We live in a universe of space and time. Events occur at a particular time, and in some location in space. In this way, space and time can be seen as a background against which things happen. Throughout most of human history, this background was seen as absolute. Each event occurs at a unique point in space and time, and in principle everyone can agree what that point is. Intuitively, it makes a lot of sense. In our everyday lives the Earth seems to be an unmoving rock, and acts as a point of reference for everything we do. Sure, we now know the Earth moves around the Sun, but it doesn’t feel that way. When Galileo and others began proposing a more sophisticated view of physics, the intuitive view of spacetime as an immutable background remained. Galileo argued that the motion of objects was relative to each other, but that motion could always be measured relative to the “fixed” space. For Galileo, speed was relative, but spacetime was not. When Newton developed his theories of physics and gravity, he also assumed that spacetime was fixed and absolute.

The success of Newton’s physics seemed to confirm the absolute nature of spacetime, and the assumption remained largely unquestioned for two centuries. But as we came to understand light, the idea became less intuitive. According to Maxwell’s equations, the speed of light is the same for all light. That’s because electromagnetic waves propagate at the same rate. But water waves propagate through water, and sound waves through air, so what do light waves propagate through?

The most popular idea was that light moved through a luminiferous aether. This aether couldn’t be observed directly, but it was thought to be stationary relative to the background of space. Some proposed that this aether could in fact be the absolute frame of reference for the universe. But if that’s the case, then your measurement of the speed of light should depend upon your motion relative to the aether.

Suppose you were on the platform of a train moving at 10 m/s (20 mph). If you measured the speed of sound in the direction you are moving, you would get a speed of 330 m/s. That’s because the sound is traveling through the air at 340 m/s, but you are traveling through the air in the same direction at 10 m/s, so the sound is moving 330 m/s relative to you. In the same way, if you measured the speed of sound in the opposite direction, you would get 350 m/s because of your motion. This is a key feature of waves traveling through a medium: they can be different in different directions because of your motion through the medium.

Then in 1887, Albert Michelson and Edward Morley performed an experiment to measure this difference in the speed of light. But what they found was the speed of light was always the same. No matter what direction light traveled, no matter how they oriented their experiment, the speed of light never changed. This was not only surprising, it violated the fundamental assumption of an absolute reference frame. It seemed the speed of light (and only the speed of light) is absolute, and this made no sense at all.

The relative nature of “now.”

This is the puzzle Einstein sought to resolve in his paper “On the Electrodynamics of Moving Bodies.” In this paper Einstein noted that in order for the speed of light to be an absolute constant, either Maxwell’s equations or Newton’s concept of space and time had to be wrong. Somewhat surprisingly, Einstein argued for the latter. Specifically, he argued that the “grid” of space and time was relative to the observer. He demonstrated this by looking at a property known as simultaneity. In Newton’s view, two events seen to occur at the same time will be seen to be simultaneous for all observers. But Einstein showed that the constancy of light required this concept of “now” to be relative. Different observers moving at different speeds will disagree on the order of events.

Rather than a fixed background, space and time is a relation between events that depends upon where and when the observer is. This relativity of space and time led to strange predictions, such as time dilation, which were later found to be true. It’s a concept that’s still difficult to fully understand, but is absolutely necessary for modern devices such as GPS.

Tomorrow: Einstein looks at the connection between matter and energy, and finds that relativity could explain the light of the stars.

Paper:  Einstein, Albert. Zur Elektrodynamik bewegter Körper. Annalen der Physik 17 (10): 891–921 (1905)

The post Lunchtime Doubly So appeared first on One Universe at a Time.

When you think of the strangest scientific theory ever, you probably think of quantum mechanics. With its particle-wave duality and collapsing wavefunctions, it can certainly be considered a strange theory. But I would argue that even more bizarre is the theory of relativity. In quantum theory objects behave strangely in space and time, but in relativity the very nature of space and time is questioned. Despite all of its consequences such as curved space, time dilation and interchange of mass and energy, we know relativity to be true. Not just “kind of” true, but provably true to a high degree of precision.

Michelson and Morley’s 1887 interferometer.
Credit: Case Western Reserve Archive

The foundational experiment for both special and general relativity is the verification that the speed of light in a vacuum is the same for all frames of reference. This was first demonstrated by the famous Michelson-Morley experiment in 1887. The idea that the speed of light is constant is deeply counterintuitive. It would be as if you are riding a skateboard at 5 mph, and you toss a ball at 15 mph, and someone standing on the sidewalk sees the ball move not at 20 mph, but 15 mph just as you do. Michelson and Morley weren’t trying to prove light speed is constant, they were actually trying to determine how the speed of light changes as the Earth orbits the Sun. Instead of observing a changing speed of light, they found no variation to the limit of their experiment, which was about 1 part in 40,000. Because of this, the Michelson-Morley experiment is sometimes called the most successful failed experiment ever.

