Cosmology Curiosity

Hawking's astronaut, a black hole, & time dilation

Gravitational time dilation is the basis of Stephen Hawking's famous illustration of an astronaut falling into a black hole.

It's in A Brief History of Time, and Hawking starts the story thus:

'Suppose an intrepid astronaut on the surface of the collapsing star, collapsing inward within it, sent a signal every second, according to his watch, to his spaceship orbiting about the star.'

At 11:00, the astronaut is to enter the black hole's event horizon. From the orbiting pilot's viewpoint, and with poetic license added:

(a) the pilot looks at the astronaut's watch, and the pilot sees '10:57', same as what his clock says;

(b) as the pilot sees the astronaut's watch tick to 10:58, he noticed that that took a full minute in his clock;

(c) the pilot then waits for the astronaut's watch to tick to 10:58 and this time, it took one full month; and

(d) the ticking of the astronaut's watch to 10:59 took even longer, at two years.

At that point the pilot heads for home. He knows that he will never see the astronaut's watch tick to 11:00.

And why is that?

Because at 11:00 when the astronaut would have entered the event horizon, no information and not even light would be able to get out.

That's how Hawking illustrated (gravitational) time dilation. 'The lower [in the gravity well], the slower [the passage of time]'.

[Images 1 & 2 [combined above] , are c/o Wikimedia Commons]

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Gravitational time dilation

Gravitational time dilation is the relative slowing down of time as a result of being in a stronger gravitational field.

This is described in Einstein's theory of general relativity.

Just like in velocity time dilation under Einstein's theory of special relativity, it's not only clocks that tick slower but the actual passage of time as well. For the person undergoing time dilation thus, things appear normal and he does not perceive that time runs slower in his particular situation.

As for experimental proof of gravitational time dilation, Wikipedia notes:

'Gravitational time dilation has been experimentally measured using atomic clocks on airplanes. The clocks that traveled aboard the airplanes upon return were slightly fast with respect to clocks on the ground. The effect is significant enough that the Global Positioning System needs to correct for its effect on clocks aboard artificial satellites, providing a further experimental confirmation of the effect. Gravitational time dilation has also been confirmed by the Pound-Rebka experiment and by observations of the spectra of the white dwarf Sirius B.'

An astronaut floating high up above the earth is aging faster thus than the rest of us.

The lower one is in the gravity well, the slower his passage of time is. 'The lower, the slower' is a mnemonic some people use.

A non-mathematical proof of gravitational time dilation can be found here.

[Image credit: Wikimedia Commons]

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The 'top-down' cosmology of Hawking & Hertog 2

Hertog & Hawking call it 'top-down' cosmology because their theory starts with the present and then they work backwards to find out what the initial conditions may had been.

The Nature article continues:

'In effect, says Hertog, the present 'selects' the past.

'Within just a few seconds after the Big Bang, a single history had already come to dominate the Universe, he explains. So from the 'classical' viewpoint of big objects such as stars and galaxies, things happened only one way after that point. Other 'histories', say, one in which the Earth formed only 4,000 years ago, have made no significant contribution to this cosmic evolution.

'But in the first instants of the Big Bang, there existed a superposition of ever more different versions of the Universe, instead of a unique history. And most crucially, Hertog says that "our current Universe has features frozen in from this early quantum mixture".'

It is interesting to note that these cosmologists consider a Young Earth view as one of the possibilities in the multiplicity of histories.

Nature continues:

'In other words, some of these alternative histories have left their imprint behind. This is why Hertog and Hawking insist that their 'top-down' cosmology is testable. Hertog says that the theory predicts the pattern of the variations in intensity of microwave background radiation [MBR] ...

'The theory also suggests an answer to the puzzle of why some of the 'constants of nature' seem finely tuned to a value that allows life to evolve. If we start from where we are now, it is obvious that the current Universe must 'select' those histories that lead to these conditions. Otherwise we simply wouldn't be here.'

As for the last point, it is apparent that 'top-down' cosmology carries with it some anthropic principle flavor.

[Image credit: Wikimedia Commons]

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Technorati Tags: anthropic principle, CMBR, cosmology, MBR, Nature.com, Stephen Hawking, Thomas Hertog, top-down cosmology

The 'top-down' cosmology of Hawking & Hertog

The question on how the universe began does not even exist, according to Stephen Hawking, in a soon to be published paper.

