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Corrected the misgendering of Dale.
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JEB
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In Dale's answer to the collision rest mass problem, how are theyis he concluding that the momentum 4-vector of the resulting particle is equal to the sum of the 4-momentums of the incoming particles. I am specifically wondering about this step in his analysis: $$R^\mu = P^\mu + Q^\mu$$

I agree with the final answer, it just seems to me that in regular collision problems we always use some form of momentum conservation (and maybe energy if collision is elastic) to find final velocities. How is Dale getting away without using conservation here? What is different to regular mechanics?

Related fact: Momentum 4-vector is a conserved quantity in special relativity.

In Dale's answer to the collision rest mass problem, how are they concluding that the momentum 4-vector of the resulting particle is equal to the sum of the 4-momentums of the incoming particles. I am specifically wondering about this step in his analysis: $$R^\mu = P^\mu + Q^\mu$$

I agree with the final answer, it just seems to me that in regular collision problems we always use some form of momentum conservation (and maybe energy if collision is elastic) to find final velocities. How is Dale getting away without using conservation here? What is different to regular mechanics?

Related fact: Momentum 4-vector is a conserved quantity in special relativity.

In Dale's answer to the collision rest mass problem, how is he concluding that the momentum 4-vector of the resulting particle is equal to the sum of the 4-momentums of the incoming particles. I am specifically wondering about this step in his analysis: $$R^\mu = P^\mu + Q^\mu$$

I agree with the final answer, it just seems to me that in regular collision problems we always use some form of momentum conservation (and maybe energy if collision is elastic) to find final velocities. How is Dale getting away without using conservation here? What is different to regular mechanics?

Related fact: Momentum 4-vector is a conserved quantity in special relativity.

Edited in response to a comment
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JohnA.
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In Dale's answer to the collision rest mass problem, how are they concluding that the momentum 4-vector of the resulting particle is equal to the sum of the 4-momentums of the incoming particles. I am specifically wondering about this step in his analysis: $$R^\mu = P^\mu + Q^\mu$$

I agree with the final answer, it just seems to me that in regular collision problems we always use these factssome form of momentum conservation (assumingand maybe energy if collision is elastic) to find final velocities. How is Dale getting away without using conservation here? What is different to regular mechanics?

Related fact: Momentum 4-vector is a conserved quantity in special relativity.

In Dale's answer to the collision rest mass problem, how are they concluding that the momentum 4-vector of the resulting particle is equal to the sum of the 4-momentums of the incoming particles. I am specifically wondering about this step in his analysis: $$R^\mu = P^\mu + Q^\mu$$

I agree with the final answer, it just seems to me that in regular collision problems we always use these facts (assuming collision is elastic) to find final velocities. How is Dale getting away without using conservation here? What is different to regular mechanics?

Related fact: Momentum 4-vector is a conserved quantity in special relativity.

In Dale's answer to the collision rest mass problem, how are they concluding that the momentum 4-vector of the resulting particle is equal to the sum of the 4-momentums of the incoming particles. I am specifically wondering about this step in his analysis: $$R^\mu = P^\mu + Q^\mu$$

I agree with the final answer, it just seems to me that in regular collision problems we always use some form of momentum conservation (and maybe energy if collision is elastic) to find final velocities. How is Dale getting away without using conservation here? What is different to regular mechanics?

Related fact: Momentum 4-vector is a conserved quantity in special relativity.

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JohnA.
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Is 4-momentum conservation used in this answer?

In Dale's answer to the collision rest mass problem, how are they concluding that the momentum 4-vector of the resulting particle is equal to the sum of the 4-momentums of the incoming particles. I am specifically wondering about this step in his analysis: $$R^\mu = P^\mu + Q^\mu$$

I agree with the final answer, it just seems to me that in regular collision problems we always use these facts (assuming collision is elastic) to find final velocities. How is Dale getting away without using conservation here? What is different to regular mechanics?

Related fact: Momentum 4-vector is a conserved quantity in special relativity.