Using speed of light to resolve inaccuracy in historical record.

[Baughn]

That isn't quite as odd as FTL breaking causality, but it definitely doesn't play well with Occam's Razor.

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One option is biting the bullet, and accepting that FTL can lead to time-travel.

This doesn't mean it would necessarily violate causality, as there are plausible physical implementations of the chronology protection conjecture; most notably virtual particle loops, which would act to cause dramatic explosions just before your ship would otherwise have formed a causal loop.

I don't see that as a violation of occam's razor. I do see it as still pretty unlikely, but we've plenty of reason by now to think that causality itself isn't necessarily unidirectional, such as various quantum eraser experiments -- of course, those could also be explained with MWI.

Regardless, it's a pretty interesting system to use for an SF story.

Lots more here: Traversable Wormholes

 

[Baughn]

A distinction that you need to make that I'm not sure that you're making is the difference between absolute characteristics of actual events and relative characteristics of actual events.

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While that's a valid way to look at it, it can be confusing. The distance and time between events changes depending on perspective? How can that be?

It only happens when you're looking at events in three dimensions plus time, ignoring that space and time are not separate. The space-only distance between two events depends on your velocity, which is to say that it literally depends on the angle your camera forms with time. That the apparent distance depends on your movement, then, shouldn't be any more surprising than that a flagpole appears to be "shorter" -- takes up less space in your photo -- if you walk up to it and point your camera upwards.

The spacetime interval between the two points is invariant; it doesn't change depending on perspective, in much the same way that the flagpole remains the same length. If you like, you could call that the 'true' distance.

It breaks your intuition a little bit, however, because it's calculated as "S^2 = t^2 - x^2 - y^2 - z^2". Two events that are three lightyears apart, and three years apart, have a spacetime interval -- a 'true distance' -- of zero.

(Which is why we don't actually call it a distance. Even though it, geometrically speaking, is.)

You will immediately notice that the spacetime interval between two points that are further apart in space than in time is an imaginary number. This makes it space-like; they're separated by more space than time. If there's more time than space, then it's time-like, and if they're equal (thus, S is zero), it's light-like.

Physicists typically punt on that, and use S^2 instead of taking the square root (in order to simplify the equations, making space-like intervals just a negative number; another reason they don't call it a distance, as the square of the distance decidedly isn't), but it's equally invariant either way.

The takeaway?

There's nothing perspective-dependent about space-time, only about your perspective. Also, faster-than-light paths are all imaginary.

 

[The Narrator]

In any case, you are correct that discovering FTL could overturn relativity rather than violating causality. However, something important to remember is that, whatever the actual rules of the universe turn out to be, they look just like Relativity under the conditions where we've been able to perform experiments. So any FTL physics would require special frames only for FTL, with no special frames for STL. Or, rather, there are special frames but the rules govern STL motion just so happen to mask the presence of those special frames.

That isn't quite as odd as FTL breaking causality, but it definitely doesn't play well with Occam's Razor.

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Although that would be a lot like what happened when we discovered relativity in the first place, where it turned out that there were principles of physics that we never noticed because their effects were imperceptible if you weren't traveling a significant fraction of the speed of light.

 

[Baughn]

So, what is the spacetime interval? What does it represent? I called it a distance, and in the four-dimensional geometry of our universe it is, but it isn't quite the same sort of thing as the distance between your keyboard and your screen.

It's the amount of time that passes, from the perspective of an object taking the path represented by that interval. It's a line segment on the worldline of that object.

Our universe is four-dimensional, which means you're a four-dimensional object. Imagine slicing a snake, but instead of snake salami there are different instances of you, at different points in time. When I say "time" I don't mean "points in the time dimension", even though that's (largely) true. I mean a line that's parallel to your worldline. Usually that ends up pointing straight ahead in the time dimension, but only because we're ~stationary...

Let's take a simpler example: A digital clock, moving from Earth to Alpha Centauri.

We'll define a function that gives us the output of the clock. f(n) = f(n-1) + 1, for all f > 0. f(0)=0.

This function doesn't exist in the clock, which is a simple mechanical clock. It exists in the laws of physics, which 'calculate' each passing moment based on the previous one. There's an equivalent function for you, although a vastly more complicated one. (And to a close approximation, one could say you are that function... but I'm digressing.)

It doesn't apply to the time dimension, which is just a (slightly odd) dimension. It applies to the worldline, and it would apply equally regardless of the direction of the worldline. If you could somehow turn it around, sending the clock hurtling backwards in time, it would still apply; f(2) would still refer to f(1), the previous point on the worldine, even though that point is in the future from our perspective. Think of a cellular automaton, where each state is entirely determined by what came before; it's like that, but without an explicit time axis, only the requirement for consistency.

