Posted on by Brian Koberlein

How We Know Gravity is Not (Just) a Force

This artist’s impression shows the exotic double object that consists of a tiny, but very heavy neutron star that spins 25 times each second, orbited every two and a half hours by a white dwarf star. The neutron star is a pulsar named PSR J0348+0432 that is giving off radio waves that can be picked up on Earth by radio telescopes. Although this unusual pair is very interesting in its own right it is also a unique laboratory for testing the limits of physical theories. This system is radiating gravitational radiation, ripples in spacetime. Although these waves cannot be yet detected directly by astronomers on Earth they can be detected indirectly by measuring the change in the orbit of the system as it loses energy. As the pulsar is so small the relative sizes of the two objects are not drawn to scale.

When  we think of gravity, we typically think of it as a force between masses.  When you step on a scale, for example, the number on the scale represents the pull of the Earth’s gravity on your mass, giving you weight.  It is easy to imagine the gravitational force of the Sun holding the planets in their orbits, or the gravitational pull of a black hole.  Forces are easy to understand as pushes and pulls.

But we now understand that gravity as a force is only part of a more complex phenomenon described the theory of general relativity.  While general relativity is an elegant theory, it’s a radical departure from the idea of gravity as a force.  As Carl Sagan once said, “Extraordinary claims require extraordinary evidence,” and Einstein’s theory is a very extraordinary claim.  But it turns out there are several extraordinary experiments that confirm the curvature of space and time.

The key to general relativity lies in the fact that everything in a gravitational field falls at the same rate.  Stand on the Moon and drop a hammer and a feather, and they will hit the surface at the same time.  The same is true for any object regardless of its mass or physical makeup, and this is known as the equivalence principle.

Since everything falls in the same way regardless of its mass, it means that without some external point of reference, a free-floating observer far from gravitational sources and a free-falling observer in the gravitational field of a massive body each have the same experience. For example, astronauts in the space station look as if they are floating without gravity.  Actually, the gravitational pull of the Earth on the space station is nearly as strong as it is at the surface.  The difference is that the space station (and everything in it) is falling.  The space station is in orbit, which means it is literally falling around the Earth.

The International Space Station orbiting Earth. Credit: NASA
The International Space Station orbiting Earth. Credit: NASA

This equivalence between floating and falling is what Einstein used to develop his theory.  In general relativity, gravity is not a force between masses.  Instead gravity is an effect of the warping of space and time in the presence of mass.  Without a force acting upon it, an object will move in a straight line.  If you draw a line on a sheet of paper, and then twist or bend the paper, the line will no longer appear straight.  In the same way, the straight path of an object is bent when space and time is bent.  This explains why all objects fall at the same rate.  The gravity warps spacetime in a particular way, so the straight paths of all objects are bent in the same way near the Earth.

So what kind of experiment could possibly prove that gravity is warped spacetime?  One stems from the fact that light can be deflected by a nearby mass.  It is often argued that since light has no mass, it shouldn’t be deflected by the gravitational force of a body.  This isn’t quite correct. Since light has energy, and by special relativity mass and energy are equivalent, Newton’s gravitational theory predicts that light would be deflected slightly by a nearby mass.  The difference is that general relativity predicts it will be deflected twice as much.

Description of Eddington's experiment from the Illustrated London News (1919).
Description of Eddington’s experiment from the Illustrated London News (1919).

The effect was first observed by Arthur Eddington in 1919.  Eddington traveled to the island of Principe off the coast of West Africa to photograph a total eclipse. He had taken photos of the same region of the sky sometime earlier. By comparing the eclipse photos and the earlier photos of the same sky, Eddington was able to show the apparent position of stars shifted when the Sun was near.  The amount of deflection agreed with Einstein, and not Newton.  Since then we’ve seen a similar effect where the light of distant quasars and galaxies are deflected by closer masses.  It is often referred to as gravitational lensing, and it has been used to measure the masses of galaxies, and even see the effects of dark matter.

Another piece of evidence is known as the time-delay experiment.  The mass of the Sun warps space near it, therefore light passing near the Sun is doesn’t travel in a perfectly straight line.  Instead it travels along a slightly curved path that is a bit longer.  This means light from a planet on the other side of the solar system from Earth reaches us a tiny bit later than we would otherwise expect.  The first measurement of this time delay was in the late 1960s by Irwin Shapiro.  Radio signals were bounced off Venus from Earth when the two planets were almost on opposite sides of the sun. The measured delay of the signals’ round trip was about 200 microseconds, just as predicted by general relativity.  This effect is now known as the Shapiro time delay, and it means the average speed of light (as determined by the travel time) is slightly slower than the (always constant) instantaneous speed of light.

