What is the 4th dimension in spirituality?

The fourth dimension, which we only guess at is our first. To understand this more easily, think of the simile used of the man who could only walk in two dimensions. We can walk in three, but in the future, there will be four—up, down, across, through. A symbol might be added to the line, the square and the cube—a hollow sphere, with other hollow and smaller spheres enclosed within it, something like the balls within balls cut by the Chinese. These spheres must be thought of, as composed of a kind of elastic fluid—the larger compressed spheres passable through the smaller and the smaller by expansion passable through the larger. Thus, each sphere can be within or without the others. Solid can become fluid, pass through solid and then resume its first form.

This power, when perfected, would give absolute power of progression in every direction and in every part of the Universe. We could pass through the heart of mountains or rise into the atmosphere to any height by altering, as it were, our own density and the density of our path—nothing would prove a hindrance. We have been taught that our world and the next world are not like two globes side by side and independent of each other, but as a spirit inhabits a body, so the next world inhabits ours. To pass from our world to the next requires transition. We cannot pass to the next world, nor the spirit to us, but in very exceptional and partial ways. But there will be a time when the limits of our visible world will be its limits no longer, and from the seen to the unseen, we shall be able to pass with the greatest rapidity and ease. The Son of Man attained to this power for a time and in a limited degree, and there have been prophecies and hints of it at different times, but in future, as easily as our thought passes from place to place, so shall we or those who come after us.

Let us call the fourth dimension interprogression, then the fifth might be called transprogression. 

As we rise from dimension to dimension, our powers are changed and increased in many ways. It is not simply an added power of progression, but an opening of new faculties in many directions. On the other side, there are beings who come over so undeveloped in any higher part that all to which they can attain is the power of passing from place to place without let or hindrance—a kind of animal life. Some linger in the atmosphere of our world, seeking to feed their feeble earthbound souls, and it is from this class that most physical manifestations are obtained—the link that binds their lower nature to earth not being yet broken. These dimensional laws begin very low down in the purely physical, and gradually rise, as the powers of the being are developed and increased. There is no sharp division between the physical and psychical, psychical and spiritual, and again between spiritual and that higher state still which we call Divine.

The sixth dimension begins to enter upon higher ground. 

The first five have to do with space—the next series has to do more directly with time. In the first time-dimension, the experience of the being is that he is no longer limited by time in the way we are—time is neither long or short—a lifetime may be lived through in a moment or a moment may extend to a lifetime—one day is with Him, as a thousand years—or a thousand years, as one day.

Do spirits need to perform any action? 

Time does not bound or hamper them. So the Master produced the wheaten bread in a moment or restored the wasted tissues of the human frame in a few brief seconds—while on other occasions the power seemed to fail Him, and He cried—I have a work to do—and how am I straitened until it be accomplished. This dimension is the normal state for higher spirits.

Next the seventh or second time-dimension. In this the being advances a stage farther—here the limitations of time fall from him more completely than before, for time may be said to have no existence. The past (or what has been called past) to him is the same as the present and only the future lies still closed to him—something of the spirit and power of the Eternal I AM is within him, and he approaches still more nearly the Divine.

Our memory is limited to those ineffaceable marks on the rock of our being made at some period by the waves of our conscious life. But to him this is not so—all things lie within his memory. More than that, they can, in a real manner, unfold themselves before him at his will. This power adds largely to the joy of those higher spheres in which he dwells. This power was hinted at by the Master when He said—

Before Abraham was—I am.

After the time-dimensions come those that belong more directly to the human will, its powers and its limitations.