Impracticality of Instantaneous Faster than Light Travel

Posted by Christopher Wojno Wed, 29 Aug 2007 16:15:00 GMT

Prompt

I enjoy various science fiction television series: Firefly (2002), StarTrek (1987), and Battlestar Galactica (2004). While watching an episode of the latter-most title, the crew demonstrated the ability to perform a “hyperlight jump.” Such a jump is the physical translocation of an object, such as the spaceship, from one point in 3D space, to another point in space without crossing any of the points in between in space or time (it was instantaneous). This circumvents Einstein’s upper bound on the velocity of matter. However, I had one lingering feeling that something is amiss.

Alright, you caught me. Yes, I was trying to figure out if such a means of travel could be implemented. Nothing in our universe has been observed that demonstrates a similar ability. Not to say it does not exist here or in another universe (assuming you believe in the multiverse theory) but merely to state a lack of templates. However, simply because something has not yet been observed does not make it impossible. However, energy requirements of such a maneuver (or lack thereof) are insurmountable.

Givens

• The First Law of Thermodynamics states: energy cannot be created or destroyed, it can only be changed
• Newton’s Law of Universal Gravitation Equation
• My math is fuzzy and error prone

Armed only with those two (the third works against me) concepts, I can deduce: if such FTL travel is physically possible, the energy requirements to perform it nullifies its practicality. Newton’s law will suffice, imperfect and non-universal as it is. It still provides a quick and dirty estimation of gravity at sufficient mass and distance.

Why the first law of thermodynamics?

Because it means that you cannot create energy for free. I propose that such a faster than light jump is a method for creating a perpetual motion/energy device unless the energy requirement is bounded by the law of gravitation.

An object in relativistic free-fall with a larger mass trades potential energy for kinetic energy until reaching a final potential energy state. You can determine the amount of potential energy gained (or lost) using the potential energy equation: U_{m~ = mgh where U}m~ is the potential energy of a mass, m is the mass of the object, g is the gravitational acceleration (varies with distance) and h is the distance between the two masses. Lets face it, if you’re trying to get passed gravity, you have at least two masses you’re trying to separate.

See Waterfall by M.C.Escher. Source: M.C.Escher GalleryIf you could theoretically teleport an object from the surface of the earth to a point in sub-orbit with less energy than it generates as kinetic energy when it falls back to earth, you have created a machine with greater than 100% efficiency: a perpetual energy device. Any one could use this technology to capture the kinetic energy and generate power (think never-ending waterfall). This violates the First Law of Thermodynamics and is widely considered to be impossible, though some venture fruitlessly and sometimes embarrassingly to develop the exception to the rule.

To compensate for the acceleration changing based on distance, turn the gravitational acceleration into a function of radial distance, then convert the potential energy formula into a function of radial distance for both height and gravitational acceleration. Then, integrate over the height.

Therefore: the total energy required of such a faster than light jump must be greater than, or equal two that equation. And that statement explains absolutely nothing until you understand one more concept. I’m assuming that the potential energy equation is universal just as the law of thermodynamics is understood to be universal.

Worst case potential energy configuration of the universe: Mass is represented by the black line, your spaceship is in blue as are some labels, the distances are in green. Source: Christopher Wojno’s GIMP Scientific Doodle Collection: 2007 So, the energy required must account for the worst case scenario: You have two bodies in all of the universe, the object and energy attempting a faster than light jump, and the rest of the universe aligned in a single file column at the atomic level. Why? The universe is not self aware. It does not keep track of its own configuration (though, that is an interesting twist on a god or gods threory). So, there is no set maximum of contiguous mass below the mass that already exists and energy capable of being converted into mass. Since one could theoretically jump from any point in space to another, with any configuration of universal masses, the worst case energy scenario must be assumed as the least amount of energy which can be expended. Unless, of course, the universe is cognizant and can plot the path of least energy through the potential energy fields that would have been traversed should the instantaneous travel been foregone and only require that amount of energy. This is highly unlikely, but if it that is the case, from a computer science stand-point, it would be interesting to see how the universe does optimization algorithms. But I digress… considerably.

This is the MINIMUM amount of energy required for a single jump. Remember, you can’t get something for nothing and there has to be an resolution of apparently dissimilar and discontinuous potential energies. It’s impossible to calculate the worst case scenario without knowing the precise mass of the universe and the desired distance to jump. But know that the greater the distance, the greater the energy that will be required. I may have jumped the gun calculating the potential energy as a function of distance because it’s clear to see that the amount of energy required to overcome the concerted gravitational pull of the entire universe, minus your insignificant (by comparison) ship and fuel, makes such a technology practically impossible.

Even if you jump inwardly toward the universe, it is also assumed the universe knows no direction of instantaneous travel. You will always be competing against the absolute lower bound of universal potential energy.

Disclaimer

This is just my theory. It’s not even well supported. I offer no other support for it at this time. If I’m wrong, please make the appropriate corrections and e-mail or comment. I really hope this isn’t the case or that there is some quantum loop-hole or unobserved phenomena that contradicts the assumptions.

Sorry if I killed your dreams of owning a spaceship with FTL capability. I know I am.

Posted in Theory | Tags einstein, energy, faster, galactica, gravity, light, newton, perpetual, than | 1 comment