Lorentz transformations

  • Thread starter Orion1
  • Start date
969
2


What is the signifigance of the first derivative of the Lorentz transformation gamma function with respect to [tex]dv[/tex]?

What type of system does this derivative represent?

[tex]\gamma'(v) = \frac{d}{dv} \left( \frac{1}{\sqrt{1 - \left( \frac{v}{c} \right)^2}} \right) = \frac{v}{c^2 \left[ 1 - \left( \frac{v}{c} \right)^2 \right]^\frac{3}{2}}[/tex]

[tex]\boxed{\gamma'(v) = \frac{v}{c^2 \left[ 1 - \left( \frac{v}{c} \right)^2 \right]^\frac{3}{2}}}[/tex]
 
142
0
I don't see any usefulness for this particular derivative. Why do you ask?

[tex]\frac{d(1/\gamma)}{dv}[/tex]
might be meaningful. It represents the change of the time-velocity [itex]cd\tau/dt}=c/\gamma[/itex] (see e.g. Brian Greene's "The elegant universe") as a function of the change of the spatial velocity [itex]v[/itex]. The function is goniometric.
 
Last edited:
969
2
Reletive Relation...


[tex]\gamma'(v)^{-1} = \frac{d}{dv} \left( \frac{1}{\sqrt{1 - \left( \frac{v}{c} \right)^2}} \right)^{-1} = \frac{d}{dv} \left( \sqrt{1 - \left( \frac{v}{c} \right)} \right) = - \frac{v}{c^2 \sqrt{1 - \left( \frac{v}{c} \right)^2 }}[/tex]

[tex]\boxed{\gamma'(v)^{-1} = - \frac{v}{c^2 \sqrt{1 - \left( \frac{v}{c} \right)^2 }}}[/tex]

[tex]\gamma'(v)^{-1} = - \frac{v \gamma}{c^2} = - \frac{ds}{dt} \left( \frac{\gamma}{c^2} \right)[/tex]

[tex]\boxed{\gamma'(v)^{-1} = - \frac{ds}{dt} \left( \frac{\gamma}{c^2} \right)}[/tex]

Are these equation solutions correct?
 

Related Threads for: Lorentz transformations

Replies
1
Views
5K
  • Posted
Replies
10
Views
1K
  • Posted
Replies
6
Views
3K
  • Posted
Replies
7
Views
2K
  • Posted
Replies
2
Views
1K
  • Posted
Replies
5
Views
2K
  • Posted
Replies
4
Views
3K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top