I Boost Generators: Physical Meaning & Observable Quantities

Click For Summary
Boosts in the Poincare group are linked to physical quantities, similar to time translation with energy and space translations with momentum. The distinction between boosts and rotations is frame-dependent, necessitating a unified understanding of both concepts. This unification leads to the identification of a relativistic angular momentum tensor that corresponds to the generators of boosts and rotations. Understanding this relationship enhances the comprehension of observable quantities in relativistic physics. The discussion emphasizes the importance of integrating boosts with rotations for a complete physical interpretation.
nicholas_eng
Messages
3
Reaction score
1
TL;DR
Do the generators of boosts correspond to anything physical?
So, all of the generators of the Poincare group are associated with pretty well-known physical quantities. Time translation is associated with energy, space translations with momentum, rotations with angular momentum, and boosts... well, boosts are generated by the "generators of boosts". Do they correspond to any observable?
 
Physics news on Phys.org
A proper understanding of boosts in the context of your question requires unifying them with rotations; note that the split between what is a "boost" and what is a "rotation" is frame-dependent. When we unify boosts and rotations, we find that there is a relativistic angular momentum tensor that corresponds to the boost/rotation generators. Wikipedia has a brief discussion:

https://en.wikipedia.org/wiki/Relat...e_generator_of_spacetime_boosts_and_rotations
 
Reply
  • Like
Likes nicholas_eng, Orodruin and Dale

Thread 'Physical Interpretation of Frame Field'

Moderator's note: Spin-off from another thread due to topic change. In the second link referenced, there is a claim about a physical interpretation of frame field. Consider a family of observers whose worldlines fill a region of spacetime. Each of them carries a clock and a set of mutually orthogonal rulers. Each observer points in the (timelike) direction defined by its worldline's tangent at any given event along it. What about the rulers each of them carries ? My interpretation: each...
View full post »

Similar threads

I How do angular displacement and rapidity relate in special relativity?
  • · Replies 3 ·
Replies
3
Views
2K
I Explore Spacetimes, Metrics & Symmetries in Relativity Theory
  • · Replies 7 ·
Replies
7
Views
3K
I Generators of translations
  • · Replies 0 ·
Replies
0
Views
2K
I Matrix Representations of the Poincare Group
  • · Replies 4 ·
Replies
4
Views
3K
Conserved quantities under the Lorentz boost
  • · Replies 11 ·
Replies
11
Views
10K
A Explicit construction of Galilean-invariant space
  • · Replies 1 ·
Replies
1
Views
1K
I Why are direct sums of Lorentz group representations important in physics?
  • · Replies 4 ·
Replies
4
Views
2K
Generator of Boosts: Classical Quantity?
  • · Replies 21 ·
Replies
21
Views
3K
I Conservation of Quantity: Noether's Theorem
  • · Replies 19 ·
Replies
19
Views
4K
I Meaning of the invariants built from the angular momentum tensor
  • · Replies 1 ·
Replies
1
Views
1K