A third effect is gravitational waves.  If stars warp space around them, then the motion of stars in a binary system should create ripples in spacetime, similar to the way swirling your finger in water can create ripples on the water’s surface.  As the gravity waves radiate away from the stars, they take away some of the energy from the binary system. This means that the two stars gradually move closer together, an effect known as inspiralling. As the two stars inspiral, their orbital period gets shorter because their orbits are getting smaller.

Decay of pulsar period compared to prediction (dashed curve). Data from Hulse and Taylor, Plotted by the author.
Decay of pulsar period compared to prediction (dashed curve). Data from Hulse and Taylor, Plotted by the author.

For regular binary stars this effect is so small that we can’t observe it. However in 1974 two astronomers (Hulse and Taylor) discovered an interesting pulsar. Pulsars are rapidly rotating neutron stars that happen to radiate radio pulses in our direction. The pulse rate of pulsars are typically very, very regular. Hulse and Taylor noticed that this particular pulsar’s rate would speed up slightly then slow down slightly at a regular rate. They showed that this variation was due to the motion of the pulsar as it orbited a star. They were able to determine the orbital motion of the pulsar very precisely, calculating its orbital period to within a fraction of a second. As they observed their pulsar over the years, they noticed its orbital period was gradually getting shorter. The pulsar is inspiralling due to the radiation of gravity waves, just as predicted.

Illustration of Gravity Probe B. Credit: Gravity Probe B Team, Stanford, NASA
Illustration of Gravity Probe B. Credit: Gravity Probe B Team, Stanford, NASA

Finally there is an effect known as frame dragging.  We have seen this effect near Earth itself.  Because the Earth is rotating, it not only curves spacetime by its mass, it twists spacetime around it due to its rotation.  This twisting of spacetime is known as frame dragging.  The effect is not very big near the Earth, but it can be measured through the Lense-Thirring effect.  Basically you put a spherical gyroscope in orbit, and see if its axis of rotation changes.  If there is no frame dragging, then the orientation of the gyroscope shouldn’t change.  If there is frame dragging, then the spiral twist of space and time will cause the gyroscope to precess, and its orientation will slowly change over time.

results_graph-lg
Gravity Probe B results. Credit: Gravity Probe B team, NASA.

We’ve actually done this experiment with a satellite known as Gravity Probe B, and you can see the results in the figure here.  As you can see, they agree very well.

Each of these experiments show that gravity is not simply a force between masses.  Gravity is instead an effect of space and time.  Gravity is built into the very shape of the universe.

Think on that the next time you step onto a scale.

Posted on by Brian Koberlein

Black Holes No More? Not Quite.

Where is the Nearest Black Hole
Artist concept of matter swirling around a black hole. (NASA/Dana Berry/SkyWorks Digital)

Nature News has announced that there are no black holes.  This claim is made by none other than Stephen Hawking, so does this mean black holes are no more?  It depends on whether Hawking’s new idea is right, and on what you mean be a black hole.  The claim is based on a new paper by Hawking  that argues the event horizon of a black hole doesn’t exist.

The event horizon of a black hole is basically the point of no return when approaching a black hole.  In Einstein’s theory of general relativity, the event horizon is where space and time are so warped by gravity that you can never escape.  Cross the event horizon and you can only move inward, never outward.  The problem with a one-way event horizon is that it leads to what is known as the information paradox.

Professor Stephen Hawking during a zero-gravity flight. Image credit: Zero G.
Professor Stephen Hawking during a zero-gravity flight. Image credit: Zero G.

The information paradox has its origin in thermodynamics, specifically the second law of thermodynamics.  In its simplest form it can be summarized as “heat flows from hot objects to cold objects”.  But the law is more useful when it is expressed in terms of entropy.  In this way it is stated as “the entropy of a system can never decrease.”  Many people interpret entropy as the level of disorder in a system, or the unusable part of a system.  That would mean things must always become less useful over time.  But entropy is really about the level of information you need to describe a system.  An ordered system (say, marbles evenly spaced in a grid) is easy to describe because the objects have simple relations to each other.  On the other hand, a disordered system (marbles randomly scattered) take more information to describe, because there isn’t a simple pattern to them.  So when the second law says that entropy can never decrease, it is say that the physical information of a system cannot decrease.  In other words, information cannot be destroyed.

The problem with event horizons is that you could toss an object (with a great deal of entropy) into a black hole, and the entropy would simply go away.  In other words, the entropy of the universe would get smaller, which would violate the second law of thermodynamics.  Of course this doesn’t take into account quantum effects, specifically what is known as Hawking radiation, which Stephen Hawking first proposed in 1974.

