Infinite mass

[JustStuit]

From what I understand as an object aproaches light speed the mass becomes greater? How does this mass change? Can some1 try to explain this to me

thnx

[CPL.Luke]

When someone says your mass gets bigger as you move towards the speed of light they mean your relative mass, this is the value you get when you solve the equation

 

E^2=(mc^2)^2+(pc)^2

 

for E, then plug e into the equation E=mc^2 and solve for mass. Basicly its not the mass changing its the energy (I know someone is going to come and say that energy is the same as mass, but its better to just think of it as energy) the reason that the energy increases is because the momentum (denoted by p) is in the equation, as p increases the energy increases.

[JustStuit]

ok thanks for the info. so its relative mass and energy which increase.

[CPL.Luke]

exactly

[5614]

As you put more and more energy into yourself it makes you heavier (due to the mass=energy thingy)... so one of the problems with going faster than the speed of light is that you'd have a more than infinte mass which you can't do! Also you can't even travel at the speed of light because then you'd have an infinite mass which you can't do either!

[Severian]

Let me explain this yet again.

 

It depends on your definition of mass. The correct definition of mass is the 'm' in E²= m² c⁴+p²c². This mass does not change with velocity and is the same in all inertial frames. It does not approach infinity as we go towards light speed.

 

The bad definition of mass, is [math]|\vec{p}|/|\vec{v}|[/math] (the magnitude of momentum divided by the magnitudes of velocity). This is sometimes used as the definition of mass out of a desire to preserve the Newtonian equation p=mv. If one uses this definition then mass is velocity dependent and will appraoch infinity as we appraoch the speed of light. However, this is a bad definition because it is frame dependent - the mass of the particle depends on who is looking at it!

 

Since [math]p=m_{\rm bad}v=\frac{1}{\sqrt{1-v^2/c^2}}m_{\rm good} v[/math] you can see that it is really the momentum which is becoming infinite as we approach the speed of light. Therefore you need to put an infinite amount of energy and momentum into the particle to make it go at the speed of light, and this is why we can never accelerate any massive object to the speed of light.

[Daecon]

Does a singularity, a zero-dimensional object, technically have an infinite mass? Is density the same as mass in that respect?