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sqljunkey
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If I had two objects with the same mass, but one had more energy than the other, would it curve space-time more than the other?
No.sqljunkey said:If I had two objects with the same mass, but one had more energy than the other, would it curve space-time more than the other?
No. The kinetic energy represented by the speed of the system is frame-dependent (you can always choose to analyze the system using a frame in which the kinetic energy is zero, and if you change the speed of the system that just means that you'll use a different frame if you want to analyze the system that way) and is completely unrelated to the heat capacity of the system.sqljunkey said:If I take away kinetic energy ( or slow down the system) that would mean I added more energy right?
@Nugatory already corrected your "or slow down the system" comment. As to the rest, they key is the net energy flow. Note the example I gave of a compressed spring versus uncompressed. There is not necessarily any change in temperature (average microscopic kinetic energy), but energy has been added to compress the spring, nonetheless. The negative heat capacity examples involve another energy 'reservoir' such that the increase in average kinetic energy in the COM frame is associated with a decrease in total energy. In the case of a gravitating system, this extra reservoir is (at least when you can use a Newtonian approximation) the potential energy. Thus, because energy has left the system, its effective gravitational mass decreases even though average kinetic energy increased.sqljunkey said:I just wanted to revisit this for a bit since I was reading something about negative heat capacity. If I take away kinetic energy ( or slow down the system) that would mean I added more energy right? That means if I "heat up" a system like this it will get cooler but the perceived mass would be greater.
Now does that mean any kind of energy added to a system, will get "stored" in the curvature of space-time? And does that mean that after a while of adding energy to a system that system would cease to have any kinetic energy at all?
The relationship between mass and energy is described by Albert Einstein's famous equation, E=mc². This equation states that energy (E) is equal to the mass (m) of an object multiplied by the speed of light (c) squared. This means that mass and energy are essentially interchangeable and can be converted into one another.
Mass affects space-time by creating a curvature in the fabric of space-time. This is described by Einstein's theory of general relativity, which states that objects with mass cause a distortion in the space-time continuum. The greater the mass, the greater the distortion, which can affect the motion of other objects in the vicinity.
According to the law of conservation of mass-energy, mass and energy cannot be created or destroyed, only converted from one form to another. This means that the total amount of mass-energy in the universe remains constant.
The concept of space-time explains gravity by showing how mass creates a curvature in space-time, and objects with mass follow the curvature of space-time. This results in the phenomenon we experience as gravity, where objects are pulled towards each other due to the curvature of space-time caused by their mass.
Understanding the interaction between mass, energy, and space-time is crucial in understanding the fundamental workings of the universe. It allows us to explain and predict various phenomena, such as gravity and the behavior of objects in space. This knowledge also has practical applications, such as in the development of technologies like GPS, which rely on our understanding of space-time to function accurately.