Faster-than-light travel

http://en.wikipedia.org/wiki/Alcubierre_drive
NASA is studying the Alcubierre drive as a possible mechanism of faster-than-light travel. Lubos Motl remarked that the drive would break the special theory of relativity:
http://motls.blogspot.fi/2013/07/relativity-bans-faster-than-light-warp.html,
though the drive is consistent with the equations of the general theory of relativity. Let us discuss if faster-than-light travel makes sense, and whether it might be possible.

Faster-than-light travel enables a time machine

The above Wikipedia article states that a faster-than-light rocket would make closed timelike curves possible, that is, the rocket could travel backwards in time. Suppose that we have a rocket that can travel at a "moderate" speed of  2 times the speed of light, relative to the frame of the Earth.

Using the formulas of time dilation and length contraction:
http://en.wikipedia.org/wiki/Time_dilation,
http://en.wikipedia.org/wiki/Length_contraction,
we can calculate how we can travel back in time with our rocket.

Suppose that stars A and B are traveling at the speed 0.99c, where c is the speed of light, relative to the Earth. They move to the direction of the vector (A, B):

A ------------ 1 light year ---------- B ------> speed 0.99c

                           O <--- the Earth

The distance of stars A and B is 1 light year, measured from the reference frame of the Earth.

The time dilation coefficient for A and B is:

             1
______________ = 1 / sqr(1 - 0.99^2) = 7.0888.
sqr(1 - v^2 / c^2)

That is, a time interval t measured at star A appears for an observer in the frame of the Earth to last 7.0888 t.

The length contraction coefficient for A and B is the same as the time dilation coefficient. That is, the distance of stars A and B in the frame of A and B is 7.0888 light years (recall it is only 1 light year in the frame of the Earth).

Suppose that we have a rocket that can move at speed 2c relative to the Earth. Let us make the rocket to fly from star A to star B. As the rocket starts from A, we also send a ray of light from A towards B.

The rocket arrives at B after 1 year of the Earth's time. But the ray of light only moves at a relative speed of only 0.01c relative to B (the speed of light observed from the Earth is always c, regardless where the light originated from). Thus, the ray of light arrives at B after 100 years of the Earth's time.

The time interval (rocket arrives at B, light arrives at B) is 99 years, relative to the frame of the Earth.

Since the time dilation coefficient is 7.0888, the time interval of (rocket arrives at B, light arrives at B) is 99 years / 7.0888 = 13.966 years in the reference frame of A and B.

But remember that the distance of A and B in their own reference frame was just 7.0888 light years. Thus, in the frame of A and B, the light arrives at B 7.0888 years later than it left A. Since the rocket arrives at B 13.966 years earlier (in the frame of A and B), we see that the rocket flew 6.877 years backwards in time!

In the calculation above, we assumed that our rocket can fly at speed 2c relative to the frame of the Earth. Since in special theory of relativity, all inertial frames are equivalent, we can let the rocket fly at speed 2c also relative to the frame of A and B. Let us make our rocket fly back from B to A at speed 2c, relative to the frame of A and B. The flight back takes 3.544 years. The rocket moved back in time 6.877 years when it flew from A to B. And it moves forward in time 3.544 years when it flies back to A. That is, the rocket arrives at A 3.433 years BEFORE it left A! Our rocket has acted as a time machine and sent us backwards in time 3.433 years on star A.

Time travel makes faster-than-light travel impossible?

If we allow faster-than-light travel only relative to the frame of the Earth or the Milky Way, then there is no time travel with respect to our frame. Ww just travel immensely fast within our galaxy.

But if we allow time travel relative to any frame, like in our calculation above, then time travel is possible, and we have to face the numerous paradoxes involved with time travel. Suppose that I use my fast rocket to travel one week back in time, and then blow up the rocket before it started its journey. How can I (or my copy) start my journey one week later? The rocket was blown up, and does not exist any more!

We instinctively believe in the principle that the past cannot be changed. If the past can be changed, then there essentially does not exist the past, because the past could be changed arbitrarily in the future. Any kind of flexible time travel, where we can transport intelligent robots to carry out missions in the past, breaks the principle that the past cannot be changed.

To avoid the paradoxed of time travel, we could use the many worlds interpretation from the philosophy of quantum mechanics. In that interpretation, the universe is constanly branching according to the results of "experiments" we perform on microscopic systems. For example, in the double-slit experiment, the branching happens according to the spot where a photon hits the screen behind the double slit.

If our time travel machine takes us to another branch of the branching universe, then no paradoxes arise. In that brach I can blow up the copy of my time travel rocket, and that does not spoil my departure with the rocket which I did from another branch of the universe. But we do have the restriction that our time travel rocket cannot take us to the past of our current branch.

A generalized travel machine: travel between universes

The previous line of thought takes us to the concept of  generalized travel machine. We already have machines that can can take us to a different position in space. We can also imagine time machines that take us to the future or the past (the past of another branch of the universe). A generalized travel machine would take us to any universe, to any place in it, and to any time in that universe. Again, our generalized travel machine cannot take us to the past of our branch of the universe, though.

