In recent 24 hours, lots of media outlets including

NY Times, The Daily Mail, Russia Today, The PK Nation, Times of India, Bend Bulletindiscuss the NASA research into faster-than-light spaceships based on "warp drive". The idea is being attributed to Mexican fantasist (rather than physicist) Miguel Alcubierre while Dr (???) Harold White is being mentioned as the most active researcher working on this ambitious project.

The proposed idea is simple: reduce the magnitude of the space-like components of the metric tensor in front of the spaceship and increase it behind the spaceship. So the space will look shorter in front of you and the general relativistic causal limit will allow the coordinate speed to be greater than it is in the vacuum. Consequently, you will move from one place to another faster than light.

Needless to say, Einstein's 1905 insights known as the special theory of relativity show that such a superluminal motion is impossible. In a different inertial system, it would look like a motion directed backwards in time. And such an invalidation of the usual chronology would produce closed time-like curves with all the "grandfather castrated before the first intercourse" logical paradoxes.

My description above indicates that the modified spacetime geometry looks like a gravitational wave of a sort and these waves can't move faster than light, either. That's really a "constructive" explanation why any would-be warp drive gadget will fail to realize its dreamed about job. The front of the wave can't move faster than light. Moreover, one may see that some negative energy density is needed in parts of the arrangement which is prohibited by the energy conditions linked to the vacuum stability, too.

However, the more universal reason why it is impossible to create a warp drive is still nothing else than special relativity. A problem for most armchair physicists, including Mr Harold White at NASA, is that they clearly seem to believe that the general theory of relativity in 1915-1916 has invalidated much of the special theory of relativity from 1905.

The truth is very different. General relativity is a generalization, not invalidation, of special relativity. Its laws may be derived by demanding the equivalence between all coordinate systems, not just the inertial frames that special relativity labels as special. On the other hand, general relativity describes gravity and you may interpret the whole structure of general relativity as the unique realization of spin-two fields, waves, or massless particles that is compatible with special relativity. The fundamental, primary principles are those of special relativity; general relativity is just a solution of certain constraints.

People generally tend to understand – or at least claim to understand – that general relativity reduces to special relativity whenever the gravitational fields may be neglected. But they don't actually understand how powerful this principle is and how diverse are the ways in which it can be exploited. So let me emphasize that the behaviors dictated by special relativity can be reconstructed in systems obeying general relativity at least in two regimes:

**short-distance physics**: in freely falling labs that are much smaller than the typical curvature radius of the surrounding spacetime, general-relativity-predicted phenomena will behave just like in special relativity**long-distance physics**: in large enough regions of the general-relativity-based flat Universe that is mostly empty so that all the regions with strong gravity only fill a vanishingly small percentage of the space, one may use special relativity so that all the high-curvature regions are described as objects or composite particles obeying the laws of special relativity

If you have a very large black hole, it creates a very strong gravitational field. For example, the red shift factor goes to zero or infinity at the event horizon. However, a freely falling observer who is much smaller than the black hole may freely fall to the black hole. As long as her spaceship is much smaller than the black hole, she won't even notice that something special is happening near the event horizon; please, assume along with your humble correspondent that there are no firewalls so that this discussion doesn't turn into complete chaos.

Special relativity appears in the lab simply because the thin tubular region of the spacetime in the vicinity of the spaceship's world line may be flattened and when it's flattened, it looks just like a straight tubular region of the Minkowski space. So in this tubular region, the gravitational field doesn't exist which means that special relativity has to be a good approximation.

The armchair physicists such as the "warp drive engineers" tend to understand this first limiting context in which special relativity emerges from the general relativity. That's why they're talking about the squeezing and stretching space that should allow faster-than-light motion. They're designing this whole story because they are apparently aware of the actual causal restrictions on motion that hold in curved space according to general relativity: massive objects have to move along time-like, and not space-like or null, trajectories.

