If you were put off Bernard by his views about time dilation, you will also be put of about mine. Time dilation, length contraction and mass increase are all illusions cause by the finite speed of light not being taken account of. This is from my web page :-

http://myweb.tiscali.co.uk/carmam/Hollings.html#lorentz
Imagine now a space rocket, which is propelled by ejecting a small amount of matter (the rocket exhaust) at high speed from the rear, so imparting a thrust in the opposite direction. We will assume that the exhaust velocity is 3,000 m/s and the mass of the rocket is 30,000 Kg (very similar to NASA's Mercury-Redstone rockets). Now we can use the Lorentz transformation to find the new mass. The velocity between exhaust and rocket is 3000 m/s, so :-

m = m0 / sqrt( 1 - ( v / c )^2)

m = mass of rocket at velocity v as measured by the essential observer

(Remember that Einstein's observer, properly called the essential observer, is always at rest relative to the motive force. In this example therefore, the essential observer is in the same frame as the rocket exhaust).

m0 = 30,000 Kg (proper mass of rocket or rest mass when v = 0)

v = 3,000 m/s - rocket's velocity relative to the exhaust

c = 300,000,000 m/s

m = 30000 / sqrt( 1 - (3000 / 3e8)^2) = 30000.0000015000000001125 Kg

The mass increase is therefore 0.0000015 Kg or 0.0015 gram which is simply not measurable compared to 30,000 kilograms. For all intents and purposes the mass increase is zero. A further point to note here is that the mass increase is measured against the exhaust which is providing the motive force, and no matter what the velocity of the rocket when measured against its starting point (or anything else for that matter), the velocity between rocket and exhaust never changes, so the rocket mass is always 30,000.0000015 Kg (disregarding the loss of mass due to fuel used). In other words, the mass is fixed at 30,000.0000015 Kg for the values used above between rocket and exhaust, and the extra 0.0000015 Kg is an insignificant amount. As there is no significant mass increase with velocity, and certainly no accumulative mass increase, there is no theoretical upper limit to the velocity of the rocket.

It therefore follows that as the mass increase is virtually zero, m approximates very closely to m0. If the acceleration is regulated to 1g for the comfort of the crew, the space ship can reach an enormous velocity, and time on this space ship will pass at exactly the same rate as back at home on earth. "The effects of gravity are indistinguishable from the effects of acceleration" [AE] (with the qualification in section 5).

I know that relativists would say that the mass increase has to be measured relative to the starting point of the rocket, but why is that? Einstein used the (essential) observer against which to measure the mass increase, with the tacit assumption that the starting point was where the propulsion unit was located, as in a particle accelerator. With that assumption, it is reasonable to refer the mass increase to the starting point. If we assume the propulsion unit (rocket motor) is remote from the rocket, then it is perfectly true that the rocket cannot exceed the speed of the rocket exhaust, as a particle in a particle accelerator cannot exceed c.

This is analogous to a space vehicle which uses light sails for propulsion. The sails are deployed in the vicinity of a star (the sun), and the light hitting the sails imparts a tiny acceleration away from the sun. This acceleration will propel the vehicle away from the sun, and the velocity will gradually but steadily increase. As the vehicle approaches light speed however, the energy from the light striking the sails gets less and less, and the acceleration gets less and less.

Quote from "Begin The Adventure" by Homer Tilton and Florentin Smarandache.

"A sailing vehicle which depends on light from the sun to accelerate it remains in that way connnected to the sun, its reference is the sun, and its speed is limited to less than the speed of light c, relative to the sun. Propulsive energy cannot reach a vehicle traveling away from the sun faster than that. It is limited to the speed of light for the same reason that a cablecar is limited to the speed of the cable pulling it."

Tom.