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jason12345
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Can the conservation of the 4-momentum be proved, or is it a postulate of special relativity?
Is conservation of the 4-momentum a postulate?
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In summary, the conservation of the 4-momentum can be experimentally verified and is a necessary consequence of the postulates of special relativity. It is a consequence of flat spacetime and time and space translation invariance.
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PeterDonis
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jason12345 said:
Yes.
If by "proved" you mean "experimentally verified", yes, tons of particle physics experiments have verified conservation of 4-momentum to high precision. (Not to mention tons of other experiments plus common experience, but most data other than particle physics is limited to the non-relativistic regime.)
As far as being a "postulate" of SR, yes, it basically is; if you want to be precise, it's a necessary consequence of the postulates of SR, since those postulates imply flat spacetime, and conservation of 4-momentum is a consequence of flat spacetime. (More specifically, conservation of 4-momentum is a consequence of time and space translation invariance, i.e., it holds in any spacetime with those properties.)
What is the conservation of 4-momentum postulate?
The conservation of 4-momentum postulate is a fundamental principle in physics that states that the total 4-momentum of a closed system remains constant over time. This means that in any interaction or process, the total 4-momentum before and after the interaction remains the same.
Why is the conservation of 4-momentum important?
The conservation of 4-momentum is important because it is a fundamental law of nature that is observed to hold true in all physical processes. It allows us to make predictions and calculations about the behavior of particles and systems, and it is a crucial concept in understanding the fundamental laws of physics.
How is the conservation of 4-momentum related to other conservation laws?
The conservation of 4-momentum is related to other conservation laws, such as the conservation of energy and the conservation of momentum. In fact, the conservation of energy and momentum are special cases of the conservation of 4-momentum, as 4-momentum includes both energy and momentum in its definition.
Is the conservation of 4-momentum always true?
Yes, the conservation of 4-momentum is a fundamental law of nature that has been observed to hold true in all physical processes. However, there are some situations, such as in quantum mechanics, where it may appear to be violated. This is due to the uncertainty principle and the fact that energy and momentum can fluctuate in small amounts.
How does the conservation of 4-momentum apply to real-world situations?
The conservation of 4-momentum applies to all physical processes, from the interactions of subatomic particles to the motion of planets in our solar system. It is used in various fields of physics, such as particle physics, astrophysics, and engineering, to make predictions and understand the behavior of systems. It is also important in the development of technologies, such as particle accelerators and spacecraft propulsion systems.
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