A typical scene on North Seymour in the Galapagos Islands. (Credit:Wikipedia-David Adam Kess). In general, tides along continental shores near the equator are much less violent than elsewhere.
Tides are a very complex phenomenon. For any particular location, their height and fluctuation in time depends to varying degrees on the location of the Sun and the Moon, and to the details of the shape of the beach, coastline, coastline depth and prevailing ocean currents. Here is a figure that shows the difference between high tide and low tide around the world.
Newton’s explanation is that, when you calculate the difference in gravity between Earth and moon at each point on the surface of Earth, you get the customary graph shown here:
This is also the shape of the ‘equipotential surface’ where mass would be in equilibrium and instantaneously ‘at rest’. There are two gravitational tides: The Body Tide and the Water Tide. The Body Tide is the response of the solid Earth to this gravitational distortion in the solid rock of Earth. The lunar body tide has a height of 0.3 meters relative to the unstressed shape of Earth while the solar body tide is about half this high. The water tides are far higher because water is lower density than rock and is free to flow around Earth’s surface with lower inertia than rock. Water tide heights can exceed 10 meters!
You would think that the solid body tide would flex the ground so severely that pipes, railroad tracks and other systems would flex and break over time. The good news is that the scale of this distortion is continent-spanning as the figure below shows.
So what does this all have to do with whether tides are found at the Equator?
Although Newton gave us the basic gravitational theory for solid body tides, his application of this theory to the behavior of water was not correct in detail. The French mathematician Laplace used Newton’s gravitational theory, but realized that its application to water tides had much more to do with the gravitational forcing of various water oscillations. Water oscillations, treated as a harmonic system with many different resonant frequencies is a much more powerful description of the details of water tides on Earth. When you combine the main lunar water tide and the solar tides acting on a complex shaped layer of water along Earth’s surface, what you get is a very different pattern of high and low water tides shown in this figure.
This figure created by Dr. Richard Ray/Space Geodesy branch, NASA/GSFC, shows the M2 lunar tidal constituent. Amplitude is indicated by color, and the white lines are cotidal differing by 1 hr. The curved arcs around the amphidromic points show the direction of the tides, each indicating a synchronized 6 hour period. Note that this response of ocean water has virtually nothing to do with the simple two-bulges, gravitational stress pattern expected from Newton’s calculation above.
So are there water tides at the Equator? Yes there are, and in fact the only locations that have very weak tides are near the poles!
At the top of this article is a figure that shows how deformed the moons shape is from a perfect sphere based on orbital data from the Lunar Orbiter spacecraft. The topography of the Moon referenced to a sphere with a radius of 1737.4 kilometers. Data were obtained from the Lunar Orbiter Laser Altimeter (LOLA) that was flown on the mission Lunar Reconnaissance Orbiter (LRO). The color coded topography is displayed in two Lambert equal area images projected on the near and far side hemispheres.
The tidal force of the Earth’s gravitational field raises solid-body tides on the Moon causing the Moon to be deformed into a non-spherical body resembling a football. The magnitude of this effect is about 20 times the solid-body tide caused by the Moon upon the Earth which is about 20×20 centimeters or 4 meters. When the Moon was first formed, it was closer to the Earth than it is now, so the tidal amplitude was quite a bit greater, moreover, the Moon was molten and so it responded even more strongly to the tidal deformation imposed upon it by the Earth’s gravitational field. As a result, the shape of the Moon is very far from being spherical. The Moon was originally rotating faster than it is now so that 3-4 billion years ago it was not orbiting the Earth as fast as it was rotating about its axis.
Over the years, however, the gravitational tidal forces acting upon the non-spherical body of the Moon have modified its non-spherical shape, and caused a systematic dissipation of the Moon’s rotational energy via friction. It costs a lot of energy to deform the Moon, and this energy is lost through the internal friction of rock rubbing against rock within the Moon to raise the solid body tides. Because the Moon may already have solidified into a football-shaped non-spherical body, there is a portion of the Moon that is always slightly closer to the Earth than other portions of the Moon. This becomes a ‘handle’ that the gravitational field of the Earth can ‘grab onto’ to apply a slightly greater force upon the Moon that at other times during the lunar orbit around the Earth. A similar deformity exists in Mercury which has aided the Sun in synchronizing Mercury into a 2:3 spin-orbit resonance. For the Moon, and the larger satellites of the other planets, a similar deformity leads to a 1:1 resonance so that the same side of the satellite always faces the planet.
So, a combination of the Moon’s initial deformation when it was molten and solidified in the Earth’s tidal gravitational field, together with the on-going tidal deformation, leads to a preferred orientation to the Moon in its orbit which the system relaxes to over billions of years.
Illustration of matter in an accretion disk falling into a black hole. (Credit: NASA’s Goddard Space Flight Center/Jeremy Schnittman). The actual image of the disk will be distorted due to the intense gravitational field and will probably look like the following image.