The original idea of Hawking radiation stems from the uncertainty principle in quantum theory.  In quantum theory there are limits to what can be known about an object.  For example, you cannot know an object’s exact energy.  Because of this uncertainty, the energy of a system can fluctuate spontaneously, so long as its average remains constant.  What Hawking demonstrated is that near the event horizon of a black hole pairs of particles can appear, where one particle becomes trapped within the event horizon (reducing the black holes mass slightly) while the other can escape as radiation (carrying away a bit of the black hole’s energy).

Hawking radiation near an event horizon. Credit: NAU.
Hawking radiation near an event horizon. Credit: NAU.

Because these quantum particles appear in pairs, they are “entangled” (connected in a quantum way).  This doesn’t matter much, unless you want Hawking radiation to radiate the information contained within the black hole.  In Hawking’s original formulation, the particles appeared randomly, so the radiation emanating from the black hole was purely random.  Thus Hawking radiation would not allow you to recover any trapped information.

To allow Hawking radiation to carry information out of the black hole, the entangled connection between particle pairs must be broken at the event horizon, so that the escaping particle can instead be entangled with the information-carrying matter within the black hole.  This breaking of the original entanglement would make the escaping particles appear as an intense “firewall” at the surface of the event horizon.  This would mean that anything falling toward the black hole wouldn’t make it into the black hole.  Instead it would be vaporized by Hawking radiation when it reached the event horizon.  It would seem then that either the physical information of an object is lost when it falls into a black hole (information paradox) or objects are vaporized before entering a black hole (firewall paradox).

In this new paper, Hawking proposes a different approach.  He argues that rather than instead of gravity warping space and time into an event horizon, the quantum fluctuations of Hawking radiation create a layer turbulence in that region.  So instead of a sharp event horizon, a black hole would have an apparent horizon that looks like an event horizon, but allows information to leak out.  Hawking argues that the turbulence would be so great that the information leaving a black hole would be so scrambled that it is effectively irrecoverable.

If Stephen Hawking is right, then it could solve the information/firewall paradox that has plagued theoretical physics.  Black holes would still exist in the astrophysics sense (the one in the center of our galaxy isn’t going anywhere) but they would lack event horizons.  It should be stressed that Hawking’s paper hasn’t been peer reviewed, and it is a bit lacking on details.  It is more of a presentation of an idea rather than a detailed solution to the paradox.  Further research will be needed to determine if this idea is the solution we’ve been looking for.

Posted on by Brian Koberlein

Why Einstein Will Never Be Wrong

Einstein Lecturing
Albert Einstein during a lecture in Vienna in 1921. Credit: National Library of Austria/F Schmutzer/Public Domain

One of the benefits of being an astrophysicist is your weekly email from someone who claims to have “proven Einstein wrong”. These either contain no mathematical equations and use phrases such as “it is obvious that..”, or they are page after page of complex equations with dozens of scientific terms used in non-traditional ways. They all get deleted pretty quickly, not because astrophysicists are too indoctrinated in established theories, but because none of them acknowledge how theories get replaced.

For example, in the late 1700s there was a theory of heat known as caloric. The basic idea of caloric was that it was a fluid that existed within materials. This fluid was self-repellant, meaning it would try to spread out as evenly as possible. We couldn’t observe this fluid directly, but the more caloric a material has the greater its temperature.

Ice-calorimeter
Ice-calorimeter from Antoine Lavoisier’s 1789 Elements of Chemistry. (Public Domain)

From this theory you get several predictions that actually work. Since you can’t create or destroy caloric, heat (energy) is conserved. If you put a cold object next to a hot object, the caloric in the hot object will spread out to the cold object until they reach the same temperature.  When air expands, the caloric is spread out more thinly, thus the temperature drops. When air is compressed there is more caloric per volume, and the temperature rises.

We now know there is no “heat fluid” known as caloric. Heat is a property of the motion (kinetic energy) of atoms or molecules in a material. So in physics we’ve dropped the caloric model in terms of kinetic theory. You could say we now know that the caloric model is completely wrong.

Except it isn’t. At least no more wrong than it ever was.

The basic assumption of a “heat fluid” doesn’t match reality, but the model makes predictions that are correct. In fact the caloric model works as well today as it did in the late 1700s. We don’t use it anymore because we have newer models that work better. Kinetic theory makes all the predictions caloric does and more. Kinetic theory even explains how the thermal energy of a material can be approximated as a fluid.

This is a key aspect of scientific theories. If you want to replace a robust scientific theory with a new one, the new theory must be able to do more than the old one. When you replace the old theory you now understand the limits of that theory and how to move beyond it.

In some cases even when an old theory is supplanted we continue to use it. Such an example can be seen in Newton’s law of gravity. When Newton proposed his theory of universal gravity in the 1600s, he described gravity as a force of attraction between all masses. This allowed for the correct prediction of the motion of the planets, the discovery of Neptune, the basic relation between a star’s mass and its temperature, and on and on. Newtonian gravity was and is a robust scientific theory.

