Black hole firewalls - real or not?

I have been combing through the web about arguments for and against so-called black hole firewalls. I will present some of my thoughts.

http://en.wikipedia.org/wiki/Firewall_(physics)
Joe Polchinski et al. caused commotion in the theoretical physics world in 2012 when they published their paper that seems to imply there is an infinitely hot "firewall" just behind the event horizon of an old black hole.

That is, assuming that black holes do not lose information, and that they radiate their information away in Hawking radiation, and assuming that the no-cloning theorem of quantum mechanics is true, then there MUST be an infinitely hot firewall just under the event horizon. The firewall prevents any observer from entering the black hole alive.

Their observation is in a stark contrast to Einstein's equivalence principle which states that a freely falling observer should not observe anything special as he falls through the event horizon (this is called the "no drama" hypothesis).

The Black Hole Information Loss Problem

http://en.wikipedia.org/wiki/Thorne%E2%80%93Hawking%E2%80%93Preskill_bet
Stephen Hawking initially claimed that black holes DO destroy information. The information would be forever lost in the singularity of the black hole. The Hawking radiation would be totally random black body radiation and would not carry away the lost information. In 2004, Hawking famously reversed his opinion and conceded that black holes do not destroy information, after all.

Information loss in a black hole is mathematically an ugly phenomenon, as it breaks the "unitarity" of quantum mechanics. That is, in quantum mechanics, time is reversible in the CPT symmetry, and the earlier state of a system is uniquely determined by a later state of the wave function. But if a black hole would destroy information, then there would be no way to deduce the early state - before the formation of the black hole - from the later state - where the black hole has already formed.

2004: Hawking Claims Black Holes Preserve Information, After All

http://arxiv.org/pdf/hepth/0507171.pdf
In 2004, Hawking presented his argument that black holes do preserve information, after all. His idea is to consider the formation and the radiating away of a black hole as a scattering experiment from the point of view of a very faraway observer. Particles are sent into the system. If the particles at some point in time become dense enough, a black hole forms. But the black hole is later radiated away in Hawking radiation.

Hawking seemed to claim that since there is a possible history where the black hole does not form at all, that is, the particles involved never condense enough to collapse into a black hole, then the information of the initial state is preserved in the wave function of that history.

Hawking's argument seemed flawed to me, and it looks like no eminent physicist has endorsed Hawking's idea. In quantum mechanics, we have to consider ALL possible histories. We cannot discard any. We cannot omit the case where a black hole forms and radiates away. The probability of black hole formation might be, say, 99.999 %. It does not help if the information is preserved in the remaining 0.001 % of cases. Unitarity must hold for all histories. It is not enough that it holds for 0.001 % of histories.

Quantum Mechanics Seems to Imply a Firewall in a Black Hole

http://arxiv.org/abs/1207.3123
In their paper, Polchinski et al. show quite convincingly that we have to give up one of the basic principles of quantum mechanics, the no-cloning theorem, or we must give up Einstein's equivalence principle that states there is "no drama" for an observer that falls freely inside a black hole.

I personally now favor the quantum mechanical point of view. Unitarity is a beautiful mathematical property. Giving up unitarity would be a much greater loss than giving up Einstein's equivalence principle.

Einstein's Solution is Mathematically Ugly

The black hole model of general relativity contains a singularity at the center of the black hole. Needless to say that a singularity is an ugly phenomenon from the mathematical point of view. As is laws of nature would break down at a point of space.

To do away with the singularity, people have suggested that some theory of quantum gravity prevents the singlularity from forming. Let us assume that there are some unknown laws of nature that stop the collapse of a black hole into a singularity. If there are some unknown laws that cause nature from differ from general relativity, it might be natural that the differing happens already at the event horizon of a black hole?

Decay of Protons in a Black hole

http://en.wikipedia.org/wiki/Virtual_black_hole
http://en.wikipedia.org/wiki/Proton_decay
As a sidenote, let us bring up the question about the decay of protons. If Hawking radiation really makes a black hole to evaporate, and the radiation is mostly photons, then we have a mechanism to turn a hydrogen atom, a proton plus an electron, into photons. That would imply proton decay. Proton decay is predicted also by some grand unified theories in physics.