Since then, the result has been confirmed numerous times. With the advent of lasers, the experiment could be performed to extremely high accuracies. The results were so precise that in 1983 the speed of light became the standard by which the meter is defined. The most recent tests of the constancy of light speed find that it varies by no more than a few parts per quintillion.

Since the speed of light is constant for all frames of reference, there should be a difference between the way time is observed in different reference frames. We can see how this works if we imagine a clock made with light. Take two mirrors and place one above the other and facing each other, then bounce a pulse of light between them. We can measure time by counting the number of times the light bounces off a mirror. Each bounce is like the tick or tock of a mechanical clock. If you could watch the pulse of light, you would see it move up and down between the mirrors at the speed of light. Up and down at a constant rate. Now suppose you took your clock on a fast moving train. Standing in the aisle of the train, you would see the light pulse move up and down at the same rate as before. Up and down at the speed of light.

Credit: John D. Norton

But an observer watching the train pass by would see something slightly different. They would also see the pulse move at the speed of light, but from their perspective the light can’t move straight up and down because it must also be moving along with you. They would see the pulse move diagonally up then diagonally down, which is a slightly longer distance between each bounce. That means it would take the light longer to travel from bounce to bounce. So from their viewpoint the ticks and tocks of your clock are slower than the ticks and tocks as you see them. Your clock appears to be running slow because of your motion relative to them.

This effect is known as time dilation, and it can be demonstrated by what is known as the Ives–Stilwell experiment. This experiment looks at the light emitted or absorbed by fast moving particles and compares them with the transverse Doppler effect. If an object speeds past you from left to right, when it is directly in front of you would you see any Doppler shift of its light? Since the relative motion along your line of sight at that moment is zero, you might think there would be no shift. But since the object is speeding past you, its time should be dilated. As a result there should be a Doppler shift. The Ives-Stilwell experiment is thus a direct test of time dilation. It was first performed in 1938, and has been improved upon over the years. Just this week, results on a new version of the experiment has confirmed time dilation to 2 parts in a billion.

Other experiments have looked at time dilation by comparing the time of two clocks in motion relative to each other. These experiments assume light obeys special relativity, so they are model dependent rather than the direct Ives-Stilwell experiments. However when comparing the relative time dilation of two atomic clocks, we find that they agree with the predictions of relativity to within one part in 10¹⁶. Special relativity makes our observations of space and time relative, but it is astoundingly accurate.

Of course relativity can be broadened to include the effects of gravity. This general theory of relativity begins with the observation that any two objects will fall in a gravitational field in the same way. It was first noted by Galileo who (according to legend) dropped lead balls of different size from the tower of Pisa. Galileo actually tested the idea by rolling balls down an inclined plane, and could find no observable difference.

Robert DuBois of Missouri Science & Tech, with an Eotvos apparatus

In 1908 Loránd Eötvös made the first precision test of the equivalence principle using a torsion balance, and found that it was true to within one part in a billion. Over the last century this result has been improved to the point that we now know the equivalence principle is true to within 1 part in 10¹⁴.
Using the equivalence principle, Einstein developed a gravitational theory even more strange than special relativity. In his theory the fabric of space and time can be bent and twisted by the presence and motion of masses. One of the first tests of the gravitational curvature of space was the deflection of starlight during a solar eclipse, first observed by Eddington in 1919. Eddington’s results supported Einstein’s model, but not very strongly. Given the radical approach of general relativity, Eddington’s results were initially disputed by some. But subsequent observations confirmed Einstein’s predictions.

A distant galaxy (blue) is gravitationally lensed by a closer galaxy (red). Credit: ESA/Hubble & NASA

The most recent tests of light bending agree with general relativity to within 0.3%. That doesn’t seem very strong, but it’s very difficult to measure accurately. At Earth’s distance, the light of a star seen at a direction 90 degrees away from the Sun is deflected by 4 milliarcseconds. That’s roughly equivalent to the width of a human hair seen from 3 kilometers away.

Our astronomical instruments have gotten so precise that even this small deflection must be taken into account. Satellites such as Hipparcos (and soon Gaia) make very precise observations of the positions of millions of stars. As the satellites orbit the Sun, measured stars are sometimes aligned more closely or more distant from the Sun. As a result, the gravitational curvature of the Sun can shift the observed position of the stars by a measurable amount. In fact, measurements of Gaia will be so precise that it could provide a more stringent confirmation of light bending.

Perhaps the weirdest prediction of relativity is that rotating masses twist space around them. This effect is known as frame dragging, and it is most dramatic around black holes. But even the Earth’s rotation twists space ever so slightly. In 2011 a spacecraft known as Gravity Probe B successfully observed this effect due to the Earth.

