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What astronomers observed in the Hulse-Taylor Pulsar was a decrease in the orbital period of the two neutron stars.

From general relativity, it was possible to predict, mathematically, how the period ought to change in time as the binary system emitted gravitational energy during the time the orbits of the neutron stars were being ‘circularized’.

The predicted, and deceptively simple, formula for the period change, dP/dt, can be found in the excellent book by Stuart Shapiro and Saul Teukolsky Black holes, white dwarfs and neutron stars, and it looks like this:

dP/dt    =    -1.202 x 10-12   M (2.8278 - M)

where M = 1.41 solar masses…the mass of one of the neutron stars determined by observation and the application of Kepler’s Laws. The units are in seconds of orbit period change per second.

The result is the predicted period change is dP/dt = -2.40 x 10^-12 and the observed value is -2.30 +/- 0.22 x 10^-12 seconds per second. This implies a better than 10 percent disagreement between theory and observation, and thereby proves that gravitational radiation leakage is the simplest explanation. No one has yet found a simpler explanation in terms of tidal friction or other non-relativity processes.

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In ordinary Newtonian physics, just about everything can be traced back to some elementary process that conserves energy and momentum. For 400 years we were taught that neither energy nor mass could be created or destroyed but had to be conserved througout some process such as the moon orbiting earth. We also learned that conservation laws applied to closed systems that you could see and systems that you could not see, from the cosmic to the atomic. Does a tree falling in the forest when no one is there to see it, still conserve energy? you bet! But then during the earth-20th century, the Roaring Twenties hit, and physics was turned upside down for a few years.

I am not going to review quantum mechanics and quantum field theory in this writing because you have probably read most of the literature about this ‘Second Pillar’ of physics. The important thing to remember is in the atomic world, a whole new set of paradighms apply that have nothing to do with Newton’s Physics except in some skelletal form. We still talk about mass, momentum and energy, but now the objects of our concern are elementary objects that behave as waves or particles depending on what kinds of experiment you put them through. Energy is no longer a Newtonian quantity but is an ‘operator’ that acts on a particle wavefunction to return a value for a particular state index. Momentum also has its own operator, and the way these operators act on a wavefunction is analogous to how a particular tuning fork vibrates in resonance to an applied force. Each vibratory mode of the wavefunction of an electron has its own energy at a particular instant in time, and a particular momentum at a particular position in space. Physicists say that energy and time ‘commute’ with each other and momentum and position do likewise. Because these wavefunctions are statistical in nature, the ‘square’ of a component of the wavefunction gives the probability that the electron will have a specific energy and momentum. But this statistical feature of an electron’s state means that the product of the conjugate variables must be greater than or equal to Planck’s constant. This gives us the famous Heisenberg Uncertainty Principle:

What these relations relate to is our ability to distinguish between each of the possible energy and momentum quantum states of an electron at a particular moment in time, and a particular location in space. In fact, because we are dealing with states that are part of an infinite harmonic series for the electrons wavefunction, we can use the mathematics of Fourier to relate frequency to wavelength for each of the states. In light and sound we have wavelength = constant / frequency where the constant is the speed of sound or light. In quantum mechanics, the wavefunction is based on similar relationships for the conjugate variables (E,t) and (p,x). The experimental problem is that because E and t are conjugate, it means that as we try to specify the momentum state, p, more accurately we steadily lose accuracy in knowing where the electron is in the x variable. Similarly, as we try to precisely determine how much energy a system has, E, we lose accuracy in knowing at which specific instant it had that energy.

What does this have to do with the energy of virtual particles?

The Heisenberg relatonship between energy and time is actually a statement of how well we can know both of these quantities for any system that has wavelike properties. In words:

The uncertainty in the total energy of a particular state decreases as the amount of time it is in that state increases.

This is often interpreted as a statement of our being able to measure the energy of the system if we only observe it for a short while. A practical example is as follows.

Initially at Time = Ti our system consists of two particles Pa and Pb which have the total energies of Ea and Eb. Then Einitial = Ea + Eb. A neighboring state at time =T2 contains the same two particles and their energies, but includes a third particle V, with the energy Ev. The final state of the system at time = Tf contains only the original two particles. According to Heisenbergs Uncertainty Principle, the change in energy between the two states is just (Ea + Eb + Ev) – (Ea + Eb) = Ev. This energy change between the two states is related to how long then state with the third particle exists according to Delta-T = h/Ev which is the minimum time the Ev energy can persist.

In quantum mechanics a system begins in an initial state at Time Ti and ends in a final state at Tf. These states contain only the original particles, in this case A and B. What happens in-between can include any other process so long as it obeys Heisenbergs Uncertainty Principle so that

Ev = h/(Tf-Ti)

If the time between the initial and final states is long, the energy fluctuation, Ev, will be very small, but if the time difference is short, the value for Ev can be very large.

So where does this energy Ev come from? You can think of it as being ‘borrowed’ from the state in which the particle V did not exist…which is called the quantum vacuum. That’s because the vacuum state is the lowest energy state of the system remaining after we remove the two original particles. What is left over is n ’empty space’ in which all of the other energy fluctuations ( interpreted as virtual particles because of E=mc^2) that come and go over time periods set by the amount of energy they contain.

Another way to think of this is to use the measurement analogy for what happens when you average together lots of measurements. When you start out with 36 measurements and average them, you get an answer but this is the mid-point of a bellcurve for these repeated measurements that has a ‘standard deviation’, which tells you the spread of the measured points around the average value. As you increase the number of measurements to 10,000 your average may not change by much, but now the shape of the bellcurve has narrowed because the standard deviation is now squareroot(10000/36) = 100/6 times smaller. The more you measure the smaller becomes the fluctuation in the parameter you are measuring. In the same way, you make 36 energy measurements of a particle state and the standard deviation is determined by Heisenbergs Uncertainty principle based on the amount of time involved in making these measurements. But when you make more measurements you increase the time between Ti and Tf and the standard deviation decreases to a smaller value.

