Thursday, 22 March 2012

Warp drives and reality: new hope for a Galactic Empire?

Very quick post today, but an article on our warp drive paper has been published in The Conversation. It's called "Warp drives and reality: new hope for a Galactic Empire?" Here's a taster:

Fans of science fiction must be disheartened when introduced to Einstein’s Special Theory of Relativity. Dreams of galactic empires, criss-crossed by roguish princesses and beautiful smugglers, go out the window with one simple rule: “thou shalt not travel faster than the speed of light”.
Even a rocket ship travelling just under the speed of light (roughly 1 billion km/h) would take more than 100,000 years to get from one side of the Milky Way to the other. That’s slightly longer than the fraction of a second required to traverse galaxies in science fiction staples such as Star Wars.

Thursday, 15 March 2012

The Event Horizon

Event Horizon was a somewhat dodgy sci-fi-horror movie that came out in the late 1990s. As the title suggests, associated with an Event Horizon is "Infinite Space, Infinite Terror". Luckily, the Event Horizon in the film as a black hole Event Horizon, and I'll leave discussing those to another time. Today, we'll try and understand the Cosmological Event Horizons.

To explain these, I am shamelessly going to use the (still) excellent cosmological figures produced by Tamara Davis. OK, let's start with this one.
To understand what this picture is telling us, we need to remember a few things. Our universe has three spatial dimensions, and any spatial point can be labelled with three numbers. In a Cartesian coordinate system, these are (x,y,z). As we are dealing with relativity, we are dealing with not only space, but space-time, and every point in the universe is labelled by 4 numbers, the three spatial coordinates and the time, t. So, every point is labelled as (t,x,y,z), and these points are called an Event.

The picture above is the evolution of our universe, the ΛCDM cosmological model, and has distance on the x-axis and time on the y-axis. The universe began at a finite time in the past (the Big Bang) and shows us (the vertical line in the centre) and other objects in the universe. At the Big Bang, distances between us and any other object is zero, and as the universe expands, objects move away from us.

The purple is the Hubble Sphere that we discussed last time. The question is, what are those other lines on there - the event horizon and the particle horizon? To answer this, we need to do a bit of mathemagic.

We need to note a couple of things. Firstly, the first picture is not the complete story, as we know that, if our current cosmology is correct, then while it was born a finite time in the past, it's going to last for ever. So really the first figure goes on for ever also.  But we can fix that and come to it in a moment.

The x-axis actually shows "physical distance". Now, the proper distance is the multiplication of the Scale Factor (which depends on time and changes as the universe evolves) and what's known as the Comoving Coordinates (which, for any individual galaxy, are fixed values).

The Scale Factor's evolution depends upon what the universe is made of, and here's a few some people made earlier
The things to see here that now is at t=0, and the scale factor was smaller in the past (things were closer together) and at some time way-back-when the scale factor was zero (the Big Bang). If we divide out the Scale Factor (so each galaxy has only its fixed comoving coordinates) we get the following picture

What are we going to do about the time axis? There is some mathemagic we can do with that also. But what, as we know that the eventual age of the universe stretches off to infinity. I'm not going to go through the gory mathematical details, but we are going to switch from the normal cosmological time to what is known as Conformal Time. For our particular universe, the cool think is that the infinite age of the universe is mapped onto a fine conformal time.

This can give you a bit of a headache, but we know lots of functions that can map the infinite onto the finite (and mathematicians, don't complain about the terminology here :), such as tanh(x). So, when we look at our universe in terms of comoving coordinate and conformal time, we get the following
Remember, in terms of time, this is the entire history of the Universe, from Big Bang to infinite future, all on one piece of paper.

Now, the cool thing, the really cool think with these coordinates is that light rays travel at 45 degrees, not at the crazy curves we see above, and we see that our event horizon is made of such straight lines, meeting at where we head into the finite conformal infinity.

So, where does this get us? Well, the event horizon forms a triangle, separating events which are inside the triangle from those outside. Remembering that light rays travel at 45 degrees on this picture, and sit down with a pencil and a ruler, what you can see what this separation of events means.

If we pick an event within the triangle (remember, this is just a dot on this page) we can draw a light ray (travelling at 45 degrees) which hits us at the origin, somewhere between the Big Bang and the infinite future.

But if we choose an event outside of the event horizon and draw another light ray heading towards us, we will see that it will not be able to cross our path between the Big Bang and infinite future.

So, this means that the event horizon separates events from those that can ever send us a signal (i.e. we can see at some point in our history) from those that can't. The proper way of saying this is that the event horizon separates events into those that can have Causal Contact with us, from those that cannot.

This might seem weird, as if you think of a distant galaxy sending our light to us from a finite distance away, then, giving the fact that the universe will be infinitely old, we must receive the light at some point? But no, because the photon is battling the expansion of the universe, and may not win and we may never see it.

There is a flip side to this and if we take the above figure and extend the red light (our light cone) to the top of the picture, we can see something quite interesting. If we set off in a standard rocket, we can never travel faster than light, and so will be always within the future red triangle. What this means is that even though we have an infinite amount of time left to play in the universe, we can only explore this finite patch (as thing we are trying to get to are being pulled away from us by the cosmic expansion).

In fact, the longer we leave it, the less and less volume there is to explore! So we'd better head off right away if we are going to see anything!

Saturday, 3 March 2012

How does the Hubble Sphere limit our view of the Universe?

Well, this caps of a busy, but successful week, but Pim van Oirschot (PhD student in the Netherlands, was my MSc student here in Australia a couple of years ago) and I just had a paper accepted for publication. It's called "How does the Hubble Sphere limit our view of the Universe?" and is basically a response to some other papers published over the last years.

