"Point four past light speed"

[Finarvyn]

Han's statement that the Falcon could go "point four past light speed" has bothered me for a long time, particularly when I try to compare Star Wars to Star Trek technology.

Bear with me for a moment -- I'm not 100% certain of the origin of the Warp Factor equation, but I do recall that as early as the 1970's the Franz-Joseph technical manual established the rule that the warp factor in Star Trek is the speed of light cubed (e.g. warp 3 is 3x3x3=27 times the speed of light). So, if one interprets "point four past light speed" as 1.4c, then the Falcon topps out at something like warp 1.1, which is pretty lame in the Star Trek universe and not too awesome for Han to brag about. However, if you go to TOS canon then warp factor 8 is the maximum speed according to TOS physics. (I know that some alien creatures topped that on occasion and that TNG established W/F 10 as the top.) This curvy graph would tell me that the "ultimate speed" would cap out at 512c.

I had an interesting thought today: what if the Star Wars scale is linear instead of cubic?

So, we have a Star Wars speed scale that starts at c and ends at 512c. What if "point four past light speed" actually represents 40% of the way along the scale to the ultimate speed? Same physics, only a different scale by which folks measure the speed compared to the speed of light.

Light speed = c = W/F 1
Point one past light speed = W/F 3.7
Point two past light speed = W/F 4.7
Point three past light speed = W/F 5.4
Point four past light speed = W/F 5.9
Point five past light speed = W/F 6.4
Point six past light speed = W/F 6.8
Point seven past light speed = W/F 7.1
Point eight past light speed = W/F 7.4
Point nine past light speed = W/F 7.7
Ultimate speed = 512c = W/F 8

This would mean that the Falcon at "point four past light speed" would be cruising at nearly W/F 6, which is typical cruising speed for the TOS Enterprise.

What say you?

TECHNICAL NOTE: I calcuated this on an Excel spreadsheet and can post numbers if anyone actually cares. There is one issue I ran into where a simple calcuation ended up with W/F 1 equal to zero, so I had to tweak the spreadsheet to calculate the correct endpoints on both ends and not just one. I also did a second calculation assuming that TOS's W/F 10 is the ultimate speed, but I don't like that TNG piece of the canon and the numbers didn't have a pattern as nice at the end. I can post those also if anyone is interested.

[Deleted]

Honestly, I say that you're putting way too much effort into trying to put meaning into a meaningless statement.

Han Solo said "She'll make point four past lightspeed" because George Lucas thought it sounded science fictiony.

He made up some $hit he thought would be fun.

[kipper]

And don't forget the Kessel run !

[Stormcrow]

Jun 13, 2015 8:04:12 GMT -6 Finarvyn said:

However, if you go to TOS canon then warp factor 8 is the maximum speed according to TOS physics.

No, warp speed was originally open-ended. The Enterprise had a cruising speed of Warp 6 and an emergency speed of Warp 8. They COULD go faster, at the risk of Scotty announcing that the engines cannae take the strain, Captain. In one story they made it to Warp 15.

The creators of Star Trek: The Next Generation wanted a way to make warp travel much faster than before, but without constantly jacking up the numbers. They hit upon the idea that the Warp scale is asymptotic, with a limit of Warp 10. To go faster and faster, they just add decimal points onto Warp 9.

This, however, ran into a similar problem very quickly, as saying "We're going Warp 9.99999!" sounded silly. So the writers began to use expressions like "maximum warp."

The Star Trek: Voyager episode where they break the "Warp 10 barrier" is stupid, not just because of the whole evolution nonsense, but because Warp 10 means infinite speed. It's not a barrier, it's an asymptote. Morons.

[Finarvyn]

Jun 13, 2015 22:37:32 GMT -6 @gronanofsimmerya said:

Honestly, I say that you're putting way too much effort into trying to put meaning into a meaningless statement.

Han Solo said "She'll make point four past lightspeed" because George Lucas thought it sounded science fictiony.

He made up some $hit he thought would be fun.

Hey, Michael! I know what you are saying here, and know from reading interviews that this is actually what happened. It's like the people who think that a "light year" is a unit of time -- the parsec sounded cool so Lucas used it.

The key is that I'm a physicist in my day job and I spend a lot of time thinking about $hit like this and how to "explain" it, assuming that Han Solo isn't a moron and that he actually knows what he is talking about.

Jun 14, 2015 9:15:36 GMT -6 kipper said:

And don't forget the Kessel run !

