probability that some unknown value X equals a singular value x)

P(NOT possible = TRUE) != 1 => P(NOT possible = TRUE) = 0 => P(NOT possible = FALSE) = 1
P(NOT possible = FALSE) = 1 => P(possible = TRUE) = 1

The first implication (red) is inaccurate. Expressed mathematically, it's blatantly foolish: P!=1, therefore P=0?! Really? What about 0.5? 0.001? 0.9999999999999?

In the case of faster than light travel, the probability that ftl is not possible is equivalent to the probability that relativity is fundamentally correct (even if not perfectly accurate), which in turn is equivalent to the probability that humanity's diverse observations of the cosmos are representative of the universe at large and that the associated scientific process is sound. As the former probability rises every time a new measurement is taken that confirms the homogeneity of physical laws in inertial reference frames, and as the latter probability rises every time new observations accurately match theoretical predictions, the resulting probability, while not precisely measurable, is certainly not zero, and likely very close to 1.

[Axiomatic]

Can't you prove, for laymen's value of prove, that FTL is impossible by saying "To go FTL, you would require an amount of energy greater than an infinite amount of energy. Since you cannot have an amount of energy greater than an infinite amount, you cannot go FTL, and therefore FTL is impossible. Thank you, goodnight."

[Simon_Jester]

The problem is that this only addresses FTL flight in Euclidean space. It does not address either the possibility of "wormhole" FTL travel (which can be established without infinite energy, though it does require the existence of negative energy density at some points in spacetime), or of "warp bubble" FTL travel in the style of the Alcubierre drive (likewise).

So it's an incomplete proof even by layman standards, because most laymen will have heard of the idea of FTL teleportation or FTL that warps space.