What Happens to Matter Inside a Black Hole?

Blog, Eugene Toth, Math, Science and Technology

by Eugene Toth
October 2, 2016Black Hole.jpghttp://www.universetoday.com/33454/how-do-black-holes-form/

A galaxy swirls around a black hole

At the center of our galaxy, gasses, stars, and nebulae swirl around a supermassive black hole, Sagittarius A.1   

Stephen Hawking explained the proportion of matter in a black hole to the matter we know.

“…the black hole would have the mass of  a mountain compressed into less than a million millionth of an inch, the size of the nucleus of an atom!” 2

For the Earth to make a black hole, it would have to be squeezed to the size of a cranberry.

In A Brief History of Time, by Stephen Hawking (New York, Bantam Books 1988) and The Black Hole War by Leonard Susskind (New York:  Hachette, 2008), two famous physicists present differing theories of what happens to matter inside a black hole.  They consider what happens to matter sucked into a black hole.  Does it disappear?

No one disputes that black holes absorb matter.   Matter is anything that has a volume and mass.  Everything we see is matter.   Matter takes five forms – plasma, gas, liquid, solid, and Bose-Einstein condensate, the coldest form of matter. 

We see light.  Light travels in waves.  Light is also matter.   Photons are packets of light that travel in waves. 

Black objects absorb light.    The capacity to absorb light produces blackness.   We can only see a black object if some photons reflect off the object.   

Nothing can escape the horizon of a black hole.   In contrast to other black objects, black holes absorb all photons.   That no light comes out of the horizon, makes the area inside the horizon black.  In space we see a huge gaping hole.  We can see only the horizon of a black hole.  Nothing inside a black hole can ever communicate with anything outside of it.  Of what is inside a black hole, physicists can only theorize.

black-hole-diagram

At the center of the horizon lies the              singularity of a black hole.    http://www.wall.org/~aron/horizon.htm

Evaporation and obliteration theory

Cambridge’s professor Stephen Hawking theorized that a black hole destroys all matter that passes the horizon.  Hawking said:

“When a black hole evaporates, the trapped bits of information disappear from our universe.  Information isn’t scrambled. It is irreversibly, and eternally, obliterated.”4

Theoretical physicists Stephen Hawking and Bill Unruh proved that black holes, just like any other pieces of matter, have a temperature.  If black holes have a temperature, then black holes radiate heat.   Hawking and Unruh called it “black body radiation.”  Hawking and Unruh reasoned that if black holes have a temperature, then black holes eventually evaporate. 

A black hole emits “Hawking radiation.”  At the surface of the event horizon a black hole creates antiparticles.  An antiparticle is counterpart of a particle.  The antiparticle of a quark an antiquark.  When a quark and an antiquark combine, they create a hadron.  The antiparticle counterpart of small particles make up the antiparticle counterparts of large particles.  For example, a neutron is made up of quarks.   Antiquarks make up antineutrons.  The destruction of a particle leaves a neutral particle and an antiparticle.  For example, the destruction of a proton leaves a neutron and a positron.

Antiparticles can also make up “anti-elements”.  For example, a positron, the opposite of an electron, and a proton make up the anti-hydrogen atom.  The anti-hydrogen atom has the same properties as a normal hydrogen atom.5

Hawking radiation consists of particles, like light.  Unlike light, however, Hawking radiation can escape a black hole.  So how does Hawking radiation escape a black hole?      At the event horizon, virtual pairs of particles separate.

Virtual pairs of particles comprise a particle and its antiparticle.  At the event horizon, one-half of a virtual pair of particles is inside the event horizon, while the other half is outside the event horizon.  The particle inside the horizon will be lost to the particle on the outside of the event horizon.  On the inside of the horizon, the singularity sucks in half of the virtual pair.   The half on the outside of the horizon escapes the black hole’s pull.  This decreases the mass of the black hole, causing the black hole to “evaporate”.6

hawkingteamu.png

“Soft hairs” form a halo around a black hole.                          http://phys.org/news/2016-06-hawking-team-soft-hair-theory.html

As a black hole evaporates, it grows hotter and smaller.  After a black hole reaches high temperatures, the black hole begins to release particles of high energy.  As the black hole gradually grows hotter and smaller, it continues to evaporate.  It grows smaller.  As it grows smaller, it grows hotter.   Physicists know almost nothing about black holes once black holes reach their last burst of evaporation. 

The Hawking theory that black holes evaporate contradicts Antoine Lavoisier’s Law of the Conservation of Mass.   In 1785, Lavoisier, in his Law of the Conservation of Mass, stated that matter cannot be created or destroyed.  

