Traveling at the Speed of Thought

Daniel Kennefick

Nov 15, 2006

LIGO facility at Hanford, Washington State

The New Look of Astronomical Observatories?

What is a Gravitational Wave?

Einstein reacts to a gravitational wave

Ripples in the Curvature of Spacetime

Gravitational Waves (in red) emerging from a binary black hole system as realized within a NASA supercomputer

Why is NASA interested?

Schematic of spacecraft arrangement in LISA mission

What are the sources for these detectors?

The antennae galaxies in the process of merging

The “Sound” of two Black Holes Merging

iota_40_10000_4_4_90_h.wav

Sources Close to HomeSources Close to Home

Stars in orbit around Sag A*, a possible black hole at the center of our Galaxy, with a mass of a million Suns

Image of the center of our Galaxy. Inset shows a blow up of the region of object Sag A*

How do we know that Gravitational Waves Exist?

They do Exist

They don’t …They do!

No, wait, they

don’t … or

maybe they do

I’m skeptical

Howard Percy Robertson

Arthur Stanley Eddington

Albert Einstein

The Power of Analogy

Accelerating charges produce Electromagnetic Waves, according to Maxwell and Hertz

Shouldn’t accelerating masses, like the Earth-Moon system, produce gravitational waves?

Shouldn’t radiating this energy away make the Earth-Moon system decay?

I told you to stop and ask for directions.

Where are we?

The Problem of the Moon and

The Problem of Longitude

In the 18th Century positional astronomy became important not because it could tell you what would happen in the future, but because it could tell you where in the world you were right now.

But there was a problem. It was actually nearly impossible to make accurate tables of the Moon’s position in the sky

The Secular Acceleration of the Lunar Longitude, or why is the Month getting shorter?

Edmond Halley

1656-1742

It’s amazing what you can learn from History

Although best known for predicting the recurrence of a comet by reading old astronomical records, Halley also was able to show that the month must have been longer in ancient times, based on ancient and medieval records of eclipses.

Apparently the Moon was now moving faster across the sky than it had done in ancient times, so presumably it must be getting closer to the Earth.

God

0-now

Newton

1643-1727

Thank Goodness Halley has shown that the Universe won’t last forever.

Perhaps Newton was wrong?

Pierre Simon de Laplace

1749-1827

No one could explain Halley’s secular acceleration.

Even when the Paris Academy offered a prize for the solution, Lagrange won by showing that there was no solution!

The only way out seemed to be to assume that Newton’s theory itself was wrong.

Laplace suggested that perhaps the gravitational force did no propagate instantaneously across space.

Perhaps there was a time lag between the “emission” of the gravitational force by one body and its “reception” by another.

Isaac Newton, 1643-1727

Hypotheses non fingo

Let’s get rid of action-at-a-distance

Isaac Newton, 1643-1727

Hypotheses non fingo

Let’s get rid of action-at-a-distance

Australian Judge, 1982

Hypotheses non Dingo

If it takes time for Gravity to travel, you have to plan ahead

Orbital Damping

Laplace concluded that this effect could explain Halley’s phenomenon if the speed of gravity was 7,000,000 times that of light.

Nowadays we can recognise Laplace’s calculation as a “back-reaction” or “radiation-reaction” kind of effect.

You can’t give in to short term thinking

Laplace later realized that the shortening of the month could be explained as a side effect of a subtle periodicity in the eccentricity in the Earth’s orbit, brought about by perturbations of the Earth’s orbit caused by the other planets (especially Jupiter).

Nowadays the slow alteration in the Earth’s eccentricity is believed to be a cause of periodic Ice Ages in the Earth’s climate, the Milankovitch cycle.

He recalculated that the speed of gravity must be 100,000,000c

Newton was right!

Napoleon Laplace presented a copy of his book to the Emperor

Where is God in your

system?I have no

need of that Hypothesis

The completion of the clockwork Universe

We’ll teach those Frogs to try to prove Newton wrong

John Couch Adams

1819-1892

In the 19th Century the English astronomer, J. C. Adams (famous for predicting the existence of Neptune), showed that Laplace had overestimated the size of his effect. It could explain only half of the observed shortening of the month.

This led to some nationalistic exchanges between the English and French astronomers, until the French astronomer Charles Delaunay proposed the answer.

Tidal Friction!

Even the best neighbors experience some friction

Today Lunar Laser Range Finding has confirmed that the Moon is getting further away, not closer to us.

The explanation is that Tidal Friction not only makes the month longer, it makes the day longer also (by slowing the Earth’s rotation). Thus there are fewer days in a month and so it appeared, to Halley, to be shorter than it used to be.

Our Clock appears to be running slow

Show me the Energy

Conservation of Energy was little understood in Laplace's time (and earlier), so it did not occur to him to ask where the energy is going if the Moon spirals towards the Earth.

For Tidal Friction the answer is heat in the Earth's shallow seas.