Interstellar travel is "almost" around the corner

Most people do not know that we already have working designs for interstellar spaceships. Designs, which are feasible with today's technology. The big obstacle is the enormous cost of these projects.

http://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)
The above Wikipedia article introduces Project Orion, which in the 1950s and the 1960s studied the design of a rocket that is propulsed by small nuclear explosions. Behind the spaceship is a pusher plate, behind which we detonate small nuclear bombs. Nuclear explosions push the spaceship to ever higher speeds. Theoretically, the spaceship can be accelerated up to 10 % of the speed of light.

Freeman Dyson's Orion design

In 1968, famous physicist Freeman Dyson performed an analysis on alternative designs of a nuclear pulse spaceship. A major problem in the design is how to cool the pusher plate after each nuclear explosion, so that the plate does not melt.

Dyson's Momentum Limited Orion rocket would contain a ship whose mass is 100,000 metric tons, and a stockpile of 300,000 hydrogen bombs, each weighing 1 metric ton. The spaceship would be huge by today's standards: the mass of the International Space Station which is currently orbiting the Earth, is only 450 tons.

The pusher plate in the Momentum Limited Orion rocket would contain an ablation coating that would slowly vaporize in nuclear explosions, and take away the excess heat.

Dyson's design would produce a rocket that runs at 3 % of the speed of light. Thus, it would only take 133 years to reach Alpha Centauri.

Dyson estimated the cost of the rocket at $367 billion, which in current dollars is roughly $3,000 billion.

Nuclear fallout is not a big problem

http://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)#Potential_problems
Freeman Dyson estimated that each launch would cause only at most 1 extra lethal case of cancer for humans. That is clearly negligible, and constitutes no reason to refrain from using nuclear pulse propulsion in rockets.

The fallout can be reduced by performing the first explosion with conventional explosives. Also, we can design hydrogen bombs where the energy from fission, and consquently the fallout, is very small.

Finding habitable exoplanets

Recent results from the Kepler space probe show that there are probably billions of Earth-like planets in the habitable temperature zone in the Milky Way. Locating such planets requires better instruments than Kepler. And we still need better instruments to determine the spectrum of the atmosphere of a potentially habitable planet.

Maybe in 20 years we will know if there are habitable planets in the vicinity of the Earth, that is, at most 15 light years away. And we will know if their atmosphere contains carbon dioxide or oxygen. If the atmosphere contains oxygen, then it might be that there is actually vegetation on the planet.

Finding a planet with vegetation would be very exciting news. With good luck, the atmosphere might be such that humans can readily breathe the air on the planet! But if we do not find any oxygen, then we need to pick a planet that contains a suitable amount of carbon dioxide in its atmosphere and "terraform" such planet for it to be easily colonizable by humans.

Terraformation of planets

It may be that the Earth is the only planet in the Milky Way that carries life. If that is the case, we will not find any planets where the atmospere contains enough oxygen for humans to breathe. But if we find a planet with water and a suitable amount of carbon dioxide in its atmosphere, we can slowly transform the planet to be suitable for humans.

The idea is that we send an unmanned spacecraft to the planet to seed there cyanobacteria and maybe also plants. If we are able to create a vegetation similar to the Earth, then it will take on the order 40,000 years to produce enough oxygen to the atmosphere of the planet, so that humans can breathe the air there.

The travel time to exoplanets is of the order of hundreds or thousands of years, and terraformation of planets takes tens of thousands of years. We are talking about really long-term projects here.

Panspermia: there might well be exoplanets that carry vegetation

The Earth formed 4.5 billion years ago, and it was under a very intense bombardment from asteroids for a few hundred million years after that. The asteroid bombardment has ejected large parts of the early Earth's crust to space, and eventually out of our solar system. Thus, much of the Milky Way has been polluted by rocks from the young Earth.

Suppose that there already was life on the Earth during the asteroid bombardment. Let us calculate how many 10 cm size life-carrying rocks from the crust might have been ejected from the early Earth in the asteroid bombardment. Suppose that 2 % of the Earth's area was ejected. Let us assume that life might have been present in the top 10 meters of crust rock. That makes:

 10 million square kilometers * 10 billion 10-cm-sized crust rocks / km^2
 = 10^17 rocks

The volume of the Milky Way is some 100,000^2 * 10,000 = 10^14 cubic light years. From the Kepler space telescope results, it has been estimated that the Milky Way might contain 10 billion planets that are friendly for life. Thus, there is an average of 10^-4 life-friendly planets in a cubic light year.

Suppose that we have a rock that drifts slowly a distance of one light year past the stars in the Milky Way. The probability of it hitting a life-friendly planet along that distance is:

 10^-4 *  (0.04 light seconds)^2 / (3 * 10^7 light seconds)^2
= 4 * 10^-21

Above we have used the fact that the diameter of an Earth-like planet is some 0.04 light seconds, and that a light year is 3 * 10^7 light seconds.

If the rock moves at a relative speed of 10 km/s past the stars in the Milky Way, then in a billion years, the rock will cover a distance of  33,000 light years.

