Light is better quantified as a relative distance.

[Eirhead]

And the "speed" of it represents the warp in time over that distance. Light will always move at the "speed of light" relative to you. Hence I theorize you should be able to bend distances and time based on your relative motion.

 

I dunno, there's probably nothing eye-popping here. Just wanted some confirmation :Glasses:

 

Assuming I'm correct, the speed of light relative to an earthly observer should be somewhat easy to break with a powerplant on a spacecraft that can maintain a 10m/s² acceleration relative to earth for 1 year constantly.

[Eirhead]

An easy test for this theory would be to set a laser on a rail to measure it's distance to a stationary object. Measure once traveling towards it, and again traveling from it (with a spot on the track set to trigger the measurement so it's a constant. The instrumentation will have to either extremely precise or the speeds on the rail exceptionally high. Preferably a combination of the 2 for best results.

[ronthepon]

Are you familiar with the Special theory of relativity?

 

You line of thought goes along it direction.

[Pyrotex]

An easy test for this theory would be to set a laser on a rail to measure it's distance to a stationary object. Measure once traveling towards it, and again traveling from it (with a spot on the track set to trigger the measurement so it's a constant. The instrumentation will have to either extremely precise or the speeds on the rail exceptionally high. Preferably a combination of the 2 for best results.

Exactly what is this experiment supposed to show? Do you expect it to confirm standard theory or violate it? Do you expect the two measurements of distance to be the same or different?

[CraigD]

And the "speed" of it represents the warp in time over that distance. Light will always move at the "speed of light" relative to you. Hence I theorize you should be able to bend distances and time based on your relative motion.

This is an excellent theory, but assuming you wrote it up well overnight, you’d be 105 years late, because, as Ron noted, this is exactly part of Einstein’s famous 1905 theory of special relativity.

Assuming I'm correct, the speed of light relative to an earthly observer should be somewhat easy to break with a powerplant on a spacecraft that can maintain a 10m/s² acceleration relative to earth for 1 year constantly.

You’re misinterpreting a consequences of special relativity.

 

Special relativity guarantees, that, assuming a spacecraft can accelerate at a sufficient rate for a sufficient duration (which turns out to be a very, very difficult practical engineering problem, which I discuss later), it can get between (nearly) any two point in space in as little time as desired according to a clock on the spacecraft. According to a clock at rest relative to its starting point (eg: on Earth), the ship will take at least slightly longer than the distance between the two points divided by the speed of light. The difference between these accelerated and un-accelerated clocks are known as time dilation.

 

With the few postulates and principles of special relativity and a bit of not-too difficult algebra, you can get a formula for distance traveled [imath]x[/imath] relative to your starting point given constant acceleration [imath]a[/imath], and time relative to the ship [imath]t[/imath],

[math]x = \frac{2 c^2}{a} \left(\cosh \left( \frac{a t}{2c} \right) -1 \right)[/math]

where [imath]c[/imath] is the speed of light and [imath]\cosh[/imath] is the hyperbolic cosine function,

[math]\cosh(x) = \frac{e^x +e^{-x}}2[/math]

where [imath]e \dot= 2.718281828459045236[/imath] is the natural logarithm base.

 

Playing with this formula, you’ll find that the “break the speed of light” time for a constant [imath]a[/imath] = 1 g (about 9.8 m/s/s) is a bit less than [imath]t[/imath] = 5 years. Since you’d likely want to arrive at your destination with about zero velocity relative to your starting point, the time needs to be doubled, giving a 10 year shipboard year trip of just a little less than 11 light years distance. For longer times, the effect is much more dramatic – a slightly longer than 56.25 year trip gets you about 2,000,000 light years, about the distance to our closest galactic neighbor, Andromeda.

 

A pretty good article on this can be read at this archive page.

 

It’s interesting to consider, using special relativity and relativistic Doppler effect calculations, what things would look like aboard such a ship.

 

This said, considering the engineering of a spacecraft that can accelerate at 1 g for anywhere near such durations pretty much rules out any powerplant that’s carried on the ship. The ship would almost certainly have to be powered externally, like an electric train, but on an interstellar scale. Even if you could do this, the problem of preventing a spacecraft moving at nearly [imath]c[/imath] from being destroyed by collisions with interstellar matter is also daunting. The ship would likely need minor planet-size ablative (eg: ice) shield, possibly replace multiple times in flight.

 

Interesting, but not easy, engineering!

 

The title of this thread, “Light is better quantified as a relative distance”, doesn’t make much sense, because light is quantified by units of energy ([imath]\mbox{mass} \cdot \mbox{distance}^2 / \mbox{time}^2[/imath]), while distance, relative or otherwise, is quantified just in units of distance.