Farewell to Reality (16 page)

There is, at present, no experimental evidence for length contraction of the kind predicted by special relativity. For ‘everyday' objects moving at physically attainable speeds, the effects are too small to measure. Subatomic objects moving close to light speed would be expected to show these effects much more clearly, but the ‘lengths' of these objects are not accessible to experiment (and, indeed, the dual wave particle nature of subatomic particles suggests that ‘length' might not be a very meaningful property for such objects).

E = mc
²
and all that

Einstein's 1905 paper on special relativity was breathtaking in its simplicity yet profound in its implications. But he wasn't quite done. He continued to think about the consequences of the theory, and just a few months later he published a short addendum.

In this second paper, he considered the situation in which a body emits two bursts of electromagnetic radiation in opposite directions. Although Einstein had already published a paper speculating on the possibility of light quanta, he refrained from introducing this concept here; in any case he did not need it — what's important is that the radiation carries
energy
in some form away from the body.

Assuming the emitted bursts of radiation behave as waves, he examined the relationship between the energy of the system (object plus emitted radiation) from the perspective of the system's ‘rest frame' and from the perspective of an observer moving at constant speed relative to the system. He found that the energies of the two situations are measurably different, and traced this difference to the kinetic energies of the body in the different inertial frames.
^*

After a little bit of algebraic manipulation, he concluded that if the total energy carried away by the radiation is E, then the mass of the body m must diminish by an amount E/c
²
, where c is the speed of light. He continued: ‘Here it is obviously inessential that the energy taken from the body turns into radiant energy, so we are led to the more general conclusion: The mass of a body is a measure of its energy content …'
⁹

Today we would probably rush to rearrange the equation in Einstein's paper to give the iconic formula E = mc
²
. But Einstein himself didn't do this. And he was not actually the first to note this possibility: five years earlier, French theorist Henri Poincaré had concluded that a pulse of light of energy E should have a mass given by E/c
²
.
¹⁰

Einstein's genius was once again to suggest that this is a general result — the inertia of a body (its resistance to acceleration), and hence the inertial mass of a body, is a measure of the amount of energy it contains. Although he was uncertain that this was something that could ever be subject to experimental test, he was prepared to speculate that the conversion of mass to energy might be observed in radioactive substances, such as radium.

Whilst E = mc
²
has become an iconic formula that demonstrates the equivalence of mass and energy, it is perhaps important to note that, as written, it is not universally applicable. It can't be applied to photons, for example, as photons are massless. If we put m = 0 into Einstein's equation we would erroneously conclude that photons possess no energy, either. This is because E = mc
²
is an approximation of a more general equation. From this general equation it is possible to deduce that photons possess energy given by their momentum multiplied by the speed of light.
¹¹

It is also tempting to push for one further conclusion regarding the nature of mass in special relativity. The equations can be manipulated to give an expression for the ‘relativistic mass' of an object, which becomes larger and larger as the object is accelerated to speeds closer and closer to that of light.

The object is not literally increasing in size. It is mass as a measure of the object's resistance to acceleration that mushrooms to infinity for objects travelling at or near light speed.
¹²
This is obviously impossible, and often interpreted as the reason why the speed of light represents an
ultimate speed which cannot be exceeded. To accelerate any object carrying mass to light speed would require an infinite amount of energy.

However, Einstein himself seems to have been cool on this interpretation, and the notion of ‘relativistic mass' remains very dubious. In a 1948 letter to Lincoln Barnett, an editor at
Life
magazine who was working on a book about Einstein's relativistic universe, Einstein wrote:

It is not good to introduce the concept of the [relativistic] mass M … of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ‘rest mass', m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion.
¹³

Spacetime: travels in four dimensions

Depending on your perspective, time dilates and lengths contract. These bizarre effects of special relativity force us to abandon our cosy Newtonian conceptions of absolute space and time and appear to threaten us with chaos. If space and time are relative and depend on the speed of a moving observer, then how can we ever hope to make sense of the universe?

We need to stay calm. Einstein was led to the principle of relativity because we demand that the laws of physics should appear to be the same for all observers, irrespective of their state of relative motion. In other words, the laws of physics are
invariant.

But how can this be if space and time are not invariant in the same way? The answer is relatively simple,
^*
and was identified by Hermann Minkowski, Einstein's former maths teacher at the Zurich Polytechnic. On 21 September 1908, he opened his address to the 80
^th
Assembly of German Natural Scientists and Physicians with these words:

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their
strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
¹⁴

The fact that relative motion causes time to dilate and lengths to contract means that time intervals and spatial intervals (distances) are different for different observers. But, Minkowski realized, if space and time were to be combined in a four-dimensional
spacetime,
then intervals measured in this spacetime would remain invariant. In Minkowski spacetime, time multiplied by the speed of light — a product which has the units of distance — takes its rightful place alongside the three spatial dimensions of common experience.

But hang on a minute. If spacetime is invariant, does this mean it is also absolute? Newton was obviously wrong about absolute space and absolute time, but was he nearly right? Does an absolute spacetime restore the idea of an independently existing ‘container' for mass and energy? Is it the existence of absolute spacetime that explains the absolute motion in Newton's bucket?

