New Channel and New Video

Just started a random science and maths channel.

May do videos every week.

Depending on how busy I am.

(so don't be surprised if I don't ever upload again :P)

Check out: A very quick intro to Calculus! Will upload a blog post later, expanding on the example given in the video.

Faster than Light Travel - September 2015

Can we ever travel faster than the speed of light?

It is a dream of the greatest physicists of our time as well as the average Joe; space exploration. The incomprehensibly vast distances involved in the universe, ever increasing due to accelerated expansion of spacetime because of dark energy, means that our planet is simply ‘a mote of dust suspended on a sunbeam’, as Carl Sagan put it. The Milky Way galaxy is 100,000 light years in diameter; meaning light would take 100,000 years to travel from one side to another. The fastest space probe so far, the NASA craft Juno, clocks in at 0.0013% the speed of light. Space colonisation seems to be an impossible feat for mankind to achieve.

But why is it impossible? Why can’t we power a spaceship to travel faster than the speed of light in a vacuum? This can actually be explained and proven geometrically using Einstein’s equation:   

E² = (mc² )² + (pc)²

Photons travel at c (the speed of light in a vacuum) as they have virtually no mass and exist as a form of energy (light energy). Therefore, the momentum term of a photon would be theoretically equal to the energy, as mass would be 0, E = pc. As the structure of the equation is like that of Pythagoras’ Theorem, we can draw a triangle with E as the hypotenuse as shown in Figure 1.

As the hypotenuse of a right angled triangle is always greater than the other sides, we can see that as long as there is mass, E cannot equal pc. With no mass the equation collapses to E = pc, as with the photon, and for static objects with no momentum in that reference frame, E = mc², the famous equation we know today.

Even if theoretically a spaceship were to travel at c, it would have adverse effects on time itself. As the laws of physics are supposed to hold true in all reference frames, logical thinking makes you assume nothing would be visible inside the spaceship as light cannot travel fast enough to catch up with your eyes as you recede from it in the spaceship at the speed of light. Einstein deduced that physics should work as normal inside the spaceship; doesn’t that mean the photons inside the ship are travelling at 2c, which violates the laws of physics? Only if space and time are absolutes. The distance between the spaceship walls and your eyes actually shortens (meaning c can remain as a constant as we are considering a smaller distance here, therefore we don’t need to cover the same amount of distance in that time) and you experience ‘time dilation’. The time perceived slows down with your speed, compared to a static observer. At small speeds like <0.1c this effect is too small to notice. However, at high speeds you would age less than your hypothetical twin who decided to not take this superluminal journey. If you perceive 2 minutes passing in a light speed spaceship, for the static observer it could’ve actually been 10 minutes. You could return to Earth and realise centuries have passed, but you haven’t aged much at all. Time dilation poses a serious logistical problem to light speed travel, and we have shown that as long as Einstein’s theories hold true to experiment and testing, an object with mass cannot travel faster than c through spacetime anyway.

Hold on; didn’t we just cover the accelerating expansion of the universe? Even in the Planck era with a second of the Big Bang the universe had expanded to astounding sizes. If this expansion has been accelerating (an observed phenomenon due to red shifts) for 13.8 billion years isn’t spacetime expanding faster than c? Doesn’t this violate the theory of general relativity? Apparently not; spacetime itself can move faster than the speed of light as it isn’t a ‘thing’ in the traditional sense. An apt analogy would be of ants, crawling around a balloon with a speed limit. They move slow, and nothing on the balloon is allowed to travel faster than the ants (the balloon symbolising spacetime), however the balloon itself can inflate very fast increasing the distances between the ants. To an ant on the balloon they would observe other ants receding at ‘faster than ant’ speeds. This concept is important to the question on ‘faster than light’ travel.

A spaceship has mass, and therefore cannot travel through spacetime faster than light as just shown. However, if we could manipulate spacetime, can we get to (for example) Alpha Centauri, the nearest star system at about 4 light years away, within the span of a human lifetime? Two theories currently exist that can help with space exploration and that do not violate the laws of physics.

Wormholes (also known more formally as Einstein-Rosen Bridges) are shortcuts through spacetime. They can connect two places across spacetime so that distances are reduced. Theoretically you could go through a wormhole and get to a place faster than light could get their if it takes the longer, ‘normal’ way. Light travelling with you through a wormhole will obviously reach the end faster as the laws of physics hold true in all reference frames. Figure 2 shows a visualisation of a wormhole.

As space and time are intrinsically connected it is thought that wormholes could allow for time travel as well. Exotic matter with negative energy density is needed to stabilise a wormhole large enough for a spaceship to get through, and this is possible under quantum field theory, however no such mechanism has been found in nature to create wormholes. The quantum foam hypothesis (a candidate for ‘fabric of the universe’) is used to theorise that miniscule, Planck scale (on the orders of magnitude many times smaller than even an electron) wormholes pop into existence and disappear spontaneously. These wormholes are not traversable and are not candidates for ‘faster than light’ travel. It is important to reiterate that none of the methods discussed are truly faster than light, as they involve manipulating spacetime, which can expand faster than light.

The Alcubierre drive, also known colloquially as a theoretical warp drive works on the principle of negative mass and energies, just like wormholes. If we had a lot of power, we could use this drive to expand the space behind a spacecraft and contract the space in front. This constant deformation of spacetime can allow an object to reach a destination faster than light would by travelling through normal space. This is entirely theoretical but it is mathematically consistent; however, it assumes that exotic matter with the correct properties exist. As we have not directly interacted with exotic matter (dark matter, negative mass etc) this theory cannot be confirmed as of yet.

The spaceship would travel in an area of ‘flat’ spacetime known as a warp bubble. The expansion behind and contraction in front is shown in Figure 3.

To change the nature of spacetime with a human invention is incomprehensible for our minds; we use 2D grids to represent the 4D nature of spacetime as we cannot comprehend more than three dimensions. The fourth dimension, time is not understood as readily as the three spatial dimensions. It is hard and counter-intuitive to think that general relativity could allow for time itself to be an observed effect and not a universal constant, that time depends on the speed you’re going at. The Alcubierre drive is such an invention that would require a huge amount of energy as well as a better understanding of exotic matter; scientific milestones that we have yet to attain.

Our understanding of dark matter and dark energy is depressingly poor; current estimates suggest that normal matter and energy, everything we perceive and see in the universe only make up 4 or 5% of the universe. There is hope however as Ray Kurzweil put it, ‘The Law of Accelerating Returns’. As our understanding grows, our capacity for learning even more increases as well, leading to an exponential cycle of understanding, and then discovery. We have seen this in action in recent times; it took only 66 years from the invention of heavier than air flight to get mankind to the moon. Mankind increases knowledge exponentially. The brightest minds of our generation have come up with mathematical frameworks and consistent theories that do not violate any laws of physics, and NASA has already begun exploration and research of Miguel Alcubierre’s theory. Colonisation of the distant stars and galaxies we see twinkling in the night sky may not be such an impossible feat after all.

New Blog

New blog from a perpetually bored Physics student, who finds a bit of pleasure in writing about science to an audience of precisely zero people.

Plenty more to come in a few years when I actually get a degree in Physics...

- Blaze