Stationary Frame: ๐‘ฃ = 0
๐‘ก = 0years
๐‘ฅ = 0lyrs
Moving Frame: ๐‘ฃ = 0๐‘
๐‘กโ€ฒ = 0years
๐‘ฅโ€ฒ = 0lyrs

Transformation
๐‘กโ€ฒ = ๐›พ(๐‘กโˆ’๐‘ฃ๐‘ฅ/๐‘ยฒ) = 0 (0โˆ’0ยท0)years
๐‘ฅโ€ฒ = ๐›พ(๐‘ฅโˆ’๐‘ฃ๐‘ก) = 0 (0โˆ’0ยท0)lyrs

Spacetime Interval (Stationary): ๐‘ฃ = 0
๐‘ ยฒ = ๐‘ยฒโ€‰๐‘กยฒโˆ’๐‘ฅยฒ
= (โˆ’)lyrsยฒ
= lyrsยฒ
Spacetime Interval (Moving): ๐‘ฃ = 0๐‘
๐‘ ยฒ = ๐‘ยฒ(๐‘กโ€ฒ)ยฒโˆ’(๐‘ฅโ€ฒ)ยฒ
= (โˆ’)lyrsยฒ
= lyrsยฒ