# 1-second Ship

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This ship allow us to travel to everywhere in the Universe in just 1 second. This is a fact, that comes out of General Relativity that has not been extensively explored in science fiction, but, according to this theory, it’s true: you can reach everywhere in the Universe in just one second (assumming a couple of very unlikely things).

One important and handy aspect of our ship is that we have a very accurate atomic clock inside it, and a perfect copy of this clock is stationed on Earth.

# Having our ship waiting for launch in a time-invariant orbit

If we need to keep a certain orbit, we have to travel at specific orbital speed. So, due to Special Relativity, turns out that this speed will impose a time dilation on our atomic clock in relation to the one on Earth. At the same time, the Earth warp space time and this warping due to Gravity also impose a time dilation in relation to anything staying away from Earth.

So, the time dilation due to gravity cancels out time dilation due to relative speed of orbit/relative speed of Earth’s surface at an orbit height of about 9,500 km above Earth center or about 3,200 km above sea level.

$t’ = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}}$

$v = \sqrt{\frac{GM}{r}}$

Replacing to account for the time dilation due to orbital speed

$t’ = \frac{t}{\sqrt{1 - \frac{GM}{c^2r}}}$

To be continued….

# Let’s assume Energy is not a problem. But…

Assuming:

• Astronaut can support any kind of acceleration.
• Ship can have infinite acceleration.
• Ship+Astronaut weights 1000 kg
• Energy is infinite.

My 1-second ship can travel at the speed of 0.999 999 999 999 999 973 26 of c (light-speed) an reach in just one second [in ship-time frame] to Alpha/Proxima centauri. The astronaut, according to Lorentz transform, is one second old during this trip, and the atomic clock only ticks 1 second. He just pushed a button and he arrived to its destination. During that time more that 4.33 years has passed on Earth.

Energy is not a problem and there is plenty of it. However, during this short trip, the mass of the ship grew to 22360679 x 1 Ton, and we passed closed to Jupiter. Did we affect Jupiter orbit? After all, we are a shooting Black-Hole !

From Special Relativity, an object of mass m at rest has a “rest-mass energy”

$E_{0} = m c^2$

If we accelerate this object to some speed v, its total energy increases too, to

$E = m \frac{c^2}{\sqrt{1 - \frac{v^2}{c^2}}} > E_{0}$

In physics, it was used to be traditional to package

$\frac{m}{\sqrt{1 - \frac{v^2}{c^2}}}$

into something called the “relativistic mass”, but nowadays, the word “mass” is reserved for m alone.

The source of gravitational curvature of space-time (and hence of the gravitational forces we feel) is ‘‘energy’’, not just mass, and to get the correct answer for ‘‘how’’ this object might curve space-time, we have to involve General Relativity, where the source of curvature is called the “stress-energy tensor”, and contains information about the object’s mass and velocity.

In principle a spaceship moving past Jupiter with a speed v extremely close to c ‘‘could’’ cause measurable gravitational effects on the planet, though it’s difficult to calculate the precise nature of these effects. In practice, we haven’t observed anything like this, and don’t encounter objects moving anything close to those speeds relative to us — at least above the subatomic level (there are Ultra-High-Energy Cosmic Rays with observed energies that imply speeds even closer to c than your numbers).

# Who is accelerating ?

Due to relativity, can’t we make the same assumption about the Earth moving and accelerating backwards, and the spaceship being the one stationed without moving ? Absolute movement does not exists so why can’t we shift the roles and say that the Earth’s clock has advanced 1 second and the ship’s clock has advanced 4.33 years ?

TO BE CONTINUED

# References

• Lawden, Introduction to Tensor Calculus, Relativity and Cosmology, 2003
• Bernard & Ira from Ask an Astrophycisist
• Santalo, Vectores y Tensores con sus aplicaciones, Eudeba, 1970
• https://www.quora.com/At-which-orbital-altitude-the-time-dilation-due-to-a-higher-speed-would-be-the-same-as-the-time-contraction-because-we-are-moving-away-from-Earth
• https://www.quora.com/What-is-the-speed-in-terms-of-c-that-a-spacecraft-need-to-reach-in-order-to-travel-to-Alpha-Centauri-in-just-1-second-from-the-point-of-view-of-the-moving-astronaut

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