We have three spatial dimensions which we can label as X, Y, and Z.
Every point in space can be described in terms of these three coordinates.
However, there is nothing special about these three particular directions,
and we can just as easily create a new coordinate system by rotating the axes.
Every point in space can now be described
in terms of the coordinates of these three new axes.
Time is also a dimension.
We therefore now have a total of four axes, but here we just show the axes
for two of the three spatial dimensions, along with the axis for time.
Every point in space and time can be described in terms of the coordinates
along the three spatial coordinates, and the coordinate along the time axis.
When an object is moving along the time axis, it is not moving through space,
but it is moving at the speed of light through time.
As before, there is nothing special about these particular directions,
and we can just as easily create a new coordinate system by rotating the axes.
But, the axis for time rotates differently than do the three axes for space.
According to Einstein’s Theory of Relativity,
all observers can believe that they are standing still,
and that it is the rest of the universe that is moving around them.
This means that when an observer travels through space and time,
their view of the axes for space-time are rotated in such a way so that
they are moving exclusively along the time axis.
But, from their point of view, the axis for time
is still at 90 degrees to the three axes for the three spatial dimensions,
and it is everyone else’s axes for time and space that have been rotated.
Different observers will therefore disagree
about the time and distance between different events.
In traditional three dimensional space,
all observers could agree on the distance between points A and B,
with the distance described by the following formula.
No matter how the three spatial axes were rotated,
the equation for distance always gave the same answer.
In the Theory of Relativity, this is no longer true.
But, what all observers will now agree on is a new parameter
called the “space-time interval”, described by the following equation.
In the Theory of Relativity,
different observers will disagree about the distance in space between points A and B.
Different observers will also disagree about
the time between an event that happened at point A,
and an event that happened at point B.
But, they will agree on this parameter called the space-time interval,
which stays constant even as the axes for time and space are rotated.
Light always travels along paths where the space-time interval is exactly zero
between every two points along the path.
This means that all observers will always agree on the speed of light.
No matter how the axes are rotated,
the speed of light will always be the same for all observers.
No matter how the axes are rotated,
the speed of light will always be the same for all observers.
Much more detailed information about Einstein’s Theory of Relativity
is available in the other videos on this channel.