**However, they seem to misunderstand or neglect the second way in which special relativity emerges from general relativity – even though the second way is, in some sense, even simpler than the first one.**

Imagine that you receive a 50-meter warp drive-driven spaceship and decide to travel from the Earth to the Sun which is 8 light minutes away. Can you get there in 5 minutes? The "warp drive engineers" like to look (at most) at the 100-meter vicinity of the spaceship. Because the spacetime geometry is warped over there, it is possible to guarantee that the spaceship moves along a time-like trajectory despite the fact that it will overcome those 8 light minutes in mere 5 minutes. But is it possible that the spaceship along with the required gravitational field around it moves this fast?

To see that the answer is No, we shouldn't look at the short-distance geometry of the spaceship only. Instead, we should look at the "big picture". Cut the 200-meter vicinity of the spaceship out of your spacetime. What is left is a nearly flat spacetime – millions of kilometers of flat emptiness – because all the hypothetical gravitational fields required to make the warp drive work were confined to the region we have omitted.

But if that's so, it must be possible to use the special relativistic approximation for this "remaining space", too. The spaceship itself (including the gravitational field in its vicinity) is just a local perturbation moving on top of a Minkowski spacetime. This Minkowski spacetime allows us to choose the different inertial frames, just like we always have a choice in special relativity. And because things can't move backwards in time in any of them, it follows that the perturbations aren't allowed to move faster than light, either.

You simply can't get to the Sun in five minutes. You may think about wonderful fantasies what is inside the warp drive spaceship or its vicinity. But before you conclude that the superluminal motion of the spaceship is compatible with the causal restrictions imposed by relativity, you should realize that relativity holds not only inside the spaceship and 50 meters away from it; it holds in the millions of miles outside the spaceship, too. The validity of relativity in the "bulk of the empty Solar System" allows you to classify any details of the inner workings of the warp drive as "irrelevant internal details of a point mass". These internal details of a point mass can't overcome the commandment of special relativity that "thou shalt not exceed the speed of light" when you are moving inside the external space. The internal details of the warp drive just don't matter at all from the long-distance, external observer's viewpoint!

Note that this second method in which special relativity emerges is valid for extreme gravitational fields such as the gravitational fields of black holes, too. If there are black holes flying through the outer space, they still behave just like other point masses from the viewpoint of distances that are much longer than the black hole radii. It doesn't matter at all that some local physics near the black holes' event horizons predicts an infinitely extreme red shift and other dramatic effects.

An alternative way to convey the same point is to say that (almost) elementary particles – nuclei, protons, neutrons, electrons, neutrinos – may also be viewed as "tiny models of a warp drive spaceship". If the spaceship were allowed to exceed the speed of light, surely the elementary particles would have the right for a perhaps tiny but nonzero "trace" of the same ability. A proton could be surrounded by warp-drive-like gravitational fields, too. Except that we know that elementary particles can't move faster than light. The same conclusion must clearly apply to spaceships – which are just large, composite elementary particles – as well.

(A much more interesting potential inner structure of a composite particle than cheap tricks and futile efforts to make it superluminal are potential wormholes or Einstein-Rosen bridges connecting the object with another, faraway object. The validity of special relativity in the bulk of the spacetime implies limitations on the possible communication between the two throats, too.)

**Loop quantum gravity share the misconceptions with the warp drive crackpots**

So the "warp drive engineers" de facto deny some key principles that special relativity taught us. They're not the only ones. A whole class of the laymen – the loop quantum gravitists and similar fans of "broken physics" – are doing pretty much the same thing very often. Whenever you hear these people criticizing the quantum field theory's and string theory's usage of a spacetime background in a calculation, you are witnessing their misunderstanding of the "survival of special relativity within general relativity".

There may be curved gravitational fields and they may be so diverse and extreme that we may be tempted to say that no background is preferred over another background. And some people also add that the physics of the Minkowski background doesn't apply because it's too special (you usually hear these things in a tendentious sentence mentioning that "it is against the philosophy of general relativity to think about the flat spacetime", and similar junk).

While the first assertion is sort of right – there are many solutions to Einstein's equations and you may treat them democratically – the second assertion is undoubtedly wrong. Einstein's equations still admit the Minkowski flat spacetime as a solution. And whenever the spacetime is "close to the Minkowski space" in any sense, physics of special relativity simply has to re-emerge and, according to any valid theory incorporating the ideas of general relativity, does re-emerge.

