[eigenschwarz]

The Average Null Energy Condition (ANEC) makes it so there can not be a traversable wormhole joining two otherwise disconnected regions of spacetime. So by construction, any infinite null geodesic (a light ray) which makes it through the wormhole must be chronal (causally connected). This means there can be no traveling faster than light over long distances by going through one.

[piker]

So that's it, then? Some thing, say, a million light years away from another thing is in practice entirely inaccessible to civilizations existing on that other thing, requiring a minimum of a million years to reach?

[nine_k]

This depends on what do you mean by 'inaccessible'.

Going there and back again, and telling your pals how things are 1000LY away is likely impossible.

Expanding your civilization to more and more habitable celestial bodies, slowly but relatively surely, is entirely possible. This is how e.g. plants colonize vast spaces, being limited by the speed of their growth often by inches per lifetime. (You should also consider the amount of resources the plats dedicate to it, and their success rate.)

[Robotbeat]

Extending human lifespan (perhaps using methods of hibernation, perhaps not) is easier technologically than basically any viable form of crewed interstellar travel.

[harimau777]

I get what you are saying, but it seems like the plant approach is mostly useless to humans. If the people on opposite sides of a galactic civilization are so far away that they cannot meaningfully interact, then it seems like that's no different than the other person not existing from their perspective.

[parksy]

Depends on the definition of useless or meaningful. If meaningfulness only extends to immediate political, social, economic or technological interactions then maybe an organic colonisation seems useless, I guess.

Unlike plants, through the power of electromagnetic communications and a culture based on shared knowledge, humans will know the others exist, even though that interaction will be slow with likely little-to-no-influence on their local evolution.

There would be huge cultural meaning even despite the lack of immediacy. Imagine living in a world where you know that there are other humans like you in space, living on other worlds light-years away. You might not be able to communicate immediately, but you know that they are there, and the universe is not so empty to you. You could look to the night sky and reminisce on your great(*n) grandpronoun whose progeny have built a thriving colony among the stars. Entire institutes would exist dedicated to collating and outlining the historical expansion of mankind among the stars, even if that knowledge takes centuries or millennia to accrue.

Also we can not say those other humans may as well not exist, because there is no telling what each new colony will go on to achieve. Their cultural, scientific and philosophical development independent of the influence of Earth's history and challenged by new environments could yield new perspectives, ways of thinking and practical inventions whose value far outweighs the large delay in communications.

If we're talking galactic scale, then the creatures who ultimately wind up on the other side of the Milky Way two hundred thousand years from now would likely bear only a passing resemblance to the humans who expanded from Earth. However barring a catastrophic event that erases their knowledge of their history, they would owe their existence in their history books to this tiny planet.

Finally, the fear that we are the only planet with human life would be vanquished, so even if we all died from pollution or meteorite, we'd know that somewhere the legacy of our species (and selected companion lifeforms) would continue, which I don't think is useless or meaningless either.

[naasking]

> I get what you are saying, but it seems like the plant approach is mostly useless to humans

Yes, and as humans are to plants, so our space faring descendents will be to us.

[therein]

But aren't there massive gaps where an intermediate celestial body to perform this jump on will be simply too far away for traditional space travel?

[jessriedel]

Probably not. On the timescales of millions of years, the only thing that really matter is whether it's physically possible, and it looks physically possible to colonize other galaxies.

http://www.fhi.ox.ac.uk/wp-content/uploads/intergalactic-spr...

I'd be pretty surprised if the jump between galactic groups is much worse.

[swebs]

On the bright side, due to time dilation, you can still make the trip in your lifetime.

[stcredzero]

You don't get much time dilation until you start hitting speeds mostly exclusive to accelerated subatomic or nuclear particles. It's nearly zero until you get past 0.5 c.

https://www.fourmilab.ch/cship/timedial.html

[zspade]

If by the bright side you mean you would only make it there it there as pure energy. Mass is converted to energy as it approaches C (Light Speed). Though getting mass to actual light speed would require infinite energy, so that point is moot.