Lavoisier conducted many experiments, in closed vessels, in which the weight remained constant, within experimental error.  He produced reactions of tin or lead with oxygen.  He analyzed mercury calx (HgO).  With large burning lenses he focused the sun’s rays to reach high temperatures to produce chemical reactions.  With a large lens Lavoisier burned a diamond and show that it produced only CO2.

Black holes differ from other objects in space.  Black holes have an extremely strong gravitational pull.  Nevertheless, black holes should not contradict the Law of the Conservation of Mass.

Pocket universe theory

Particle physicist Leonard Susskind teaches at Stanford.  He considered but rejects a theory that inside the black hole, a piece of space breaks off and forms a universe, isolated from our perception of spacetime. 

One of the most trusted principles of physics states that information is never lost. 7    According to the pocket universe theory, information that falls into a black hole goes into a baby universe. According to the pocket universe theory, a black hole does not obliterate information.   A black hole stores the information in the pocket universe.    This theory solves the problem with Hawking’s theory, that information cannot be created or destroyed.  If a black hole evaporated, then the information in the pocket universe would become completely unobservable. 

The pocket universe theory fails because it requires a change of energy.   To create a pocket universe would require a change of energy.   A quantum fluctuation is a temporary change in the amount of energy in a point in space.   Physicists Leonard Susskind, Thomas Banks, and Michael Peskin all agree that quantum fluctuations would transform into thermal fluctuations, changes in thermal energy.  Thermal fluctuations would almost instantaneously heat the universe to impossibly high temperatures. 

Wormholes

The pocket universe theory suffers a second problem.  The only way information could enter a pocket universe would be through a wormhole.  A wormhole is a theoretical passageway through space.  For example, the Einstein-Rosen Bridge is a passageway from one universe to the other through a singularity.   The singularity acts as a wormhole. John Archibald Wheeler, of John Hopkins University showed, by mathematics, that wormholes would open and closein so a short amount of time that nothing could pass through.   Susskind cites Wheeler’s wormhole as evidence that wormholes creating miniature universes would not be possible.

Information Vault Theory

Some speculate that black holes stop evaporating once they reach the Planck Mass.   The Planck mass is the combined mass of the number of particles in a Planck unit.  A Planck unit is the maximum allowed mass to contain one elementary charge.   The Planck mass is about 0.0217651 milligrams.   Physicists believe that once a black hole reaches this size, it stops evaporating.  It becomes an infinitely small information vault, containing all the information it absorbed.  This theory conforms to the Law of Conservation of Matter more than Hawking’s theory.  By the information vault theory, information is not destroyed. 

Susskind disagrees with the information vault theory.  He states that a particle containing potentially infinite amounts of information would have infinite entropy. The Second Law of Thermodynamics states that entropy constantly increases.   Entropy is decay into disorder.  Water eroding a rock creates entropy.  An ice cube melting causes entropy.  Susskind defines entropy as:

“Entropy is a measure of the number of arrangements that conform to some specific recognizable criterion.”8

 According to the First Law of Thermodynamics, heat balances itself, by flowing into cold objects.  Heat raises the temperature of cold objects and lowers the temperature of hot objects until a system has a uniform temperature.  Infinitely entropic particles would cause a thermodynamic disaster. The infinite entropy caused by the information vaults would burn up the universe.

The bathtub option

entropy.jpg

                 Entropy                  http://www.michelecoscia.com/?p=1041

Susskind compares a black hole to a bathtub.  Susskind analogizes matter entering a black hole to drops of ink spilling into a bathtub of water.   Before an ink drop falls into the water, the ink drops are sharply defined.  One can easily differentiate between the ink and the water.  As the ink falls into the water, the ink drops dissolves.  The difference between ink and water blurs.  The water becomes cloudy.  Soon all that remains is a uniform tub of slightly gray water. 

If the inky water evaporates, the molecules of ink and water continue to exist.  They enter the air.  They scatter and separate from each other.  Susskind’s “bathtub option” edits Stephen Hawking’s theory to conform to the Law of Conservation of Matter. 

Conclusions

Both Hawking and Susskind believe that, at the center of a black hole, the singularity, along with all the other matter inside the black hole, eventually evaporates.   Hawking theorized that a black hole destroys and obliterates all matter which enters the horizon.   Susskind’s bathtub option predicts that the matter is scattered.  

FOOTNOTES

         1. Henderson, Mark “Astronomers confirm black hole at the heart of the Milky ‘Way'” London: Times Online. (December 9, 2008) (Accessed 10/2/2016).  “…[L]urking at the center of our galaxy is a supersized black hole with a Schwarzschild radius of about 100 million miles – about the size of the Earth’s orbit around the Sun.”  Susskind, Leonard The Black Hole War, My Battle with Stephen Hawking to make the World Safe for Quantum Mechanics (New York: Hachette Book Group, 2008) p.32.