In particular, weak enough gravitational waves may always be viewed as waves of the field \[

h_{\mu\nu} = g_{\mu\nu} - \eta_{\mu\nu}

\] i.e. the difference of the full (curved) metric tensor and the special relativistic (flat) constant metric tensor. The physics of such weak gravitational waves simply has to respect all the restrictions that you may derive from spin-2 waves propagating in a flat spacetime of special relativity. In plain English, the gravitational waves

*are*spin-2 waves in a pre-existing external spacetime. This is not the only way how the identity of gravitational waves may be described but it is

*a valid way*and all conclusions derived from this valid way of looking at things are right and important.

If your theory contradicts the conclusions arising from this approach, and LQG does, then your theory is dead and you can't "resuscitate" it by confusing or demagogic comments about background independent and similar misinterpreted buzzwords. General relativity

*is*a generalization or deformation of special relativity and if your theory doesn't respect the conclusions of special relativity whenever it should, i.e. in all the appropriate limits, then your theory contradicts the principles of general relativity as well because general relativity is something that

*must include*and

*does include*special relativity as a special case!

## snail feedback (52) :

"In particular, weak enough gravitational waves may always be viewed as waves of the field

hμν=gμν−ημν i.e. the difference of the full (curved) metric tensor and the special relativistic (flat) constant metric tensor."

Well,

we can formally write things like that, but can a curved space-time be

completely compatible with a flat one? Does not that mean the "weak h" may become too strong to get to "g"?

Dear Vladimir,

a generic, not too refined prescription how to deal with curved fields special relativistically will fail once the "h" becomes comparable to "eta". However,

1) in real situations, the gravity waves have "h" dozens of orders of magnitude smaller than "eta" which means that any relative error in the special relativistic predictions must also be 10^{minus dozens}

2) when one deals with the curvature more accurately, the relationship actually holds exactly even for finite - not just infinitesimal -"h".

Concerning the latter point, the gravitational self-interactions of the "h" field with itself - non-linearities of general relativity - are actually not only compatible with special relativity but they are dictated (at the right values) by special relativity, too.

Moreover, "g" in any finite-energy disturbance has to approach "eta" at a sufficient distance from the center of the disturbance. So one can make the deviation from any naive predictions of special relativity arbitrarily low by cutting a sufficiently large neighborhood of the "object" from the spacetime.

One could write a few more pararaphs like that. To summarize, when one is careful about what the objects actually are and how they're allowed to interact, the special relativistic description is not only 100% accurate but also implied by special relativity even for finite, strongly curved fields.

LM

Sorry for the off-topic comment: Are you ok with this: http://meta.physics.stackexchange.com/questions/2810/community-promotion-ads-2013/4645#4645 ?

Apologies, could you please be more specific about what I am OK or not OK with?

I meant the ad proposal on meta.physics.SE (since it is an ad of your blog).

Dear dimension10, thanks if I should thank ;-) but there are still too many question marks.

I am just not getting it. Which website places ads on which website, why, and who pays for that? Do you have the right to determine such things or is that a contest in which your proposal has almost no chance? Do you need my picture in higher resolution or a permission to promote my blog elsewhere? You surely have or may have the latter two. ;-)

There are too many unknowns and I don't have time to study everything I need to study to understand what you're really asking me about.

It's supposed to be a proposal for an ad on Physics.SE like the other ads there. Nobody pays : ) . It's just like the "Looks like you have a question for..." ads on Physics.SE.

What I was asking you is whether you are ok with there being an ad of your blog on Physics. SE.

"to promote my blog elsewhere?"

Yes. That was what I was asking for. Whether you would be ok if the ad works? , .

Yup, of course I would be OK with that! I would also bet that you won't succeed. ;-) Thanks, anyway.

Thanks.

Dear Lubos, while GR surely forbids stable wormholes to exist (without negative energy densities) superstrings make their existence almost compulsory (http://arxiv.org/abs/1108.3003). The questions I have to you are: how to use the aforementioned GB action to engineer such a stable bridge? More specifically, how modern cosmological data constrain the the coupling strenght among that dilatonic field and usual matter? Would it be possible to excite (and how) the dilatonic field in a lab? Many thanks

Dear NumCracker, the GB term only starts to matter at extremely short distances related to the coefficient (or coefficients' ratio) of this GB term or shorter which most likely means at distance scales close to the Planck length or string length. So a traversable wormhole solution may formally exist but it corresponds to an object that is so thin or so hugely curved that all of quantum gravity effects become relevant at the same moment. You can't make it macroscopic and smooth AFAIK. The non-traversability of the Einstein-Rosen bridge is a key requirement for the consistency of the Maldacena-Sussind picture, for example.