Does a Black Hole Have an Interior at All?

http://en.wikipedia.org/wiki/Holographic_principle
If there is searing hot firewall just behind the horizon of a black hole, we can ask if the black hole has an interior at all. According to Bekenstein and Hawking, a black hole is the structure which has the maximal possible entropy in a given area of space. The entropy is NOT proportional to the volume of the enclosed space, but proportional to the area of the black hole. This has been taken as evidence for the holographic principle that the universe really has only two large spatial dimensions and a 3D universe is an illusion.

Since the black hole, in a way, reveals the holographic nature of the universe, it does not sound too far-fetched to speculate that a black hole does not have an interior at all in the sense of our 3D universe. Maybe material falling in a black hole gets distributed in some exotic form on the horizon of the black hole, and the "inside" of the black hole does not exist at all.

Is a Black Hole Analogous to an Atom for Quantum Mechanics?

The hydrogen atom is an example of an object which can superficially be viewed as a classical ball from a long distance. For example, if hydrogen atoms form ideal gas, the atoms in the gas seem to behave like in classical mechanics. But when we go close to the atom and start to study its internal structure, we notice that classical mechanics does not work at all. We have to study the structure of a hydrogen atom in quantum mechanics to get right results.

Maybe a black hole is an "atom" of universe in the way that its internal structure can only be understood through quantum mechanics? That is, we have to forget about the theory of general relativity when we study the internal structure of a black hole. In the previous section, we argued that since black holes reveal the holographic nature of our universe, it might be that they have to be treated in a quantum mechanical way and we must forget about general relativity in their internal structure.

Attempts to Reconcile Quantum Mechanics and the Equivalence Principle

After Polchinski et al. published their seminal paper about firewalls, there has been a flurry of papers where different authors try to get rid of firewalls by reconciling quantum mechanics and Einstein's equivalence principle in some way.

http://arxiv.org/abs/1306.0533
Juan Maldacena and Leonard Susskind suggest that entangled systems in quantum mechanics are not separate entities after all, but are connected through a wormhole in general relativity. Then the interior of a black hole would NOT be separate from the exterior, and the no-cloning theorem for an infalling observer is not violated. That is, we do not need any firewall behind the event horizon. The observer falls with no drama inside the black hole. The authors coin a slogan "ER = EPR".

http://arxiv.org/abs/1402.5674
In another paper, Leonard Susskind suggests that the no-cloning principle is preserved in the way that it is exceedingly hard to compute the state of the interior of a black hole from the Hawking radiation. That is, though the no-cloning principle is violated, it is impossible for anyone to see the violation because the calculation to show the violation would require too big computing resources.

To my mind, the two above suggestions to do away with firewalls sound as complicated and far-fetched as hidden variable theories that try to revert quantum mechanics back to classical physics.

http://arxiv.org/abs/1401.5761
Trying to solve the firewall problem, Stephen Hawking himself suggests that a black hole does not contain an event horizon at all, but just an "apparent horizon". Then there would be no need for a firewall, as there does not exist a true black hole in the classical sense. If Hawking is able to form a mathematical theory from his ideas, it would be a nice solution to the problem. If I understand correctly, the "firewall" in Hawking's solution is the matter that is densely packed very close to the apparent horizon of his quasi black hole.

Fuzzballs

http://en.wikipedia.org/wiki/Fuzzball_(string_theory)
A fuzzball is an attempt to explain a black hole as a string theoretic object. A fuzzball does away with the singularity in the black hole, and it predicts that information is not lost in a black hole. Maybe a fuzzball is the right description of a black hole, if we abolish Einstein's equivalence principle and use quantum mechanics as our guide?

Conclusion

I have been browsing the World Wide Web for a few days now, and it is obvious that there is no consensus among physicists whether black hole firewalls exist or not. A large number of papers have been published in the past two years, and many of them try to do away with firewalls. But none of these papers seems convincing enough. My guess at the moment is that we really have to give up the equivalence principle and treat black holes as purely quantum mechanical objects. Maybe that involves a firewall or maybe we have to assume that a black hole has no interior at all.

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.