michaellee8 · October 1, 2017 02:13
diff --git a/propsoal-gravitational-circular-transport-system b/propsoal-gravitational-circular-transport-system
 # Theoretical Proposal of Gravitational Circular Transport System

 ## Inspiration

 In the recent discuss with Professor Chu Ming Chung, we concluded that theoretically, if we can produce sufficient gravitational wave from a massive object that is moving in an extreme speed, it is possible to achieve faster-than-light travel relative to a inertial reference frame. 

 ![Gravitational wave from a pair of neutron stars orbiting.](https://upload.wikimedia.org/wikipedia/commons/b/b8/Wavy.gif "Gravitational wave from a pair of neutron stars orbiting.")
 Two-dimensional representation of gravitational waves generated by two neutron stars orbiting each other. From Wikipedia., licensed under Public Domain.

 ![Relativistic Doppler effect of light wave](https://upload.wikimedia.org/wikipedia/commons/d/d4/Velocity0_70c.jpg "Relativistic Doppler effect of light wave")
 A source of light waves moving to the right, relative to observers, with velocity 0.7c. The frequency is higher for observers on the right, and lower for observers on the left. From Wikipedia, attribution "By en:TxAlien - en:Image:Velocity0 70c.jpg, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1066460".

 The concept is quite simple, because of the relativistic Doppler effect, given a very fast gravitational wave source, those gravitational wave produced will contract along the moving direction of such object, and expand opposite the moving direction of such object. It is believed that these gravitational wave will distort space-time to contract and expand respectively. It is believed that these non-symmetrical distortion to space-time will allow faster-than-light travel relative to a far apart reference frame, but remains slower than light in the current reference frame. Such an idea is in fact referenced from the idea of warp engine (Alcubierre drive), but inspired distortion to space-time is caused by **Doppler effect of gravitational wave** instead of the space-time expansion due to negative mass.

 ## Difficulties

 However, such approach is extremely difficult to turn into practice. 

 ![Mass-energy warps spacetime.](https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Gravitation_space_source.svg/869px-Gravitation_space_source.svg.png "Mass-energy warps spacetime.")
 Mass-energy warps space-time. From Wikipedia.

 It is known that even a neutron star can only distort space-time at a ratio of $10\%$, which means such object have to be extremely massive, i.e. black hole. 

 <iframe src="//commons.wikimedia.org/wiki/File:Warped_Space_and_Time_Around_Colliding_Black_Holes_(Courtesy_Caltech-MIT-LIGO_Laboratory,_produced_by_SXS_project).webm?embedplayer=yes" width="854" height="480" frameborder="0" webkitAllowFullScreen mozallowfullscreen allowFullScreen></iframe>
 Warped space-time around colliding black holes.

 Scientist also observed that even in a extremely large-scale gravitational event like merge of black-holes, only a small proportion amount of energy, approximately $3\%$ is converted into gravitational energy, and hence far from enough to cover the length contraction and time dilation effect due to the distortion to time-space of normal gravity, which actually slow down the object for a far apart observer. i believe a much bigger ratio is required for that.

 Moreover, given a massive enough star, it will take a very large amount of energy to move it in a speed that Doppler effect can be significant.

 Therefore, it is nearly impossible to achieve that kind of mass, acceleration and speed in the same time if we are talking about a linear motion, but what about **circular motion**?

 ## The binary star system

 It is discussed in Wikipedia that a binary star system can generate gravitational wave. As stated above, to generate such non-symmetrical distortion to time-space, a combination of extreme mass, acceleration and speed is required. Due to my insufficient mathematics skill to analysis such acceleration due to gravitation field, I would like to provide an approximate algebra approach with Newton's law of gravitation and proper acceleration for relativistic circular motion here. Such equation is given by $a={GM}/{\left(2r\right)^2}= \gamma^2 {v^2}/{2r} $, resulting in: 

 $$GM\propto \left(\gamma v\right)^2 r =  \left(\gamma \omega \right)^2 r^3$$

 Note that such $r$ refers to the radius of orbit. It describes a very complex mathematical relationship, causing such system very hard to construct. To achieve a large $v$ to approach speed of light, it requires a large $r$ since a large $\omega$ can cause our massive object to leave its orbit. However, if $r$ is actually too big, $M\propto \left(\gamma v\right)^2 r $ implies that $v$ have to be small, especially when the gravitational constant $G$ is too small. And what even worse, look at that acceleration $a$, it is inversely proportional to $r^2$, which means if we get the radius big, we will have no acceleration to get enough gravitational wave.

 Fortunately, there are a mathematics solution to that. Just increase $M$ is enough, right? But we faces two practical problems here. Where in universe can you **get an object with that mass**? I suppose you can get something like a neutron star or black hole to do that, how on Earth can you **find enough energy to push it into that kind of velocity**?

