(July 23, 2019 at 8:59 am)comet Wrote:(July 23, 2019 at 8:36 am)polymath257 Wrote: No, you cannot just add energy to a system. To add energy, you have to apply a force. In other words, you have to interact with the system by some other system. Interactio between particles can, and does, change the dynamic properties of the particles involved. This includes energy and momentum, for example.
Energy is a property of the particles, not something that can be separated from them. Energy doesn't exist as a 'thing in itself', but solely as a property of such things: quantum particles.
You accelerate a car by applying a force to it. That force comes from a system other than the car (the force of the road on the car).
Yes, the total energy of the 'system' changes *if* you consider the system to be the car. If you consider the system to be the car plus the road, then not.
And, when it comes to cosmology, there are some inherent difficulties involved in even talking about the 'total energy of even a universe of finite extent. That is because the energy is one component of a four dimensional vector and there is no single way to parallel transport a vector in a curved spacetime. So, in some ways, energy is *less* fundamental than, say, charge, which is the same for all observers.
I don't think so. The energy isn't a "fourth vector". The different types of energy can be thought of as vectors and the total energy is the resultant vector. the vector quantities themselves might change but the result's magnitude will always be the same.
you are right and wrong with the car. The reaction force of the street is in response to the car. Yeah, you can say the friction coming from the street is adding to the car but then look at the car and street surface as the system. we can do this all the way down or all the way up.
I think your base claim that energy is a component vector is wrong. "total energy" is the resultant vector, not a component vector. and its magnitude will always be the same. KE + PE. the components that you are talking about are the components of KE and PE.
I think your base understanding is incomplete. are you trained in this stuff?
No, you misunderstood. Energy is NOT a vector. It is a *component of* a vector. More specifically, it is the time component of the energy-momentum 4-vector. So, in that sense, it has *exactly* the same 'reality as momentum. In other words, it is a *property* of the particles involved.
The PE and KE are not 'components in the vector sense. They are scalars that add up to be the total energy. But, you are working classically, and classical physics is ultimately wrong. When you get to relativistic physics, energy is one component of a four dimensional vector associated with the particle. And, in fact, the energy-momentum vector for a particle always has a (relativistic) length associated with the rest mass of the particle. That is where the equation E^2 = m^2 c^4 +p^2 c^2 comes from (the correct version of E=mc^2 to apply to moving and/or massless particles).
