Undergrad Is a Time Rotation Operator Analogous to Spatial Rotations Possible?

  • Thread starter Thread starter member 743765
  • Start date Start date
  • Tags Tags
    Hamiltonian
Click For Summary
The discussion explores the concept of a time rotation operator and its potential analogy to spatial rotations. It highlights that a true "time rotation operator" cannot exist independently, as time is a single dimension that cannot be rotated without involving spatial dimensions. Lorentz boosts are identified as the relevant analogues, combining time and space dimensions in their application. The conversation emphasizes the necessity of integrating spatial dimensions to conceptualize any form of rotation involving time. Ultimately, the relationship between time and space in physics necessitates a multidimensional approach.
member 743765
We studied about the time translation operator and that its generator is the hamiltonian the question is could there be a time rotation operator in analogy with rotations in space and what would be it's relation to relativity?
 
Physics news on Phys.org
Lorentz boost seems what you are looking for.
 
Reply
  • Like
Likes member 743765 and Hill
phyahmad said:
could there be a time rotation operator in analogy with rotations in space
There can't be a "time rotation operator" in the sense of just "rotating time" and not affecting "space" at all, because (heuristically) "time" is only one dimension and it makes no sense to "rotate" in just one dimension; you need at least two. So you need to include at least one dimension of space in the rotation.

As @anuttarasammyak points out in post #2, Lorentz boosts are the "time-space rotation" analogues of rotations in ordinary space. Boosts require two dimensions, one of "time" and one of "space" (the "space" dimension is the spatial direction in which the boost is applied).
 
Reply
  • Like
Likes member 743765

Thread 'One does not “prove” the basic principles of Quantum Mechanics'

I am slowly going through the book 'What Is a Quantum Field Theory?' by Michel Talagrand. I came across the following quote: One does not" prove” the basic principles of Quantum Mechanics. The ultimate test for a model is the agreement of its predictions with experiments. Although it may seem trite, it does fit in with my modelling view of QM. The more I think about it, the more I believe it could be saying something quite profound. For example, precisely what is the justification of...
View full post »

Similar threads

Undergrad How is Graphene's Hamiltonian rotationally invariant?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Hamiltonian of a particle in a magnetic field
  • · Replies 10 ·
Replies
10
Views
4K
Graduate Time-dependent unitary transformations of the Hamiltonian
  • · Replies 9 ·
Replies
9
Views
6K
Undergrad Interpreting Unitary Time Evolution
  • · Replies 10 ·
Replies
10
Views
1K
Graduate Jaynes-Cummings Hamiltonian: Where did the time dependence go?
  • · Replies 4 ·
Replies
4
Views
2K
Generator of Boosts: Classical Quantity?
  • · Replies 21 ·
Replies
21
Views
3K
Undergrad What's the relation between spinor space and SO(3) vector space?
  • · Replies 53 ·
2
Replies
53
Views
4K
Graduate How to derive the quantum detailed balance condition?
  • · Replies 0 ·
Replies
0
Views
1K
Graduate Does the quantum space of states have countable or uncountable basis?
  • · Replies 67 ·
3
Replies
67
Views
7K
Graduate Please help me clarify my misconception involving generators
  • · Replies 10 ·
Replies
10
Views
1K