Let's say you get to 96% C. You would experience 28% of the journey. Taking into account the the time to speed up and slow down from C, you're looking at over 290k years from the perspective of the passengers.

At 99% C, you would experience over 14% of the journey (About 142k years).

[stcredzero]

Mass is converted to energy as it approaches C (Light Speed).

Not so much.

https://www.youtube.com/watch?v=LTJauaefTZM

Try this thought experiment. Let's say you had a magic Bussard Ramjet rocket which scoops up energy and reaction mass from space and can accelerate forever. There are no special reference frames. So what happens if the rocket accelerates then shuts off its engine at the point where the "relativistic mass," as measured by an un-accelerated observer, should make the rocket disappear behind an event horizon?

From the POV of people on the rocket, they accelerated, then stopped accelerating. From the observer's POV, the rocket turned into a black hole? One reference frame now seems "privileged" or different somehow. How do we square this with relativity? Also, what happens if the rocket turns around, then decelerates? Wouldn't that constitute them returning from inside of an event horizon?

The answer, is that "relativistic mass" is actually just a pedagogical fiction.

(EDIT: Also, a lot of the redonkulousness in the thought experiment sneakily comes from rockets that can magically accelerate without worrying about where the fuel and energy come from. If you worked out how much fuel and reaction mass would be needed by a real rocket to perform such a feat, you'd get "unphysical" amounts of matter.)

[zspade]

I stand corrected. That's what I get for trying to make an offhand joke based on some some bad info. The rest of the time comment stands though.

[raattgift]

Don Lincoln's point boils down to momentum being a frame-dependent quantity even in plain old Newtonian mechanics, that the special-relativistic correction for momentum is simple. The point he is making about mass is, in essence, that one has to be careful in understanding equivalence relations E = m, E = p, E = hf, E = h/\lambda (here all are with c=1) as an overloading of "energy". In the last three of these there is a frame-dependent quantity: momentum, frequency, wavelength. In the first there is a non-frame-dependent quantity, the invariant mass, m_{0}. It is not the same species as a frame-dependent quantity m_{relativistic}, and at 6m57s into the video, he shows some of the dangers of "punning" them.

Your related comment says that m_{relativistic} is a pedagogical fiction. No, it is just a quantity that is non-identical to m_{0}. That students frequently forget (or do not know) that is a teaching failure.

However, you've introduced a gravitational event horizon, which is not something you can find in Special Relativity (whose spacetime is everywhere non-curved, that is, it is free of any gravitational effects at all).

If we pick out the globally flat background of Special Relativity and drop a test particle into it -- electrically neutral, low mass, and classically pointlike -- the latter generates the stress-energy tensor. Dropping indices and factors, G=T=0 -> G=T!=0, where G is the Einstein curvature tensor and T is the stress-energy tensor.

The stress-energy tensor is generally covariant: observers anywhere in spacetime, no matter how they are moving, agree on the total value of T at the point occupied by our test object. However, they are free to disagree on the quantities in the components of the stress-energy tensor.

The components of T can be written as a 4x4 matrix representing the flux of row-momentum into the column-direction. If (row,column) specifies a component of this matrix, and we count rows and columns 0..3, and we specify that our spacetime dimensions run 0...3 with 0 being the timelike dimension t, then a positive value of T (remember at a specific point in spacetime) in (0,0) and zeroes in all the other components means that momentum from the past of that point is flowing in the future of that point.

If at point p = (0,0,0,0), T^{00} = 1 and all the other components of T are zero, then at p' = (1,0,0,0), T^{00} = 1.

From Noether, a quantity that is invariant in time is conserved like the Newtonian conservation of energy.

An observer moving with our test particle generating T^{00} = 1 would relate the T^{00} quantity to the particle's rest mass (or invariant mass, if you like).

Let's call our 1 rows and columns "x" after the Cartesian direction

On a spacetime diagram, our test particle develops a worldline vertically along the t axis and not at all along the x axis.