         2.  Hawking, Stephen A Brief History of Time (New York: Bantam Books, 1998). p 112

         3.   Susskind, Leonard The Black Hole War, My Battle with Stephen Hawking to make the World Safe for Quantum Mechanics, supra, p.32   

         4.  Susskind, Leonard, The Black Hole War, My Battle with Stephen Hawking to make the World Safe for Quantum Mechanics, supra, p. 185

         5.  Wikipedia, “Antiparticle,” https://en.wikipedia.org/wiki/Antiparticle

         6. Strassler, Matt “Virtual Particles, What are they?” https://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/

         7.  Susskind, Leonard, The Black Hole Warsupra, p. 179 “Smaller than an atom, smaller than a quark, smaller even than a neutrino, the single bit may be the most fundamental building block.  Without any structure, the bit is just there, or not there. John Wheeler believed that all material objects are composed of bits of information.” The Black Hole War, supra, p.136

         8.  Susskind, Leonard, The Black Hole War, supra, p. 131

BIBLIOGRAPHY

            Cain, Fraser, “How Do Black Holes Form?”  Universe Today http://www.universetoday.com/33454/how-do-black-holes-form/ (Dec. 23, 2015) (Accessed 10/2/16)

           Hawking, Stephen, A Brief History of Time (New York: Bantam Books, 1998).

           Henderson, Mark “Astronomers confirm black hole at the heart of the Milky ‘Way.'” London: Times Online. (December 9, 2008) (Accessed 10/2/2016)

            Strassler, Matt, “Virtual Particles, What are they?” https://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/.

           Susskind, Leonard, The Black Hole War, My Battle with Stephen Hawking to make the World Safe for Quantum Mechanics ( New York:  Hachette Book Group, 2008).

            Wikipedia, “Antiparticle,” https://en.wikipedia.org/wiki/Antiparticle. (Accessed 10/2/2016).

            Yirka, Bob, “Hawking team updates soft hair theory to help solve black hole information paradox.” http://phys.org/news/2016-06-hawking-team-soft-hair-theory.html#jCpf. June 9. 2016 (Accessed 10/2/2016)

The Quadratic Formula

Alwin Peng, Authors, Math, Uncategorized

 

By Alwin Peng

The quadratic formula is used in order to find the value of x in an equation such as ax^2 + bx + c = 0.

It is x = (-b + (b^2 – 4ac)^(1/2))/2a.

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It simplifies a more complicated way to solve the expression. Below, I will show you why the formula works by explaining how it was derived.Deriving the quadratic formula goes as follows:

ax^2 + bx + c = 0

ax^2 + bx = -c .We subtract both sides by C

x^2 + bx/a = -c/a .We divide both sides by A

x^2 + bx/a + (b^2)/(4a^2) = -c/a + (b^2)/(4a^2) .We add (b^2)/(4a^2) to both sides   so that the left side of the equation is factorable

(x + b/2a)^2 = -c/a + (b^2)/(4a^2) We factor the left side

(x + b/2a)^2 = -4ac/(4a^2) + (b^2)/(4a^2) We multiply the top and bottom of the fraction -c/a by 4a so that it can be added with (b^2)/(4a^2), achieving the common denominator of 4a^2 in both fractions.

(x + b/2a)^2 = (-4ac + (b^2))/(4a^2) We now add the like terms

x + b/2a = (((b^2) – 4ac)^(1/2))/2a We square root both sides

At last, we subtract both sides by b/2a, isolating x and getting the quadratic formula:

x = (-b + (b^2 – 4ac)^(1/2))/2a

The method  that we just used to obtain the quadratic formula is known as “completing the square”, but just plugging values into the quadratic formula is a faster and simplified way to complete the square.

 

Fibonacci Sequence

Authors, Eugene Toth, Math, Miscellaneous, Science and Technology, Uncategorized

Fibonacci Numbers

by Eugene Toth

Fibonacci numbers are an amazing sequence of numbers which appear all throughout human history and throughout nature.  One may see fibonacci numbers in the great pyramid or a nautilus’ shell.  This amazing sequence of numbers have a simple pattern but a stunningly complex role in the world around us.

Pascal’s Triangle

Authors, Eugene Toth, Math, Miscellaneous, Science and Technology, Uncategorized

Pascal’s Triangle

by Eugene Toth

Mathematicians named Pascal’s triangle after the French mathematician Blaise Pascal.    Pascal’s triangle is a triangular graph.

In Pascal’s triangle each number is the sum of the two directly above it.  The numbers in each row are numbered beginning with 0 for the first row. Each number is positioned either to the left or to the right of the numbers in the rows above. The sum of the elements of a single row is twice the sum of the row preceding it.  A Pascal’s triangle can expand infinitely.