Is there a relationship between energy and time? What is it?
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7$\begingroup$ energy is the component of momentum in a time-like direction $\endgroup$– ChristophDec 6, 2014 at 2:32
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3$\begingroup$ According to Noether's theorem, the conservation of energy is a result of the physical laws governing the universe not changing with time (technically, energy is conserved in a any system with a time-translation invariant Lagrangian.) $\endgroup$– jabiraliDec 6, 2014 at 2:45
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$\begingroup$ So without energy, there is no momentum? Therefore time stops??? What is the math or equation behind this? I have only taken mostly classical mechanics from high school and want to try to learn a bit more. $\endgroup$– Chanho BakDec 6, 2014 at 2:49
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$\begingroup$ This question is too broad. One could answer with the time-energy uncertainty relation, with energy conservation through Noether's theorem as jabirali, with the Hamiltonian being the generator of time translations, and surely a host of other, related, but not identical relations. $\endgroup$– ACuriousMind ♦Dec 6, 2014 at 12:53
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$\begingroup$ @ACuriousMind: Sorry, 3 years old, but just a quick question. So yes, all these limited separate relations like the uncertainty principle, the Noether theorem, etc. suggest a universal relation that I call the time-energy symmetry. Something like them being Fourier conjugates. Are you aware of a way to formulate such a universal relation? $\endgroup$– safesphereSep 2, 2017 at 18:32
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4 Answers
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Energy is the name physicists give to the Noether Charge that is conserved when a physical system's description through its Lagrangian is unchanged by time shifts. Or, in more everyday language, most physics does not depend on where one puts the $t=0$ time co-ordinate origin. The laws are invariant when we shift our time origin back and forth. Noether's theorem tells us that there is one conserved quantity (in this case energy) for every continuous symmetry (in this case the continuous displacement of the time origin without effect on the Lagrangian) of a system.
Time shift invariance corresponds to conservation of energy. Likewise invariance with respect to spatial origin shifts implies conservation of momentum: one scalar component for each basis direction of displacement. Rotational invariance implies conservation of angular momentum.
answered Dec 6, 2014 at 4:48
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The units of energy is $\dfrac{ML^2}{T^2}$ so that way energy is inversely proportional to square of time. But in most equations of energy, time is never present. Energy is a simpler way to relate work done in complicated systems with variable force. That is found by work-energy theorem. Work is $$\text{force*distance}$$.
There is also Noether's theorem that states that all forms of energy is always conserved as the physical laws governing the universe does not change with time. Simply energy is not something abstract nor is it a fundamental property of objects. Sure potential energy, kinetic energy exists but we define such quantities to find the work done by a force. Energy is the capacity of a body to do work and nothing more.
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$\begingroup$ By implication, were time added to the equation we would have a far better understanding of statics and mechanics of physics. If the force is towards the ground but time displacement is horizontal to the force then direction is changed and closed equilibrium becomes variable. $\endgroup$– RhodieAug 1, 2022 at 7:39
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Here is a model for the relation between energy and momentum, based on classical physics:
A particle at rest receives a linear acceleration. After this acceleration process it is moving, it has kinetic energy which corresponds to a momentum.
For calculating the energy, you consider the length of the path the force of acceleration was applied:
ekin = f x s
For calculating the momentum, you consider the time during which the force of acceleration was applied:
p = f x t
As a result you see that energy and momentum are somewhat symmetric, and energy includes time in the same way that momentum includes space.
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Time is not directly related to energy itself, but it is definitely related to many aspects of energy.
For example, the direction of time (from past to future) can be determined by the flow of energy in the universe. This concept is known as entropy. Our universe is gradually moving from a state of energy concentration (where some regions of our universe contain more energy than other regions) to a state of energy distribution (where all energy in the universe would be equally distributed). The evenness of energy distribution is known as entropy. So our universe is gradually moving from a state of lower entropy to a state of higher entropy.
Gravitation fields have an impact on the speed of time flow. If you replace matter for energy (using E=mc²) it would imply that the speed of time flow would be different for regions of higher energy concentration and regions of lower energy concentration. However, remember that this is a very very vague (some might consider it outright false) interpretation because you are taking energy as mass. While they are definitely interchangeable, their properties aren't the same.
