Howdy, This is my first post. Please be gentle. ;-) I have been thinking about the speed of light. Scenario 1: I'm on a train travelling at the speed of light. Everything in the train immediately about me appears normal. The reflection in the windows, looking down at myself, indeed anything locally around me. However, outside the train things are different relative to the observer. This I accept. Now, were I to run along inside the train carriage at 10mph, I would be running precisely 10mph within the train - not lightspeed + 10mph. So my questions are: - Would an observer see the train travelling at the speed of light with me running an additionally fast 10mph? - Were I to run and jump out of the train, would I then be travelling at lightspeed+10mph? The e=mc^{2} seems to be to be spot on if related to the speed at which information travel or can be transmitted. So as long as this is not violated then, space can expand faster then the speed of light for instance. Scenario 2: I understand that as I travel ever faster toward the speed of light, the energy required to get me there becomes infinite because my mass also becomes infinite. Is my mass a result of other gravitational bodies? Is there a measurable increase with the shuttle and its ohms burns? In my mind, if I kept applying that ohms burn, eventually I would get faster and faster, but why would my mass increase with no other influences? All thoughts welcome. :) Thanks, Adam
Since you cannot travel at c, your question makes no sense. Were you travel CLOSE to the speed of light and add another speed to it, as you described, they do NOT "add" in the way you think. Look up "relativistic speed addition" Since, as you assumed, this topic has been discussed here approximately 14,138 times, why not do a forum search?
Your mass does not change as you increase in speed. You can see this by using the full form of Einstein's equation. I'd type it in, but I'm on my phone and cannot. However, the equation includes a term for momentum on the right side so that the energy of an object depends on both the mass and the momentum. So while mass stays the same as you increase in speed, momentum increases, which means total energy increases without any need for mass to change.
To add to what Drakkith said, consider this: all motion is relative so talking about it only makes sense by defining the frame of reference that you are using. BUT ... regardless of what frame of reference you use, YOU are always in your own frame of reference. It then follows that according to the guy standing next to you, you are not moving at all and according to an accelerated particle at CERN, you are moving at almost the speed of light. SO ... according to your understanding, the guy next to you is convinced that your mass is the same amount that you think it is whereas the particle thinks you have a HUGE mass. How could they both be right in any absolute sense? Do you feel any more massive just because the particle thinks you are?
The correct formula to add a passengers speed (relative to the train) [itex]v_{relative}[/itex] to the speed of the train [itex]v_{train}[/itex] to find its speed relative to the ground [itex]v_{passenger}[/itex] , assuming both passenger and train are moving in the same direction, is [tex]v_{passenger}=\frac{v_{relative} + v_{train}}{1+\frac{v_{relative}\times v_{train}}{c^2}},[/tex] where c is the speed of light.