L2 transformation reduces to the L1 transformation

In summary, the conversation revolves around understanding and showing the relationship between the L2 and L1 transformations in the context of two reference frames in standard configuration. The L2 transformations involve a unit vector and the L1 transformations do not, and both are viewed in the S' frame. The conversation also clarifies that "standard configuration" refers to both reference frames moving in the direction of the x-axis.
  • #1
Pyrokenesis
19
0
Hello.

I am having trouble answering the following question:

"Show that the L2 transformation reduces to the L1 transformation when the two reference frames are in standard configuration."

Am I wrong to assume that r = xi + yj + zk

Any help would be beautiful!

Thanx much
 
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  • #2
"Show that the L2 transformation reduces to the L1 transformation when the two reference frames are in standard configuration."

I assume that the source of this question defines what the L2 and L1 transformations are, as well as what two reference frames are being compared. Please elaborate.
 
  • #3
The L2 transformations are as follows:

r' = r + γv^[(1 - 1/γ)(r.v^) - βct];

ct' = γ(ct - r.β);

where β = v/c & v^ is the unit vector in the direction of v.

The L1 transformations are:

x' = γ(x - βct);
y' = y;
z' = z;

ct' = γ(ct - βx);

where β = v/c.

All are viewed in the S' frame.
 
  • #4
We should also require that you define "standard configuration" but I'm going to assume that is with both reference frames moving in the direction of the x-axis :smile:.

Yes, you are correct to right r= xi+ yj+ zk. Notice that the difference is that "xi+ yj+ zk" assumes some particular coordinate system ("standard configuration") while "r" does not.

You may also assume ("standard configuration") that v= vi+ 0j+ 0k and that v^= i+ 0j+ 0k.
 
  • #5
Sorry. Yes standard configuration is when both reference frames move in the direction of the x-axis.

Thanks I think I can solve it now.
 

What is L2 transformation?

L2 transformation refers to a mathematical process that involves converting a data set into a new representation, typically with the goal of simplifying or reducing the complexity of the data.

What is L1 transformation?

L1 transformation is a similar process to L2 transformation, but with a different set of mathematical rules. It also aims to simplify or reduce the complexity of the data, but uses a different approach to achieve this.

How does L2 transformation reduce to L1 transformation?

L2 transformation reduces to L1 transformation when the mathematical rules of L2 transformation are simplified or approximated to those of L1 transformation. This may occur when the data set has certain characteristics or when the desired outcome can be achieved with a simpler approach.

What are the benefits of L2 transformation reducing to L1 transformation?

The main benefit of L2 transformation reducing to L1 transformation is that it allows for a simpler and more efficient way of representing and analyzing data, which can save time and resources. It can also make complex data easier to interpret and understand.

Are there any limitations to L2 transformation reducing to L1 transformation?

Yes, there may be limitations to this process as it involves approximating or simplifying mathematical rules, which may not always be accurate or appropriate for the data. Additionally, the results of L1 transformation may not be as accurate or precise as those of L2 transformation.

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