We know that there are only 3 spacial dimensions because if we light a light bulb, we are able to measure the energy at any point in the 3 spacial dimensions and we can see that no energy is leaking into a 4th spacial dimension. Can the same thing be said for the time dimension? If we flash a flash bulb, can we measure the dwindling of energy over time in the same way? Is all the energy accounted for? Or is some of it leaking into another time direction?
It would be possible to measure the amount of energy emanating from the lightbulb over time if desired (a photometer or similar device could be used). As to your question, according to the law of conservation of energy for an isolated system (say, our lightbulb and the area immediately around it), energy is conserved in the system over time. By Noether's theorem, continuous time translation symmetry (which exists in this situation, the local curvature of spacetime is negligible) implies that the energy in this system is conserved. As such, no energy is leaking into another time dimension (we are currently unaware of any additional time dimensions anyhow). The law of conservation of energy is fundamentally defined by the passage (and symmetry) of one time dimension.