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Comment by lisper | Hacker News Reader

The right way to think of this: the speed of light is not a speed limit, it's a speed reference. Everything is always moving at the speed of light through spacetime. When you "move" through space, you're not changing the magnitude of your velocity vector, only its direction. So the more you move through space, the less you move through time.

If you could move through space at the speed of light your velocity through time would be zero and you would appear (to yourself) to be moving infinitely fast, or equivalently, to be everywhere at once, or (again equivalently) that the universe had no spatial extent in your direction of travel due to an infinitely large Lorenz contraction.

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This explanation is wrong, and is not what the article is talking about at all. This article is about creating a warp bubble using negative energy, which changes the distance between two points. You can think about it sort of like creating a kink in a piece of metal with a piece of dust inside of it, the kink then propagates through the metal by distorting the geometry of the larger object in such a way that the distance traveled by the piece of dust is less than the original distance between the start and end point of the kink. The reason this works has nothing to do with special relativity, it comes from the fact that if you plug negative energy into the equations of general relativity, you get warp bubble solutions which travels between two points faster than light could travel between the two points if there was no warp bubble.

A few years ago I actually read through most of the original paper[1], and worked out a lot of the equations.

Although I don't see it mentioned in the article, and I'm speculating here, the reason the approach described in the article might work out for photons is that negative energy has been discovered at the quantum scale in something called the Casimir effect[2]. The Casimir effect happens when you have two conducting plates which are placed very very very close to each other, then in the space between the plates, something which behaves exactly like negative energy exists[3], and it causes an attractive force to be exerted between the two plates.

A natural thing to try would be to harness this type of negative energy to create a tiny warp bubble, and try somehow to stick a quantum particle like a photon in it.

[1] http://arxiv.org/abs/grqc/0009013

[2] http://en.wikipedia.org/wiki/Casimir_effect

[3] http://physics.stackexchange.com/questions/47922/can-negativ...

I will explain why lisper's explanation of light speed is wrong. The fundamental problem is that it violates the premise of relativity and is a classic example of appealing to an absolute frame.

Velocities are only measured relative to other objects. The explanation given by lisper requires an absolute reference frame. Otherwise, you have no way to figure out how much you're actually moving through space, and thus, through time because you can never figure out your "true" speed.

Relativity tells me that no matter what speed I travel at, I will experience time at the same rate. From my frame of reference, I will perceive things to happen in other reference frames at different rates. When we calculate time dilation and length contraction, we're determining that if something took time "t_a" in Frame A, it will appear to have taken time "t_b" to an observer in Frame B.

Furthermore, it's impossible under relativity to have a frame of reference that moves at the speed of light in any other frame.

Thanks for the great explanation! Would you be willing to write up your summary of this paper in the form of a gist? http://sciencegist.com/arxiv/gr-qc/0009013

That's a fantastic explanation. I did a Physics undergrad and masters, and somehow I never heard this particular metaphor for it, but using a velocity vector through spacetime makes for a very clear image of what's going on. Is that from general relativity? (I only did special relativity)

This is just special relativity (space need not be curved for this description to work).

Brian Greene's "Fabric of the Cosmos" gives a good layman's exposition of this idea, using a loaf-of-bread metaphor (this was the first time I saw it explained this way and it made a huge impact on my way of thinking about SR)

He does the same in "The Elegant Universe", using the metaphor of a car driving at a fixed speed (c) across field that is space in one direction and time in another. That was my big "aha" moment with special relativity: understanding that "space" and "time" are dimensions in essentially the same way that "length" and "width" are dimensions -- with the caveat that we always have this tremendous velocity (c) across one or the other.

Then you contemplate the kinetic energy that must be associated with c, and e=Mc^2 pops right out at you. Absolutely blew my mind when I first grokked that intuitively.

In the end, Greene failed to convince me that string theory was particularly interesting, but his descriptions of relativity are absolutely first-rate.

These are actually sometime the worst things to read if you actually want to understand stuff. The publishers of these kind of popular science books enforce the rule for authors that no equations should ever appear. If authors get really upset with that they allow printing one equation, usually, E=Mc^2. This leads even talented authors to water down everything with faulty and many time absurd metaphors. There is no real substitute to reading real physics books. On a lighter side, check this out: http://www.youtube.com/watch?v=w5VVEw4ZSRI

Well, having an intuitive understanding goes a long way too. Being able to derive formulae rather than just having them memorized is good. Of course, I don't want a book that doesn't include the formulae, but I want to know the "why" of it as well.

Special relativity.

