mr. vodka
May15-11, 09:29 AM
Hello,
I was wondering if the following quote by Wikipedia (http://en.wikipedia.org/wiki/Four-velocity section "Interpretation") makes sense:
In other words, the norm or magnitude of the four-velocity is always exactly equal to the speed of light. Thus all objects can be thought of as moving through spacetime at the speed of light. This provides a way of understanding time-dilation: as an object like a rocket accelerates from our perspective, it moves faster through space, but slower through time in order to keep the four-velocity constant. Thus to an observer, a clock on the rocket moves slower, as do the clocks in any reference frame that is not comoving with them. Light itself provides a special case- all of its motion is through space, so it does not have any "left over" four-velocity to move through time. Therefore light, and anything else traveling at light speed, does not experience the "flow" of time.
Cause I would think it doesn't make sense: in this reasoning they're acting as if the norm is something like a^2+b^2+c^2+d^2, so that if b^2+c^2+d^2 is big ("rocket [...] moves faster through space"), then to keep the norm constant, a^2^ should be smaller ("slower through time in order to keep the four-velocity constant"). But of course that is not the structure of the norm, so I don't think this reasoning works out. It would even lead to an opposing answer: due to the minus sign in the norm, the "speed through time" should increase along with the spatial speed! (indeed reflected in \eta^0 = \frac{c}{\sqrt{1-u^2/c^2^}}).
I'm not sayig the four velocity is contradicting time dilation, I'm just trying to argue that their reasoning makes no sense. Or if it does, I have something new to learn, so please correct me!
I was wondering if the following quote by Wikipedia (http://en.wikipedia.org/wiki/Four-velocity section "Interpretation") makes sense:
In other words, the norm or magnitude of the four-velocity is always exactly equal to the speed of light. Thus all objects can be thought of as moving through spacetime at the speed of light. This provides a way of understanding time-dilation: as an object like a rocket accelerates from our perspective, it moves faster through space, but slower through time in order to keep the four-velocity constant. Thus to an observer, a clock on the rocket moves slower, as do the clocks in any reference frame that is not comoving with them. Light itself provides a special case- all of its motion is through space, so it does not have any "left over" four-velocity to move through time. Therefore light, and anything else traveling at light speed, does not experience the "flow" of time.
Cause I would think it doesn't make sense: in this reasoning they're acting as if the norm is something like a^2+b^2+c^2+d^2, so that if b^2+c^2+d^2 is big ("rocket [...] moves faster through space"), then to keep the norm constant, a^2^ should be smaller ("slower through time in order to keep the four-velocity constant"). But of course that is not the structure of the norm, so I don't think this reasoning works out. It would even lead to an opposing answer: due to the minus sign in the norm, the "speed through time" should increase along with the spatial speed! (indeed reflected in \eta^0 = \frac{c}{\sqrt{1-u^2/c^2^}}).
I'm not sayig the four velocity is contradicting time dilation, I'm just trying to argue that their reasoning makes no sense. Or if it does, I have something new to learn, so please correct me!