Now let's complicate this a bit by having the test particle chuck a bit of itself out its back, engaging a classical notion of conservation of momentum. We'll call the 1 dimension backwards-and-forwards, or x, compared to our timelike 0 axis t. T^{01}, if positive, encodes the momentum coming from the past and leaving the point in the forwards direction.

Assuming coordinates (t,x,y,z) that absorb the emitted units:

At p = (0,0,0,0) we have T = 1, and T^{00} = 1.

Let's keep things normalized so that our particle is always at the origin of x.

At p' = (1,0,0,0) we have T = 1, and T^{00} = 0.9 and T^{01} = 0.1.

At P = (2,-1,0,0) we have the boosted exhaust: T^{01} = 0.1; at p'' = (2,0,0,0) we have the particle T^{00} = 0.9. Thus at p''' = (3,0,0,0) we have the particle still T^{00} = 0.9, and the exhaust P'' = (3,-2,0,0), T^{0,1} = 0.1.

But notice that this picture depends on coordinate conditions: the "rocket" particle at x=0 always, tracing out a vertical worldline on a spacetime diagram. The exhaust does not remain at x=0, and so traces out a worldline that has an angle from vertical.

If we flip this so the exhaust is at x=0, then we would say that the exhaust is at P = (2,0,0,0), P'' = (3,0,0,0) etc and its |T^{00}| remains 0.1 and it traces out a vertical worldline on the spacetime diagram. The "rocket" on the other hand is at p'' = (2,1,0,0), p''' = (3,1,0,0) etc and its |T^{01}| is 0.9.

What component(s) stress-energy appears in depends on the choice of coordinate basis.

Likewise, if we draw a spacetime diagram with the exhaust always at x=0, it traces a vertical worldline up the t axis, while the "rocket" traces out a worldline at some angle, because it is not at a constant x coordinate.

A completely different observer holding itself at x=0,y=0,z=0 would calculate different coordinate-values for particle/rocketing-particle/exhaust (changing the coordinates of p, p', p'', ... and P, P', .... However, it would agree that a normalized value of the whole T at p and p' is 1 but that the value of T at p'' is 0.9 while the value of T at P is 0.1. However, the total of 1, 0.9, or 0.1 respectively could be allocated to different components of T in 4x4 matrix form.

Technically, since T is nonzero at several points in spacetime (all those p and P points) spacetime is not flat. However, in any timelike hypervolume of this nearly empty spacetime, the total stress-energy will be 1.

Even if we move the "rocket" and its exhaust apart ultra-relativistically, the sum of their stress-energies at any time will remain 1. In Newtonian terms, what's being described is a total conservation of energy, and an unchanging centre-of-mass in a deforming system. Your rocket/bussard is similar: there is a system of ship + fuel + exhaust (+ waste heat + ...) whose observer-independent (or generally covariant) total is constant at any time. Thinking in a more field-like way, there are rocket-bits, fuel-bits, exhaust-bits (etc) which generate nonzero stress-energy at various points in the spacetime. The stress energy at each point in spacetime can be agreed by all observers, however they are free to disagree about how the stress-energy at a point is distributed among the various tensor components.

In order to form an event horizon we would need a much larger quantity of stress-energy in a small region, and that is not what is described in your posting, which is more about extremizing components of the tensor (at various points) rather than the whole tensor itself.

[saagarjha]

> Mass is converted to energy as it approaches C (Light Speed).

Uh, I think it's the other way around: the energy you pump in becomes additional mass.

[stcredzero]

Look at my sibling comment to yours. Relativistic mass is mostly just a pedagogical fiction.

[nkrisc]

Well, theoretically they could load their civilization up on a giant ship and move their civilization there over the course of a million years. Likelihood of success? Probably not great, but possible.

[xvector]

Everyone is missing the obvious solution. If we're talking about tech this fantastical, the best idea is to ditch our ephemeral biological bodies, jump onto a synthetic medium, and call it a day.

Hit pause so the journey takes a fraction of a second, or spend 1000Y in a VR - do whatever you want. I don't see a future where we're this advanced yet still content with our frighteningly fragile bodies.