Hawking's work with Thomas Hertog of CERN was written about in a Nature article:

'... the Universe had no unique beginning. Instead, they [Hawking & Hertog] argue, it began in just about every way imaginable (and maybe some that aren't).

'Out of this profusion of beginnings, the vast majority withered away without leaving any real imprint on the Universe we know today.

'Only a tiny fraction of them blended to make the current cosmos, Hawking and Hertog claim.

'That, they insist, is the only possible conclusion if we are to take quantum physics seriously. "Quantum mechanics forbids a single history," says Hertog.'

On the matter of multiple histories, it may be recalled that Richard Feynman once said that the two-slit experiment contains the essential and only mystery of quantum mechanics.

In essence, Feynman's sum-over-paths explanation says that the photon did pass through one slit, but also through the other slit at the same time, and more astonishingly through all imaginable paths within the room before passing through the slits, including a path that went through the Andromeda galaxy first and elsewhere before entering the slit.

The Nature article continues:

'The key point is that not all paths contribute equally to the photon's behaviour: the straight-line trajectory dominates over the indirect ones.

'Hertog argues that the same must be true of the path through time that took the Universe into its current state. We must regard it as a sum over all possible histories.'

[Image credit: Wikipedia]

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Einstein's E=mc², Brian Greene, and the joust

Brian Greene has an interesting article in Edge.org, entitled, 'That Famous Equation and You'.

Some excerpts [long, but interesting]:

'Here's a story for E = mc². Two equally strong and skilled jousters, riding identical horses and gripping identical (blunt) lances, head toward each other at an identical speed. As they pass, each thrusts his lance across his breastplate toward his opponent, slamming blunt end into blunt end. Because they're equally matched, neither lance pushes farther than the other, and so the referee calls it a draw.

'This story contains the essence of Einstein's discovery. Let me explain.

'Einstein's first relativity paper, the one in June 1905, shattered the idea that time elapses identically for everyone. Instead, Einstein showed that if from your perspective someone is moving, you will see time elapsing slower for him than it does for you. Everything he does - sipping his coffee, turning his head, blinking his eyes - will appear in slow motion.

'This is hard to grasp because at everyday speeds the slowing is less than one part in a trillion and is thus imperceptibly small. Even so, using extraordinarily precise atomic clocks, scientists have repeatedly confirmed that it happens just as Einstein predicted. If we lived in a world where things routinely traveled near the speed of light, the slowing of time would be obvious.

'Let's see what the slowing of time means for the joust. To do so, think about the story not from the perspective of the referee, but instead imagine you are one of the jousters. From your perspective, it is your opponent - getting ever closer - who is moving. Imagine that he is approaching at nearly the speed of light so the slowing of all his movements - readying his joust, tightening his face - is obvious. When he shoves his lance toward you in slow motion, you naturally think he's no match for your swifter thrust; you expect to win. Yet we already know the outcome. The referee calls it a draw and no matter how strange relativity is, it can't change a draw into a win.

'After the match, you naturally wonder how your opponent's slowly thrusted lance hit with the same force as your own. There's only one answer. The force with which something hits depends not only on its speed but also on its mass. That's why you don't fear getting hit by a fast-moving Ping-Pong ball (tiny mass) but you do fear getting hit by a fast-moving Mack truck (big mass). Thus, the only explanation for how the slowly thrust lance hit with the same force as your own is that it's more massive.

'This is astonishing. The lances are identically constructed. Yet you conclude that one of them - the one that from your point of view is in motion, being carried toward you by your opponent on his galloping horse - is more massive than the other. That's the essence of Einstein's discovery. Energy of motion contributes to an object's mass.

'As with the slowing of time, this is unfamiliar because at everyday speeds the effect is imperceptibly tiny. But if, from your viewpoint, your opponent were to approach at 99.99999999 percent of the speed of light, his lance would be about 70,000 times more massive than yours. Luckily, his thrusting speed would be 70,000 times slower than yours, and so the resulting force would equal your own.

'Once Einstein realized that mass and energy were convertible, getting the exact formula relating them - E = mc² - was a fairly basic exercise, requiring nothing more than high school algebra. His genius was not in the math; it was in his ability to see beyond centuries of misunderstanding and recognize that there was a connection between mass and energy at all.

