- #1
ramcg1
- 31
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Spacetime raises many questions.
Three-dimensional space is easy to visualise. We live in it. We can denote orthogonal axes as x, y and z and have oodles of fun with three-dimensional geometry.
One wonders, is there really a fourth dimension and is that dimension time?
Newtonian physics has a time parameter. All of space exists at the same unique point in time and moves, as a unit, forward through time at a constant rate.
Spacetime tells us that that an event occurs at a unique point in spacetime with a set of coordinates such as (t, x, y, z). From there we can we can use a lot of advanced mathematics to have oodles of fun with four-dimensional space.
Being inquisitive and sceptical by nature, I ask myself what this fourth dimension "t" really represents.
When I boil down the introductory explanations to spacetime, I find that the "t" represents how long it takes electromagnetic radiation (light) to travel from one spacetime event to another. This velocity is taken because it leaves the spacetime interval invariant under changes of coordinates. Thus, one unit along the "t" axis represents one second of flight time for electromagnetic radiation. That's it, end of story, now get on with the mathematics of spacetime.
Take an imaginary empty sphere with a shell that emits no electromagnetic radiation. Inside the sphere, there is nothing, no matter and no electromagnetic radiation. This sphere has volume so it has the three Cartesian dimensions. Allow the outer surface of the sphere to reflect light. I can see the sphere and it exists in the linear Newtonian time that I am used to. If there has been and never will be any electromagnetic radiation within the sphere, how can I assign the speed of light to the conversion factor between space and time? Does spacetime have any meaning if there is no electromagnetic radiation? Should I now assign zero the conversion c reducing four-dimensions to three-dimension? However, a division by zero would render the spacetime transformations meaningless.
To be able to have flight times (where the velocity is c - the speed of light) between imaginary clocks there must be electromagnetic radiation. If there is no electromagnetic radiation then there are no flight times (where the velocity is c) between imaginary clocks.
All electromagnetic radiation must have a source. From a point source, an electromagnetic wave front would be spherical. Does spacetime have any meaning before the formation of the electromagnetic radiation? Is negative time only relevant to the current position of an existing wavefront or photon?
When I turn on my bedroom lamp (assume it a point source that illuminates in all directions at once) the wave front of the light is a sphere moving a velocity c. I can represent the position of any photon on that sphere by the four coordinates (t, x, y, z) where t is the time of flight. Things to note:
• This t has no meaning before the lamp is turned on
• Before the lamp was turned on the light had no existence and no velocity
My neighbour can turn on his bedroom lamp and achieve the same result.
I can extend this to an infinite number of neighbours and for every one of these point sources I can either have an expanding sphere of light or nothing.
Now normally turning on and off point sources would be a random event and each point source would be independent from all the others. I could allocate these events to positions on a linear time scale. I could explore the maths of flight times between positions on the expanding spheres and between expanding spheres, but that is not a good model of spacetime. I would have positions in my four-dimensional space that do not have expanding spheres of light.
Alternatively, I could switch them all on. Now I have an infinite number of expanding spheres. I can measure the distances between two point sources by the linear three-dimensional distance between them and by the time, it would take the light to reach the other point source. Thus, I can construct a four-dimensional vector for light traveling from one point source to the anther point source.
Now that I have my four-dimensional vector, a model of spacetime, I can go on to play with it mathematically and do all the wondrous things of spacetime. Does this mean that Minkowski space is a model of the surface area of an infinite number of electromagnetic expanding wave fronts originating from an infinite number of point sources?
Not a good model of time as a fourth dimension though, is it, not in the same ilk as the Cartesian dimensions, quite Newtonian actually.
Three-dimensional space is easy to visualise. We live in it. We can denote orthogonal axes as x, y and z and have oodles of fun with three-dimensional geometry.
One wonders, is there really a fourth dimension and is that dimension time?
Newtonian physics has a time parameter. All of space exists at the same unique point in time and moves, as a unit, forward through time at a constant rate.
Spacetime tells us that that an event occurs at a unique point in spacetime with a set of coordinates such as (t, x, y, z). From there we can we can use a lot of advanced mathematics to have oodles of fun with four-dimensional space.
Being inquisitive and sceptical by nature, I ask myself what this fourth dimension "t" really represents.
When I boil down the introductory explanations to spacetime, I find that the "t" represents how long it takes electromagnetic radiation (light) to travel from one spacetime event to another. This velocity is taken because it leaves the spacetime interval invariant under changes of coordinates. Thus, one unit along the "t" axis represents one second of flight time for electromagnetic radiation. That's it, end of story, now get on with the mathematics of spacetime.
Take an imaginary empty sphere with a shell that emits no electromagnetic radiation. Inside the sphere, there is nothing, no matter and no electromagnetic radiation. This sphere has volume so it has the three Cartesian dimensions. Allow the outer surface of the sphere to reflect light. I can see the sphere and it exists in the linear Newtonian time that I am used to. If there has been and never will be any electromagnetic radiation within the sphere, how can I assign the speed of light to the conversion factor between space and time? Does spacetime have any meaning if there is no electromagnetic radiation? Should I now assign zero the conversion c reducing four-dimensions to three-dimension? However, a division by zero would render the spacetime transformations meaningless.
To be able to have flight times (where the velocity is c - the speed of light) between imaginary clocks there must be electromagnetic radiation. If there is no electromagnetic radiation then there are no flight times (where the velocity is c) between imaginary clocks.
All electromagnetic radiation must have a source. From a point source, an electromagnetic wave front would be spherical. Does spacetime have any meaning before the formation of the electromagnetic radiation? Is negative time only relevant to the current position of an existing wavefront or photon?
When I turn on my bedroom lamp (assume it a point source that illuminates in all directions at once) the wave front of the light is a sphere moving a velocity c. I can represent the position of any photon on that sphere by the four coordinates (t, x, y, z) where t is the time of flight. Things to note:
• This t has no meaning before the lamp is turned on
• Before the lamp was turned on the light had no existence and no velocity
My neighbour can turn on his bedroom lamp and achieve the same result.
I can extend this to an infinite number of neighbours and for every one of these point sources I can either have an expanding sphere of light or nothing.
Now normally turning on and off point sources would be a random event and each point source would be independent from all the others. I could allocate these events to positions on a linear time scale. I could explore the maths of flight times between positions on the expanding spheres and between expanding spheres, but that is not a good model of spacetime. I would have positions in my four-dimensional space that do not have expanding spheres of light.
Alternatively, I could switch them all on. Now I have an infinite number of expanding spheres. I can measure the distances between two point sources by the linear three-dimensional distance between them and by the time, it would take the light to reach the other point source. Thus, I can construct a four-dimensional vector for light traveling from one point source to the anther point source.
Now that I have my four-dimensional vector, a model of spacetime, I can go on to play with it mathematically and do all the wondrous things of spacetime. Does this mean that Minkowski space is a model of the surface area of an infinite number of electromagnetic expanding wave fronts originating from an infinite number of point sources?
Not a good model of time as a fourth dimension though, is it, not in the same ilk as the Cartesian dimensions, quite Newtonian actually.