Calculating the Travel Time of High-Energy Particles Across Our Galaxy

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SUMMARY

The discussion focuses on calculating the travel time of high-energy protons across the Milky Way galaxy, which spans approximately 100,000 light-years. The participant utilized the equations E² = p²c² + m²c⁴ and K = mc²(γ-1) to derive the velocity of a proton with an energy of 10¹⁹ eV. The participant encountered discrepancies in results, specifically obtaining a velocity equal to the speed of light (c) and exceeding it, prompting a request for guidance on resolving these inconsistencies.

PREREQUISITES
  • Understanding of relativistic physics concepts, particularly energy-momentum relations.
  • Familiarity with the Lorentz factor (γ) and its implications in relativistic velocity calculations.
  • Knowledge of kinetic energy equations in the context of particle physics.
  • Basic understanding of the structure and scale of the Milky Way galaxy.
NEXT STEPS
  • Study the derivation and implications of the Lorentz factor (γ) in relativistic motion.
  • Explore the relationship between energy and momentum in high-energy particle physics.
  • Learn about the limitations of classical mechanics when applied to relativistic speeds.
  • Investigate the concept of superluminal speeds and the theoretical implications in physics.
USEFUL FOR

Students and researchers in physics, particularly those focusing on particle physics and relativistic mechanics, will benefit from this discussion.

senatorarmstrong
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Homework Statement



Our galaxy is about 10^5 light-years across, and the most energectic particles known have an energy of about 10^19 eV. How long would it take a proton with this energy to traverse the galaxy as measured from (a) the galaxy and (b) the particle?

Homework Equations



I attempted to use the relationship between energy and momentum. E2 = p2*c2 + m2*c4

I also tried solving the problem with relativistic kinetic energy. K = mc2(γ-1)

The Attempt at a Solution



I used both equations and got similar results...

I figured what I could do is use the energy given and then solve for u in γ. Knowing the relativistic velocity, I could then find how long it would take this proton to zip across the milky-way.

If I am solving for u in γ, I am obviously solving for the velocity of the particle (b) and not the velocity of the particle with respect the galaxy (a).

What throws me off is using the two equations up there, I got u to be equal to c. When I used the kinetic energy equation, u > c! Can't be...

Any hints?

Thanks!
 
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