'A little known fact about Einstein's September 1905 paper is that he didn't actually write E = mc²; he wrote the mathematically equivalent (though less euphonious) m = E/c², placing greater emphasis on creating mass from energy (as in the joust) than on creating energy from mass (as in nuclear weapons and power stations).

'Over the last couple of decades, this less familiar reading of Einstein's equation has helped physicists explain why everything ever encountered has the mass that it does. Experiments have shown that the subatomic particles making up matter have almost no mass of their own. But because of their motions and interactions inside of atoms, these particles contain substantial energy - and it's this energy that gives matter its heft. Take away Einstein's equation, and matter loses its mass. You can't get much more pervasive than that ...' [emphasis added]

[Image credit: Wikimedia Commons]

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White hole cosmology

A white hole (also called anti-blackhole) is a black hole running backwards in time.

While a black hole acts as a point mass that absorbs any nearby matter, a white hole acts as a point mass that repels or even ejects matter.

Two white hole scenarios are presently thought of.

The first is a white hole that is paired with and is on the opposite end of black hole. A wormhole is theorized to be interconnecting the two.

The second type of white hole is a stand alone one. Some say that this cannot exist as it would seem to violate the second law of thermodynamics.

Just the same, there's a new theory in cosmology that proposes that the Big Bang was actually a white hole. An opposing view can be found here.

Related post: Humphreys' 'white hole' cosmology

[Images 1 & 2 c/o Universe-review.ca]

Technorati Tags: anti-black hole, black hole, General Relativity, relativity, Schwarzschild geometry, Schwarzschild wormhole, white hole, worm hole

Been mulling over Einstein's E=mc²

E=mc² says that given the mass, the object's stored energy can be known.

Consider: if all of a paper clip's atoms were converted into energy, it would yield 18 kilotons of TNT (more powerful than the Hiroshima bomb of 1945). And the payload of the most powerful ICBMs consists of hydrogen gas barely enough to fill a party balloon.

It's interesting to note that the equation's original format was M=e/c². Which means that Einstein's original tack was primarily to explain mass in terms of energy rather the other way around.

In everyday life, M=e/c² would mean that:

(a) a rock on a table when lifted overhead (thus having gained potential energy), would have increased its mass;

(b) a rubber band when stretched (thus having stored elastic energy) will increase in mass; and

(c) any moving object having been imputed with kinetic energy will gain mass.

The gain in mass in the above examples are negligible. But in certain scenarios, the effect can be quite dramatic. For instance, a puny marshmallow if can be speeded up to c would gain such a huge mass that it can blast the Earth to bits.

Just some qualifications on what 'mass' is. Any object has an invariant mass [m₀] and it's independent of its velocity [v]. Its relativistic mass [m_r] on the other hand, rises with v and approaches infinity as v nears lightspeed [c]:

m_r = e/c²
m₀ = sqrt (e²/c⁴ - p²/c²)

where e is energy, p is momentum and c is the speed of light in a vacuum.

Note that when an object is at rest, p would be zero and the second equation is then reduced to m₀ = e/c², same as in m_r.

In ending, reiterating physicist Frank Wilczek's remarks on E=mc² may be fitting:

'So right from the beginning Einstein was thinking about the question of could you explain mass in terms of energy [i.e., more along M=e/c²]. It turned out that the realization of that vision, the understanding of how not only a little bit of mass but most of the mass, 90 percent or 95 percent of the mass of matter as we know it, comes from energy. We build it up out of massless gluons and almost massless quarks, producing mass from pure energy. That's the deeper vision.'

[Images 1, 2, & 3 c/o Wikimedia Commons & Wikipedia]

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Einstein's E=mc² explained

HEAR how ten top physicists describe Einstein's E=mc² to curious non-physicists.

A text version is also available.

The physicists featured are: Nima Arkani-Hamed, Janet Conrad, Sheldon Glashow, Brian Greene, Alan Guth, Tim Halpin-Healy, Lene Hau, Michio Kaku, Neil deGrasse Tyson, and Frank Wilczek.