[nkrisc]

Perhaps it's because building a giant ship that can carry countless generations of inhabitants many light years is really more of just an engineering problem. All the challenges (of which there are plenty) all have reasonably known solutions. There's not really all that much novel technology required. Just better tech than we have, and a lot of it, to be sure.

Uploading a consciousness into a computer and have it remain "you"? That's completely foreign to what we know today. I'm not saying it's categorically impossible; to your point, if a civilization has advanced to the point where the above is ship is feasible, surely they must have picked this up along the way? Maybe, but maybe not. We don't even know if it is possible. But keep a shitload of people alive in space for a long time? Sounds plausible, even if it is enormously difficult.

[p1esk]

Or we can relax the requirement that “it remains you”, and be content with the idea of cloning the mind. This should be somewhat easier to achieve.

[throwawaymath]

If you are okay with that, you no longer need to upload anything, and your problem becomes one of imitation rather than continuity. You can dispense with the philosophical question of identity entirely and obviate away the problem of interfacing with a mind.

Find a way to decompose an individual's personality into progressively more granular dimensions of behavior. Model stimulus -> response reactions as transformations. Sample enough responses from each type of behavior, make linear approximations of the transformations until you achieve a 1:1 simulacra, and derive a basis for the response basis. Your human mind will be a matrix representation of the map between the stimulus and response spaces.

As unrealistic as all of that sounds, it still sounds significantly easier to me than uploading (or even interfacing with) a mind.

[stcredzero]

Or we can relax the requirement that “it remains you”, and be content with the idea of cloning the mind.

How do we know that the incomprehensibly weird and advanced minds running our ships and habitats in those unimaginably distant points of space and time won't just decide that virtual smiley faces with our names written on them are close enough to, "it remains you." How do we know they won't one day do a "slightly lossy compression" of the human race?

[cgriswald]

The future you don’t see describes the present. We are (at very great, politically untenable cost, to be sure) capable of sending a ship full of humans and supplies elsewhere at a reasonable fraction of c. Our ability to do this continues to grow; although due to resource scarcity it’s not clear if efficiency gains will ever make it cheaper to do in the future than now.

We don’t even know where to start replacing our bodies. AI? Genetics? Cybernetics?

[xvector]

> capable of sending a ship full of humans and supplies elsewhere at a reasonable fraction of c

I am not sure of this. Even if we pooled the Earth's resources into constructing a generation ship, we still are not sure we are capable of making a ship that is sustainable both socially and technologically.

We do not know if our tech can last hundreds of years. Even if that wasn't the problem, we do not know if we can maintain a self-sustaining environment that lasts hundreds of years. Even if that wasn't the problem, we don't know what failure modes need to be accounted for. Even if that wasn't the problem, we don't know how to keep humans sane on such a journey. It is, after all, unethical to have new humans born on a journey they never signed up for. We do not have the right to determine the fate of our progeny.

An upload to a synthetic medium is perhaps the only sane and ethical way to accomplish this goal.

[XorNot]

I mean at that point you don't have to choose - you do all those things, plus have some more of you spend a bunch of time figuring out the philosophical ramifications of bringing it all back together.

Add some check processes which periodically restore an old backup and have a conversation to see if the backup agrees to a merge as the moral monitoring system.

[mirimir]

Or better yet, do the "Contact" thing, and just transmit information. Start with something to generate interest. Then maybe some (hopefully appreciated) knowledge and/or technology. Then instructions for building VR or robots, and data to load them with.

[krapp]

>So that's it, then? Some thing, say, a million light years away from another thing is in practice entirely inaccessible to civilizations existing on that other thing, requiring a minimum of a million years to reach?

"We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far." -- H.P. Lovecraft, 'Call of Cthulhu'

We're just a random species of ape too smart for its own good, only here to ponder the universe at all because an asteroid happened to wipe out the dinosaurs 65 million years ago. The universe doesn't owe us anything.

At least we have telescopes and science fiction, though. The dinosaurs didn't have either.

