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You're completely right that there is nothing revolutionary about viewing a point in spacetime as a point (x,y,z,t) in 4 dimensions. If that was what special re
by jules 8y ago
You're completely right that there is nothing revolutionary about viewing a point in spacetime as a point (x,y,z,t) in 4 dimensions. If that was what special relativity was about then it would be very boring!
The x,y,z directions are connected to each other, because the x direction can be rotated into the y direction by rotating in the xy-plane. What special relativity is about is that the t direction can be rotated into the x direction by "rotating" in the tx-plane. Rotating in the tx-plane is acceleration in the x direction. That's what causes all the weird relativistic effects such as time dilation and length contraction when you accelerate objects. Creatures that don't intuitively understand that the x and y directions form a whole could come up with a similar theory: if you rotate an object in the xy-plane it gets x-dilated and y-contracted. The only mathematical difference between a rotation in the xy-plane and a rotation in the tx-plane is a minus sign in the formula for rotation. So the t direction is not exactly like the x,y,z directions, but the only difference is that terms involving t^2 get a minus sign. For example, the squared distance in 3D is x^2 + y^2 + z^2, but the squared "distance" in the weird 4D spacetime geometry is x^2 + y^2 + z^2 - t^2.