0
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ I am just now reading Rovelli's "The Order of Time". On page 134, he says "One (variable) does not vary: the total amount of energy in an isolated system. ... knowing what the energy of a system may be... is the same as knowing how time flows because the equations of evolution in time follow from the form of it's energy." I believe that this helps to answer my question above, but I'm still going to have to figure out how something that does not vary (total energy in a system) can have any relation to time. Intuitively it seems the exact opposite. $\endgroup$ – foolishmuse Oct 17 '18 at 17:09
1
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ The curvature of spacetime normally can be represented by the potential gravitational energy, so the Noether theorem holds and energy is conserved. For example, the Earth rotating around the Sun in a curved spacetime doesn't break energy conservation. In cases where the curvature is dynamic and the process is irreversible, it is hard to introduce the potential energy in a meaningful way. For example, we say that energy is lost to the redshift in the expanding universe, because we don't account for the potential energy of the expansion. Although there is no redshift in the frame of the emitter. $\endgroup$ – safesphere Aug 31 '18 at 17:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.