[airstrike]

You're correct, at least according to Kurzgesagt

https://www.youtube.com/watch?v=ZL4yYHdDSWs

[maxerickson]

According to physics as we currently understand it, yes.

[BartBoch]

As always, soon we will discover another way, or there will be a different theory that will allow bending the rules.

[lupire]

Not always. Faster than light travel has never been bent.

[BartBoch]

Well, we are able to research FTL for only a few decades. Give it a few more due to complexity. Few ages ago people thought that the world is flat...

Also, there are theories of FTL: https://en.wikipedia.org/wiki/Faster-than-light

[earenndil]

> Few ages ago people thought that the world is flat...

Ah, no they didn't. Scientific consensus has been the earth is round for thousands of years.

[craftinator]

As the word 'age' is used in the original comment, a likely synonym is 'millenia', so you are in aggreement with the poster.

[psionides]

They didn't really, that's a common misconception: https://en.wikipedia.org/wiki/Myth_of_the_flat_Earth

[smoyer]

And suddenly people think the earth is flat again ... we need to keep science more relatable to the general population and that starts with being realistic.

I'm not arguing with your idea ... just that it should start with a caveat ... "there are no current theories that support FTL but we're hoping ..."

[jcoffland]

Shadows can move faster than light.

[saagarjha]

Shadows are an abstract concept (namely, the absence of light), not a physical thing.

[smoyer]

I would argue that shadows are a very physical effect.

[TotempaaltJ]

That's an interesting assertion... Why would shadows be able to move faster than light?

[virgilp]

It's perfectly correct and does not contradict physics. Think about it in the opposite direction - say you have a perfect laser, with perfect pointing ability. You pick two planets that are far away from each other but at roughly the same distance from Earth, and make an angle of 10 degrees with it; it will take you a few seconds to "move" the laser 10 degrees and thus move the spot from one planet to the other - in the process making the spot "travel" millions of light years in a few seconds. However, the light itself has not traveled at faster-than-light speeds (it still takes a lot of years for the light from your laser pointer to reach any one of those two planets).

[jcoffland]

Say you're standing in front of the sun and you wave your arm. As the light travels away from you, your shadow will get larger and move faster. Eventually the movement of the shadow will exceed the speed of light. In theory it will approach infinity.

The light itself will continue to travel at normal speed but if you waited for the light to bounce back from distant planets you could observe the shadow moving FTL.

[hinkley]

I'm kind of relieved by this.

The last wormhole conversation I had with someone, I imagined a weapon using a short-distance wormhole with the ends opposed 180 degrees, and using a star's own gravity to tear chunks out of it. Everybody dies from massive solar flares.

Of course time travel books, wormhole researchers, and myself all make the same mistake over and over: If you made a wormhole or traveled in time, why do we assume that the frame of reference of the system is our star? Sol is whirling around our galaxy and an alarming rate, and that's moving through the universe at a huge velocity. Why would the hole you're trying to make in space move along with our solar system?

If I traveled back to five minutes ago I'd die in hard vacuum. I'd have just enough time to realize how stupid I am. Similarly, every time I try to use the same wormhole it would be farther from where I am and the other end farther from where I want to be.

[andrewflnr]

AIUI wormhole mouths don't have a direction. They're spherical.

The picture of a wormhole as a bell-shaped indentation in a sheet, like the graphic on this article, is an artifact of trying to explain 4-d concepts in 3-d shapes (in 2-d images). For a being in the 2-d sheet, the wormhole is a circularly symmetric spot of weird-shaped space. In real 3-d space, a wormhole is a spherically symmetric spot of weird-shaped space.

[hinkley]

True. You could still use this to make two Lagrange points near the surface, mucking up everything. The fact that the hole has to be longer than the distance traveled would greatly reduce the gravitational field coming out of the hole.

You could still drop one end of the hole into the sun... (and I’ve just realized this was a Farscape plot and therefore how the idea got into my head in the first place)

[olemartinorg]

Presumably, if you're smart enough to make a time machine, you'd be smart enough to calculate the target position in both time _and_ space.

