Quantum
The ultra-violet 'catastrophe'
By the end of the nineteenth century, scientists working on the way energy is radiated from a hot body had a problem. Their theory told them that, for a body at a given temperature, the amount of energy (e.m.radiation) radiated was proportional to its frequency. Unfortunately, this means that all the energy should be radiated at infinite frequency, which does not happen.
The curve, for 5000 degrees K, for this 'classical' theory is shown in black in the graph below. (This graph has wavelength, rather than frequency, as the x-axis so that the region of interest is near the origin) The curve for 5000 degrees K, found by experiment, is shown in blue.
The discrepancy was known as the 'ultra-violet catastrophe' as the experimental curve dips sharply at ultra-violet frequencies whereas the theoretical curve keeps on increasing. This was obviously a 'catastrophe' for the theory. The discrepancy between the curves for 5000 degrees K actually starts to become significant at wavelengths shorter than 3 micrometres.
In
the early years of the 20th Century, Max
Planck and others found that the experimental curve can be explained
if energy is emitted, and absorbed, in discrete amounts (quanta) where the size
of a quantum is proportional to the frequency of the radiation.
The
black body radiation curves
Is the quantum explanation appropriate for all frequencies?
Process versus principle
Although
in principle the quantum explanation works for all frequencies, do we
need to use this explanation for frequencies lower than infrared? Do
we need to consider the processes involved at those frequencies as
having a quantum nature? I would suggest not, unless we consider
space and time to be quantised which would mean motion occurs in
steps. Otherwise, there are at least four processes that produce e.m.
radiation.
Oscillating
electrons – microwave and radio
Radiation
produced by
oscillating electrons, in an electrical circuit for instance,
does not seem to come in quanta. This radiation comes in a
continuous wave,
bearing in mind that this could be an emergent property.
Internal
molecular vibration – mid-infrared wavelengths
Radiation produced by
vibration of chemical bonds in a molecule may be considered to be a
half-way-house between continuous oscillation and a quantum effect.
The molecule absorbs energy which causes its chemical bonds to
vibrate in one or more modes. The vibration can be initiated either
by radiation from other molecules, or by mechanical jostling by
adjacent molecules. The frequency of these modes does not change but
the amplitude may, so this radiation should not be considered to be
quantised.
It's similar to the ringing of a bell. This can be due to a nearby bell ringing at the same frequency (sympathetic vibration) or by striking the bell with a hammer. The energy of the hammer blow does not have to be a specific amount to cause the bell to resonate.
Electron
jumps within an atom – infrared, visible, ultraviolet and x-rays
Some infrared, visible,
ultraviolet and some x-rays are produced by an electron changing
energy levels within an atom. The energy differences between these
levels are fixed so the radiation comes in fixed quanta.
Nuclear
processes – x-rays and gamma radiation
Gamma and some
x-radiation is produced by processes in the nuclei of atoms and is
quantised as a result of the nature of these processes.
Is the received photon the same one that was emitted?
A Two-Slit experiment can
be set up so that light quanta (photons) are registered at the target
one at a time. Over time an interference pattern builds up at the
target.
In Quantum Theory this is
interpreted as a photon emitted from the source, spreading out as a
'wave-function', passing through both slits, then interfering with
itself. A 'collapse of the wave-function' is necessary for the
photon to be in a single state and be absorbed by an atom in the
target.
However, the fact that
one photon at a time is detected at the target does not mean that
photons leave the source one at a time nor that discrete photons move from the source to the target.
All that is required for
the target to register the arrival of a photon is that an electron in
a target atom undergoes a transition to a higher energy level.
Is there another way of looking at this process?
Scenario
A Two-Slit experiment is
be set up as described previously. An electron in a source atom
undergoes a transition to a lower energy level, emitting a quantum of
energy. Electromagnetic radiation (what I call the 'presence' of
the transition) spreads out through the apparatus. By the time it
reaches the target it is attenuated and cannot, by itself, cause an
electron in a target atom to undergo a transition to a higher energy
level.
However, the combined
presence of many 'simultaneous' source transitions can produce the
necessary conditions for such a target transition. The presence of the
source transitions can pass through both slits and continue to the
target. Then, if a target atom is in the right place and in the right energy state, a
photon will be registered as arriving at the target. An interference
pattern builds up over time.
In other words the photon does not have to be a discrete entity that moves from the source to the target. In this scenario there is no 'wave-function' and so no 'collapse of the wave-function' is necessary for a photon to be absorbed.
A potential problem
However,
there is a problem with this idea. If many source atoms have to
change state simultaneously for one target atom to change state, many
other target atoms ought to change state simultaneously as well. So
how can it appear that one photon at a time reaches the target?
Solutions
- The combined presence of many source transitions is required at a target atom for a quantum to be absorbed. Due to the different path lengths between source atoms and target atoms, simultaneity will only be achieved at a minority of target atoms.
- The atoms in the source and the target oscillate, due to the temperature of the apparatus. These oscillations cause changes in the frequency of the incoming presence at the target atoms. Since the target atoms will only undergo a transition to a higher energy level at a certain frequency, this limits the number of target transitions.
- Not all target atoms will be in the correct energy state to absorb an incoming quantum.
- The source emission is adjusted so that only one photon at a time is detected at the target.
For
a combination of these reasons it may be possible for only one photon at a
time to be detected at the target.
The effect of detecting a photon at one of the slits
If the
experimenter tries to detect which slit the photon passes through, the interference pattern disappears. Why should
this be? Consider the following explanation.
The
experiment is set up so that photons can be detected as they pass
through one of the slits. When
an electron in a slit detector atom undergoes a transition to a higher
energy level, the conditions for an electron in the target atom to
undergo a transition may not be not met. Detecting
a photon at one of the slits changes the conditions at the target.
The apparatus behaves as though it has only one slit and no
interference pattern builds up.
Mike Holden - Nov 2015