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actionintegral
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Does anyone have a brief explanation of why the gamma is necessary in the Lorentz transformation.
in order to account for relativistic effects like time dilation, doppler shift...actionintegral said:Does anyone have a brief explanation of why the gamma is necessary in the Lorentz transformation.
actionintegral said:But the constancy of the speed of light is preserved simply by
x'=x-vt and t'=t-vx/cc. I'm trying to see where the scaling factor comes in.
Gamma, or sometimes called the Lorentz factor, represents the relationship between relativistic time and proper time or relativistic length and proper length.actionintegral said:Does anyone have a brief explanation of why the gamma is necessary in the Lorentz transformation.
nakurusil said:Comes from preserving dx^2 -( c dt )^2
you are perfectly right. in the paperactionintegral said:But the constancy of the speed of light is preserved simply by
x'=x-vt and t'=t-vx/cc. I'm trying to see where the scaling factor comes in.
actionintegral said:Fair enough - but why would I want to preserve THAT?
actionintegral said:nakurusil said:Comes from preserving dx^2 -( c dt )^2
Fair enough - but why would I want to preserve THAT?
actionintegral said:But the constancy of the speed of light is preserved simply by
x'=x-vt and t'=t-vx/cc. I'm trying to see where the scaling factor comes in.
pervect said:We _also_ want the transforms to have the property that the inverse is generated just by changing the sign of v.
actionintegral said:Does anyone have a brief explanation of why the gamma is necessary in the Lorentz transformation.
Gamma (γ) is a mathematical factor used in the Lorentz transformation equations to account for the effects of time dilation and length contraction in special relativity. It is often referred to as the "relativistic factor" or "dilation factor."
Gamma is calculated using the formula γ = 1/√(1 - v^2/c^2), where v is the relative velocity between two reference frames and c is the speed of light. This formula is derived from the principles of special relativity and is used to adjust measurements of time and space between two frames of reference moving at different velocities.
Gamma is important in Lorentz transformation because it allows us to accurately describe the effects of time dilation and length contraction on objects moving at high velocities. It is a crucial component in the equations that enable us to reconcile the differences in measurements between different reference frames in special relativity.
Gamma and the speed of light (c) are directly related through the Lorentz transformation formula. As the relative velocity between two frames approaches the speed of light, the value of Gamma approaches infinity, meaning that time dilation and length contraction become more pronounced. This is a fundamental concept in special relativity.
Yes, Gamma can be greater than 1. In fact, when an object is moving at a significant fraction of the speed of light (v/c), Gamma will always be greater than 1. This indicates that time will appear to pass slower and lengths will appear shorter in the moving frame of reference compared to a stationary frame, as observed in the famous "twin paradox" thought experiment.