None of this is meant to be taken seriously. There’s a million crackpot theories generated everyday, and this one is mine

In the latest Bobiverse book (book 6 – The Infinite Extent), they describe a warp drive where time dilation is “reversed” compared to regular space travel.

Naively plotting this, we get a time dilation that looks something like this:

(In the book they give us enough data points to estimate the function, but it’s not important here)

Let’s see if we can put together a physics model that seems plausible. We have discontinuity at v=c, so we aren’t going to find a ‘nice’ formula, instead it’s going to have a phase transition. So perhaps something like:

BUT:

• It’s hard to justify any of these options. They aren’t “pretty”
• It’s not even clear what “v” is (at least to me). I’m not sure if you could define it nicely.
• They have the huge problem that they break causality. You could go back in time and kill yourself as a baby.

To fix, we really need a “preferred frame of reference”. We could say that there really is a true “rest frame”, for example the rest frame for the Cosmic Microwave Background.

Leaving known physics behind, this makes for a natural “preferred frame of reference“, and we could hypothesize that all Warp travel was in reference to this frame. So when you say “Warp 3”, you’re specifying your speed relative to this preferred frame of reference.

With this, we need to throw away the suggested possible formulas for v > c.

But then where on earth do we start? Let’s just consider what would be “pretty” – often a handy guide in physics:

• Assume there is a true “at rest” frame of reference (e.g. CMB)
• We need a ‘phase’ transition. Something must jarringly happen when switching from below c to above c.
• Examples seen elsewhere is the spin of an electron. It can spin up, or it can spin down. There’s no smooth transition. It’s either one or the other.
• Nature loves symmetries. Here we want a ℤ_2 symmetry – i.e. we want to say that all the laws of physics remain unchanged when switching to warp, if we also changed something else. If we changed both of these things (whatever that “something else” is) then we’d have no way of knowing that we’re in warp, and everyone going below warp would look like *they* are the ones in warp. A real physics example is if someone was going backwards in time AND you made the charges flip (e.g. electrons were positively charged) AND you mirorred everything, then everything would look exactly the same. A person in such a universe would not know they are in the “backwards time” universe (https://en.wikipedia.org/wiki/CPT_symmetry)

So, enforcing a symmetry, let’s say:

χ = ln v/c

And then instead of making up random formulas for what warp could be, we say it looks like -χ

Then we get:

This is beautifully symmetry, but our time dilation for v > c doesn’t match the books where we want a dilation of 1. Lets adjust slightly:

Okay, we’ve got a mathematical symmetry, and this gives us a nice match to the books…. except our ship would explode, because in the ‘warp phase’ all the laws of physics are broken. What we really want is the warp phase to be completely normal for people inside. i.e. we want the laws of physics to appear unchanged. Which means that if you ‘warped’ in the warp phase, that would be the same as unwarping. And everyone unwarped would appear warped to you!

Let’s insist that the laws of physics remain the same. We need to break from the standard model to do this, by defining using some “cosmic time” instead of time – e.g. the time that someone at rest relative to the CMB would measure.

Okay, this is nice. But it does deviate from the standard model. That means we could detect whether we are in this universe where we can warp. The different is really subtle, but measureable.

We move at 300 km/s relative to the CMB. So β=cv​≈0.001234, so dT/dτ​=1−β2​≈0.9999992384, so all our clocks we would running slightly too slow. We’d lose 68 milliseconds a day. Which is pretty huge.

Now by itself, we couldn’t detect this. After all, all the clocks would be moving slower, so how would you tell? The problem is when you have things moving. For example, GPS satellites moving at 3.9 km/s would drift by 1.4ms per day, meaning that our GPS would give you the wrong location by c * 1.4ms = 420km.

So.. can we state that we DON’T live in a Bobiverse universe where we could build drives that do usable warp?

Yes. Unless you like ugliness in your physics equations.

(I kid, I doubt I’ve even scratched the surface. I’m already out of my depth).

Symmetry Breaking

I did assume that physics while ‘warping’ was the same. What if it was almost the same, but not quite?

This is what’s called symmetry breaking. We possibly see this in our real universe. E.g. Why is there more matter than anti-matter? Our physics standard model says that there’s a symmetry, so should have the same amount of both. Yet we don’t observe that, and we aren’t sure why.

Another real example is that:

In 2002 Oscar Greenberg proved that, with reasonable assumptions, CPT violation implies the breaking of Lorentz symmetry.
— https://en.wikipedia.org/wiki/CPT_symmetry

So we do know that our really beautiful symmetries don’t completely mesh with each other, even though we can’t find where or how.

Maybe CPT symmetry is actually CPTW symmetry, where W means Warp, and all the anti-matter is warping around.