Many contemporary physicists and philosophers believe so. In
The Fabric of the Cosmos,
American theorist Brian Greene writes:

Special relativity does claim that some things are relative: velocities are relative; distances across space are relative; durations of elapsed time are relative. But the theory actually introduces a grand, new, sweepingly absolute concept:
absolute spacetime.
Absolute spacetime is as absolute for special relativity as absolute space and absolute time were for Newton …
¹⁵

Gravity and the curvature of spacetime

We come, at last, to the second problem that Newton was obliged to sweep under the carpet: the problem of the origin of his force of gravity, which was required to act instantaneously between objects and at a distance.

It is such a common, everyday experience that it is hard to believe that Newton couldn't explain it. When I drop things, they fall. They do this because they experience the force of gravity. We are intimately familiar with this force. We struggle against it every morning when we
get out of bed. We fight against it every time we lift a heavy weight. When we stumble to the ground and graze a knee, it is gravity that
hurts.

In the clockwork universe described by Newton's laws of motion, force is exerted or imparted by one object impinging on another. But there is nothing slamming hard into the moon as it swoons in earth's gravitational embrace. There is nothing out at sea pushing the afternoon tide up against the shore. When a cocktail glass slips from a guest's fingers, it seems there is nothing to grab it and force it to shatter on the wooden floor just a few feet below.

Newton was at a loss. In the
Principia
he famously wrote:

Hitherto we have explained the phænomena of the heavens and of our sea, by the power of Gravity, but have not yet assigned the cause of this power… I have not been able to discover the cause of those properties of gravity from phænomena, and I frame no hypotheses.
¹⁶

Part of the solution to this riddle would come to Einstein during an otherwise average day at the patent office in November 1907, by which time he had been promoted, to ‘technical expert, second class'. He later recalled: ‘I was sitting in a chair in my patent office at Bern. Suddenly a thought struck me: If a man falls freely, he would not feel his weight.'
¹⁷

Suppose you climb into an elevator at the top of the Empire State Building in New York City. You press the button to descend to the ground floor. The elevator is, in fact, a disguised interstellar transport capsule built by an advanced alien civilization. Without knowing it, you are transported instantaneously into deep space, far from any planetary body or star. There is no gravity here. Now weightless, you begin to float helplessly above the floor of the elevator.

What goes through your mind? Your sensation of weightlessness suggests to you that the elevator hoist cables have been suddenly cut and you're free-falling to the ground.

The aliens observing your reactions do not want to alarm you unduly. In true
Star Trek
style, these are beings of pure energy. They reach out with their minds, grasp the elevator/capsule in an invisible force field and gently accelerate it upwards. Inside the elevator, you fall
to the floor. Relief washes over you. You conclude that the safety brakes must have engaged, and you have ground to a halt. You know this because, as far as you can tell, you're once more experiencing the force of gravity.

Einstein called it the ‘equivalence principle'. The local experiences of gravity and of acceleration are the same.

The special theory of relativity is ‘special' in the sense that it deals only with inertial frames at rest or moving at constant velocity relative to one another. Einstein had sought ways to deal theoretically with situations involving acceleration, and the equivalence principle suggested a strong connection between acceleration and gravity. But it would take him another eight years to figure out precisely how the connection works.

The equivalence principle suggested at least one consequence, however. In an elevator that is rapidly accelerating upwards, a beam of light emitted from one side of the elevator would strike the other side slightly lower down, because in the time it takes for the light to travel from one side to the other, the elevator has moved upwards. The acceleration has caused the light path to bend. And if acceleration cannot be distinguished from gravity, then we would expect to see precisely the same result if the elevator were stationary in a gravitational field. Einstein concluded that light is bent near large gravitating objects, such as stars and planets.

On its own, this was not a particularly astounding revelation. If, like Newton, we were to assume that light is composed of tiny corpuscles, then we would expect them to carry a small mass and so be affected by a gravitational field. Newton's corpuscular theory actually predicts a shift in the light from distant stars passing close to the sun of about 0.85 arc seconds. As we now know, photons are massless but they still possess momentum and energy, and this makes them susceptible to gravitational forces (because ‘m' = E/c
²
).

But there is a second effect, as Einstein discovered. It originates in the understanding that light travels in straight lines, but what constitutes a straight line has to be amended in the vicinity of a large gravitating object.

Our general experience of distances and lines is formed by our local geometry, which is ‘flat' or Euclidean. In Euclidean geometry the shortest distance between two points is obviously the straight line we
can draw from one to the other. But what is the shortest distance between London and Sydney, Australia? The answer, of course, is 10,553 miles. But this distance is not, in fact, represented by a straight line. The surface of the earth is curved, and the distance between two points on such a surface is not a straight line, it is a curved path called a
geodesic.

Now comes a leap of imagination that is truly breathtaking. What if the space near a large mass isn't ‘flat'? What would happen if it is curved? Light following the ‘straight line' path through a space that is curved would appear to bend. Einstein realized that he could finally eliminate the curious action-at-a-distance suggested by Newton's gravity by replacing it with curved spacetime. An object with mass (and hence energy) warps the spacetime around it, and objects straying close to it follow the ‘straight line' path determined by this curved spacetime.

‘Spacetime tells matter how to move; matter tells spacetime how to curve,' explained American physicist John Wheeler.
¹⁸
And this is a short, but eloquent, summary of Einstein's general theory of relativity.