I have a theory about that as well, and was actually going to start a thread on in in a day or two once some of the chatter from this one died down. Assuming we get much actual chatter or debate on the issue.

How about this: Suppose there is a region near Kessel which is full of asteroiods or planetary masses such that hyperspace travel is impossible. This would mean that the Falcon would have to rely on regular-space engines. So, perhaps the Falcon is moving fast enough to let relativity kick in and the distance between Kessel and some standard location gets relativistically shrunk from its usual to "less than 12 parsecs."

See, science rules!

[randyb]

Jun 15, 2015 5:30:01 GMT -6 Finarvyn said:

Jun 14, 2015 9:15:36 GMT -6 kipper said:

And don't forget the Kessel run !

I have a theory about that as well, and was actually going to start a thread on in in a day or two once some of the chatter from this one died down. Assuming we get much actual chatter or debate on the issue.

How about this: Suppose there is a region near Kessel which is full of asteroiods or planetary masses such that hyperspace travel is impossible. This would mean that the Falcon would have to rely on regular-space engines. So, perhaps the Falcon is moving fast enough to let relativity kick in and the distance between Kessel and some standard location gets relativistically shrunk from its usual to "less than 12 parsecs."

See, science rules!

My favorite explanation for this one is that Han Solo was trying to pull a fast one on what he saw as a couple of desert rubes. (Not original to me, but I forget where I saw it.)

[kipper]

Jun 15, 2015 9:53:43 GMT -6 randyb said:

Jun 15, 2015 5:30:01 GMT -6 Finarvyn said:

I have a theory about that as well, and was actually going to start a thread on in in a day or two once some of the chatter from this one died down. Assuming we get much actual chatter or debate on the issue.

How about this: Suppose there is a region near Kessel which is full of asteroiods or planetary masses such that hyperspace travel is impossible. This would mean that the Falcon would have to rely on regular-space engines. So, perhaps the Falcon is moving fast enough to let relativity kick in and the distance between Kessel and some standard location gets relativistically shrunk from its usual to "less than 12 parsecs."

See, science rules!

My favorite explanation for this one is that Han Solo was trying to pull a fast one on what he saw as a couple of desert rubes. (Not original to me, but I forget where I saw it.)

I think that's more-or-less explicitly stated in one version of the actual script.

[Deleted]

Just look at the expression on Obi-Wan's face after Han says it.

[Deleted]

Finn, you have way too much free time to come up with theories.

I always assumed that Lucas just made science errors. The notion of it being a way for Han to try to con Luke never crossed my mind.

[Mushgnome]

The explanation is clear if you watch the deleted scenes. Han Solo was being a wiseacre because Luke and Ben interrupt just as he is about to score with a lovely dark haired Tatooinisita.

www.inquisitr.com/1450847/star-wars-raw-footage-reveals-han-solos-other-woman-in-cantina-scene/

[krusader74]

Jun 13, 2015 8:04:12 GMT -6 Finarvyn said:

Han's statement that the Falcon could go "point four past light speed" has bothered me for a long time... What say you?

My own theory is that "point four past light speed" means 1.4 c, short for √2 c ≈ 1.4142135623730951 c, because at that speed, something very special happens mathematically---the Lorentz factor gamma (γ) becomes -i, the negative of the imaginary unit. When this happens, space turns into time and vice versa, while length contraction and time dilation vanish. Let me spell this out in more detail...

In special relativity, the spacetime metric is

dτ^2 = (dx⁰)^2 + (dx¹)^2 + (dx²)^2 + (dx³)^2

where the superscripts indicate components of a contravariant 4-vector (not exponents) and x⁰ = i c t. This is really important: Notice the factor i = √-1. In Minkowski space, the time coordinate x⁰ is an imaginary number!

The Lorentz factor, gamma, is computed as

γ = 1 / √(1 - β^2) where β = v/c

Keep in mind that i^2 = i i = -1 and that we can clear an imaginary unit out of the denominator of a number  by multiplying the number by i/i = 1.

If v = √2 c, then β = √2, and so β^2 = 2, and so γ = 1/i = i / i^2 = -i. If c < v < √2 c, then γ would still be imaginary but |γ| > 1. And if v > √2 c, then γ would still be imaginary but 0 < |γ| < 1. For example, if v = 1.400 c, then γ = -1.02 i. And if v = 1.428 c, then γ = -0.98 i. When v = √2 c ≈ 1.4142135623730951 c, then γ = -i exactly.