But we're sending this clock to Alpha Centauri, on a very fast rocket. A rocket so fast, it gets there at 99% the speed of light! This means it crosses a five light years distance in 5.05 years, from our perspective.

What's the length of the clock's worldline? The spacetime interval between <clock launches from earth> and <clock arrives at alpha centauri>? Well, that's simple: In years, it's sqrt(5.052​ - 5.002​) = 0.5025 That's in years. Or light-years, if you prefer; they're really the same thing.

Accordingly, the clock will have measured just over half a year passing. Its worldline is shorter than if it had been stationary; it's literally smaller than a clock that stayed put, in four dimensions, because the distance between Earth and (Alpha Centauri + 5 years) is shorter than the distance between Earth and (Earth + 5 years).

That's what the spacetime interval is. Not the distance on a meterstick, but the true, four-dimensional distance between events.

 

[tedr]

Alright, let me try a thought experiment. Please disregard any technical/engineering feasibility and only consider the science under it.
Suppose i have a telescope pointed at our nearest star Proxima centaur. As it is four light years away, we are receiving an image of the star that is 4 years old.yes/no?
Suppose i have a mirror on that star. Suppose that mirror is always pointed towards us, such that it reflects the earth, just like we can see our self in our bath room mirror.
Will the image of earth that we see will be of the earth as it is now or of the earth 8 years ago?
Now take this Mirror and put it further away, and won't the image of earth reflected from it simply be the image of earth in its Past? And by this system, we can effectively see into the past of earth provided we had a mirror at sufficient distance?

 

[Baughn]

Alright, let me try a thought experiment. Please disregard any technical/engineering feasibility and only consider the science under it.
Suppose i have a telescope pointed at our nearest star Proxima centaur. As it is four light years away, we are receiving an image of the star that is 4 years old.yes/no?
Suppose i have a mirror on that star. Suppose that mirror is always pointed towards us, such that it reflects the earth, just like we can see our self in our bath room mirror.
Will the image of earth that we see will be of the earth as it is now or of the earth 8 years ago?
Now take this Mirror and put it further away, and won't the image of earth reflected from it simply be the image of earth in its Past? And by this system, we can effectively see into the past of earth provided we had a mirror at sufficient distance?

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Of course it would work. The mirror would have to already be there, that's the only problem.

 

[TheLastOne]

How would you place that camera there?

Fly there and put it there? But with a physics-adhering propulsion, you need to fly for at least 18 years to get to that point, at which point you have to catch up with the light signal by another 18 years.
As @The Narrator noted, you need FTL for that.

But... since FTL travel necessarily implies time travel, why don't you just travel into the local past and watch it happening right there?

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There could be any number of reasons ether practical or social to not actually create timelike-loops.

 

[Cadis]

I guess my question is how am I going to measure how much time has passed.

In a more general sense, I'm trying to figure out the difference between actual events and our perception of these events.

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This is why it is called relativity. Everything is relative except light and depends on your frame of reference.

 

[SeptimusMagisto]

This is why it is called relativity. Everything is relative except light and depends on your frame of reference.

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I guess I'm still not sure if it's the actual events that are relative or just the way information about those events gets to me. It seems like light could only possibly affect the latter, but it might be the former through some mechanism I'm just not getting.

 

[linkhyrule5]

I guess I'm still not sure if it's the actual events that are relative or just the way information about those events gets to me. It seems like light could only possibly affect the latter, but it might be the former through some mechanism I'm just not getting.

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Light doesn't directly have to do with the fact that events are relative. It's just that the fact that the speed of light is a constant has implications about the way we add velocities, which after a bit of math reveals that spacetime is a thing and events are relative.

It's less "speed of light is a constant, therefore events are relative," and more "the constancy of the speed of light was a clue we used to discover the fact that events are relative."

 

[bluepencil]

I've always been fond of the saying "The Speed of Light is not so much as a speed limit but it's how fast the universe is capable of updating itself."

If the Sun were to vanish right now, we would still get eight more minutes of sunlight and only afterwards would the Earth start careening off into the void because if gravitons existed they could still only travel as fast as light.

 

[Quadhelix]

While that's a valid way to look at it, it can be confusing. The distance and time between events changes depending on perspective? How can that be?

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I agree with you that the best/correct way of thinking about Relativity is that it's the result of us living in a 3+1 dimensional spacetime. However, I think that starting out with that explanation, without laying any further foundations, risks throwing people into the deep end while they're still learning to float.

Also, faster-than-light paths are all imaginary.

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*mic drop*
*air horns*
*"Turn Down for What"*

I guess I'm still not sure if it's the actual events that are relative or just the way information about those events gets to me. It seems like light could only possibly affect the latter, but it might be the former through some mechanism I'm just not getting.

