How long does it take the light to get from the Sun to the Earth?
A: No time all. You will hear the answer ‘8 and a half minutes’ but that is from our perspective on Earth. From the perspective of the light, it takes no time at all! So it takes the light no time, be we see it as taking over 8 minutes.
Relativity is that all observations are relative to the perspective of the observer.
The point is that time itself is relative to the observer. Acceleration changes the perspective of an observer, so as an observer changes speed, time changes. For perspective to change significantly, you have to be travelling at incredible speed, as the change is determined by your speed as a fraction of the speed of light. The light itself, in the above example, is actually travelling at infinite speed from the perspective of light. But relativity means time distorts and any observer not also travelling at the speed of light, will observe the light travelling at the fastest speed anything will appear to be travelling at, the speed of light.
Yes, you can go faster than 300,000km/s (lightspeed), it just doesn’t look that way to others.
You may read that the approximately 300,000km/s (the speed of light) is the fastest speed there is. In reality this depends on point of view). You will also read that if you travel fast enough time will pass more slowly and if you travel the over 4 light years to the nearest star fast enough, that although it will still take over 4 years on Earth, only 1 year will pass for you, and fellow travellers. So you would then have travelled over 4 light years in 1 year of your time. If you divide distance travelled by time you get 4 light years per year- or 4x the speed of light at 1,200,000km/s. The trap is that, for someone who stayed back on earth, over 4 years will have passed, so they will see you as having travelled only slightly below the speed of light.
But for you, the traveller, it is possible to start accelerating and just keep on accelerating at constant acceleration with everything appearing normal. You could keep accelerating to 1 times speed of light, 2 times, 4 times and even faster. It is those that do not come for the ride who will see your speed as just getting closer and closer to the speed of light, you never reaching the speed of light.
This is not the deepest analysis, but was produced in response to a specific question.