Some Key Concepts from Relativity and Quantum Mechanics
Relativity and Quantum Mechanics are two areas of physics that deal with realms far
removed from our daily experience. Relativity applies to very high energy realms:
fast moving objects (fast = near the speed of light) and/or large masses
(large = solar mass). Quantum mechanics applies to the realm
of very small particles (small = atoms). If we extend these theories
into our normal, everyday experience, they provide tiny (usually insignificant)
corrections to Newton's laws, but the departure from Newtonian physics can be
extraordinary in the domains that these theories were developed to describe.
The behavior of physical systems in these realms can appear bizarre and
counter-intuitive, even paradoxical. Nevertheless, it should be understood that
these theories are well supported by observations and experiments, and that they
are widely accepted as "the best" theories currently available. And to understand
some of the phenomenon in astronomy, it is necessary to come to terms with a few
of their more important concepts.
Special and General Relativity
- Energy and matter are eqivalent. They are different forms of the same "stuff".
All energy has mass, and all mass can (under proper conditions) be converted to
energy. The conversion between mass and energy happens according to the famous equation
E = mc2
where E stands for energy, m is mass, and c is the speed of light.
- Time and space are not distinct entities, but are differently perceived aspects of
a 4-dimensional "spacetime". How this spacetime is perceived depends on the state
of the observer.
- All observers will measure the same speed for a beam of light
(c = 3x108m/s), regardless of their motion relative to
other observers.
- Observers who are moving with respect to each other will perceive time and space
differently.
- Time Dilation - Moving clocks run slow.
- Length Contraction -
Moving objects shrink along the direction of their motion.
- Accelerated motion and gravitational fields can "warp" spacetime.
- Observers who are at rest or moving at constant velocity (inertial observers)
will see a "flat" space-time geometry. The space around them will obey the laws of
Euclidean geometry.
- Observers who are accelerating will observe a curved (bent or warped) spacetime
geometry. Euclidean rules will not apply.
- A gravitational field is observationally equivalent to a uniform acceleration.
(An isolated observer, in a sealed room, would not be able to tell the difference
between a room on the surface of the earth, with gravity of 9.8 m/s2, or
in a spaceship accelerating through deep space with a constant acceleration of
9.8 m/s2.) Thus, gravity warps spacetime, and any object with mass
bends the spacetime surrounding it. The stronger the gravitational field, the greater
the effect on spacetime.
- Light always travels along straight lines in the local spacetime (geodesics).
If a light ray passes through a region of curved spacetime (near a massive star, for
instance) it will appear to bend as it follows the contours of the curved spacetime.
Quantum Mechanics
- A particle in a confined physical system (e.g.: an electron in an atom) can
exist only in certain discrete states. This is the principle that gives rise to
the energy levels of the hydrogen atom (see Chaisson & McMillan, chapter 4).
- On the sub-atomic scale, there are two kinds of particles: bosons and fermions.
They are distinguished by their behavior. Two identical bosons (e.g.: photons) are
capable of being in the same physical state (having the same energy, momentum,
location, etc.), while two identical fermions (e.g.: electrons, protons, neutrons,
atomic nuclei) cannot exist in the same state. It is for this reason that
there can be only 2 electrons (one spin "up" and one spin "down") in each "shell"
of an atom (note that this is responsible for the difference in chemical behavior of
different atoms).
- The behavior of global observables (temperature, pressure) of a many-particle system
(typically >1023 particles) will depend on the total energy in the
system and the type of particles.
-
If there is sufficient energy in a many-particle system, all particles will be freely exchanging
between higher and lower energy states, and most energy levels will not be "filled"
at any given time. Such a system will follow classical laws of thermodynamics.
In particular, pressure will be proportional to temperature (thermal pressure),
and can vary throughout the system.
- If there is insufficient energy in a many-particle system, then most of the
particles will be confined to the lower energy states (for bosons, they will all be
in the ground state; for fermions, they will fill up all energy states below some
threshold energy level). In the case of fermions, these lower energy levels will all
be filled, and the particles will be severely restricted in their ability to exchange
energy. Such a system is said to be degenerate. The thermodynamics of a
degenerate system does not obey classical laws. In particular, there is no longer
any relationship between temperature and pressure, which will be the same throughout
the degenerate system. The degeneracy pressure in such a system is limited
by the quantum mechanical properties of the particles that supply the pressure.
- Quantum mechanics allows particles of one type to change to another type,
either by emitting or absorbing (or both) additional particles. One possible
transformation is
proton + electron --> neutron + neutrino
Dr. Scott C. Smith
Last modified: Tue Nov 08 11:33:39 Eastern Standard Time 2005