Gravity Probe B tests general relativity. Credit: Gravity Probe B Team, Stanford, NASA

The frame dragging effect of Earth is so small that it’s astounding we can perceive it at all. To observe these effects, the team had to create quartz spheres so precise that their surface varied no more than 40 atoms from a mathematically perfect sphere. They were then covered with a thin layer of niobium so they could be suspended within an electric field. Their rotation created a small magnetic field, which was measured by superconducting quantum interference devices. Of course all of this is packed into a probe and shot into space for an 18 month mission. Over the duration of the experiment, the rotation of the spheres had to be measured with milliarcsecond precision. Despite the challenges, Gravity Probe B confirmed the Earth’s gravitational curvature of space to within 1% of predictions, and confirmed frame dragging to within 19%.

Decay of a binary pulsar’s orbital period over time.

Despite all these successes, there is one confirmation of relativity which still eludes us: direct observation of gravitational waves. According to general relativity, when large masses such as neutron stars or black holes orbit each other, they should create ripples in spacetime. These ripples should radiate outward as gravitational waves. Because these waves carry energy away from the system, the orbits of these massive objects should decay. We’ve seen this kind of orbital decay in binary pulsars, so we’re pretty certain these gravitational waves exist. But to truly be certain we’d like to detect them directly.

In principle we should be able to observe their effect as an oscillation in the separation distance of two mirrors. But even if the mirrors were separated by 4 kilometers, the variation in their distance would only be about 10^-18 meters, or about a thousand times smaller than the width of a proton. We haven’t confirmed gravitational waves yet, but with projects such as LIGO, and the proposed space-based LISA, we will likely succeed.

Of course, these experiments are only possible using lasers, and the knowledge of the invariant speed of light. Perhaps it is fitting that we use the first triumph of relativity to strive for its last great confirmation.

Note: This post originally appeared at Starts With A Bang!

The post The Strangest Theory We Know Is True appeared first on One Universe at a Time.

There’s been a couple of questions about the possibility of traveling faster than light, so let’s explore that a bit today.  The short answer to whether one can travel faster than light is no.  The inertial speed of an object can never exceed the speed of light.  This means if you measure the speed of an object passing you, it will always be less than the speed of light.  The longer answer is “it’s complicated.”

The reason it’s complicated is because we like to think of speed as the motion of an object in some absolute, universal reference frame.  In our every day experience, this works just fine.  In general, however, it doesn’t work.  For one thing, motion is relative, so an object’s “speed” depends who’s measuring it.  At speeds approaching light, special relativity also comes into play, which leads to strange things like time dilation and length contraction.

To demonstrate this, suppose we had a rocket that could accelerate at a constant 1 gee.  This would mean the passengers of our rocket would experience the same “weight” they feel on Earth.  To travel to another star, we simply accelerate toward our destination until we are halfway there, coast just long enough to flip the ship around, then decelerate for the second half of our journey so that we stop at the end of our journey.

The nearest star system is Alpha Centauri, which is 4.3 light years away.  The trip on our 1-gee rocket would take about 5.8 years from Earth’s point of view, and our ship would reach a maximum speed of 0.948 c, or just shy of 95% of light speed.  From the point of view of the passengers, the trip would take only 3.56 years.  From the point of view of our passengers, they traveled 4.3 light years in 3.56 years, which is an average speed 1.2 times faster than light!

Things get more strange if we take a trip to Gliese 876, a star system 15.3 light years away with 4 known planets.  Seen from Earth, the rocket will take 16.7 years to reach Gliese, and reach a maximum speed of 0.993 c.  For our passengers, however, the trip will only take 5.6 years, so their perceived average speed is 2.7 c.  I’ve plotted the travel time of our passengers as a function of the distance of their trip in the figure below.  You can see that the farther they go, the more dramatic this effect gets.  Taken to extremes, our passengers could travel to the Andromeda galaxy (2 million light years away) in only 28 years from their point of view.

So what’s really going on here?  One thing all observers can agree upon is that the speed of light (in a vacuum) is constant from their point of view.  A lab on Earth and a lab on our accelerating spaceship will both measure the same speed. The only way for an Earth lab and a lab moving at nearly the speed of light to agree on light speed is for time and distance to depend on your point of view. In other words, space and time are relative.

As the rocket speeds up, observers on Earth would see that time for the passengers is slowing down.  So Earth observers would say the trip to Gliese actually took 16.7 years, but the slowing of the passenger’s time means only 5.6 years passed for them.  From the view of the passengers, the distance between the Earth and Alpha Centauri appears to get shorter as they speed up.  At any point in their trip they would still measure their speed to be less than light, its just that the faster Earth and Gliese are moving relative to them, the shorter their separation distance appears to be.

Clearly our rocket is not real, so you might be inclined to think that this is all speculation, but these effects have been observed on a smaller scale.  In fact, the GPS in your phone has to correct for these effects in order to work properly.

The upshot of all this is that “speed,” “distance,” and “time” depend on your point of view, and they change in such a way that all observers measure the same speed of light.

Of course if you add gravity to the mix, things get even more interesting.  But I’ll save that for another time.

The post Faster Than Light appeared first on One Universe at a Time.