 However, how if what we get isn't a pair of binary stars, but **a bunch of stars orbiting in a an orbit**?. 

 ## The "flying horses" system
	# Theoretical Proposal of Gravitational Circular Transport System

	## Inspiration

	In the recent discuss with Professor Chu Ming Chung, we concluded that theoretically, if we can produce sufficient gravitational wave from a massive object that is moving in an extreme speed, it is possible to achieve faster-than-light travel relative to a inertial reference frame.

	![Gravitational wave from a pair of neutron stars orbiting.](https://upload.wikimedia.org/wikipedia/commons/b/b8/Wavy.gif "Gravitational wave from a pair of neutron stars orbiting.")
	Two-dimensional representation of gravitational waves generated by two neutron stars orbiting each other. From Wikipedia., licensed under Public Domain.

	![Relativistic Doppler effect of light wave](https://upload.wikimedia.org/wikipedia/commons/d/d4/Velocity0_70c.jpg "Relativistic Doppler effect of light wave")
	A source of light waves moving to the right, relative to observers, with velocity 0.7c. The frequency is higher for observers on the right, and lower for observers on the left. From Wikipedia, attribution "By en:TxAlien - en:Image:Velocity0 70c.jpg, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1066460".

	The concept is quite simple, because of the relativistic Doppler effect, given a very fast gravitational wave source, those gravitational wave produced will contract along the moving direction of such object, and expand opposite the moving direction of such object. It is believed that these gravitational wave will distort space-time to contract and expand respectively. It is believed that these non-symmetrical distortion to space-time will allow faster-than-light travel relative to a far apart reference frame, but remains slower than light in the current reference frame. Such an idea is in fact referenced from the idea of warp engine (Alcubierre drive), but inspired distortion to space-time is caused by Doppler effect of gravitational wave instead of the space-time expansion due to negative mass.

	## Difficulties

	However, such approach is extremely difficult to turn into practice.

	![Mass-energy warps spacetime.](https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Gravitation_space_source.svg/869px-Gravitation_space_source.svg.png "Mass-energy warps spacetime.")
	Mass-energy warps space-time. From Wikipedia.

	It is known that even a neutron star can only distort space-time at a ratio of $10\%$, which means such object have to be extremely massive, i.e. black hole.

	<iframe src="//commons.wikimedia.org/wiki/File:Warped_Space_and_Time_Around_Colliding_Black_Holes_(Courtesy_Caltech-MIT-LIGO_Laboratory,_produced_by_SXS_project).webm?embedplayer=yes" width="854" height="480" frameborder="0" webkitAllowFullScreen mozallowfullscreen allowFullScreen></iframe>
	Warped space-time around colliding black holes.

	Scientist also observed that even in a extremely large-scale gravitational event like merge of black-holes, only a small proportion amount of energy, approximately $3\%$ is converted into gravitational energy, and hence far from enough to cover the length contraction and time dilation effect due to the distortion to time-space of normal gravity, which actually slow down the object for a far apart observer. i believe a much bigger ratio is required for that.

	Moreover, given a massive enough star, it will take a very large amount of energy to move it in a speed that Doppler effect can be significant.

	Therefore, it is nearly impossible to achieve that kind of mass, acceleration and speed in the same time if we are talking about a linear motion, but what about circular motion?

	## The binary star system

	It is discussed in Wikipedia that a binary star system can generate gravitational wave. As stated above, to generate such non-symmetrical distortion to time-space, a combination of extreme mass, acceleration and speed is required. Due to my insufficient mathematics skill to analysis such acceleration due to gravitation field, I would like to provide an approximate algebra approach with Newton's law of gravitation and proper acceleration for relativistic circular motion here. Such equation is given by $a={GM}/{\left(2r\right)^2}= \gamma^2 {v^2}/{2r} $, resulting in:

	$$GM\propto \left(\gamma v\right)^2 r = \left(\gamma \omega \right)^2 r^3$$

	Note that such $r$ refers to the radius of orbit. It describes a very complex mathematical relationship, causing such system very hard to construct. To achieve a large $v$ to approach speed of light, it requires a large $r$ since a large $\omega$ can cause our massive object to leave its orbit. However, if $r$ is actually too big, $M\propto \left(\gamma v\right)^2 r $ implies that $v$ have to be small, especially when the gravitational constant $G$ is too small. And what even worse, look at that acceleration $a$, it is inversely proportional to $r^2$, which means if we get the radius big, we will have no acceleration to get enough gravitational wave.

	Fortunately, there are a mathematics solution to that. Just increase $M$ is enough, right? But we faces two practical problems here. Where in universe can you get an object with that mass? I suppose you can get something like a neutron star or black hole to do that, how on Earth can you find enough energy to push it into that kind of velocity?

	However, how if what we get isn't a pair of binary stars, but a bunch of stars orbiting in a an orbit?.

	## The "flying horses" system