/sci/ - Science & Math

Cosmology requires that use its models in the intended context. There still aren't any answers to the big picture mysteries.

>>15027439
>not intuitive
It is intuitive. Everyone knows what velocity is; it's speed associated with a direction. In relativity, we call "velocity" the 3-velocity to differentiate motion through 3D space from motion through 4D spacetime. 4D motion is quantified as the 4-velocity: a vector with four components instead of three. It is some weird property of the universe (Lorentz invariance) that the 4-velocity of any physical object in spacetime is normalized so that its square is always (ALWAYS!) equal to the speed of light squared. In one's own reference frame, the frame in which one is still or motionless, one observes one's 3-velocity to be zero and all of one's normalized 4-velocity has to get made up by the 1-velocity, which is the rate of time passing. However, relative (as in RELATIVITY) to another observer in a frame moving with respect to one's own frame, one's 3-velocity through space is non-zero and one's 1-velocity through time has to decrease to maintain the overall normalization of the 4-velocity. This slowing down of the 1-velocity is called "time dilation." This is weird because one's "proper time" (the time on a stopwatch in the frame where one's 3-velocity is zero) always goes at a constant rate. Due to the effect I mentioned, which is called time dilation, the passage of time measured by two stopwatches moving with respect to each other will usually not agree for relativistic 3-velocities. Since the speed of light is so high and the square of the 4-velocity is always equal to the speed of light squared (for some reason), we don't notice time dilation between frames which move non-relativistically with respect to one another.

As a counterexample, it is said that time stops as one's 3-velocity approaches the speed of light, or that clocks don't tick in a frame comoving with a photon, because the 3-velocity squared is already equal to the speed of light squared. There's no normalized, Lorentz invariant 4-velocity left over to have some 1-velocity.

>>15027439
>not intuitive
It is intuitive. Everyone knows what velocity is; it's speed associated with a direction. In relativity, we call "velocity" the 3-velocity to differentiate motion through 3D space from motion through 4D spacetime. 4D motion is quantified as the 4-velocity: a vector with four components instead of three. It is some weird property of the universe (Lorentz invariance) that the 4-velocity of any physical object in spacetime is normalized so that its square is always (ALWAYS!) equal to the speed of light squared. In one's own reference frame, the frame in which one is still or motionless, one observes the 3-velocity to be zero and all of one's normalized 4-velocity has to get made up by the 1-velocity. However, relative (as in RELATIVITY) to another observer in a frame moving with respect to one's own frame, the 3-velocity through space is non-zero and the 1-velocity through time has to decrease to maintain the overall normalization of the 4-velocity. This slowing down of the 1-velocity is called "time dilation." This is weird because one's "proper time" (the time on a stopwatch in the frame where one's 3-velocity is zero) always goes at a constant rate. Due to the effect I mentioned, which is called time dilation, the passage of time measured by two stopwatches moving with respect to each other will usually not agree for relativistic 3-velocities. Since the speed of light is so high and the square of the 4-velocity is ALWAYS equal to the speed of light squared (for some reason), we don't notice time dilation between frames which move non-relativistically with respect to one another.

As a counterexample, it is said that time will stop when one's 3-velocity reaches the speed of light, or that clocks don't tick in a frame comoving with a photon, because the 3-velocity squared is already equal to the speed of light squared. There's no normalized, Lorentz invariant 4-velocity left over to have some 1-velocity, which is the rate of time passing.

>>14835870

What did he mean by this?