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@linkhyrule5 beat me to the punch on this, but it bears repeating that the invariance of the speed of light is a consequence of the geometric rules of spacetime, not the cause. @Baughn has explained several times over the past few pages that the fundamental explanation behind Special Relativity is that we live in a universe of 3+1 dimensions -- three spacial dimensions, plus time -- and Special Relativity is a description of the geometry of this 3+1 dimensional spacetime.

The invariance of the speed of light is a consequence of the fact that spacetime intervals are invariant and something traveling at the speed of light traces out a spacetime interval with a magnitude of 0. Because spacetime intervals are invariant, something that traces out a spacetime interval of length 0 will do so according to all observers, and thus all observers will measure that something as traveling at c.

Events being relative isn't just about how information from those events reaches, but neither is it a consequence of how light behaves. Rather, both the behavior of light and the relative measurement of events are consequences of the underlying geometry of spacetime.

 

[linkhyrule5]

One of these days I'm going to write up a big effortpost about rapidity and why anyone who wants to understand relativity should study hyperbolic geometry and trigonometry.

That day is probably not today, though.

 

[Baughn]

Nothing quite beats fiction for building intuition, and that's just as true for relativity as anything else. That's why I linked to Greg Egan on the previous page. You have to find the right fiction, but it isn't nonexistent.

Besides that, the more (ahem) perspectives you get on relativity, the more likely it is that you'll successfully put all the pieces together in your head.

So for the ones that already have, I'm going to post a picture from said books...



On top, there's a rotating, rigid square in our universe. On bottom, there's a rotating, rigid square in two particular dimensions in Dichronauts... but the same diagram would be valid for a rotating, rigid square in our universe which happens to lay flat in the time dimension, stretching west-east as well as past-future.

This, too, is a way of demonstrating time dilation. It's why FTL is impossible, and why Lorentzia length contraction happens. In the end, it's all geometry.

It's fun watching a group of misfits using the phenomenon we'd call "time dilation" to make their ladder tall enough that they can rescue a prisoner held on the second floor, however.

 

[We Just Write]

I actually once did a paper-napkin analysis of how a ship equipped with a warp drive could end up in the past/future of its destination, using a half-assed lorentz transformation. There are basically three cases, determined by the ship's realspace velocity relative to the destination.

Case 1: Ship is stationary relative to destination before going to warp

In this case, things behave more or less how they do in most space opera; elapsed time onboard the ship is basically consistent with elapsed time at the destination, assuming they got word of your departure using a wormhole communication link. There's a bit of wiggle room

Case 2: Ship is moving towards destination before going to warp

In this case, the trip takes less time from the perspective of those aboard, however the elasped time at the destination will be noticeably increased. The closer the ship's realspace velocity is to c, the more pronounced the effect is. This can go up to the point where there's basically no point to turning on the warp drive since either way you're pretty much a lighthugger.

Case 3: Ship is moving away from destination before going to warp

At low levels, this is the inverse of Case 2, trading increased elapsed time aboard the ship for lower elapsed time at the destination. However, when the realspace velocity away from the destination becomes equal to the inverse of the warp drive's rating in c, elapsed time at the destination becomes zero. Go any faster away from your destination, and from their perspective you will arrive prior to a wormhole-sent message of your departure, possibly being able to use the wormhole to send mail to your past selves. Worth noting is that this seems to hard cap at one year into the past per light-year traveled.

 

[mastigos]

Yeah, half suspected it was wrong/incomplete, but relativity is fucking confusing.

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Then here's a simpler way to understand it:

• Most people vaguely understand the concept that as you approach the speed of light, your time slows down
• For things actually travelling at the speed of light, time is outright frozen. They experience no time between leaving Point A and arriving at Point B
• Therefore, the speed of light is the speed of teleportation. It is the speed of instantaneous travel with no time between leaving and arriving
• Therefore to go faster than the speed of light means to arrive before you left
• Thus all ftl allows time travel

 

[Vorpal]

Then here's a simpler way to understand it: ...

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Things should be as simple as possible, but not simpler. The explanation is very mistaken on several levels, starting from a confusion about coordinate and proper time: lightspeed is not instantaneous in an inertial reference frame, despite the lightspeed limit taking zero proper time.

Lightspeed and instantaneous speed are very different things; on a spacetime diagram, lightspeed is along the diagonal and instantaneous (infinite) speed the horizontal; cf. the (u,x) diagram posted above to make this clear (pretend u is time).

Finally, it is not correct that FTL is automatically time travel; this is again obvious on the diagram, because going backwards in time (in a fixed inertial frame) would be going below the x-axis, while there are plenty of FTL spacetime directions between the x-axis and the lightspeed diagonals.

