Heisenberg uncertainty principle at relativistic velocities Would the Heisenberg uncertainty principle, the energy of h-bar in particular, be affected by the Lorentz factor at relativistic velocities from an external pov?
If a rocket were to speed by at relativistic velocities and if we could see inside it, or if we could view the environment close to a black hole, would quantum effects be more pronounced there?
That is to say, would the magnitude of h-bar increase in a similar way that the Lorentz factor increases the magnitude of momentum and kinetic energy at relativistic velocities?
My thought process stems from H bar = 1.054571817×10−34 joules x sec, yet mass and energy are equivalent. So if the Lorentz factor can intensify mass and energy shouldn't H bar be affected as well?
 A: 
Would the Heisenberg uncertainty principle, the energy of h-bar in particular, be affected by the Lorentz factor at relativistic velocities from an external pov?

There is no reason why Planck's constant (in this case the reduced Planck's constant which is just $\frac{h}{2\pi}$) would change even in relativistic velocities. What you mean by the "energy of $\hbar$" is not obvious.

If a rocket were to speed by at relativistic velocities and if we could see inside it, or if we could view the environment close to a black hole, would quantum effects be more pronounced there?

In terms of quantum effects near a black hole, the rate of particle-antiparticle creation and annihilation is increased dramatically near its event horizon. But this is due to the immense gravitational energy caused by the black hole on space-time itself. What this has to do with $\hbar$ is not obvious.

That is to say, would the magnitude of h-bar increase in a similar way that the Lorentz factor increases the magnitude of momentum and kinetic energy at relativistic velocities?

No. There is no reason why $\hbar$ would increase, let alone change in any way.

My thought process stems from H bar = 1.054571817×10−34 joules/sec, yet mass and energy are equivalent. So if the Lorentz factor can intensify mass and energy shouldn't H bar be affected as well?

No. It should not. And $\hbar$ has units $J\cdot sec$ and is referred to as “action”. The mechanism you explain here seems to connect two separate things. The equivalence of mass and energy has no direct bearing (that is obvious to me anyway) on what the value of $\hbar$ is. If you could elaborate on what you mean here in the comments, I would be happy to edit this answer in order to answer your question.
A: Planck constant $h= 6.62607015\times 10^{−34}$ Js (i.e. Joules times second and not Joules per second) in SI units. See here. As such it has the units of action. Although energy transforms as a result of Lorentz transformations, the Planck constant does not. There may be some interesting effects of special relativity (or general relativity) on the uncertainty principles, but as far as we know this does not include a variation in the value of $h$.
