Where is point zero in the universe? At what velocity are we relative to point zero? In which direction do we accelerate to increase our velocity? How close are we to the speed of light? Is this theoreticly even possible to calculate? Maybe the speed of light is not that far away relative to point zero?

Hi Erich.

Your questions are a bit off topic, but good ones nevertheless. In order not to deviate too far from the topic of this thread (relativistic acceleration), I have replied to your questions in a new FAQ thread in this Blog. Click this link to read.

So essentially Mass and Force are constant, but Acceleration is relativistic. So given the equation F=ma, the acceleration decreases as velocity approaches the speed of light for a constant force and mass. This is why objects with mass can't reach c. So what is the physical interpretation of the smaller acceleration? Where does the energy go that ordinarily would have gone into kinetic energy 1/2MV²?

Quote: "So essentially Mass and Force are constant, but Acceleration is relativistic…. Where does the energy go that ordinarily would have gone into kinetic energy 1/2MV^2?"

The energy still goes into kinetic energy, but just with a different equation, i.e., KE = mc^2/sqrt[1-(v/c)^2]-mc^2, where mc^2 is the rest energy. It is easy to verify that if v << c, then KE ~ ½ mv^2. However, if v tends to c, then KE tends to infinity.

In relativity, it's the total energy, which is loosely speaking: rest energy + kinetic energy + thermal energy + pressure energy, etc. that causes inertia and not just the mass.

I realize this question might not make sense, but why should it be that it takes more energy to accelerate an object the faster it's moving? I know you're right and the equation you've put there is correct (relativistic energy), but I from a qualitative understanding I'm lost.

I picture someone using energy to accelerate an object from rest to close to the speed of light. The object is then left alone and allowed to travel at this speed for a while and then energy is used to bring the object to rest.

Using that equation you gave seems to indicate that it took more energy to accelerate the object than it did to decelerate it. So was energy lost?

Hi Roger,

Apart from energy lost due to drag, inefficiencies, etc., it takes the same amount of energy to stop a relativistic particle than it took to accelerate it, provided we are talking about both in the same inertial frame. Although it's old-fashioned, the easiest way to get to grips with this is the 'moving mass' that increases with velocity and decreases again under braking.

The more correct view is that the relativistic kinetic energy increases and that one can use that energy when you stop the mass. They do this in particle accelerators to achieve (and use) the kinetic energy in collisions to make other fundamental particles.

Then there is an unorthodox view (don't tell a scientist I said this). The speed limit "c" is just a measurement limitation and in reality the particle just keeps on accelerating, but we are unable to measure that. Scientists have a term for this 'speed': they call it 'rapidity' and it can approach infinity, because light's rapidity is infinite.

AFAIK, rapidity cannot be used directly in ½mc² to calculate kinetic energy. The one beauty of it is that it can be added together linearly!