It's essentially impossible to explain how FTL leads to time travel without considering what Lorentz boosts do in spacetime, which is basically a rotation along hyperbolas (or their lightspeed asymptotes) rather than circles, as again illustrated in the above animation.

So here's an alternative explanation instead:

(1) If some future-directed sublight velocity is possible, then they all are.​

This is an almost trivial statement but it's illustrated in the animation in that Lorentz boost can 'rotate' any event on the upper branch of the twin hyperbolas into any other event on it. ... The direct analogue of this statement is:

(2) If some right-directed superluminal velocity is possible, then they all are.​

Again in the the animation illustrating that any event on the right branch can be rotated into any other on it. Now, there's nothing physically special about the left branch (unlike the bottom, which represents sublight past-directed directions in spacetime), and indeed with more spatial dimensions turning around is easy, so those directions should be possible as well. Notably, this includes directions below the x-axis as well as instantaneously fast ones (horizontal in the diagram).

Therefore, if FTL is possible, then any direction except those in the bottom branch are fair game, and it's easy to make loops in spacetime that break causality (e.g.: say you're at rest; from the origin, send an instantaneous right-moving signal to a relay, and let the relay re-send it using a left-moving signal that goes below the x-axis, which intersects the time axis at a negative time coordinate, so you've just sent a signal into your own past).

 

[Baughn]

Yup. Though I'd add:

- "Rotating a world-line" sounds abstract, but the way to do so is acceleration. Any rocket engine will do. (Though if you want to reach high angles, it had better be antimatter-powered.)

- The most obvious reason why we cannot reach superluminal velocities is that there's no way to rotate past the forty-five degree angle, i.e. the speed of light. That's often expressed as "reaching C requires infinite acceleration", but it's a statement about geometry. The dimensions don't join up smoothly, so to speak.

- Therefore, if we had any means to translate past it, we could probably accelerate superluminally until our world-line is pointed towards the bottom-right, then translate again to put us in the bottom triangle.

This would turn the ship into antimatter, but more intriguingly would also point its direction of casuality directly against the rest of the universe. I doubt that would end well, so perhaps it's for the best that we can't.

(However, The Arrows of Time deals with this scenario. Not this exact one, as it's set in a true euclidean 4D universe, but it's still really interesting.)

All of that being said... Here's one of my favorite graphs:


All right, that's matter annihilation. Now tilt your head ninety degrees... Wait for it... Suddenly it's showing a photon bouncing off a mirror!

That isn't a trick. They're the same thing.

 

[The Narrator]

That's often expressed as "reaching C requires infinite acceleration"

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Don't you mean infinite force?

 

[We Just Write]

Yeah, an alcubierre-derived warp field would basically be the translating within reference frame that Baughn described. Thing is, since the warp field pretty much closes off the ship in its own isolated spacetime when in transit, any concerns about annihilating like antimatter are pretty severely mitigated.

 

[Quadhelix]

Don't you mean infinite force?

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Not really -- due to how velocities add in Relativity, an object/observer undergoing constant acceleration* will asymptotically approach the speed of light.

*Within its own frame of reference -- or, rather, within each of the inertial frames of reference that it passes through as it accelerates.​

Thus: "infinite acceleration"

 

[The Narrator]

Not really -- due to how velocities add in Relativity, an object/observer undergoing constant acceleration* will asymptotically approach the speed of light.

*Within its own frame of reference -- or, rather, within each of the inertial frames of reference that it passes through as it accelerates.​

Thus: "infinite acceleration"

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So when they said "infinite acceleration" they actually meant "finite acceleration for an infinite length of time."

 

[Baughn]

So when they said "infinite acceleration" they actually meant "finite acceleration for an infinite length of time."

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The amount of time doesn't matter. If you could think of a way to do it in finite time, that's fine; the summed-up acceleration is infinite either way. But even infinite acceleration will only take you to the speed of light, not past it.

 

[mastigos]

Things should be as simple as possible, but not simpler. The explanation is very mistaken on several levels, starting from a confusion about coordinate and proper time: lightspeed is not instantaneous in an inertial reference frame, despite the lightspeed limit taking zero proper time.

Lightspeed and instantaneous speed are very different things; on a spacetime diagram, lightspeed is along the diagonal and instantaneous (infinite) speed the horizontal; cf. the (u,x) diagram posted above to make this clear (pretend u is time).

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0 proper time and instantaneous are synonymous. Infinite speed is NOT synonymous with them. Travel at the speed of light is instantaneous from the reference of the traveler, because it takes 0 proper time. Travel at infinite speed is much much weirder than that, and was not what I was discussing.

Finally, it is not correct that FTL is automatically time travel;

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Hence I used the word "allows" instead of "is"

 

[DrGilga]

that game was perfect trek