Outside the black hole, it depends on what form the matter takes. If it happens to be in the form of gas that has been orbiting the black hole in a so-called accretion disk, the matter gets heated to very high temperatures as the individual atoms collide with higher and higher speed producing friction and heat. The closer the gas is to the black hole and its Event Horizon, the more of the gravitational energy of the gas gets converted to kinetic energy and heat. Eventually the atoms collide so violently that they get stripped of their electrons and you then have a plasma. All along, the gas emits light at higher and higher energies, first as optical radiation, then ultraviolet, then X-rays and finally, just before it passes across the Event Horizon, gamma rays.
Here is what a model of such a disk looks like based on a typical calculation, in this case by physicist Kovak Zoltan (Phys Rev D84, 2011, pp 24018) for a 2 million solar mass black hole accreting mass at a rate of 2.5 solar masses every million years. Even around massive black holes, temperatures run very hot. The event horizon for this black hole is at a distance of 6 million kilometers. The first mark on the horizontal axis is ‘5’ meaning 5 times the horizon radius or a distance of 30 million km from the center of the black hole. This is about the distance from our sun to mercury!
If the matter is inside a star that has been gravitationally captured by the black hole, the orbit of the star may decrease due to the emission of gravitational radiation over the course of billions of years. Eventually, the star will pass so close to the black hole that its fate is decided by the mass of the black hole. If it is a stellar-mass black hole, the tidal gravitational forces of the black hole will deform the star from a spherical ball, into a football-shaped object, and then eventually the difference in the gravitational force between the side nearest the black hole, and the back side of the star, will be so large that the star can no longer hold itself together. It will be gravitationally shredded by the black hole, with the bulk of the star’s mass going into an accretion disk around the black hole. If the black hole has a mass of more than a billion times that of the sun, the tidal gravitational forces of the black hole are weak enough that the star may pass across the Event Horizon without being shredded. The star is, essentially, eaten whole and the matter in the star does not produce a dramatic increase in radiation before it enters the black hole. Here is an artist version of such a tidal encounter.
Once inside a black hole, beyond the Event Horizon, we can only speculate what the fate of captured matter is. General relativity tells us that there are two kinds of black holes; the kind that do not rotate, and the kind that do. Each of these kinds has a different anatomy inside the Event Horizon.For the non-rotating ‘Schwarzschild black hole’, there is no way for matter to avoid colliding with the Singularity. In terms of the time registered by a clock moving with this matter, it reaches the Singularity within a few micro seconds for a solar-massed black hole, and a few hours for a supermassive black hole. We can’t predict what happens at the Singularity because the theory says we reach a condition of infinite gravitational force.
For the rotating ‘ Kerr Black holes’, the internal structure is more complex, and for some ingoing trajectories for matter, you could in principle avoid colliding with the Singularity and possibly reemerge from the black hole somewhere else, or at some very different future time thousands or billions of years after you entered.
Some exotic theories say that you reemerge in another universe entirely, but physicists now don’t believe that interpretation is accurate. The problem is that for black holes created by real physical events, the interior of a black hole is awash with gravitational radiation which makes the geometry of space-time very unstable, preventing just these kinds of trips.
For the simplist non-rotating Schwarschild black holes, even they offer a mind-numbing prospect. The mathematics says that outside the event horizon, a particle will experience space and time normally. The particle (and you!) can travel freely in space along the R, radial coordinate, but have no control over your progression in time along the T coordinate. You can speed it up or slow it down a bit through the time dilation effect of high-sped travel, but you can not travel backwards in time. At the event horizon, something amazing happens. The mathematical variables we have been using for time and space, that is R and T, reverse their rolls in the equations that define the separation between points in spacetime. What this means is that the space coordinate, R, behaves like a time coordinate so that you have no freedom to maneuver and not be crushed at the Singularity at R=0. Meanwhile you have some freedom to move along the T coordinate as though it acted like the old familiar space coordinate out side the event horizon.
For Schwarschild black holes that form from supernovae, you have another problem. The event horizon in the mathematics only appears a LONG time after the implosion of matter. In fact it is what mathematicians call an asymptotic feature of the collapsing spacetime. What this means is that if you fell into the black hole long after the supernova created it, the collapse is still going on in the frame of someone far away with the surface of the star trying to pass inside the horizon, but this process has not yet completed. For you falling in, the bulk of the star is still outside the horizon and the black hole has not yet formed! The time dilation effect is so extreme at the horizon that the star literally freezes its motion from the standpoint of the distant observer and becomes a frozen-in-time, black star. As seen from the outside, it will take an eternity for you to actually reach the horizon, but from your frame of reference, it will only take an hour or less depending on where you start! Once you pass inside the horizon, the time to arriving at the singularity is approximately the gravitational free-fall time from the horizon distance. For a supermassive black hole this could take hours, but for a solar mass black hole this takes about 10 microseconds!
