system
Given the following post, respond as if you're commenting on Reddit:
human
Is energy actually momentum in the time dimension instead in one of the three space dimensions?

The formula for work done on an object is dW = F dx. And F=dp/dt. And work done is energy E measured in joules. So this gives dE dt=dp dx. Doesnt relativity tell us that space and time are similar,( except for a conversionfactor c and a minussign in the invariant spacetime interval). So energy is simply momentum in the time direction.
gpt
Actually kind of yes. In relativity, there's a quantity called 4-momentum, which is a 4D vector consisting of energy and the three components of momentum. Energy is the time-like component.

P^μ = (E/*c*, p^(x), p^(y), p^(z))

There's also four-position:

x^μ = (*c*t, x, y, z),

four-velocity:

u^μ = γ(*c*, v^(x), v^(y), v^(z)) where γ = 1/sqrt(1-(v/c)^(2)) and v^x = dx/dt etc.

and others

Four-vectors obey Lorentz transforms by construction. If you "square" them by multiplying them by themselves and the Minkowski metric matrix (ignoring GR here)

|A^(μ)|^2 = (A^(0))^2 – (A^(1))^2 – (A^(2))^2 – (A^(3))^2

you get a Lorentz-invariant quantity: something that's the same in all reference frames.

The (square root of) this quantity for 4-momentum is called invariant mass:

E^2 – p^(2)*c*^(2) = m^(2)*c*^(4)