If you measure time in seconds, and speed in units of C, then vx^2+vy^2+vz^2+vt^2 is always a constant (in flat spacetime). So you have no choice over the matter. If you are stationary, time passes at a rate of 1 second / stationary second. If you move in space, rate of passage changes exactly by the amount required to compensate. So in a way, you always move at the same speed through spacetime, speed of light, and can only choose the direction.

The reason is that time dilation factor is the lorenz factor, (1-u^2/c^2). This is how much time will pass in your watch per one second of a stationary clock.

http://en.wikipedia.org/wiki/Four-velocity

Just remember that this is true only in special relativity.

It is NOT true in general relativity, which means it's true only as an idea to understand things - the real universe does not follow that equation.

It does, locally.

Not under the influence of gravity it doesn't. Gravity causes time dilation without a corresponding velocity.

Yes it does. Gravity changes spacetime, so the locally flat spacetime at the bottom of a gravity well isn't the same as the locally flat spacetime at the top of a well, but it's still flat in both cases.

How does that cause a change in velocity?

Or are you implying there is no time dilation?

It's actually

  vx^2 + vy^2 + vz^2 - vt^2

the minus sign in front of the vt is very important and gives the SR (hyperbolic) structure of flat spacetime. The rotating a vector thing is just an analogy to euclidean space rotations.

I really really want to understand this, but I can't get past your third sentence. No fault of your own, just me. But if you have anything I can read that explains it better I would be grateful!

If you were heading due north at 100m/s, then changed your bearing to head slightly east without changing your overall speed, then you'd now be heading a bit less than 100m/s north and a bit more than 0m/s east.

This is the same kind of thing, except that when "at rest" in space (relative to some fixed point) you're moving at the speed of light in a pure time direction. When you move in space, you divert some of that speed from the time direction into the space direction you're moving in. Overall you're still doing the speed of light, just in a different "direction".

Here's an illustration, if it helps: http://imgur.com/YrlKW4Z

The length of the red arrow is always the same. When your velocity is zero, your "time speed" is 1.0. As you begin to move faster, the arrow tilts towards the X axis, decreasing your "time speed".

It's not a great way of describing it though.

The biggest issue is that the interchange between speed and time is not linear. So that graph doesn't make sense as displayed.

At a minimum you have to understand that the time scale on the side of the graph is not linear, but rather exponential. And graphs with exponential scales are not easy to understand.

Making it worse is that there are other things that can slow down time - namely acceleration.

Oop. You're right. I overlooked that. I put about 2 minutes into the illustration and didn't think it over very much (I probably should have).

I was mostly responding to TomGullen's confusion about the GP's statement, rather than trying to paint a super-accurate picture.

I wasn't really criticizing you as much as the concept of describing relativity as a tradeoff between the two. I don't think that helps enough to overcome the misunderstandings it can cause.

I feel the same way. Every time I try to understand the speed of light and correlation between time/space, my brain just hits a dead end.

"When you "move" through space, you're not changing the magnitude of your velocity vector, only its direction. So the more you move through space, the less you move through time."

I can understand what is being said here word-by-word, but the concept as a whole does not make much sense to me.

Try this:

http://blog.rongarret.info/2011/09/faster-than-light-probabl...

Think of it like falling. If you fall straight down at your terminal velocity you always head for one point. If you are able to move side to side at a very large speed, you can theoretically fall towards all points under you at once. Or, if you will, 'stop' falling towards any one point at all.

What bugs me about this explanation is the following: aren't we moving quite a bit all the time? We go along the earth as it's rotating around itself, then revolving around the sun, then the solar system revolving around the milky way, then the milky way probably moving somehow and so on.

If we could somehow "get off" earth, "stand still" and let it "float away", would time would appear to move faster?

In any given reference frame you have a velocity vector that's some part space and some part time but has magnitude 1. It's just rotated.

There's nowhere to "stand still" in the universe. But if you pick a reference frame where you're moving less fast in space your velocity has more of a time component to make up for it. If you pick one where you move very quickly in space (maybe one that doesn't follow the Earth's orbit) then you have less motion in time. That observer sees you experience less time.

And if they pick a reference frame where you move the speed of light - where your velocity vector is fully in space; with '1' for space and '0' for time - they don't see you experience any time.

There's no way to stand still per se, but we can tell the difference between someone who accelerates and someone who doesn't - that's the resolution of the "twin paradox". So if one person travels around in a circle and their twin stays still (by magically floating above the earth without following its rotation, or by staying suspended at a particular point in the earth's orbit for a year while the earth goes around), then they have accelerated less than their twin and should therefore have aged slightly more.

What I don't understand is: does this still apply under General Relativity, or does proximity to the massive earth redefine acceleration?