Based on tons of scientific data and decades of research, here is an artist’s impression of the Milky Way Galaxy, as seen from above the galactic “North pole”. (Credit: NASA. JPL-Caltech/R. Hurt (SSC/Ca)
All of the basic elements have been established including its spiral arm pattern and the shape of its central bulge of stars. To directly answer this question, however, is a difficult, if not impossible, task. The problem is that we cannot directly see every star in the Milky Way because most are located behind interstellar clouds from our vantage point in the Milky Way. The best we can do is to figure out the total mass of the Milky Way, subtract the portion that is contributed by interstellar gas and dust clouds ( about 1 – 5 percent or so), and then divide the remaining mass by the average mass of a single star.
From a number of studies, the mass of the Milky Way inside the orbit of our sun can be estimated to an accuracy of perhaps 20 percent as 140 billion times the mass of the Sun, if you use the Sun’s speed around the core of the galaxy. Radio astronomers have detected much more material outside the orbit of the Sun, so the above number is probably an underestimate by a factor of 2 to 5 times in mass alone.
Now, to find out how many stars this represents, you have to divide by the average mass of a star. If you like the sun, then use ‘one solar mass’ and you then get about 140 billion sun-like stars for what’s inside the sun’s orbit. But astronomers have known for a long time that stars like the sun in mass are not that common. Far more plentiful are stars with half the mass of the sun, and even one tenth the mass of the sun. The problem is that we don’t know exactly how much of the Milky Way is in the form of these low-mass stars. In text books, you will therefore get answers that range anywhere between a few hundred billion and as high as a trillion stars depending on what the author used as a typical mass for the most abundant type of star. This is a pretty embarrasing uncertainty, but then again, why would you need to know this number exactly?
The best estimates come from looking at the motions of nearby galaxies such as a recent study by G. R. Bell (Harvey Mudd/USNO Flagstaff), S. E. Levine (USNO Flagstaff):
Using radial velocities and the recently determined proper motions for the Magellanic Clouds and the dwarf spheroidal galaxies in Sculptor and Ursa Minor, we have modeled the satellite galaxies’ orbits around the Milky Way. Assuming the orbits of the dwarf spheroidals are bound, have apogalacticon less than 300 kpc, and are of low eccentricity, then the minimum mass of our galaxy contained within a radius of 100 kpc is 590 billion solar masses, and the most likely mass is 700 billion. These mass estimates and the orbit models were used to place limits on the possible maximum tangential velocities and proper motions of the other known dwarf spheroidal galaxies and to assess the likelihood of membership of the dwarf galaxies in various streams.
Again, you have to divide this by the average mass of a star…say 0.3 solar masses, to get an estimate for the number of stars which is well into the trillions!
Another factor that confuses the problem is that our Milky Way contains a lot of dark matter that also produces its own gravity and upsets the estimates for actual stellar masses. Our galaxy is embedded in a roughly spherical cloud of dark matter. Various theoretical calculations show that these should be very common among galaxies. Here is an example of such a model in which the luminous galaxy is embedded in a massive DM halo. (Credit:Wikipedia-Dark Matter Halo N-body simulation)
By using the motions of distant galaxies astronomers have ‘weighed’ the entire Milky Way and deduce that the dark matter halo is likely to include around 3 trillion solar masses of dark matter.
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.
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.
Gravity can certainly warp and distort the ‘straight-line’ path of a light ray. This Hubble image is of the Einstein Ring LRG 3-757 in which the central massive galaxy has warped the image of a background galaxy into a ring of light. (Credit: ESA/Hubble & NASA)
The speed of light is something measured with a local apparatus in an inertial reference frame, using the same meter stick and clock. A gravitational field has zillions of such ‘locally inertial reference frames’ which are described by freely-falling observers for short intervals of time and small regions of space. In all of these tiny domains, an observer would measure the same velocity for light as guaranteed by special relativity. To ask what the speed of light is over a domain where gravitational forces make a reference frame ‘non-inertial’ and not moving at a constant speed, is an ill-defined question in special relativity. As soon as you try to measure the speed of such an impulse, you would be using a clock and a meter stick which would not be the ‘proper time and space’ intervals for the entire region where the gravitational field exists.
Gravity can affect the speed of light. If you measure the speed over a large enough region that special relativity and its requirement of a flat spacetime is not satisfied. In the presence of curved spacetime, conventional local measurement techniques do not work and so you cannot define the speed of light in exactly the same way that you do under laboratory conditions in ‘flat’ spacetime. In fact, in curved spacetime even the concept of conservation of energy is not easily defined because the curvature of space itself changes the definition. Conservation of energy only works in flat spacetime.
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.
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.
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.
An astronomer's point-of-view on matters of space, space travel, general science and consciousness
