Special relativity from different angle

[exponent137]

If we accelerate one body with mass m0 on a distance dx, then, we need energy dW:
dW = a m0 dx = dv/dt m dx = m0 dv v
Energy dW, which we gives weight dW= dm c^2
If we put this in differential equation, solvation is
dm/m0 = v dv /c^2
and
(m/m0)=exp(v^2/(2c^2))
But this calculation does not give that m is infinity at v = c.

What failing to my calculation?

(I know normal derivation of special relativity equation)

 

[pervect]

You are assuming that in SR, F=ma, where m is the 'relativistic mass'.

This formula is fundmanetally wrong. See for instance

https://www.physicsforums.com/showpost.php?p=687759&postcount=71

Careful here. At relativistic speeds, F no longer equals ma, even if you replace m by the "relativistic mass". Assuming that the force and acceleration are in the same direction as the object's velocity, and that the acceleration a is that measured by an inertial observer who measures the object to be moving at speed v, the relationship would be:
$$F = m \gamma^3 a$$
where m is the usual invariant ("rest") mass. ($m \gamma^3$ is sometimes called the longitudinal mass.)

You can also take a look at http://www.math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

in the addendum "what is the relativistic version of F=ma"

 

[exponent137]

I found another formula for relativistic mass which works:
c^2 dm = m v dv gama^-2
where
gama=(1-(v/c)^2)^-1/2

The result is m = gama m0
Where m0 is mass at v=0.
This give the same formula of relativistic mass in longitudinal direction as in horizontal direction. This gives hint that absolute explanation is possible. This means slower time-run in rocket which moves very fast is consequence of larger mass in rocket and so means that we see mans in rocket moving slow. But how to explain that peoples in rocket see us that our clock run slow?

I understand that two main postulates of relativity,
1.speed of light is the same in every inertial system
2. All system are equally valid.
But one explanation should to exist, if we suppose that our system is privileged. Suppositions are more involved than with points 1 and 2, but some explanation should to exist.

 

[exponent137]

Above mentioned relativistic mass (longitudinal = transverzal) is useful, because it is alternative explanation for time dilatation:
Because mass is larger, everything is moving slower and this gives slower time running.
But how this concept explain that someone in moving rocket see time dilatation on earth?
I suppose that that classical special relativity is only the most simple view on special relativity, but it is not the only one.


P.S
I think that this question of beginners, but thread was moved.