Can a Particle with Rest Mass Travel at the Speed of Light?

Click For Summary
SUMMARY

A particle with rest mass cannot travel at the speed of light, as established by the equation m = (E² - (pc)²)^(1/2) / c². As velocity approaches the speed of light (v=c), both energy (E) and momentum (p) approach infinity, leading to a scenario where mass effectively becomes zero. However, the method of handling infinities in calculations is incorrect, as one cannot simply subtract infinities. The discussion emphasizes the physical impossibility of assigning infinite energy to a particle.

PREREQUISITES
  • Understanding of relativistic energy equations
  • Familiarity with momentum in physics
  • Knowledge of the concept of rest mass
  • Basic grasp of limits and infinity in mathematical contexts
NEXT STEPS
  • Study the derivation of the relativistic energy-momentum relation
  • Explore the implications of massless particles, such as photons
  • Investigate the concept of energy limits in special relativity
  • Learn about the physical interpretations of infinity in physics
USEFUL FOR

Students of physics, educators teaching special relativity, and anyone interested in the fundamental principles of particle physics.

Qyzren
Messages
41
Reaction score
0
What is the rest mass m of a particle traveling with the speed of light in the laboratory frame?

i believe m = (E² - (pc)²)^.5 / c² is the correct equation to use?
as velocity goes up, so does energy and momentum? so when velocity is at speed of light, E = infinity and momentum = infinity? so we have infinity - infinity on the numerator? so this gives mass = 0? is any of this correct? thanks for help.
 
Physics news on Phys.org
The answer turns out to be correct, but the method is not. For one thing, you can not simply subtract off infinities in the manner that you just did.

What is the formula for the relativistic energy of a particle of rest mass, m? Write this down. Now if v=c, this gives you the result you (incompletely) stated above, namely that E = infinity, unless _______ (fill this in).

Ask yourself: Is it physical for a particle to be given an infinite amount of energy?
 

Similar threads

Special relativity - kinematics
  • · Replies 2 ·
Replies
2
Views
2K
Special relativity - Maximum mass
  • · Replies 3 ·
Replies
3
Views
1K
Rest Mass of Compound Object after Collision
  • · Replies 18 ·
Replies
18
Views
2K
How to Calculate Invariant Mass for Negligible Particle Mass?
  • · Replies 9 ·
Replies
9
Views
3K
How Does Special Relativity Affect Photon Emission Angles?
  • · Replies 4 ·
Replies
4
Views
2K
Maximum rest mass in particle collision
  • · Replies 2 ·
Replies
2
Views
4K
How is Rest Mass Affected in the Process of Rocket Propulsion?
  • · Replies 1 ·
Replies
1
Views
1K
Probability distribution of outgoing energy of particle
  • · Replies 1 ·
Replies
1
Views
2K
Photon beam is incident on a proton target produces a particle
  • · Replies 4 ·
Replies
4
Views
2K
How Close to Light Speed Do Protons Move in the LHC?
  • · Replies 33 ·
2
Replies
33
Views
4K