In the realistic vacua, the dilaton - and all other scalar fields - have to be stabilized. That means that there exists a potential V(phi) for the dilaton and the Universe sits near a minimum of phi. The excitations around this minimum look like massive scalar particles, exactly like for the Higgs boson that we already know (although the mass of the dilaton and moduli is likely to be much greater than for the Higgs). A massless dilaton would imply a time dependence of the fine-structure constant and new long-range forces contradicting the tests of the equivalence principle. We pretty much know that those things aren't there. So at very long distances, there's only the pure GR (plus electromagnetism and, more speculatively, U(1) groups for a dark sector) without any dilatons or other scalar fields.

Lubos, slightly off topic, but not really since it deals with general relativity. In http://physics.stackexchange.com/questions/3986/newtons-bucket/4004#4004

you said, "the bucket - and all other objects - know how to behave and whether they're spinning because they interact with the metric tensor".

But, you also say, "The equivalence principle guarantees that the effect of gravitational fields is indistinguishable from the effect of inertial forces resulting from spin or acceleration."

So, can we really say that the bucket knows whether it's spinning? I'd think that the equivalence principle means that we can't determine that we're spinning because the effect is indistinguishable from a gravitational field. In fact, isn't this supposed to be the whole point of general relativity: One can't perform an experiment to determine if they are accelerating? e.g. accelerated reference frames are equivalent to inertial frames?

Best wishes Lubos

This popular science article explains the physics behind the negative energy space-time bubble

http://www.zamandayolculuk.com/cetinbal/pdfdosya/wormholesjan.pdf

It may be explaining a science-fiction novel but it is not explaining anything about the actual Universe because those things are prohibited in Nature.

Dear Justin, a good question and No, this is not the point of general relativity.

General relativity doesn't say that you can't distinguish acceleration from non-acceleration. General relativity says that you can't distinguish acceleration relatively to an inertial frame from acceleration relatively to a freely falling frame in a gravitational field - the latter "accelerated" motion may very well be a static position within a gravitational field.

General relativity doesn't say that the metric tensor doesn't exist. It says that its deviations from the flat metric tensor may be interpreted either as an artifact of using a non-inertial coordinate system *or* as a sign of a gravitational field within a possibly inertial system. The latter is more general and has to be used whenever the curvature invariants are nonzero, of course, but locally, up to the first space-and-time derivatives of the metric around a given point, the latter may always be perfectly emulated by the former.

We can surely say whether the bucket is in a flat space and not spinning. In that case, the water level will remain flat.

Years ago, Bob Lazar explained just how faster-than-light spaceships operate, as he had help reverse-engineer at least one of them.

Hoi Lumo,

A higher resolution picture of you would be good and the graphic as a whole should be quadratic if I remember this correctly.

Too many sourball downvote all string theory related community promotion adds ... :-/. If their score gets below the freezing point they should probably get removed because seeing the TRF or the official ST site add with a negative net score would be too painful. Non of these two sites deserves being treated like this by knownothings and dimwits!

I am horrified to discover that my fav physics blogger is a space-time substantivalist. :_( I would like to see you explain the hole argument away: http://plato.stanford.edu/entries/spacetime-holearg/

People cannot forget Gauss Lemma!

It's a potentially important point and an interesting paper. But I still

have some trouble with it. For example, they have clearly not switched

to the reasoning rooted in the ER-EPR correspondence yet.

hcg recipes phase 2 pdf

"the causal restrictions imposed by relativity"One of the letter writers under the article in the New York Times made that point, too. He said to think of the speed of light not like the speed of a thing that could be exceeded by the speed of another thing -- a Toyota and a Formula 1 race car -- but as the "speed limit of causality", with the actual speed of photons almost an afterthought.

