Mass increases with speed so to maintain a constant acceleration the force has to increase to infinity. You can exert a constant force but its acceleration will decrease with velocity.

Acceleration is dv/dt. Velocity is dx/dt. Special relativity says that dx an dt are both adjusted by gamma. As velocity approaches C, dx/dt^2 gets smaller, thus acceleration must reduce. Force is mass times acceleration. Force may constant. As velocity increases, acceleration drops and mass increases by equal factors.

In order to have constant force change in mass compensate with acceleration to fix is constant

I agree with John Moll’s explanation

To address the second question first – surely I can exert a constant force on an object simply by holding it motionless against the force of gravity?
And, consequently surely I could claim that the object was undergoing a constant acceleration of zero? Hmmm…!?

You can exert a constant force on an object, but since F = ma and m increases as the object accelerates, the acceleration will decrease when constant speed is applied.
But ot maintain the constant acceleration we have to increase F (numerically, delta_F/delta_t = m_0 * a^2). Theoretically I don’t see why we can’t achieve constant acceleration this way, but in practise it will take too much force I guess.

As you accelerate away from me you move faster and faster with respect to me. As a result I see your time dilating and so your acceleration diminishes: you see yourself continuing to accelerate with 1 m/s^2 for example but I see your second lasting longer so the amount I see you accelerate in MY second is smaller. There is no need to introduce the concept of relativistic mass to explain this diminished acceleration at higher relative speeds.

Too much force is required to achieve constant acceleration. SRT has add-on concepts, but there seem to be limits.

Even if we conceive in a black hole that it can continue to achieve greater acceleration, these events seemed to have mostly already occured in merger and aquisitions of earlier times of the universe.

Quasar activity involved with black holes chewing apart stars has quieted universally. Not stopped, but remnants are the energy echoes of earlier times.

Constant force continues to make black holes the gravitational centers of universes.

The only way for that to achieve constant acceleration is by mergers and it seems that phase has largely occured and has quieted in the Universe.

LIGO reports and charts many collisions, in incredible science. In younger days of the universe when even the Milky Way grew from 5 collisions, constant acceleration seems to have occured at the Galactic core.

But the grass has been cut. The trees are all pruned, and our quasar activity has ceased into Fermi Bubble remnants.

For black holes to have a constant force, this is possible.

Constant acceleration seems to no longer be possible. Dark energy expansion contradicts this.

If the universe is expanding, we have the constant acceleration in that action of dark energy.

As you accelerate away from me you move faster and faster with respect to me. As a result I see your time dilating and so your acceleration diminishes: you see yourself continuing to accelerate with 1 m/s^2 for example but I see your second lasting longer so the amount I see you accelerate in MY second is smaller. There is no need to introduce the concept of relativistic mass to explain this diminished acceleration at higher relative speeds.

when you apply an even force to an object its speed and mass will remain the same. where as if an object alone is at speed it will be affected by so many other forces drag, gravity, light pressure, etc., etc., the force applied by you keeps ahead of these other forces.

Thanks to Alumni Syed for the clarity of his answer.

My Egyptian friends call themselves Said, spelled differently.

Keep up the great work! The force and energy of Special relativity always need more clarity.

However, are you also familiar with the Law of exponential return, opposite the Diminishing return? 🙂

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