Understanding Conservation of Energy: Time vs Distance vs Position

[pivoxa15]

Conservation of energy => energy does not change wrt time

But does it also imply energy does not change wrt distance or position as well?

In the definition they only specify wrt time.

 

[londonrulz]

Conservation of energy => energy does not change wrt time

But does it also imply energy does not change wrt distance or position as well?

In the definition they only specify wrt time.

It would take atleast some time to change distance or position anyway!

 

[neutrino]

Do you have any examples in mind where you think total energy may change with distance/position?

 

[marlon]

Conservation of energy => energy does not change wrt time

But does it also imply energy does not change wrt distance or position as well?

In the definition they only specify wrt time.

Conservation of energy means, err, conservation of energy. So, the energy value of your classical system does NOT change at all. That's it.

marlon

 

[daniel_i_l]

What do you mean by "change with time" or "change with position"? The total energy in a system is constant over time, but the energy can move around the system, is that what you mean?

 

[MaWM]

Conservation of energy says that the total energy of a closed system does not change in time. If the "closed system" is spatially constrained (and many real world systems are), then the energy will always be spatially constrained as well. However, the energy is free to move around within the confines of the system as it sees fit. Clearly, if energy was always constant at every point in space, the universe would be entirely without motion. (And a preferred frame of rest would be created, but that's going a bit afield.)

 

[pivoxa15]

Lets take a system. The only way a system can change is wrt time. Correct? If it can change wrt distance than it is not a system but a subsystem. And we can extend it to a whole system. Hence by ensuring the total energy does not change wrt time we have guranteed conservation of energy.

The issue arose actually in QM when d<H>/dt=0 <=> energy conservation
where H is the Hamiltonian operator.

So time is a varible that is omnipresent in any system? Or is it just in QM that the system change wrt time only.

 

[pivoxa15]

In my textbook it states, QM adopts the broader interpretation of a conserved quantity as one whose average value does not change over time, no matter what may be the initial state of the system.

So I infer that in the conserved classical system the value at all times do not change.

Hence time seems to matter in the conservation of energy. So does space as well?

 

[Danger]

As long as the space is all within your 'system', no. There are a couple of things that (in my opinion) can mess up the general statement.
First, remember that mass and energy are interchangeable. Something like anti-particle interactions can increase the energy content... at the cost of decreased mass. Mass/energy is conserved. Second, the energy density will definitely change with varying volume of the 'system' due to the inverse square law. Third, most practical systems are not actually closed because of losses to the 'outside'.