Most other commenters trotted out the usual tired clichés -- "Dare to dream," "Lord Kelvin said there was nothing left to be discovered," "They told the Wright Brothers their plane would never fly." The "best" one of these was a fellow who explained that in a 1950's science-fiction story, the problem of anti-gravity was solved by telling a team of scientists that the opposing side in the war had already done it and now they had to reverse-engineer that solution. But in reality, no one had yet solved anti-gravity! But that didn't matter! Because telling them there was a solution freed the scientists of their mental and psychological inhibitions. And so, this fellow triumphantly concludes, the "problem" of anti-gravity was solved!!!

I look forward to your film review of "interstellar", which comes out next year and is about worm holes.

It is being co-produced by Christopher Nolan and Kip S. Thorne. They are trying to make a realistic science fiction film.

Seeing in terms of Lagrangian, one understands the travel methodology currently used by satellites, and current space travel, of course, the idea is to reduce the amount of travel time to these distant places.

How that is done is the continued question with which commonsense is being asked to be used here? So any ideas, Lubos?

Nice article why are there no comments ?

Dear Lumo, could the first F-Theory paper somehow adress the issue how string theory (I know that string theory is not F-theory :-) ...) could work without supersymmetry but without the correspodning vacua lying in the swampland? I thout the first part of this article is interesting for my question here http://physics.stackexchange.com/q/64740/2751 too and therefore linked to it in a commment :-P

Just reading the abstracts of the too black hole information papers I could immediately see which is the bad one and which is the (almost?) good or better one too :-D, and I liked reading the nice explanations why this is in the rest of the article.

BTW you give me really a hard time to catch up reading all the nice TRF articles at present, as you can see I have fallen behind LOL :-D

Cheers

It was always my understanding the the so called "warp drive" could not be self contained. A space-time "track" has to be set up in advance. I thought that was a well known requirement (though it is not sufficient, it still needs impossible negative energy density).

Of course, with proper preparation, it *is* possible to fly from Earth to Pluto in less than a minute. Simply have someone tow Pluto closer to Earth. That would certainly be far cheaper than large changes to the metric.

I'm not even sure that the "warp" isn't really just moving the end points, hiding the fact with obfuscated coordinates and impossible matter distributions. In other words, it's a magic trick. The apparent inconsistency with SR is a (not so) plausible distraction.

Dear Stephen, sorry to have disappointed you. I don't understand the would-be philosophical - I would say plain armchair popular - argument on the page above.

It seems to promote some Einstein's 1913 views. Whatever they were, they were rendered obsolete by the final form of general relativity in 1915-16.

Coordinate transformations produce the "same physics" but the vacuum isn't empty. It just inevitably has some information in it - the metric tensor field - and one may invariantly distinguish a flat spacetime from a curved one and many other, more detailed things.

If Leibniz's point were that the vacuum has to be "really free of information", GR and proofs behind it made it totally clear that he was wrong.

You are making very good points that I am trying to take into account. The hole argument is not trivial and is still an on-going subject of research. My point is that the vacuum is still not well understood and thus making claims about it, such as what you argue in this article, may be a bit premature.

Dear Stephen, yes, the vacuum is rather complicated, especially relatively to people's naive ideas, but I have studied the vacuum for something like 25 years.

Indeed, particle physics says that the vacuum already contains the ingredients for everything that may exist within it. Virtual particles arise and disappear. The vacuum is a bit like the 2484 AD "amarouns" food from the Visitors sitcom,

http://www.youtube.com/watch?v=SqlAP8Sit00

Yes, but to borrow an analogy from the very entertaining video, we must not assume that the Jello is all we have to think about. IMHO, we need to look at the process that generates the Jello in a way that is consistent with GR.

The recent discussion of Black Hole Complementarity may be just the thing to give us good insights into this question. For example, if the craft with an Alcubierre drive is behind an event horizon, the discussion of whether or not it is moving FTL is mute.

We should be careful that our proscriptions of possible FTL travel do not assume an observer that can acquire information about things that no physical system can measure. There is no such thing as causation for the universe as a whole as it is impossible to define a Cauchy hypersurface that is consistent with QM (aka the initial data problem).

