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

AI Thread Summary
The discussion focuses on calculating the travel time of high-energy protons across the Milky Way, which spans approximately 100,000 light-years. The participant attempts to use energy-momentum relationships and relativistic kinetic energy equations to determine the proton's velocity. They encounter confusion when the calculations suggest a velocity equal to the speed of light (c) and even greater than c, which contradicts the principles of relativity. The participant seeks guidance on resolving these discrepancies and understanding the correct approach to the problem. Clarification on the calculations and methods is requested to ensure accurate results.
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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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Please show exactly what you did. Then we will be able to guide your thinking.
 

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