[hinkley]

I suspect if you had that much understanding of orbital mechanics, you'd be a billionaire already and not worry so much about time travel.

[TeMPOraL]

No sensible protagonist or villain use time travel to become a billionaire. There are usually better pursuits involved.

[VRay]

Except Biff of course

[lenocinor]

Maybe this sounds a bit silly, but this is honestly one of the most mind-blowing thoughts I've read on Hacker News. Thanks, I can't believe I never thought of this myself in the past. :)

[FakeComments]

You don’t really explain how the assumption leads to the conclusion — and I’m left with the impression you used many words to say “they just assumed you can’t”.

Could you elaborate?

Edit:

Looking into energy conditions further, they are literally assumed restrictions on the equations because physicists felt some predictions were unphysical.

I’d really like if someone could explain if there’s any justification to what I was responding to beyond “well, because we assumed it should work that way”.

I think it behooves the physics community to be honest which claims are conclusions and which are their assumptions, and the specific reasoning that leads from assumption to conclusion.

[eigenschwarz]

I definitely get your point. One difference between theoretical physics and just math is we have since we use math as just a tool to describe the world, we still have to input physical assumptions to make any sense of what we see. There are many instances of things being mathematically "OK" but we don't think physically exist. See "White Hole" for instance.

I will try to give a better explanation later today! Funny enough, I am off for the section for the QFT2 that Daniel teaches right now, hah. I can also ask him personally questions later in the week.

[lupire]

Who is the "we" who thinks White Holes don't exist?

https://en.wikipedia.org/wiki/GRB_060614

[nine_k]

Black holes are hard to notice, except by side effects, but we know great many of them, end even portrayed one.

White holes would be relatively hard to miss, because they must be shining very brightly. One of the current theories suggests that the big bang (or "a big bang") was a white hole: every black hole is a white hole producing a big bang a parallel universe. We've already had ours, and are lucky enough to still register its echo as the CMB.

[Filligree]

Without negative matter, it's impossible to build a wormhole that's shorter than the distance through normal space.

This piece of math shows that it may still be possible to build a wormhole which isn't shorter than that distance. Obviously that wouldn't be much of a shortcut, but the potential research and (maybe) real-world applications are still impressive.

[FakeComments]

That’s not what I was asking.

I was asking about the particular usage of the average null energy condition as justification to rule out wormholes: why isn’t that just begging the question by assuming your conclusion? and how does that particular assumption actually lead to the conclusion there can’t be wormholes?

It’s interesting the downvotes for asking someone to support a scientific claim, and be clear where they’re making assumptions versus reaching empirical conclusions.

[lupire]

That's right. When you have a mathematical theory, there are often extremal cases that predict strange things that have never been observed. At this point you have a choice to make:

1) Assume the mathematical theory is too permissive, and rule out the things you have no reason to exist, and hope to find a more elegant theory (on the controversial metaphysical assumption that simpler/elegant theories are more likely to be correct)

2) Assume that the mathematical theory is pointing you in a direction to search for a new phenomenon, and build things like superconducting supercolliders to search for empirical evidence.

With wormholes, we're a bit stuck in that we are decades to centuries away from empirically testing the theories, so physically the Average Null Energy Condition is moot -- it's fine math to do, as groundwork/scaffolding for future physics, but it doesn't say anything physically until we get empirical evidence for or against it.

[FakeComments]

Okay — and just to be clear, there’s nothing problematic to me about simplifying assumptions or effective theories.

Both are important tools for making predictions tractable.

But when we lose sight of what are conclusions, what are strongly justified assumptions, and what are simplifying assumptions we don’t have justification for (or even know to be untrue), we begin to create fundamentally inaccurate models or wrongly shut down others’ avenues of inquiry.

This happens in economics and business quite often, but simplifying assumptions become orthodox truth with surprising frequency in hard sciences like physics, as well.

[empath75]

If that condition didn’t hold, we would expect to see a lot of phenomena that we don’t see, which makes it a poor model for reality.