Let's start with the basics, as in what is the Hubble Sphere? For gory details, I recommend the classic paper by Ed Harrison, but simply put, the Hubble Sphere is the distance from us which objects are moving (relative to us) at the speed of light.

We know the Universe is expanding, and that expansion is measured in terms of the Hubble Constant, which is about 72 km/s/Mpc. What this means is objects 1Mpc away are moving away from us at 72km/s, those at 10Mpc are moving at 720km/s, 100Mpc at  7200km/s etc etc. So, if you go far enough, objects will be traveling at the speed of light, and then even further go faster than the speed of light.

This often freaks people out, basically because people get taught special relativity first, with the mantra of "you can't travel faster than light", and then don't know how to understand this statement in terms of the curved space-time of general relativity.

I grabbed the above picture from Tamara Davis, who wrote an excellent paper on misconceptions in cosmology a few years ago. The important one is the top picture which presents the history of the universe in terms of distance along the bottom and time up the side.

The dotted lines are objects in the universe (i.e. other galaxies) at at the Big Bang the distance between all objects is zero, so they all are at the origin. The Hubble Sphere chops the universe into those objects moving slower than the speed of light (with respect to us) and those moving faster.

The light cone is the path of a light ray from the Big Bang to us today. The thing to note is that the light ray changes directions from moving away from us to be moving towards us at the Hubble Sphere.

Here's my version from my paper;
The dashed line is today, the blue is the distance to the Hubble Sphere, and red are light rays. As you can see, we've gone into the future, to 90 billion years after the Big Bang. As, in the future, we are going to be dominated by dark energy, the Hubble Sphere asymptotes to a fix distance, but light rays still change direction when crossing the Hubble Sphere.

Now, this recent paper says that there is something important about the Hubble Sphere, namely that light rays we receive today have never been out to distances greater than the Hubble Sphere today. This appears to be the case in the above picture.

But the above picture assumes that we have a "cosmological constant" acting as dark energy. If we change the properties of dark energy, namely making it Phantom Energy instead, then something cool happens.

At the start, things look the same, but into the future, the Hubble Sphere actually starts to contract. And as you can see, light rays that we receive in the future will have gone out to a much larger distance than the Hubble Sphere is when the photons are received, showing that the previous claims are not generally true.

We've got a bit of history dealing with some claims about the Hubble Sphere, and I might write about them sometime. For now, I'm going to enjoy another soggy weekend in Sydney.

How does the Hubble Sphere limit our view of the Universe?

Geraint F. Lewis, Pim van Oirschot
It has recently been claimed that the Hubble Sphere represents a previously unknown limit to our view of the universe, with light we detect today coming from a proper distance less than this "Cosmic Horizon" at the present time. By considering the paths of light rays in several cosmologies, we show that this claim is not generally true. In particular, in cosmologies dominated by phantom energy (with an equation of state of \omega < -1) the proper distance to the Hubble Sphere decreases, and light rays can cross it more than once in both directions; such behaviour further diminishes the claim that the Hubble Sphere is a fundamental, but unrecognised, horizon in the universe.

Thursday, 1 March 2012

The Alcubierre Warp Drive: On the Matter of Matter

I think I am over the yearly battering with Australian Research Council Discovery Grants with the grant now submitted. The release is matched with the acceptance of a paper from left-field, and so, to quote Monte Python, "And now for something completely different".

Last year, Brendan McMonigal was an honours student with me, and we took a look at the Alcubierre warp drive, a method to travel globally faster than the speed of light, while being quite happy with Einstein's General Theory of Relativity. This stuff often freaks people out, because they get special relativity beaten into them first, without realizing what this actually means in terms of general relativity.

Whatever other people think, I love General Relativity. What you can do with the universe is actually pretty cool.

So, the warp drive, in hand waving terms, travels at arbitrary speed by messing about with space-time. But what Brendan looked at it the question of what happens to all those particles and photons that get caught up in the warp bubble.

What he found is that as the warp drive sweeps through the universe and collects up all the particles, the ions and lone electrons, and microwave background photons, and whatever else is lying around.

And then when you slow down, they all get released in a burst, which will fry all of the people waiting to meet you. This is not good (not if Nanna has come all the way to meet you at the space port).

You can read more at universetoday, but if you are interested, check out the paper. Well done Brendan!

The Alcubierre Warp Drive: On the matter of matter

Brendan McMonigal, Geraint F. Lewis, Philip O'Byrne
The Alcubierre warp drive allows a spaceship to travel at an arbitrarily large global velocity by deforming the spacetime in a bubble around the spaceship. Little is known about the interactions between massive particles and the Alcubierre warp drive, or the effects of an accelerating or decelerating warp bubble. We examine geodesics representative of the paths of null and massive particles with a range of initial velocities from -c to c interacting with an Alcubierre warp bubble travelling at a range of globally subluminal and superluminal velocities on both constant and variable velocity paths. The key results for null particles match what would be expected of massive test particles as they approach +/- c. The increase in energy for massive and null particles is calculated in terms of v_s, the global ship velocity, and v_p, the initial velocity of the particle with respect to the rest frame of the origin/destination of the ship. Particles with positive v_p obtain extremely high energy and velocity and become "time locked" for the duration of their time in the bubble, experiencing very little proper time between entering and eventually leaving the bubble. When interacting with an accelerating bubble, any particles within the bubble at the time receive a velocity boost that increases or decreases the magnitude of their velocity if the particle is moving towards the front or rear of the bubble respectively. If the bubble is decelerating, the opposite effect is observed. Thus Eulerian matter is unaffected by bubble accelerations/decelerations. The magnitude of the velocity boosts scales with the magnitude of the bubble acceleration/deceleration.