Now consider the Lorentz transformation and its corollaries, time dilation and length contraction: spacetime coordinates change from one inertial frame using unprimed coordinates (x⁰, x¹, x², x³) to primed (x'⁰, x'¹, x'², x'³) coordinates with relative velocity v like so:

x'⁰ = γ (x⁰ - v x¹ / c^2)
x'¹ = γ (x¹ - v x⁰)

Note that v x¹ / c^2 = β x¹ / c. The ratio β=v/c is unit-less, and the ratio x¹ / c has units space/(space/time)=time. And time coordinates always have a factor of i. So, WLOG, let v x¹ / c^2 = i θ where θ is some real number.

If γ = -i, then x'⁰ = γ (x⁰ - v x¹ / c^2) = -i (i c t - i θ) = c t - θ, which is a space coordinate, rather than a time coordinate, because time always has a factor of "i" in it, but this a real number. An imaginary value of gamma transforms time into space! Similarly, it can be shown that if γ = -i, then x'¹ is a time coordinate, not a space coordinate!

Time dilation: Δt' = γ Δt where

Δt' ≡ time between ticks as measured in the rest frame of the clock
Δt ≡ time between ticks (t₀, t₁) as measured in the rest frame of the clock, i.e., Δt = i c (t₁ - t₀)

If γ = -i then Δt' = -i i c (t₁ - t₀) = c (t₁ - t₀), which is a space interval, rather than a time difference, because time always has a factor of "i" in it, and this a purely real number.

However, notice there is no "dilation" because |γ| = 1. Dilation only occurs when |γ| > 1.

Length contraction: Δx' = Δx/γ

Again, if γ = -i, then Δx' = Δx/γ = Δx/-i = -i Δx / i^2 = i Δx, which is a time difference, not a space interval, due to the factor of i.

And again, notice there is no true "contraction" either because |γ| = 1. Contraction only occurs when |γ| > 1.

Simple mathematical explanation: In the complex plane, multiplying by -i is equivalent to a 90° clockwise rotation.

So if γ = -i, then "time dilation" (multiplication by gamma), rotates the time axis 90° clockwise into the space axis. And "length contraction" (division by gamma), multiplies by i, rotating the space axis 90° counterclockwise into the time axis.

In other words, traveling at exactly v = √2 c (≈ 1.4 c or "point four past light speed") "turns" time into space and space into time!

Moreover, it rotates with no rescaling (contraction/dilation), because |γ| = 1 exactly.

---

Here's something else tricky to think about:

A long time ago in a galaxy far, far away....

A long time ago, distances between galaxies (and stars and other stuff in the cosmos) were a lot shorter, because the cosmos was smaller, because Hubble's law, v = H₀ D.

So does this prologue mean: "A long time ago in a galaxy that's now far, far away"? Or is it not that long ago after all? Or is there a contradiction in the statement?

Moreover, Star Wars happened in the distant past. Star Trek in the future. Therefore, to get from point A to point B in the same amount of time, the Millenium Falcon didn't really need to travel as fast as the USS Enterprise. And Voyager had to travel even faster than Enterprise. That's why Voyager had to break the "Warp 10 barrier"!

---

Anyway, here's someone else's explanation of "point four past light speed"... While not canon, the following reference indicates "point four past light speed" actually means 1.4 x 100000c or 140000c.

Lightspeed was a slang term referring to the speed at which a starship traveled through hyperspace. In reality though, lightspeed, or traveling through hyperspace with a class 1.0 hyperdrive motivator was actually over one hundred thousand times faster than the speed of light, allowing a ship to cross the galaxy in a matter of days. Light speed could be dangerous without the right coordinates.

Quoted from Lightspeed at Wookieepedia, the Star Wars Wiki. See also: Hyperspace and Hyperdrive.

Again, my issue with this explanation is the tacit assumption that distances between points were the same "A long time ago" as they are now, so the MF had to go really fast. But the cosmos is expanding, faster and faster, so distances were smaller "A long time ago" and the MF didn't really have to go as fast then as it would now.

---

It should also be noted that there are several canonical "warp factor" scales used Star Trek. They are detailed in the following three references:

Warp factor at Memory Alpha
en.memory-alpha.wikia.com/wiki/Warp_factor

Warp factor at Memory Beta
memory-beta.wikia.com/wiki/Warp_factor

Warp Speed Anomolies at the Daystrom Institute Technical Library
www.ditl.org/article-page.php?ArticleID=17&ListID=Articles