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Posted 26 August 2007

Einstein was right, but...

by Frikkie de Bruyn

"Astronomers are physicists who study the universe and the laws which govern it".
- South African Astronomical Observatory quoted at the 50th meeting of the South African Institute of Physics.

The physicist’s attitude towards time is conditioned by experiments proving general relativity’s treatment of time as correct in hundreds of experiments. Time is not regarded as a sequence of events which happen, but rather the past and future are all here. Time doesn’t flow. There is no past; we have memories of events that are spatially separated from what we call now. Nor does the future exist; it is all here, it simply is now. Time is interwoven with space in the theory of relativity. It is spacetime. Spacetime is elastic. It can be stretched and bent. Space and time are mutually distorted. If space is stretched time is shrunk. This resulted in spacetime warps. The stronger the gravity, the more pronounced is the spacetime warp. The gravitational pull of some very massive stars are so strong that they leave behind a black hole, where it is thought that a singularity at the centre of the black hole marks the end of time and matter no longer exists in the form known to us. Time in this context must not be confused with the concept of time that arises as a result of the second law of thermodynamics; the tendency of all systems, including the universe, to increase its entropy or disorder.

General relativity liberated time from the universality attributed to it by Newton, which allowed each observer’s time to continue independently and freely, to each observer observing his own time. This means that there can be no agreement between two observers about their ‘now’. In the well known ‘twins paradox’ one member of the twins went on a space trip at a speed very close to the speed of light and return to earth to find that his brother who remained behind, has aged ten years to his one year. The relatively high speed at which he travelled enabled him to experience one year for every ten years on earth. This is known as the time dilation effect which has some far reaching consequences for physics and cosmology. General relativity treats the universe as a ‘causal universe’, meaning that every event must have been caused by another event, not outside the light history of the event. The drawing hereunder illustrate event P which can only be causally influenced by events inside the light cone A. The light cone illustrates the finite speed of light and that nothing can exceed the speed of light.

In the sketch above the light cone A lies in the past of the event P and the light cone C lies in the future of the event P. Only events inside light cone A can influence events at P. Events lying outside light cone A can have no effect on event P since it would have to travel faster than the speed of light to do so.

The predominance of the speed of light has important consequences for cosmology. During the exponential expansion of the universe, generally referred to as the big bang, the universe expanded faster than the speed of light. This does not mean that Einstein’s relativity is wrong. It means that nothing with rest mass can travel as fast or exceed the speed of light. What it does mean is that there are parts of the universe we cannot see since the light emitted did not have enough time to reach us. That is why we refer to the observable universe, the part of the universe we can see. The universe may therefore be infinite or finite in extent. We cannot tell. Since more light reaches us everyday from parts of the universe previously inaccessible to us, we can really say ‘tomorrow we shall know more’.

General relativity taught us that the member of the twins speeding off in a spaceship at a speed very close to that of light will experience a slowdown of his time relative to that on earth and that the spaceship and the astronought will become more and more massive. Energy is converted into matter and that is why the spaceship cannot reach or exceed the speed of light. Particles, such as a photon with no rest mass, travel at the speed of light and does not age one second. According to a photon which theoretically travelled from the big bang will record the time spent on travelling to us as NIL. What Einstein could, however, not have foreseen was what is happening inside the accelerating spaceship. A brilliant young Canadian physicist, Bill Unruh, then barely out graduate school, found that due to the quantum theory and relativity there must be a universal effect whereby any accelerating object must have the feeling that it is embedded in a sea of hot photons. The temperature is proportional to the acceleration. The relation T and the acceleration a is known. The formula derived by Unruh is

T = a(ħ/2πc)

Where ħ is Planck’s constant and c is the speed of light. How do we explain this phenomenon? Quantum mechanics tells us that no particle can remain absolutely still; there would always remain some intrinsic motion called the zero point motion. But this principle also applies to fields that permeate space, such as the electric and magnetic fields. Applying the uncertainty principle to say the electric and magnetic fields, if you measure the precise value of the electric field in one area of space, you have to be completely ignorant of the magnetic field. Therefore the value of both the electric and magnetic fields in one area of space cannot be zero. No matter how cold space is, there is still a random fluctuation in the electric and magnetic fields. This is known as the quantum fluctuations of the vacuum. Quantum fluctuations cannot be detected, they carry no energy. But the amazing thing is they can be detected by an accelerating detector because the accelerating detector provides a source of energy. It is these random fluctuations that register an increase of the temperature on thermometers carried in the accelerating spaceship. It still does not fully explain the random motion of particles. The explanation has to be found in the fact that particles can be correlated in that if you measure the properties of one, you get a complete description of the properties of another. In the case of the accelerating astronought the particle detected by her thermometer is correlated to a particle beyond her horizon (see next paragraph for explanation of the astronought’s event horizon). This means that the particles observed by her thermometer are intrinsically random. Random motion means heat, therefore her thermometers register heat!

The accelerating astronought develops what is called an event horizon. Stars that he observed early in his flight now disappear from his sight. If he slows the speed of the spaceship down, he will find that the stars become visible again. This is known as Bekenstein’s law which states that with every horizon that forms a boundary separates an observer from a region which is hidden from him. There is nothing new about a horizon. All observers have their own horizons. The hidden region consists of all those events that he cannot receive information from. What is interesting about the event horizon experience by an accelerating astronought is that he can access information again beyond his event horizon when he decelerates the spaceship. I must stress that the two phenomena of heat developing inside an accelerating spaceship and the event horizon occurring as a result of acceleration has not been observed.

Frikkie de Bruyn

Books used in research for this article

Hawking SW, The Universe in a Nutshell. Transworld Publishers, London 2001
Smolin L, Three Roads to Quantum Gravity. Orion Books Ltd London 2003                 

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