What does "4D + 1" mean?
The shorthand "4D + 1" can be confusing, but it is simply an informal way of saying "4‑dimensional spacetime plus 1 extra spatial dimension." The result of this addition is a 5‑dimensional spacetime.
Breaking it down
When physicists discuss dimensions, they almost always refer to spacetime dimensions—the combined number of spatial dimensions plus the dimension of time. Our everyday experience is of a universe with 3 spatial dimensions (up/down, left/right, forward/backward) and 1 time dimension. This is correctly called 4‑dimensional spacetime, often written as (3+1) dimensions, and informally referred to as "4D."
The original Kaluza‑Klein theory proposes adding one additional spatial dimension to our familiar three. Therefore, we start with the familiar 4D spacetime (3 space + 1 time) and add one extra spatial dimension. The mathematics becomes: (3 spatial + 1 time) + 1 extra spatial = (4 spatial + 1 time). A universe with 4 spatial dimensions and 1 time dimension has a total of 5 dimensions, correctly called 5‑dimensional spacetime or simply "5D."
Thus, when the previous explanation used the phrase "4D + 1 graviton," it meant: the graviton existing in the full 5‑dimensional spacetime (which is our 4D spacetime plus one extra spatial dimension). When observed from the perspective of our familiar 4‑dimensional spacetime, that single 5D object appears to split into multiple particles.
Summary of dimensional terminology
The following table clarifies how these terms relate to one another:
| Phrase Used | What it Represents | Total Spatial Dimensions | Total Spacetime Dimensions |
|---|---|---|---|
| 4D | Our familiar spacetime | 3 | 4 (3 Space + 1 Time) |
| 4D + 1 (extra space) | Our spacetime plus one extra spatial dimension | 4 | 5 (4 Space + 1 Time) |
| 5D | The resulting 5‑dimensional spacetime | 4 | 5 (4 Space + 1 Time) |
In short, "4D + 1" is a convenient shorthand for building a 5‑dimensional world from our familiar 4‑dimensional one by adding one extra dimension of space.
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