For orbital decay due to a finite speed of propagation of gravity the answer is ...

Gravitational Waves.

Those Mercurial Gravitational Waves

Henri Poincare 1854-1912

The next great master of celestial mechanics was the man who coined the term

“gravitational waves”

He wondered if these new fangled and highly speculative waves might be able to explain another very famous and intractable obstacle of celestial mechanics

The Perihelion Advance of Mercury

The Anomalous Perihelion Advance of Mercury

In the 19th Century astronomers noticed that calculations of planetary perturbations of Mercury's orbit about the Sun were unable to explain a small part of Mercury's

Perihelion Advance

In Newton's theory of gravity planets (in the absence of perturbations from other planets) should have closed orbits which do not precess.

Mercury's unexplained precession was all of

43” per century

Vulcanology

Mr. Spock c. 2245-2285

If Mercury's orbit was precessing, perhaps the explanation was an undiscovered planet, which was given the name

Vulcan

19th Century Astronomers boldly went in search of it, and a great many of them actually saw it!

The Race is to the Swift

Poinare pointed out that Mercury is the fastest moving planet, being the closest to the Sun, and thus would be expected to emit the strongest gravitational waves, if they exist.

The loss of energy due to this radiation might cause a slow inward spiral which could explain the failure of the orbit to be closed, except that the numbers did not quite work out.

Surprise! This time Newton was wrong

In 1915 Einstein was able to show that his new theory of gravity

General Relativity

predicted that orbits of planets in strong gravitational fields (with noticeable curvature of spacetime) would not be closed.

His prediction for Mercury precisely matched that of the unexplained observations.

Albert Einstein 1879-1955

But what about Gravitational Waves?

Karl Schwarzschild 1873 - 1916

In early 1916 Einstein wrote to the astronomer Karl Schwarzschild that gravitational waves did not exist in his new theory.

Within 6 months he had changed his mind (and poor Schwarzschild was dead).

How does orbital damping due to Gws depend on v, the speed of the orbiting body (e. g. Mercury)?

Laplace v/c

Poincare (v/c)2

Einstein (v/c)5

Arthur Stanley Eddington 1882-1944

Gravitational Waves Travel at the Speed of Thought

The English Astrophysicist Eddington was somewhat skeptical of Einstein's paper on gravitational waves.

He showed that there did appear to be some real gravitational waves which, according to the theory, traveled at speed of light, c.

But he also showed that certain other proposed waves were spurious, they could be made to travel “at the speed of thought.”

Nathan Rosen Joe Weber 1909-1995 1919-2000

Einstein Changes His Mind Again

“Next term we are going to have your temporary collaborator Infeld here in Princeton, and I am looking forward to discussions with him. Together with a young collaborator, I arrived at the interesting result that gravitational waves do not exist, though they had been assumed a certainty to the first approximation. This shows that the non-linear general relativistic wave field equations can tell us more or, rather, limit us more than we had believed up to now.”

-Albert Einstein to Max Born, written in mid-1936.

John T. Tate 1889-1950

Excuse me, Dr. Einstein

Einstein in High Dudgeon

Draft of Einstein's reply to Tate (in German)

Dear Sir,

We (Mr. Rosen and I) had sent you our manuscript for publication and had not authorized you to show it tospecialists before it is printed. I see no reason to address the- in any case erroneous - comments of your anonymous expert. On the basis of this incident I prefer to publish the paper elsewhere.

respectfully,

P.S. Mr. Rosen, who has left for the Soviet Union, has authorized me to represent him in this matter.

The Referee Strikes Back

Robertson fills Tate in on what transpired after Einstein withdrew his paper

Einstein never published in the Physical Review again.

The Binary Pulsar

1963 Freeman Dyson proposes that binary neutron stars might be constructed by alien civilizations, and thus SETI should focus on gravitational wave sources

1967 Discovery of first pulsar

1974 Discover of first binary pulsar

PSR1913+16

1978 Measurement of Orbital Decay

agrees with Einstein's quadrupole formula prediction of 1918

2003 Discover of Double Pulsar

both pulsars are visible from Earth and the binary is an even closer one with much faster rate of orbital decay

Joseph TaylorNobel Laureate, 1993

Keep in mind how rare these systems are. A neutron star binary is only a good source of gravitational waves if the stars are much closer together then two main sequence stars could manage to be, given their size.

Since neutron stars once were main sequence stars, how can such extremely close binaries come into existence in the first place?

If LIGO can see out as far as the VIRGO supercluster of galaxies, it should be able to see several of these inspiralsper year.

Looking for needles in Haystacks

LISA

In Space, Everyone Can Hear Your Inspiral

LISA, on the other hand, will be inundated by signals from within our own galaxy and from stars spiralling into supermassive black holes at the center of distant galaxies.

All of these are too low frequency to be detectable by any Earth-based gravitational wave detector.

LISA, if it flies, will genuinely open a “new window on the Universe.”