So when people say: 'I am approaching the speed of light, and to get to 100% light I would need infinite energy' they are essentially saying that this situation is impossible?
Yes.
I read this in Hawking's book and confused me because I assume when he says 99.9% speed of light, he means 99.9% speed of light in relation to someone outside observing?
Yes, but note that $c$ is a universal constant. If something is traveling at the speed of light, it is traveling at the speed of light to everyone (except other photons traveling parallel, see my answer to this question).
I just cannot understand this notion of needing more and more energy to get closer to light as absolute velocity does not exist? (in that it is a purely relative concept).
It boils to relativity. The energy of a particle is related to the velocity, $v$, via the relation
$$
E=\gamma mc^2=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}
$$
As $v\to c$, $E\to\infty$, but gives an indeterminate operation at $v=c$.
Surely the ability to accelerate further cannot possible be impeded because speed is all relative, there should be no limit to acceleration? If I 'accelerate' a further 50MPH, will I get to the destination exactly 50 miles early?
(a) 50 mph is a speed, not an acceleration and (b) you can't get somewhere "50 miles early." If your trip is 300 miles, you can't get there in 250 miles. You can get there in a shorter amount of time.
From what I can gather you 'can' accelerate FTL (sort off) but instead space bends towards you so you will get to your destination 'ftl' but only due to the curvature in space? So in effect, you can go light years in seconds (lets forget the practicals for a second), but from anyone observing, this will ALWAYS take light years.
The 2nd postulate of special relativity states that $c$ is invariant of reference frame (constant for everyone), so nothing can accelerate to speeds faster than light.
Also, if for me I am going 'FTL', does outside observers see me as going light speed, or is it 99.999%.. is there a specific number?
Faster than light means that you have a speed $v>c=2.9979\times10^{10}$ cm/s. If you have done this, then kinematics suggest you have a complex velocity (as in the imaginary number complex) which is utter nonsense since velocity is a physical (real) quantity.
Further to Timaeus's Answer, the second postulate follows from the first postulate if we know about light. Otherwise, the second cannot follow from the first in a strict sense.
However, even if you don't know about light, there is still a way whereby the second postulate can be strongly motivated by the first, as follows.
The first postulate is essentially Galileo's notion of relativity as explained by his Allegory of Salviati's Ship.
If you assume:
- The first relativity postulate; and
- A concept of absolute time, i.e. that the time delay between two events will be measure to be the same for all inertial observers; and
- Homogeneity of space and time so that linear transformation laws between inertial frames are implied (see footnote)
Then these three assumptions alone uniquely define Galilean Relativity.
However, if you ask yourself "what happens to Galileo's relativity if we relax the assumption of absolute time" but we keep 1. and 3. above, then instead we find that a whole family of Lorentz transformations, each parametrised by a parameter $c$, are possible. Galilean relativity is the limiting member of this family as $c\to\infty$. The study of this question was essentially Einstein's contribution to special relativity. You can think of it as Galileo's relativity with the added possibility of an observer-dependent time. I say more about this approach to special relativity in my answer to the Physics SE Question "What's so special about the speed of light?".
It follows from this analysis that if our Universe has a finite value of $c$, then something moving at this speed will be measured to have this speed by all inertial observers. However, there is nothing in the above argument to suggest that there actually is something that moves at this speed, although we could still measure $c$ if we can have two inertial frames moving relative to each other at an appreciable fraction of $c$. It becomes a purely experimental question as to whether there is anything whose speed transforms in this striking way.
Of course, the Michelson Morley experiment did find something with this striking transformation law.
Footnote: The homogeneity of space postulate implies the transformations act linearly on spacetime co-ordinates, as discussed by Joshphysic's answer to the Physics SE question "Homogeneity of space implies linearity of Lorentz transformations". Another beautiful write-up of the fact of linearity's following from homogeneity assumptions is Mark H's answer to the Physics SE question "Why do we write the lengths in the following way? Question about Lorentz transformation".
Best Answer
To understand this you need to understand what we mean by speed.
If I want to measure positions and times I need to set up a coordinate system. For example I can take my stopwatch and my metre rule and construct some Cartesian axes $t$, $x$, $y$ and $z$, then I can describe every point in spacetime by its position in my coordinates $(t,x,y,z)$. Once I have done this I can calculate the velocity of some object by watching how its position measured using my coordinates changes with the time measured using my coordinates. So for example if something is moving along my $x$ axis the speed is just:
$$ v = \frac{dx}{dt} $$
All very well, but why did I repeatedly use the phrase measured using my coordinates in the paragraph above? Well, it's because my coordinate system is just one way of measuring out spacetime and it doesn't necessarily have any fundamental physical significance. That means the speeds determined by my coordinates don't necessarily have any fundamental physical significance either.
To look into this a bit farther let's stick to flat spacetime so we don't have the complications introduced by general relativity. The obvious coordinates to choose are those of an inertial frame, and you'll meet the phrase inertial frame over and over again in studying relativity. In these coordinates the speed of light is always $c$.
But now suppose I'm accelerating with some acceleration $a$. There's nothing to stop me choosing coordinates where I remain at the origin i.e. I measure all distances and times relative to me. This would be a non-inertial frame, and as you'd expect if I use a non-inertial frame all sorts of weird things can happen e.g. Newton's laws no longer apply.
To make this concrete suppose I am accelerating along the $x$ axis and I measure the velocity of a light beam travelling along the $x$ axis using my non-inertial coordinates. I get the result:
$$ v_\text{light} = c\,\left(1 + \frac{a}{c^2}x \right) \tag{1} $$
I won't go thorough the derivation, but the accelerating coordinates are known as Rindler coordinates and the speed of light is calculated using an equation called the Rindler metric.
Anyhow, what I find is that the velocity of light now changes with the distance along the $x$ axis away from me. When the product $ax$ is positive (i.e. ahead of me) the velocity of light is greater than $c$ and when $ax$ is negative (behind me) the velocity of light is than than $c$. In fact when $ax = -c^2$ the velocity of the light slows to zero and there is an event horizon there (called the Rindler horizon).
But it's the same light in the same spacetime, just described using two different sets of coordinates. So what then is the real speed of the light. And here we reach the key point: there is no real speed. Relativity tells us that any set of coordinates is as valid as any other set of coordinates - you cannot say the inertial coordinates are right and the accelerating coordinates are wrong because they are equally valid ways of describing the same spacetime.
There is one last point to make. Suppose we take my equation (1) for the speed in the accelerating coordinates and calculate the speed at my position i.e. at $x=0$. The value is:
$$ v_\text{light} = c\,\left(1 + \frac{a}{c^2}\,0 \right) = c $$
So even though the speed of light is variable, at my position the speed is equal to $c$. And this is another absolutely key point: although the speed of light may vary in some coordinate systems, if you measure the speed of light at your position you will always get the value $c$. So the speed of light is always locally constant, it's just not globally constant.