Then in the early 1900s Einstein proposed a different model known as general relativity. The basic premise of this theory is that gravity is due to the curvature of space and time by masses.  Even though Einstein’s gravity model is radically different from Newton’s, the mathematics of the theory shows that Newton’s equations are approximate solutions to Einstein’s equations.  Everything Newton’s gravity predicts, Einstein’s does as well. But Einstein also allows us to correctly model black holes, the big bang, the precession of Mercury’s orbit, time dilation, and more, all of which have been experimentally validated.

So Einstein trumps Newton. But Einstein’s theory is much more difficult to work with than Newton’s, so often we just use Newton’s equations to calculate things. For example, the motion of satellites, or exoplanets. If we don’t need the precision of Einstein’s theory, we simply use Newton to get an answer that is “good enough.” We may have proven Newton’s theory “wrong”, but the theory is still as useful and accurate as it ever was.

Unfortunately, many budding Einsteins don’t understand this.

Binary waves from black holes. Image Credit: K. Thorne (Caltech) , T. Carnahan (NASA GSFC)
Binary waves from black holes. Image Credit: K. Thorne (Caltech) , T. Carnahan (NASA GSFC)

To begin with, Einstein’s gravity will never be proven wrong by a theory. It will be proven wrong by experimental evidence showing that the predictions of general relativity don’t work. Einstein’s theory didn’t supplant Newton’s until we had experimental evidence that agreed with Einstein and didn’t agree with Newton. So unless you have experimental evidence that clearly contradicts general relativity, claims of “disproving Einstein” will fall on deaf ears.

The other way to trump Einstein would be to develop a theory that clearly shows how Einstein’s theory is an approximation of your new theory, or how the experimental tests general relativity has passed are also passed by your theory.  Ideally, your new theory will also make new predictions that can be tested in a reasonable way.  If you can do that, and can present your ideas clearly, you will be listened to.  String theory and entropic gravity are examples of models that try to do just that.

But even if someone succeeds in creating a theory better than Einstein’s (and someone almost certainly will), Einstein’s theory will still be as valid as it ever was.  Einstein won’t have been proven wrong, we’ll simply understand the limits of his theory.

Posted on by Brian Koberlein

Why Our Universe is Not a Hologram

Superstrings may exist in 11 dimensions at once. Via National Institute of Technology Tiruchirappalli.

Editor’s note: This article was originally published by Brian Koberlein on G+, and it is republished here with the author’s permission.

There’s a web post from the Nature website going around entitled “Simulations back up theory that Universe is a hologram.” It’s an interesting concept, but suffice it to say, the universe is not a hologram, certainly not in the way people think of holograms. So what is this “holographic universe” thing?

It all has to do with string theory. Although there currently isn’t any experimental evidence to support string theory, and some evidence pointing against it, it still garners a great deal of attention because of its perceived theoretical potential. One of the theoretical challenges of string theory is that it requires all these higher dimensions, which makes it difficult to work with.

In 1993, Gerard t’Hooft proposed what is now known as the holographic principle, which argued that the information contained within a region of space can be determined by the information at the surface that contains it. Mathematically, the space can be represented as a hologram of the surface that contains it.

That idea is not as wild as it sounds. For example, suppose there is a road 10 miles long, and its is “contained” by a start line and a finish line. Suppose the speed limit on this road is 60 mph, and I want to determine if a car has been speeding. One way I could do this is to watch a car the whole length of the road, measuring its speed the whole time. But another way is to simply measure when a car crosses the start line and finish line. At a speed of 60 mph, a car travels a mile a minute, so if the time between start and finish is less than 10 minutes, I know the car was speeding.

A visualization of strings. Image credit: R. Dijkgraaf.
A visualization of strings. Image credit: R. Dijkgraaf.

The holographic principle applies that idea to string theory. Just as its much easier to measure the start and finish times than constantly measure the speed of the car, it is much easier to do physics on the surface hologram than it is to do physics in the whole volume. The idea really took off when Juan Martín Maldacena derived what is known as the AdS/CFT correspondence (an arxiv version of his paper is here ), which uses the holographic principle to connect the strings of particle physics string theory with the geometry of general relativity.

While Maldacena made a compelling argument, it was a conjecture, not a formal proof. So there has been a lot of theoretical work trying to find such a proof. Now, two papers have come out (here and here) demonstrating that the conjecture works for a particular theoretical case. Of course the situation they examined was for a hypothetical universe, not a universe like ours. So this new work is really a mathematical test that proves the AdS/CFT correspondence for a particular situation.

From this you get a headline implying that we live in a hologram. On twitter, Ethan Siegel proposed a more sensible headline: “Important idea of string theory shown not to be mathematically inconsistent in one particular way”.

Of course that would probably get less attention.