scottbekerham said:
General relativity states that our universe is four dimensional curved space so time dimension is not separated from space dimensions .Why then is the time dimension different from the 3 space dimensions ? and why there must be 3 space dimensions and not 4 for example ?
It is not difficult to regard at least one universe model as one consisting of four spatial dimensions. The 4-D universe is populated by 4-dimensional objects. A typical characteristic of these 4-D objects is that they are very short along their X1, X2, and X3 dimensions (we can describe their sizes in the first 3 dimensions using the inch unit). But the size of the 4-D objects along their X4 dimension may be of the order of 10^13 miles or much more. So, one thing making the 4th dimension so different is the shape of the objects occupying the 4-D space (long along X4 and short along X1, X2, and X3).
But the most remarkable aspect of this model is that some aspect of observers exhibits a 3-D characteristic that moves along the observer's X4 axis at the speed of light. And as the observer moves along X4 he experiences a continuous sequence of 3-D worlds. And special relativity theory tells us that observers moving at different velocities relative to each other experience different instantaneous 3-D cross-section views of the 4-D universe.
So, time is associated with the 4th dimension only because nature, for some inexplicable mysterious reason moves the consciousness along the 4th dimension at light speed. That does not make X4 a time dimension--no more than a path along a highway is regarded as a time dimension just because you can mark off clock times along the highway corresponding to the time when points along the highway points are passed.
Here is a sketch showing a black coordinate system and a blue coordinate system. The blue system represents the inertial frame for a blue guy moving at relativistic speed relative to the black frame. We identify an instant of time for each observer which represents "NOW" for each observer. But notice that the instantaneous 3-D space experienced as "NOW" for each observer is different. At that instant of time, the observers are occupying two different 3-D worlds.
So, the blue guy's 3-D world intersects an earlier time along the black X4 axis as compared to the "NOW" time for his own blue X4 axis. Thus, the blue guy sees the black X4 clock running slower than his own. But, the black guy sees the blue guy's clock running slower. But, these effects are strictly a result of the different 3-D cross-section views of the two observers. So, time dilation simply results from differences in continuous sequences of 3-D cross-section views of 4-D objects in a 4-D universe.
assionflower: no, time is not a dimension -atty: yes, it is.