On the Conservation of Energy

[JoeyC]

Could energy be created if it was destroyed in the same amounts, simultaneously?
Say you have 5 J of heat energy.
You observe 5 J of heat energy through whatever tool you're using.
But what if that energy was being destroyed and created at the same time?
You still only observe 5 J of heat energy.

Would the reasoning behind the Conservation of Energy allow this?

[Name]

Could energy be created if it was destroyed in the same amounts, simultaneously?
Say you have 5 J of heat energy.
You observe 5 J of heat energy through whatever tool you're using.
But what if that energy was being destroyed and created at the same time?
You still only observe 5 J of heat energy.

Would the reasoning behind the Conservation of Energy allow this?

I think so? From my understanding matter and antimatter particles can spontaneously appear due to quantum fluctuations and instantly annihilate so therefore energy is conserved (this is also how Hawking radiation of black holes work). So I don't think what your saying would violate the conservation of energy. I could be wrong though.

[JoeyC]

Doing some research on this (already having a very basic, very fundamental - AKA enough to know what the theories are but not why- knowledge of quantum physics and virtual particles) this seems to be correct.

Supposedly the 4 fundamental forces don't violate these laws because when their forces (e.g. gravity/EM force) is exerted, the kinetic energy imparted to a particle is made up for by a decrease in potential energy. While these potential energy fields for each force seem a good solution, what about dark matter? How does that work? On that topic, why don't black holes act on dark matter?

[Name]

Doing some research on this (already having a very basic, very fundamental - AKA enough to know what the theories are but not why- knowledge of quantum physics and virtual particles) this seems to be correct.

Supposedly the 4 fundamental forces don't violate these laws because when their forces (e.g. gravity/EM force) is exerted, the kinetic energy imparted to a particle is made up for by a decrease in potential energy. While these potential energy fields for each force seem a good solution, what about dark matter? How does that work? On that topic, why don't black holes act on dark matter?

I'm not 100% sure about what you're asking, but I'll try and answer this. The current accepted cosmological model is ΛCDM, with CDM referring to cold dark matter. CDM interacts extremely weakly with EM force/normal matter, but it should interact the same gravitationally. It played a huge role in galaxy formation because galaxies wouldve coalesced around areas of higher densities, and the gravitational effec6s can be seen today in the rotational curves of galaxies. Dark matter should interact with black holes as well, we simply just cannot see dark matter interacting with bhs.
Also dark matter is still only a theory. Other theories have been proposed (ex modified Newtonian dynamics) although most evidence point to ΛCDM model being correct.
The Astronomy DSO the bullet cluster is a interesting read about dark matter if you're interested.

[PM2017]

Here's another interesting point -- conservation of energy doesn't hold in all situations.

Here's a good video explaining it: https://www.youtube.com/watch?v=cnGYMe6GBeQ
Here's some more on Noether's theorem: https://www.youtube.com/watch?v=04ERSb06dOg

I'm not going to pretend I understand much of this either... :\