What are the physics definitions for time and energy? [duplicate]

Question

I'm a student of physics. Please could someone give me the explanations of the observed physical phenomena of time and energy. Especially, the differences between the two and how they relate to oneanother. Many thanks.

Answer 1

Time is no more than a coordinate. It could seem as it is special regarding the physical universe in a classical sense, dissociating time and space, but long years of physics develompent and the theory of relativity have proved this point of view wrong. You can't untangle time from space, so it must be regarded as just another coordinate labelling an event, and the universe, as a four-dimensional spacetime.

In some sense, time IS special compared to the spatial coordinates, since it is time the only non-homogenous and ever-advancing coordinate (meaning, you can choose any point in space and the properties of it will remain the same, but not every point in time is the same).

There's a deeper meaning to the word time as well. In the two above paragraphs I have been talking about time as a coordinate, but one can also refer to time as a parameter of the evolution of a particle (or a system, or a body). If you were to parametrize the evolution of a certain system, according to the laws of physics and in the absence of forces (let's make it easy to understand), you will verify that bodies take "the shortest path" between their starting and finishing points. Allow me to clarify with an example from classical mechanics: Suppose you're in vacuum, in the absence of any field and throw a ball with some speed $v$ from point A, and stop it at point B. There's no way the ball is going to make weird shapes! It will follow a straight line to its destination. This simple "mental experiment" can be extrapolated to quite more difficult problems via the principle of least action, which is only a fancy way of saying that bodies follow the "shortest" trajectories between their initial and final points. These trajectories can be mathematically parametrised (just as you would parametrise an arbitrary curve), and one can find that there's usually a favourite parameter to choose, which is time. If you apply this explanation to not only space $(x,y,z)$ but to spacetime $(t,x,y,z)$, you'll find what the shortest path in the evolution through time and space of a particle (or a system) is, and you'll find the optimal parameter to choose for it is the proper time of it: The measure of its own "pace" through spacetime.

I think the discussion of why there is a favourite parameter is waaaay beyond the scope of this question, but you'll get to it eventually (and I hope you find it as interesting as I do!)

Now, just for the sake of the truth, I must correct myself and say that this "proper time" parameter sometimes cannot be used. This is, when we're treating massless particles, as photons are. This is another way of checking how time (proper time) doesn't exist for light particles, and it's a shocking result of general relativity. However, one can surely assign a time coordinate to a light event.

Now energy, that's quite the tricky concept. In a classical sense, one often regards energy as some sort of "capacity" or "potential" of a system to perform some work. It only depends on the state of a system, never on how it got there (we say it's a state function because of this). It's responsible of determining a system's evolution through spacetime, since it carries information of where the system stands in the phase space, which is the precise way of calling the ensemble of velocities and positions of the particles in a system.

Let's start the discussion regarding a single particle and a single kind of force acting over it, which we will imagine to be electrostatic since that's an easy one. If we were to have a fixed negative charge in the origin of our space and our particle was positively-charged, now it's easy to think of it as being attracted to the fixed negative one. This means, if you were to place our positive particle at some point in space, it will start accelerating towards the fixed charge in the origin. As you can see, placing the positive particle anywhere around the negative one, will make it accelerate towards it. In the opposite direction, trying to move the positive particle away from the negative one won't be free, you'll have to exert some force on it. That's cause you're acting against the force between these two particles. As you will probably know already if you're studying physics, energy is conservated, and as that force you're exerting on the positive particle is costing you some energy, this must be transferred to the outwards-moving positive particle, as it will have now more potential of accelerating back to the negative charge at the origin. This is an easy visualization of how energy quantifies the potential of a system.

Energy though, is very far from being this easy, and not for anything is the central topic of discussion in every physics course, at least as far as I've come. It can be manifested in many forms, but the most important aspect of it is, doubtless, the fact that it's preserved and that it naturally tends to stay at a minimum, which relates, again, to our principle of last action, given the fact that the "crazy paths" a ball can take from point A to point B, or a planet orbiting around its star doing an 8 shape, imply quite a bigger energy fluctuation (though in the end it would be preserved) than the natural straight line or elliptical orbit they would take in nature. This is not coincidence, since time and energy are geometrically related in a way that time labels the evolution of energy, and energy governs the evolution of systems through time.

Actually, and this is quite advanced as well, energy conservation comes from the fact that, when you make the leap from traditional 3 dimensional space and time physics to the 4 dimensional space-time physics, you find that the time-component of the 4 dimensional momentum of a system is precisely the energy.

I know I never got to truly define in a straight clear way neither time or energy in this discussion, and that most of the concepts I introduced here aren't rigorously treated nor absolutely correct, but I hope this fulfilled the scope of the question and you got a bit of a deeper understanding on what time and energy are and how are they related.

Answer 2

It's recommended that you learn about energy to start with, looking up the definition of the unit of energy, the Joule and learning about mechanical energy or 'work done'. You could then move on to find out about other types of energy.

Time is different and you probably won't find a simple explanation of what it actually is. The physics unit of time is the second.

Power is also a physics quantity that you could look into, in the equation for power, time and energy are both there.

$Power = \frac{energy}{time}$

Depending on how deeply you are thinking of looking into all this, you might want to see another question here Intuitive explanation for why time symmetry implies conservation of energy?