A Starship Bathed in Heat, and not a Star Nearby

posted by Jeff Lee on December 24, 2012

Einstein’s Special Theory of Relativity tells us that the speed of light, c, is nature’s speed limit. All particles of pure energy are locked at this speed, and all matter particles always move more slowly than c. Thus, running a fair race[1] with a light beam is not only a fool’s errand, but it would constitute proof that a village somewhere is missing its idiot. However, physics doesn’t prevent us from getting arbitrarily close to the speed of light. 99% of c is perfectly okay, as is 99.9999% of c. There is simply no way to gain that “last 9” to bring us to light speed.

Although the speed of light is very fast (a whopping 300,000 kilometers per second), the stars are very far away. Thus, the exploration of distant star systems begets the obvious requirement for very fast subluminal (slower than light speed) starships.

 

“I Feel the Need…The Need for Speed”[2]

As a ship approaches the speed of light, the remarkable phenomenon of Time Dilation becomes prominent. The astronauts on board a relativistic starship would age less, maybe very much less, than the rest of humanity left behind on Earth. With sufficient speed, a vehicle manned by its intrepid crew could voyage across the Milky Way galaxy within a crew member’s lifetime. However, the speeds needed to complete such a journey within a human lifespan are indeed daunting.

For instance, at half the speed of light (5000 times greater than the fastest spacecraft the human species has ever launched), only 15% more time passes on Earth than on the spacecraft. At 90% of light speed, 2.29 years pass on Earth for every one year on the ship. For 100 years to pass on Earth for every one year on the starship, it must travel at 0.99995c.

Time dilation . The spacecraft clock shows less elapsed time than the Earth clock. For the depicted times, the spacecraft is moving at 0.80c.

Time dilation[3]. The spacecraft clock shows less elapsed time than the Earth clock. For the depicted times, the spacecraft is moving at 0.80c.

 

Conceptualizing a starship capable of a sustained 1g acceleration is a useful thought experiment. Such a vessel would almost certainly need to be constructed in space, powered by some likely as-of-yet undiscovered means, and would embark on its awe-inspiring voyage. After accelerating in this way for about a year, this ship would be moving very close to the speed of light.

If the objective is to land astronauts or robotic probes on an alien world, it would continue accelerating until the midpoint of the journey. It would then decelerate at 1g until arriving at the destination. Such a starship will have spent most of the voyage very close to the speed of light, and time will have slowed tremendously.

Such a ship could reach our nearest stellar neighbor (Proxima Centauri, 4.24 light years away) in 3 years and 7 months (ship time). The other side of the Milky Way Galaxy (80,000 light years away) would be reached in 22 years (ship time). Even intergalactic travel is possible for such a hypothetical starship, as our neighboring galaxy, M31 (2.2 million light years away), could be reached in 28 years (ship time).

An obvious drawback of this approach is that the discoveries made by the crew (human or robotic) upon arriving at the other side of the Milky Way galaxy would be of little use to the rest of humanity. The waiting time for a radio message from the recently arrived astronauts would be 80,000 years. By the time such a message arrived on Earth, 160,000 years will have passed since the astronauts’ departure. Of course, this assumes that the ship could generate an electromagnetic signal that could be received after traveling across the galaxy. On their way to embarkation, those valiant travelers may glance at a sign at the spaceport that reads “Say your goodbyes now. None of us will be here when you return”.

Although futuristic methods of propulsion may someday make possible speeds very close to the speed of light, the energy costs would be truly enormous. However, propulsion is not the only challenge.

 

A Remnant of the Big Bang

Arno Penzias and Robert Wilson were awarded the 1978 Nobel Prize in Physics for their 1964 serendipitous discovery of the Cosmic Microwave Background (CMB) radiation. This vestige of the Big Bang permeates the entire visible universe. Thus, any starship on any heading would always be approaching (and also receding from) the CMB radiation. Any approaching radiation source is Doppler shifted to higher frequencies (i.e. blue shifted) and thus higher energies, much as the whistle of an approaching train is increased in pitch. In addition to being blue shifted, the incoming radiation undergoes a “narrowing” due to what is called “relativistic beaming”. The faster the starship travels, the more blue shifted and the more narrow the beam of incoming radiation will be.

