how to show that 2 seccessive Lorentz Trasformations ,in general,are non-commutative?

[ploum]

thank you for giving me the answer :)

[cristo]

I doubt anyone will just give you the answer without you putting some effort in. For example, try writing what you know about lorentz transformations, how you might go about answering the question, etc..

Why should someone spend time answering a question that you have not even asked properly?

[dextercioby]

HINT: Lorentz boosts along the same space axis do form an uniparameter group.

Daniel.

[mjsd]

long way of doing things: Lorentz transformations form a group, if this group is non-abelian then you original problem is answered. may need to work out multiplication table of this group to show that... or perhaps there are smarter way to do things? I'll leave that to you.... but one final remark: if all you need to show is that they are in general such as such....just show by examples

[robphy]

From the way you posed the question, you just need to find one counterexample to commutativity.

Note that a spatial rotation is a particular Lorentz transformation. Hopefully you know that spatial rotations in three-dimensional [Euclidean] space are also generally noncommutative. There's a famous example with rotating a book by 90 degrees along two different axes successively, then comparing the results when the order is reversed.

You're probably asking about Lorentz boosts. You might try the analogue of the preceding example... implicit in the hint by dextercioby.