The Lorentz factor gamma and proper time

Click For Summary
SUMMARY

The discussion centers on the Lorentz factor, denoted as ##\gamma##, and its implications for proper time along light-like curves in special relativity. It is established that proper time along a light-like curve is zero, as ##\gamma## becomes infinite when the velocity ##v## equals the speed of light ##c##. The confusion arises from the structure of ##\gamma## rather than any fundamental issue with proper time itself. Proper time is defined for timelike paths, and its undefined nature for null paths is a deliberate choice for mathematical convenience, not a reflection of physical reality.

PREREQUISITES
  • Understanding of special relativity concepts, particularly the Lorentz factor ##\gamma##.
  • Familiarity with the mathematical formulation of proper time, including the equations $$\Delta\tau=\Delta t/\gamma$$ and $$\Delta\tau=\Delta t\cdot\sqrt{1-(v/c)^2}$$.
  • Knowledge of light-like and timelike curves in Minkowski spacetime.
  • Basic grasp of the implications of massless particles in the context of spacetime geometry.
NEXT STEPS
  • Study the derivation and implications of the Lorentz factor ##\gamma## in detail.
  • Explore the mathematical properties of proper time and its applications in various physical scenarios.
  • Investigate the concept of affine parameters and their role in parameterizing null geodesics.
  • Review Sean Carroll’s Lecture Notes on General Relativity for deeper insights into proper time and spacetime geometry.
USEFUL FOR

Physicists, students of relativity, and anyone interested in the mathematical foundations of spacetime and the behavior of light in the context of special relativity.

  • #31
Trysse said:
What is the distinction between "not experiencing time" and "experiencing ZERO time"? Does it not amount to the same?
Worrying about that isn't physics.
 
Physics news on Phys.org
  • #32
Trysse said:
What is the distinction between "not experiencing time" and "experiencing ZERO time"? Does it not amount to the same?
I don't know. It's a question of semantics, not physics.

The important distinction here is that for anything traveling at speed ##c## the passage of time is not defined. That is very different from saying that the passage of time is zero.

In the parlance of physics you have three types of intervals: timelike, lightlike, and spacelike. The passage of proper time is defined, and makes sense, only for timelike intervals. For a lightlike (as well as a spacelike) interval it is not possible to define the notion of proper time. It is therefore a sloppy use of terminology to say that no time passes for something traveling at light speed. Moreover, that sloppy use of terminology can lead to misconceptions.
 

Similar threads

Undergrad Understanding Lorentz Factor & Proper Time Invariance
  • · Replies 32 ·
2
Replies
32
Views
4K
Undergrad Are the Lorentz Transformations False?
  • · Replies 54 ·
2
Replies
54
Views
4K
High School Am I understanding the concept of proper frame of reference?
  • · Replies 33 ·
2
Replies
33
Views
1K
Undergrad A Hidden Zero in Einstein's Simple Derivation
  • · Replies 22 ·
Replies
22
Views
3K
Undergrad Understanding Relation of Proper & Vector Quantities
  • · Replies 23 ·
Replies
23
Views
2K
High School Confusion in notation of Lorentz Transformations
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Escape velocity near a black hole: Newtonian or Special Relativity?
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad What is the definition of proper time interval according to Wikipedia?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad What Is the Proper Time in Curved Space?
  • · Replies 48 ·
2
Replies
48
Views
5K
Undergrad Def Proper Time GR: Half or Integral Along Path?
  • · Replies 17 ·
Replies
17
Views
3K