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1. Fill in the gap in your lecture notes: Given x' = y (x-vt) and x = y (x'+vt'), show t=y (t'+(v/c²)x') and t' = y (t-(v/c²)x).

1. Fill in the gap in your lecture notes: Given x' = y (x-vt) and x = y (x'+vt'), show t=y (t'+(v/c²)x') and t' = y (t-(v/c²)x).

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1. Fill in the gap in your lecture notes: Given x' = y (x-vt) and x = y (x'+vt'), show t = y (t'+(v/c²)x') and t' = y (t-(v/c²)x). 2. What do we mean when we say something is invariant under a Lorentz Transformation? Use the Lorentz Transformations to show that (Ax)² + (Ay)² + (Az)² - (cAt)² is invariant. 3. When v is small (i.e. v<<c), show that the Lorentz Transformations become the Gallilean Transformations. What is the physical implication of this observation?
Transcribed Image Text:1. Fill in the gap in your lecture notes: Given x' = y (x-vt) and x = y (x'+vt'), show t = y (t'+(v/c²)x') and t' = y (t-(v/c²)x). 2. What do we mean when we say something is invariant under a Lorentz Transformation? Use the Lorentz Transformations to show that (Ax)² + (Ay)² + (Az)² - (cAt)² is invariant. 3. When v is small (i.e. v<<c), show that the Lorentz Transformations become the Gallilean Transformations. What is the physical implication of this observation?
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