[MikeS (OP)]

If space were empty and frictionless then an object could accelerate unimpeded.  Presumably it would take little energy to accelerate an object up to approaching the speed of light. 
Relativity tells us it is not like that.  If more and more energy is required to accelerate the object as light speed is approached then it would seem this must be due to some form of friction in space, space itself being viscous.
The things we know that occupy space are time, gravity, the quantum energy field, photons and neutrinos. 

The question is what is causing this viscosity that makes it difficult for objects to accelerate to near light speed?

[Bored chemist]

Presumably it would take little energy to accelerate an object up to approaching the speed of light. 
No, even without relativity, it would take rather a lot of energy.
" it would seem this must be due to some form of friction in space"
It doesn't seem that way to me.
Since there is, as you say, nothing obvious that can cause this "viscosity" then the effect must be due to something else.

[Geezer]

If the mass remained constant and you continuously applied a small force for a very long time, the object would attain very high speeds. Unfortunately, the mass increases exponentially, so you have to keep increasing the force exponentially to maintain the acceleration. Pretty soon you've used up more energy that the Universe contains to maintain the acceleration.

(That's an an approximation - no doubt some smartypants will point out some serious flaws in my description.)

[damocles]

[/i][/b]

If the mass remained constant and you continuously applied a small force for a very long time, the object would attain very high speeds. Unfortunately, the mass increases exponentially, so you have to keep increasing the force exponentially to maintain the acceleration. Pretty soon you've used up more energy that the Universe contains to maintain the acceleration.

(That's an an approximation - no doubt some smartypants will point out some serious flaws in my description.)

What a challenge! -- all right I will be the smartypants.

The increases in mass and required force are asymptotic, not exponential.

With an exponential increase, any resulting velocity v could be achieved with a finite input of a^v

An asymptotic increase is worse, because the force increases as ac/√(c² − v²), which becomes infinitely large as v approaches c, and meaningless if v exceeds c

[yor_on]

Nice one 

[Geezer]

[/i][/b]

If the mass remained constant and you continuously applied a small force for a very long time, the object would attain very high speeds. Unfortunately, the mass increases exponentially, so you have to keep increasing the force exponentially to maintain the acceleration. Pretty soon you've used up more energy that the Universe contains to maintain the acceleration.

(That's an an approximation - no doubt some smartypants will point out some serious flaws in my description.)

What a challenge! -- all right I will be the smartypants.

The increases in mass and required force are asymptotic, not exponential.

With an exponential increase, any resulting velocity v could be achieved with a finite input of a^v

An asymptotic increase is worse, because the force increases as ac/√(c² − v²), which becomes infinitely large as v approaches c, and meaningless if v exceeds c

Ah right! An obvious slip of the pen.

[MikeS (OP)]

Thank you guys but none of the above answers the question.
To accelerate to light speed requires an asymptotic amount of energy. Why?
Nice word damocles, thanks.

As you approach the speed of light time dilates.
At light speed, time would be infinitely dilated.
An asymptotic amount of energy is requires to accelerate mass up to light speed.
Infinite energy is equivalent to infinite mass (E=mc²)
Infinite mass infinitely dilate time (as in a black hole for example).
So infinite energy is required to infinitely dilate time.

If you are not happy with the term infinity then think a little bit less than light speed.

What do you think?

[Bored chemist]

A little bit less than light speed is perfectly possible. Things like the LHC do it.
And, btw, the word asymptotic describes the way in which the speed approaches, but never quite reaches C. It doesn't mean infinite.