Mass and Energy Conservation in Relativistic Frames

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In summary, the conversation discusses the concept of a free electron losing a photon and getting slower when observed from the Earth frame, but appearing to gain energy and move faster when observed from a frame moving with the initial velocity of the electron. The conversation also brings up the idea of an oscillating electron in an electrical field and how it would perceive its own motion. The conservation of four-momentum is suggested as a concept to explore further in understanding the relationship between mass, energy, and momentum in these scenarios.
  • #1
ankitpandey
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watching from Earth frame, i see an electron lose a photon and get slower. but if i consider a frame still moving with initial velocity of electron, what do i see? the electron looses a photon,but moves faster. hence its relativistic mass is also greater than rest mass.total energy has increased in both ways. how is sum of mass and energy conserved here?
 
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  • #2
Bravo, you have just shown a single free electron cannot emit a single photon.
 
  • #3
What if it is not free but oscillating due to an alternating electrical field? Does it still see itself in freefall, emitting photons for no reason? or does it "feel" itself accelerating since the field is not gravitational?
 
  • #4
A stationary accelerometer in the oscillating electron's rest frame would register an oscillating acceleration, so you know that the frame is non-inertial and therefore the electron would "feel" itself accelerating.

To the OP: you may want to look into the conservation of four-momentum, which encapsulates the conservation of energy and conservation of momentum in one nice convenient Lorentz-invariant package.
 
  • #5
well then let us assume electron and neutron moving in direction of electric field.then, with respect to nuetron, is electron gaining energy when it is actually becoming slower relative to earth?
 
  • #6
What does conservation of the four-momentum tell you?
 

1. What is the principle of mass and energy conservation in relativistic frames?

The principle of mass and energy conservation in relativistic frames states that the total mass and energy of a closed system remains constant, regardless of any transformations or interactions within the system. This is based on the famous equation E=mc^2, which relates mass and energy as two forms of the same physical quantity.

2. How does the concept of mass and energy conservation change in the theory of relativity?

In classical physics, mass and energy were considered as separate and independent quantities. However, in the theory of relativity, they are interconnected and can be transformed into one another. This means that the total mass and energy of a system can change, but their sum must always remain constant.

3. Can mass be converted into pure energy and vice versa?

Yes, according to the famous equation E=mc^2, mass can be converted into energy and vice versa. This has been demonstrated in nuclear reactions and is the basis for technologies like nuclear power and nuclear weapons.

4. How does the theory of relativity affect our understanding of the conservation of mass and energy?

The theory of relativity revolutionized our understanding of mass and energy conservation by showing that they are not separate and fixed quantities, but rather interconnected and relative to the observer. This means that the conservation laws must be applied in all frames of reference, even in high-speed or gravitational scenarios.

5. What are some practical applications of the principle of mass and energy conservation in relativistic frames?

The principle of mass and energy conservation in relativistic frames has numerous practical applications, such as in nuclear energy production, particle accelerators, and understanding the behavior of objects in extreme conditions like black holes. It also plays a crucial role in the development of space travel and exploration.

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