When approaching the speed of light, distances are shortened due to length contraction, so if you are travelling at the speed of light wouldnt that make all distances shrink to nothing? meaning that you exist everywhere in the universe? I'm starting physics at school this year and im just curious :)
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Length only contracts in the direction of travel. If you accelerated a ship toward the speed of light and it was a tall skinny rocket with its nose pointed in the direction of travel, it would appear to an outside observer that the rocket was getting squished: that it was getting shorter but not wider or longer.
However, length contraction does degenerate to omnipresence. If you're in space, where the distances that objects are from you can be separated into x, y, and z components, then their distance is
r = sqrt( x^2 + y^2 + z^2), from the three-dimensional form of the Pythagorean Theorem
If you're traveling in the x-direction, then as you approach the speed of light their distances shorten to
r = sqrt( y^2 + z^2)
The only cases where you zoom up next to something is when it's on the x-axis (aligned with your direction of travel), where y = 0 and z = 0. So you're only able to zoom up on the direction you're moving towards and the direction you're moving from (ironic).
This interpretation agrees with time dilation: if the straight-line distance between two points approaches zero, then the time it takes to travel between them must approach zero.
An under-appreciated argument against faster-than-light is that length contraction implies you would be shorter than zero! (Mathematically, you would have imaginary length)
EDIT: Yes, a consequence of relativity is that the simultaneity of events can be different depending on the frame of reference. Person A could see two events as simultaneous while Person B sees them as sequential (though cause and effect must be preserved), if they are moving at some speed relative to one another.
However, length contraction does degenerate to omnipresence. If you're in space, where the distances that objects are from you can be separated into x, y, and z components, then their distance is
r = sqrt( x^2 + y^2 + z^2), from the three-dimensional form of the Pythagorean Theorem
If you're traveling in the x-direction, then as you approach the speed of light their distances shorten to
r = sqrt( y^2 + z^2)
The only cases where you zoom up next to something is when it's on the x-axis (aligned with your direction of travel), where y = 0 and z = 0. So you're only able to zoom up on the direction you're moving towards and the direction you're moving from (ironic).
This interpretation agrees with time dilation: if the straight-line distance between two points approaches zero, then the time it takes to travel between them must approach zero.
An under-appreciated argument against faster-than-light is that length contraction implies you would be shorter than zero! (Mathematically, you would have imaginary length)
EDIT: Yes, a consequence of relativity is that the simultaneity of events can be different depending on the frame of reference. Person A could see two events as simultaneous while Person B sees them as sequential (though cause and effect must be preserved), if they are moving at some speed relative to one another.