We get that the probability for a single rock to hit a life-friendly planet in 1 billion years is roughly 10^-16.  Since there were 10^17 such rocks, we get that 10 rocks will hit a life-friendly planet during a billion years.

Life may spread further from these 10 exoplanets if there is sufficient asteroid bombardment of those planets. That way, we may get a chain reaction where life spreads exponentially through the Milky Way. In 10 billion years, most of the 10 billion life-friendly planets in the Milky Way might get seeded with life.

Currently, it is not known if bacteria can survive a billion years in space inside a rock of size 10 centimeters. But it is well possible that bacteria could stand such conditions. Also, we do not know if bacteria can survive the heat when the rock falls through the atmosphere of the planet.

We do not know if life originated on the Earth, or if it started on some exoplanet in the Milky Way, and was seeded to the Earth inside a rock that was ejected from some exoplanet. If life originated on the Earth, and it originated only after the big asteroid bombardment of the Earth, then it may be that the Earth is the only life-carrying planet in the Milky Way.

But if life originated on the Earth or some exoplanet before the asteroid bombardment of that planet, then rocks containing seeds of life have polluted the Milky Way. In that case, it is possible that we will find many exoplanets that already carry life. Furthermore, that life may be related to the life on the Earth. Exoplanets may harbor life where the DNA structure and much of the chemistry of living cells is similar to the Earth. We might even find planets where there are plants and animals that look like ones on the Earth. In that case, sci-fi stories about strange planets with jungle-like vegetation and dinosaur-like creatures might actually be more realistic than we could imagine!

Ball lightning, does it exist?

http://en.wikipedia.org/wiki/Ball_lightning
The Wikipedia article talks about the ball lightning as "an unexplained atmospheric electrical phenomenon". I am going to argue that the ball lightning almost certainly does not exist as a physical phenomenon. Instead, most sightings of the ball lightning are probably optical after-images in the eye of the observer.

Advent of camera phones and the ball lightning

According to the Wikipedia article, in year 1960, 5 % of U.S. population claimed having seen the ball lightning. The phenomenon is described as a light ball lasting up to 20 seconds. Sometimes the ball lightning appears indoors. I personally had a close relative who said that he had seen a ball lightning hovering above their kitchen stove.

Now that almost everybody is carrying a camera phone in their pocket, we would expect to see an explosion in the number of photographs and videos of the ball lightning. Thousands of such pictures should be snapped every year!

But from the Internet I can find few modern pictures of the ball lightning. A Google image search brings up some old drawings of the ball lightning inside a house, and some outdoors shots of various lights. Looks like the ball lightning has become very "shy" at the advent of camera phones. It no longer appears so often. The simple explanation for this is that the phenomenon never existed physically.

Ball lightning likes houses and humans?

The classic ball lightning story is that it enters a home through a chimney, moves around in a room, and throws small objects, like books, around. The father of my best friend told that as a child, during World War II he was reading a newspaper, when a ball lightning appeared and behaved just like in the classic story. He said that he did not notice any ball lightning by himself, but the other people present in the room were terrified and told this story afterwards to him.

The question is, why does a ball lightning enter homes? Is the ball lightning an intelligent being who likes to frighten humans? If a ball lightning by chance goes inside through a narrow chimney, we should have at least a thousand times more ball lightnings circling around in the yard of the house! The simple explanation is that the phenomenon does not exist physically, but only in the minds of humans.

Automatic cameras

There are probably millions of surveillance cameras in the world which record video. Using a Google search, I was not able to find a single surveillance video which would contain a ball lightning. This is in a huge contrast to the fact that several percent of people claim to have observed a ball lightning, often only a few meters away.

Scientific explanations for the ball lightning

Wikipedia lists several hypotheses which attempt to explain the ball lightning as a physical phenomenon. For some of the hypotheses, there exist laboratory experiments that create some kind of a glowing ball. But there is no adequate explanation how the glowing ball could form in nature, or even inside a house. For example, the vaporized silicon hypothesis has hard time explaining how the burning silicon can enter houses.

Ball lightning as an after-image in the eye

I believe the after-image hypothesis can explain many ball lightning observations. A lightning strikes close to the observer, and the bright flash of lightning leaves an after-image in the eye of the observer. The after-image may appear like a glowing ball to the perplexed observer. After-images in  the eye tend to "float" slowly as the eye turns. That would explain the typical floating slow movement which is reported about ball lightnings.

Ball lightning as a sociological phenomenon

It is natural for a human being to be impressed by the power of a thunderstorm, a giant and violent act of nature. Stories of ball lightning can spice up ordinary stories of thunder. This may explain why people like to interpret what they see as a semi-mystical phenomenon. They like to tell about these experiences to other people.

Relationship to UFO's and ghosts

The ball lightning could be classified as a subcategory of UFO's, Unidentified Flying Objects. Stories of the ball lightning can also be compared to stories of ghosts. Stories of UFO's, ball lightnings, and ghosts serve a psychological and sociological purpose. What are the common characteristics of these stories, and what are the differences? I will later write some thoughts about this.