Some interesting excerpts:

'Before Einstein, before E=mc², there was no even possible thought that just a hunk of material, any old hunk of material, was pregnant with enormous quantities of energy that you could release if only you could harness it ... yet these amazing facts about the world can just be sitting all around us waiting for the correct eye, for the correct angle to understand them properly. So that's the legacy that theoretical physicists are trying to carry on today.' -- Nima Arkani-Hamed (Theoretical physicist, Harvard University)

'E=mc² is not the whole of the equation that Einstein wrote down ... the whole equation is E is equal to mc², the amount of energy the particle would have if it was sitting still, plus the extra energy that it would have if it has any motion. And if you think about it in that equation, if you now say E is equal to mc² plus this energy of motion, you could set the mass equal to zero [e.g., as in a neutrino or a photon] and you still have energy.' -- Janet Conrad (Experimental physicist, Columbia University)

'Of course, energy and mass themselves have nothing whatever to do with light, so it is a little peculiar to find c, the speed of light, sitting in this all-important formula that relates energy to mass. What I guess is the easiest way of describing the excuse for that is that c in special relativity is not just the speed of a certain object that's called light. C is the limiting velocity of any motion in special relativity.' -- Alan Guth (Theoretical physicist, MIT)

'E=mc² famously suggests the idea that you can get a lot of energy out of a small amount of mass. But that's not what Einstein had in mind, really, and you won't find that equation in the original paper. The way he wrote it was M=e/c² and the original paper had a title that was a question, which was, "Does the inertia of a body depend on its energy content?" [the answer is "yes"] So right from the beginning Einstein was thinking about the question of could you explain mass in terms of energy. It turned out that the realization of that vision, the understanding of how not only a little bit of mass but most of the mass, 90 percent or 95 percent of the mass of matter as we know it, comes from energy. We build it up out of massless gluons and almost massless quarks, producing mass from pure energy. That's the deeper vision.' -- Frank Wilczek (Theoretical physicist, MIT)

[Image by Shizhao, per Creative Commons Attribution ShareAlike License v. 2.0.]

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Christian views on cosmology & life's origin

The main Christian cosmology views are: (a) young earth creation; (b) progressive creation or old earth creation; and (c) theistic evolution.

An Origins.org article by Rich Milne and Dr. Ray Bohlin provides a good primer:

'The first view of science and earth history we will discuss is the recent or literal view. This position is often referred to as scientific creationism, creation science, or young earth creationism. Young earth creationists believe that the earth and the universe are only tens of thousands of years old and that Genesis gives us a straightforward account of God's creative activity.

'The second position, progressive creationism or day-age creationism, holds that the earth and the universe are billions of years old. However, progressive creationists believe that God has created specifically and ex nihilo (out of nothing), throughout the billions of years of earth history. They do not believe that the days of Genesis refer to twenty-four hour days, but to long, indefinite periods of time.

'A view traditionally known as theistic evolution comprises the third position. Theistic evolutionists essentially believe that the earth and the universe are not only billions of years old, but that there was little, if any, intervention by God during this time. The universe and life have evolved by God-ordained processes in nature. Theistic evolutionists, or evolutionary creationists, as many prefer to be called, believe that the first chapter of Genesis is not meant to be read historically, but theologically. It is meant to be a description of God as the perfect Creator and transcendent over the gods of the surrounding ancient Near Eastern cultures.'

Bibleandscience.com has an article on the organizations affiliated with each school of thought.

[Image credit: Wikimedia Commons]

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Technorati Tags: cosmology, creation, creation science, creationism, day age theory, evolution, old earth creation, progressive creationism, theistic evolution, young earth creation

Gerald Schroeder's cosmology 3

Here's the chronology of Gerald Schroeder's cosmology:

Day One of Genesis lasted 8 billion years, Day Two 4 billion, Day Three 2 billion, Day Four 1 billion, Day Five 0.5 billion, and Day Six 0.25 billion. The total is 15.75 billion years, like what modern cosmology says.

Schroeder's cosmology is a variant of the 'day-age' theory. As for the initial event of creation, Schroeder uses the inflationary version of the Big Bang model.

Here's a sampling of responses to Schroeder's cosmology --

Reasons to Believe: 'Response to Genesis and the Big Bang'

Answers in Genesis: 'Gerald Schroeder and his new variation on the “day-age” theory'

The Panda's Thumb: 'Confronted with critique, Schroeder lost voice'

Amazon.com: see the book's customer reviews [yours truly's review is dated 12 June 2006, by 'CosmologyCuriosity_dotcom']

Schroeder's talks on cosmology are available as free video: (a) Genesis One - A Physicist Looks at Creation [1 hr+], and (b) Beyond Intelligent Design - the Scientific Case for a Creator [31 minutes].

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Technorati Tags: big bang, cosmology, day-age theory, Gerald Schroeder, inflation