Relativity :

Readings: Special Relativity
Time Dilation
Spacetime
Mass Energy Equivalence

  • relativity resolves Newtonian physics at extreme energies
  • new type of science for the times since it required sophisticated technology to test
Einstein's theory of relativity deals with Newtonian physics when energies or velocities are near the speed of light. Relativity is usually thought of as modern physics since it was developed at the start of the 20th century and could only be tested in the realm available to scientists by high technology. However, relativity primarily completes the revolution that Newton started and is also highly deterministic as is much of classical physics.

  • relativity redefined fundamental constants, such as mass and length, to be variable
  • these parameters did not become uncertain (quite the opposite) only relative
  • relativity is broken into two parts:
    1. special relativity involving inertial frames
    2. general relativity involving accelerated or gravitational frames
In the holistic viewpoint of relativity theory, concepts such as length, mass and time take on a much more nebulous aspect than they do in the apparently rigid reality of our everyday world. However, what relativity takes away with one hand, it gives back in the form of new and truly fundamental constants and concepts.

The theory of relativity is traditionally broken into two parts, special and general relativity. Special relativity provides a framework for translating physical events and laws into forms appropriate for any inertial frame of reference. General relativity addresses the problem of accelerated motion and gravity.


Special Theory of Relativity :

  • experiments with electromagnetic wave properties of light finds contradictions with Newtonian view of space and time
  • Michelson-Morley experiment shows speed of light is constant regardless of motion of observer (!)
By the late 1800's, it was becoming obvious that there were some serious problems for Newtonian physics concerning the need for absolute space and time when referring to events or interactions (frames of reference). In particular, the newly formulated theory of electromagnetic waves required that light propagation occur in a medium.

In a Newtonian Universe, there should be no difference in space or time regardless of where you are or how fast you are moving. In all places, a meter is a meter and a second is a second. And you should be able to travel as fast as you want, with enough acceleration.

In the 1890's, two physicists (Michelson and Morley) were attempting to measure the Earth's velocity around the Sun with respect to Newtonian Absolute space and time. This would also test how light waves propagated since all waves must move through a medium. For light, this medium was called the aether.

The results of the Michelson-Morley experiment was that the velocity of light was constant regardless of how the experiment was tilted with respect to the Earth's motion. This implied that there was no aether and, thus, no absolute space. Thus, objects, or coordinate systems, moving with constant velocity (called inertial frames) were relative only to themselves.

In Newtonian mechanics, quantities such as speed and distance may be transformed from one frame of reference to another, provided that the frames are in uniform motion (i.e. not accelerating).

  • Einstein makes constant speed of light key premis to special relativity
Considering the results of the Michelson-Morley experiment led Einstein to develop the theory of special relativity. The key premise to special relativity is that the speed of light (called c = 186,000 miles per sec) is constant in all frames of reference, regardless of their motion. What this means can be best demonstrated by the following scenario:

  • special relativity interprets light as a particle called a photon
  • photon moves at speed of light and has zero mass
  • speed of light is an absolute limit, objects with mass must move at less than speed of light
This eliminates the paradox with respect to Newtonian physics and electromagnetism of what does a light ray `look like' when the observer is moving at the speed of light. The solution is that only massless photons can move at the speed of light, and that matter must remain below the speed of light regardless of how much acceleration is applied.

In special relativity, there is a natural upper limit to velocity, the speed of light. And the speed of light the same in all directions with respect to any frame. A surprising result to the speed of light limit is that clocks can run at different rates, simply when they are traveling a different velocities.

  • space and time are variable concepts in relativity
  • time dilation = passage of time slows for objects moving close to the speed of light
This means that time (and space) vary for frames of reference moving at different velocities with respect to each other. The change in time is called time dilation, where frames moving near the speed of light have slow clocks.

  • Likewise, space is shorten in in high velocity frames, which is called Lorentz contraction

Space-Time Lab

  • relativity leads to some strange consequences, such as the twin paradox
  • however, all these predictions have been conferred numerous times by experimentation
Time dilation leads to the famous Twins Paradox, which is not a paradox but rather a simple fact of special relativity. Since clocks run slower in frames of reference at high velocity, then one can imagine a scenario were twins age at different rates when separated at birth due to a trip to the stars.

It is important to note that all the predictions of special relativity, length contraction, time dilation and the twin paradox, have been confirmed by direct experiments, mostly using sub-atomic particles in high energy accelerators. The effects of relativity are dramatic, but only when speeds approach the speed of light. At normal velocities, the changes to clocks and rulers are too small to be measured.


Spacetime:

  • relativity links where and when (space and time) into a 4 dimensional continuum called spacetime
  • position in spacetime are events
  • trajectories through spacetime are called world lines
Special relativity demonstrated that there is a relationship between spatial coordinates and temporal coordinates. That we can no longer reference where without some reference to when. Although time remains physically distinct from space, time and the three dimensional space coordinates are so intimately bound together in their properties that it only makes sense to describe them jointly as a four dimensional continuum.

Einstein introduced a new concept, that there is an inherent connection between geometry of the Universe and its temporal properties. The result is a four dimensional (three of space, one of time) continuum called spacetime which can best be demonstrated through the use of Minkowski diagrams and world lines.

  • determinism is hardened with the concept of spacetime since time now becomes tied to space
  • just as all space is `out there', so is all time
Spacetime makes sense from special relativity since it was shown that spatial coordinates (Lorentz contraction) and temporal coordinates (time dilation) vary between frames of reference. Notice that under spacetime, time does not `happen' as perceived by humans, but rather all time exists, stretched out like space in its entirety. Time is simply `there'.


Mass-Energy Equivalence:

  • if space and time are variable notions, the momentum must also be relative
  • in order to preserve conservation of energy, mass must be connected to momentum (i.e. energy)
Since special relativity demonstrates that space and time are variable concepts, then velocity (which is space divided by time) becomes a variable as well. If velocity changes from reference frame to reference frame, then concepts that involve velocity must also be relative. One such concept is momentum, motion energy.

Momentum, as defined by Newtonian, can not be conserved from frame to frame under special relativity. A new parameter had to be defined, called relativistic momentum, which is conserved, but only if the mass of the object is added to the momentum equation.

This has a big impact on classical physics because it means there is an equivalence between mass and energy, summarized by the famous Einstein equation:

  • mass increases as one nears the speed of light, which explains the limit to the speed of light for material objects, you need infinite acceleration to move an infinitely increasing mass
The implications of this was not realized for many years. For example, the production of energy in nuclear reactions (i.e. fission and fusion) was shown to be the conversion of a small amount of atomic mass into energy. This led to the develop of nuclear power and weapons.

As an object is accelerated close to the speed of light, relativistic effects begin to dominate. In particular, adding more energy to an object will not make it go faster since the speed of light is the limit. The energy has to go somewhere, so it is added to the mass of the object, as observed from the rest frame. Thus, we say that the observed mass of the object goes up with increased velocity. So a spaceship would appear to gain the mass of a city, then a planet, than a star, as its velocity increased.

  • mass-energy equivalence is perhaps the most fundamental discovery of the 20th century
  • photons have momentum, i.e. pressure = solar sails
Likewise, the equivalence of mass and energy allowed Einstein to predict that the photon has momentum, even though its mass is zero. This allows the development of light sails and photoelectric detectors.