Dear Stephen, I didn't understand your comments about the process that created the jello. Perhaps you took the video analogy too seriously? The vacuum was created by some processes when the Universe was a newborn but the current properties of the vacuum may be studied independently of that pre-history.

A 100-meter-large spaceship localized in an otherwise flat Universe can't be behind any event horizon. If there were an event horizon, it would be one around the spaceship which means that the spaceship would be a black hole. Black holes' classical properties are completely determined by their charges etc. - they can't behave as spaceships that could "spit" astronauts again because nothing can escape from a black hole. The shape is determined to be spherical, too.

When you incorrectly say that the ban on FTL can be lifted because the spaceship is hidden behind an event horizon, what's actually hiding behind the event horizon is you. You use nonsensical words about event horizons to protect yourself and your misconceptions against any traces of rational thinking.

No, there cannot be a single instance of a process that created the vacuum in any absolute sense, this is what I was trying to point out with my words about the initial data problem. We must reason as if the vacuum is specified every time we make a measurement (that involves the vacuum's effects - which is most of the time). Let's forget about the subtleties of event horizons and BHs for now, although I wish you would think of these questions in those terms.

The vacuum is ever-present and, I contend, continuously generated. The creation of the vacuum is continuous, not a "special" magic event that only happened once in the history of the universe because otherwise we are assuming some metaphysics that are indistinguishable from passages in some religious text and ignoring the fact that in physics measuring what is going on in some very small region of space-time and/or very high energy regime is equivalent to measuring what occurred in some very early epoch of the Big Bang. Observables do not come with time stamps.

Very interesting what the US governement decides to spend its money for, whereas at the same time in a table I have seen in the journal of our German physics society about the changes to the funding of different sciences in the US, the entry concerning HEP is the only one (!) that appears with the wrong sign ... :-/

I like the "course grained" explanation of why no warp drive can work, regardless how hard the warp drive engineers will try ... :-)

Interesting words. I just don't know how to read them so that these words agree with anything I know about Nature.

What do you operationally mean by a continuous creation of the vacuum? How are you suppose to find evidence that this is occurring? What does it follow from? I have simply no idea what you're talking about,.

Lubos, then the LHC is up and running and protons are scattering off each other, how can they tell what epoch (of the universe) they are in? All they (metaphorically speaking) can know is that there is so much energy, charge, momentum, etc. Similarly, how does the vacuum "know" what time it is? Can it know that it is 2 hours after the Big Bang? No. All it knows is what quantum numbers are involved in defining it. Therefore to make any claim that the BB vacuum is somehow special is assuming a prefered frame of reference. There is no preferred frame nor basis of Nature.

Dear Stephen, the laws of physics are time-translationally-symmetric so they don't change at all when you wait. That's why there's no fundamental way to measure the "epoch", either.

The environment does change as a function of time. For example, since the Big Bang, the Universe was in the process of global cooling so the temperature of the outer space (and other quantities) may be used as a proxy of time since the Big Bang.

Because it goes to the question of the state of the vacuum. We have theories that tell us that space-time inflated at an astonishing rate that pulled apart particles faster than the speed of light. What prevents that scenario from causing causality violations? We cannot appeal to an environment that is time reparametrization invariant. My point is that the vacuum does not have a timestamp that tells it what epoch it is in, it only 'sees' local data. Who is to say that the vacuum cannot be induced to, in some local area, that is is inflating at some amazing rate and all of the "stuff" riding on that inflation would never notice that it was traveling FTL.

Dear SPK, as I said, the laws of physics are time-translationally-invariant but what is actually out there - the state of the physical system, whether it's the Universe or something smaller, may and does depend on time and situation.

So the vacuum still contains fields that have some values. They include the metric tensor which remembers whether the space is curved or not etc. In the same way, the vacuum always contains the electromagnetic field. And it also contains the inflaton field PHI whose value determines whether the Universe is just expanding or not.

The inflationary expansion implies the existence of horizons - and therefore faster-than-light coordinate motion of places from each other - but those evolutions don't contradict the causal restrictions of relativity as refined by geberal relativity. In particular, the mutual speed of objects just "meeting" each other is never faster than the speed of light.