 

Cosmic radiation background

The temperature variations in the Cosmic Microwave Background Radiation.

 

Results which I presented at the 2012 100YSS Public Symposium showed that even for speeds in excess of 5 parts per million below the speed of light[4], Doppler shifting of the CMB radiation would not present a hazard to starships. My work involves examining whether blue shifted CMB radiation would be hazardous on similar journeys to much farther destinations.

Of course, only a significant breakthrough in subluminal propulsion physics would allow us to reach such speeds anytime in the foreseeable future.

 

Temperature – A Simple Idea that’s Really Not So Simple

Temperature is a familiar concept; everyone knows what it means to be hot or cold. Hot = molten lava, the surface of the sun, a summer’s day in south Texas. Cold = a food freezer, the backside of the moon, a January day in Green Bay, Wisconsin. Temperature is conveniently defined as the average kinetic energy of molecules. The faster those molecules move (on average), the hotter the material is. In most everyday situations, this idea works well. However, complications arise when the temperature is either very low (close to absolute zero), very high (like that found within a star), when there is no matter present (e.g. the “vacuum” of space), or when an observer is moving close to the speed of light.

The temperature of interstellar space is a frigid 2.7 Kelvin[5]. That is to say, an object that isn’t generating any of its own internal heat will, if left for a long time in deep space, reach and remain at a temperature of 2.7 Kelvin. What little heat the object does receive would come from such sources as the light from distant stars, the radiation given off by ionized interstellar atomic hydrogen, and the CMB radiation.

As a starship accelerates toward the speed of light, the normal background temperature of 2.7 Kelvin is Doppler inflated, and a rapidly warming heat bath surrounds the spacecraft. However, like so many things in life, this picture is not quite so simple. There’s controversy in the literature about how different observers measure temperature. My research supports the contention that at speeds very close to the speed of light, the temperature of this heat bath is high enough to melt all known materials. Thus, Doppler temperature inflation seems to place technological speed limits on subluminal interstellar spacecraft.

 

Drag in Space

Since interstellar space is not actually vacant of matter, drag would occur as a result of impacts with free electrons, interstellar atomic hydrogen, so-called thermalized photonic gases, etc.

However, there is another source of drag – radiation pressure. As a relativistic starship moves through interstellar space, it would encounter photons from numerous sources including the CMB, ionized atomic hydrogen, stars, quasars, the occasional gamma ray burst, etc. During ultra-fast subluminal travel, these radiations would create significant drag on the bow of the starship.

Although photonic drag on a non-relativistic spacecraft is negligible, a different picture emerges for starships traveling close to the speed of light. Some of my work is investigating the drag forces on ultra-high speed interstellar spacecraft, as well as whether different bow geometries could help mollify photonic drag.

Fashioning a “ship in a bottle” by enclosing a spacecraft in a “warp bubble” would isolate it from the hazards of space. However, for any ultra-fast starship not protected by an “amniotic sac” of spacetime, the surrounding maelstrom of radiation and heat cannot be flouted.

 

[1] Investigations are currently being done to determine whether it may be possible to “cheat” in such a race, and take a “shortcut” through spacetime (e.g. “warp bubbles” and Lorentzian wormholes).

[2] Top Gun, 1986.

[3] From: http://claesjohnsonmathscience.files.wordpress.com/2012/01/t_dilation.gif

[4]  The maximum speed attained by a ship accelerating/decelerating at 1g to the exoplanet Kepler 22b, 620 light years away.

[5] In comparison, liquid helium is 4 Kelvin; liquid nitrogen is 77 Kelvin.


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2 Responses to A Starship Bathed in Heat, and not a Star Nearby

  1. MJ says:

    Could the CMB radiation at high speeds be used to power the engine, much like the concept of the scramjet?

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