If we could somehow "get off" earth, "stand still" and let it "float away", would time would appear to move faster?

A qualified yes, but it depends which time you mean by "time would appear to move faster". If you were "still", then those observed in motion would appear to have time pass more slowly.

Astronauts who spend time on the international space station age slightly less than people on earth (by 0.007 seconds behind for every 6 months) - time on earth goes faster than for them relative to those of us "stationary" on earth.

When two observers are in relative uniform motion and uninfluenced by any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock. The faster the relative velocity, the greater the magnitude of time dilation. This case is sometimes called special relativistic time dilation.

http://en.wikipedia.org/wiki/Time_dilation

(The whole Wikipedia "Time Dilation" article is worth reading)

That's a nice explanation, but this hypothetical device doesn't move through space, it warps space. It's based on general relativity. It's gotten a lot of attention, and its practicality has been critiqued quite a bit, but everybody seems to agree that the math is right.

> its practicality has been critiqued quite a bit

That is quite the understatement. From the original article:

"[I]t depended on large amounts of a little understood or observed type of “exotic matter” that violates typical physical laws"

But other than that, there's no problem :-)

No argument there, just saying it doesn't seem to violate fundamental principles.

The exotic matter is negative mass. In theory there is such a thing, and a quantum effect produces it at a very small scale. Whether it will ever be possible to produce it in large quantities is another matter.

But at least the quantity required isn't quite as large as it used to be. The original configuration need a negative Jupiter mass. Now it's down to several tons.

I'm sure Niantic can hook them up.

There's another explanation to go with this one:

Suppose all objects have an 'energy', whatever that is, given by a vector sum of two components: P and M. Now every object may be distinguished by the distribution among those components: if, for a given norm, the energy is all in P, we say it is spacelike, it's energy is all in the space component. If it's in M then it's timelike.

So for us massive timelike objects at rest, E=M (in natural units) and for spacelike objects, E=P. Then it becomes clear that, since the mass is an instrinsic property of objects, any given object with M>0 cannot be spacelike: the energy vector will always have a time component, and likewise light cannot be timelike. You can however increase the spacelike component of the object and make it approach spacelikeness, measured by, for instance, the angle teta=arctg(P/M) with diminishing returns for each unit of energy (if you visualize it, you'll se at the start the return is linear -- teta ~ P/M and then it becomes very hard).

So the explanation above is telling in the sense that if you could be spacelike things would be weird, but doesn't reveal why you can't have massive spacelike objects -- namely, because we have a finite supply of energy.

The problem with that explanation from a pedagogical point of view is that you have left the word "energy" deliberately undefined. Because it's undefined, your explanation is isomorphic to this one:

"Suppose all objects have a 'snorble' (whatever that is) give by a vector sum of two components..."

You also haven't defined M and P. I know you mean mass and momentum, but only because I already understand this stuff. If your target audience is someone who doesn't already understand it, you need to define your terms or your explanation won't be effective.

Awesome!

Based on my layman's understanding of relativity, I intuited this model on my own, but no physicist I've spoken with has verified it as a valid model. It just seemed so obvious to me based on the constraints. Thanks for verifying my intuition on the topic. :)

Just for the record, I'm not actually a physicist.

Bummer. Maybe it's only a non-physicist's mental model then. :|

Interesting explanation. What happens at the other end of your example? If you reduce movement through space to zero, would time move infinitely fast?

You move through time at the maximum speed, c.

If it makes any sense ;-)

Obviously finitely, at constant speed.

No. That is your normal state of affairs: when you're "sitting still" in space, you're "moving through time" at the speed of light. I'm using scare quotes here because, of course, there is no such thing as "sitting still in space" because all motion is relative. The point here is that "light is always moving at the speed of light relative to you (no matter how you're moving)" is the same as saying "you are always moving at the speed of light relative to light (no matter how you're moving)". The way that works is, as I said, that this constant speed is a measure of your motion through spacetime, not through space alone or time alone.

I get the space-time vector thing. You said that, when moving at the speed of light, one moves through time at a velocity of zero, thus giving the appearance of infinitely fast movement. So if one was able to achieve zero movement (which would probably require achieving zero energy?), wouldn't time also appear to be moving infinitely fast (even though it was actually moving at the speed of light).

> when moving at the speed of light, one moves through time at a velocity of zero

When moving through space at the speed of light one moves through time at speed zero. Likewise, when moving through space at speed zero one moves through time at the speed of light, which is one second per second. This is the normal state of affairs that you experience day to day. It is not possible to achieve zero movement through spacetime. In this universe, everything is always moving through spacetime at the speed of light. The only thing that changes is the direction of motion: more through space, less through time, and vice versa.

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