How does the Inflaton field know what epoch it is in? How does the vacuum in some region of space-time know the "time"? What does the bulk of space-time have to do with what is happening inside some small region of the universe? This is why I brought up the Hole Problem. We need to be careful making arguments that assume a frame of reference that is effectively "outside" of the universe and yet can 'see what is going on inside'.

I looked into Harold White, he apparently does have a PhD but it's in planetary physics, not GR.

http://search.proquest.com/docview/304509845

Harold White does have a PhD, but it's in planetary physics and not GR.

http://search.proquest.com/docview/304509845

Party pooper.

Thanks. I always thought it was weird the way popular science writers popularised this. As you said, their arguments are always on the lines of "Right here, in this reigon, the spaceship seems to..." .

I once read the Alcubierre paper. All he shows is that if there was such a wave, traveling faster than light, then a material particle would be carried along with it. It remains the case that the wave itself can't travel faster than light according to special and general relativity. A pretty meaningless result.

It seems that the quickest way to debunk the warp drive idea is the fact that that geometry around the ship is essentially a configuration of gravitons and so if the geometry is moving it can only move at the speed of light (at best) since the gravitons can only move at the speed of light.

I want so badly for FTL travel to be possible so we can all go exploring the galaxy but unfortunately it seems like it's impossible.

Those who believe Quantum Field Theory know that nothing can travel faster than light because in QFT everything is made of fields and "Fields don't move infinitely fast. Changes in a field propagate in a 'laborious' manner, with a change in intensity at one point causing a change at nearby points, in accordance with the field equations". This quote is taken from "Fields of Color: The theory that escaped Einstein" by Rodney Brooks. Check it out at quantum-field-theory.net/fields of color.

I'm confused...

If F-theory is essentially just a formalism and is exactly equivalent to Type IIB String Theory (right? Taking an S^2 compactification should mean the T-dual of the T-dual which is the same theory in the end), why is it so useful in phenomenlogy? How can it give rise to such nice phenomenology when Type IIB string theory doesn't (right?)?

Just adding an S^2 torus results in all the phenomenology? Even though the theories are equivalent?

.

"Dear Lumo, could the first F-Theory paper somehow adress the issue how string theory (I know that string theory is not F-theory :-) ...) could work without supersymmetry"

I don't think this is possible. From what I understand, the "non-supersymmetric F-theory" was probably used just as, maybe a toy model, or something? Right?

Dear Dimension10, it is a formalism equivalent to type IIB string theory in a general enough sense of "type IIB" but it shows - and allows an elegant mathematical analysis of - much more general vacua than were thought to exist in type IIB e.g. in the 1980s.

The issue is that the shape of the 2-torus may depend on the "large" 9+1 dimensions and there may be weakly coupled and strongly coupled regions. Not only that, the shape may undergo SL(2,Z) monodromies when one goes around a 7-brane-like locus. This monodromy group contains Z_2 that switches the strong and weak coupling - so if you just go around, a weakly coupled theory becomes an S-dually equivalent strongly coupled one, and so on.

Because the shape parameter tau is complex and its holomorphic dependence is natural, one may use the mathematical formalism of complex manifolds to analyze the compactifications as if they were 12-dimensional geometries.

In some sense, the singular 7-branes with monodromies of many kinds are the main addition of F-theory relatively to "old type IIB", so all phenomenologically viable F-theory compactifications are previously neglected braneworlds. One must add that for the bulk of F-theory compactifications that are semirealistic, the 12-dimensional manifold is smooth but the base of the eliptic fibration has singular fibers.

I suppose that by S^2, you meant T^2, the torus. S^2 is a sphere. There's no known way to compactify the 2 infinitesimal directions of F-theory on a sphere.

Thanks a lot, I get it now!

Wait, why did my username change to "Guest"

?

Is it possible that, even if the drive cannot move _faster_ than light, that it could move _AT_ the speed of light, or at least so darn close it might as well be at that speed? As you mention, gravity waves move at the speed of light. This would not violate causality, and although it's not as good as going faster than light, it would still get us to the nearest star in 4.3 years instead of 100,000, which is obviously a big improvement, I'd think. With 100 years' travel, we could reach any star in 100 light-years -- and that's a LOT of stars!

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