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Not completely. Gravity is a distortion in the geometry of space. This illustration (Credit: LIGO/T. Pyle) shows how gravity waves from colliding black holes distort this geometry in a way that electric and magnetic waves do not.

First of all, gravity is what is called a tensor force while electromagnetism is a vector force. That difference means that it is impossible to reproduce all of the properties in gravity using a simpler force field. Moreover, gravity is not at all a force in the usual sense. It is a purely geometric effect in spacetime.

Gravity provides ONLY a force of attraction between all forms of matter and energy. Electromagnetism provided ONLY attractive or repulsive forces between matter which carries electric charge. It is possible to get the acceleration of gravity and the force of gravity by using two charged particles of opposite charge, but numerically all you would have is a force field that mimics one feature of gravity. Take away the charges and the similarity immediately vanishes.

Contrary to what some science fiction stories might imply, we know of no electromagnetic analog of gravity. We can however create electromagnetic force fields with charged matter that can alter the total forces they feel due to gravity. We can levitate charged particles in magnetic fields and so on.

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The biggest difference is that a gravitational field is mathematically classified as a tensor field while magnetic fields, or actually electromagnetic fields, are vector fields. This means that it takes 4×4=16 components to define a gravitational field in general while it only takes 4 components to define an electromagnetic field. The number 4 comes up because spacetime is 4-dimensional.

Gravitational fields are determined only by the mass ( or mass-energy) of a body. Charged and uncharged massive particles produce the same gravitational field pound for pound ( well…the electromagnetic energy has its own mass so it does contribute a bit ).

Magnetic fields are produced by charged particles in motion, and depend on the charge and velocity of these particles, but not on their mass. Magnetic fields are ‘polar’ fields with a North and South polarity.

Gravitational fields have no polarity at all. At large distances, gravitational fields diminish as the inverse square of distance from their source.

Magnetic fields at large distances from their source, decrease as the inverse cube of the distance.

You can only detect magnetic fields by using charged particles to measure their deflection.

Gravitational fields can be detected by using anything to measure a change in velocity.

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It depends entirely on what you mean by knowledge. This figure (Credit:NASA/Conceptual Image Lab) shows magnetic field lines and the graded decrease of Earth’s gravity in an artistic rendition. We know how both of these work in considerable detail.

Our theories for gravity and magnetism allow us to describe the essential physics of systems from nearly the size of the universe, to events at a scale of nearly one million times smaller than the nucleus of an atom. The latter phenomenon is explained by quantum electrodynamics which routinely makes predictions correct to 10 decimal places. For gravity, we can accurately describe systems as vast as the universe and its evolution, all the way down to the surfaces of black holes a few dozen kilometers across.

From a practical point of view we understand these two forces almost perfectly, and to our best current ability to measure.

A charged particle sitting in your reference frame motionless produces a pure electric field like the figure above.As you get farther from the center, the number of imaaginary field lines is conserved through each spherical surface and so the strength of the field decreases as the reciprocal of te surface area of the sphere. This is the relationship if space is 3-dimensional and explains the inverse-square law.

Where does this electric field come from? It comes from the electromagnetic force which is a quantum phenomenon explained in great detail by a theory called Quantum Electrodynamics. Every charged particle is surrounded by a cloud of virtual photons that are exchanged between other charged particles to produce the familiar electrostatic force.

Here is a common diagram (Credit: Wikipedia) showing the exchange of just one of these virtual particles (the wavy line) exchanged between two electrons. This ‘Feynman Diagram’ is a only symbolic representation of the mathematical terms that have to be multiplied together to calculate the probability that this reaction will occur. It is not meant to be a ‘photograph’ of what is actually going on.

A magnetic field is what we observe in our frame of reference as an electric field passes by traveling at a speed relative to us. The movement of these charges is called an electric current, and all electric currents produce magnetic fields so long as the speed of the current is not zero. But a magnetic field is not fundamentally a new field in nature, its just the familiar electric field seen in a different reference frame. Our understanding of ‘electromagnetic’ fields is virtually perfect to the extent that its bass is in quantum mechanics is a solid foundation.

Gravitational fields are very different. We call them ‘fields’ because that is a left-over description from Newtonian physics and it serves us well in most things that we come into contact with in our solar system and local universe. But this is not the correct way to think about gravity. It is neither a field nor is it a force, although it resembles both of these in rough terms.

General relativity is our most sucessful theory for describing gravity, but it is a purely geometric theory and not one that looks anything like quantum electrodynamics. Instead, 4-dimensional spacetime is the ‘field’ that describes gravity and distortions in it lead to the experiences of accellerations as particles try to travel in straight lines through the geometry. At the same time, matter (and energy) also creates these geometric distortions. General relativity is a theory of the geometry of worldlines and not some mythical background space into which gravity is embedded. The biggest flaw in general relativity is that it does not tell us exactly how matter creates gravity. The only other theory that we have that describes how forces are produced is called Quantum Field Theory of which quantum electrodynamics is the most successful one.

There is no similar theory for gravity, so we do not really know how gravity is created by matter. Because the field for gravity is called spacetime, what we have to imagine is a theory that describes where spacetime ‘comes from’ in other words how matter produces space and time!!!

If you are asking a more metaphysical question about our knowledge, then we don’t really understand ANYTHING about gravity at the deepest level, such as why does gravity exist? Is it a quantum field? What is the nature of space-time?

In terms of the human sphere of activity, we understand enough about these two fields that we will never have much practical need for better theories than the ones we now have.