| The laws list: T |
The laws list T
tachyon to twin paradox.
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T.
- tachyon
-
- A purely speculative particle, which is presumed to
travel faster than light. According to Einstein's equations of special
relativity, a particle with an imaginary rest mass and a velocity greater
than
c
would have a real momentum and energy. Ironically, the greater the kinetic
energy of a tachyon, the slower it travels, approaching
c
asymptotically (from above) as its energy approaches infinity.
Alternatively, a tachyon losing kinetic energy travels faster and faster,
until as the kinetic energy approaches zero, the speed of the tachyon
approaches infinity; such a tachyon with zero energy and infinite speed is
called transcendent.
Special relativity does not seem to specifically exclude tachyons, so
long as they do not cross the lightspeed barrier and do not interact with
other particles to cause causality violations. Quantum mechanical analyses
of tachyons indicate that even though they travel faster than light they
would not be able to carry information faster than light, thus failing to
violate causality. But in this case, if tachyons are by their very nature
indetectable, it brings into question how real they might be.
-
- tachyon paradox
-
- The argument demonstrating that
tachyons
(should they exist, of course) cannot carry an electric charge. For a
(imaginary-massed) particle travelling faster than
c,
the less energy the tachyon has, the faster it travels, until at zero energy
the tachyon is travelling with infinite velocity, or is transcendent. Now a
charged tachyon at a given (non-infinite) speed will be travelling faster
than light in its own medium, and should emit
Cherenkov radiation. The loss of this energy will naturally reduce the
energy of the tachyon, which will make it go faster, resulting in a runaway
reaction where any charged tachyon will promptly race off to transcendence.
Although the above argument results in a curious conclusion, the meat of
the tachyon paradox is this: In relativity, the transcendence of a tachyon
is frame-dependent. That is, while a tachyon might appear to be transcendent
in one frame, it would appear to others to still have a nonzero energy. But
in this case we have a situation where in one frame it would have come to
zero energy and would stop emitting Cherenov radiation, but in another frame
it would still have energy left and should be emitting Cherenkov radiation
on its way to transcendence. Since they cannot both be true, by relativistic
arguments, tachyons cannot be charged.
This argument naturally does not make any account of quantum mechanical
treatments of tachyons, which complicate the situation a great deal.
-
- tardon
-
- A particle which has a positive real mass and travels
at a speed less than
c
in all inertial frames.
Compare
tachyon,
luxon.
-
-
- tau-theta paradox (1950s)
-
- When two different types of kaons, tau and
theta (today tau refers to a completely different particle) decay, tau
decays into three particles, while the theta decays into two. The tau and
theta differ only in parity; and at the time, it was thought that parity was
strictly
conserved, and that particles differing only in parity should behave
exactly the same. Since the two decay differently, a paradox ensued. The
paradox was resolved when experiments carried out according to F. Yang and
T.D. Lee's theoretical calculations indeed indicate that parity is not
conserved in weak interactions.
-
- tesla; T (after N. Tesla, 1870-1943)
-
- The derived
SI unit of
magnetic flux density, defined the magnetic flux density of a magnetic flux
of 1 Wb
through an area of 1
m2;
it thus has units of
Wb/m2.
-
- thermodynamic laws
-
-
- First law of
thermodynamics
-
- The change in internal energy of a system is the sum of the heat
transferred to or from the system and the work done on or by the system.
-
- Second law of
thermodynamics
-
- The entropy -- a measure of the unavailability of a system's energy
to do useful work -- of a closed system tends to increase with time.
-
- Third law of
thermodynamics
-
- For changes involving only perfect crystalline solids at absolute
zero, the change of the total entropy is zero.
-
- Zeroth law of
thermodynamics
-
- If two bodies are each in thermal equilibrium with a third body,
then all three bodies are in thermal equilibrium with each other.
-
- Thomson experiment; Kelvin effect
(Sir W. Thomson [later Lord Kelvin])
-
- When an electric current flows through a
conductor whose ends are maintained at different temperatures, heat is
released at a rate approximately proportional to the product of the current
and the temperature gradient.
-
- Tipler machine
-
- A solution to Einstein's equations of general
relativity that allows
time travel. An extremely dense (on the order of the density of neutron
star matter), infinitely-long cylinder which rotates very rapidly can form
closed timelike curves in its vicinity, which will allow time travel and
possible subsequent
violations of causality.
-
- transition temperature
-
- The temperature (dependant on the
substance involved) below which a
superconducting substance conducts electricity with zero resistance;
consequently, the temperature above which a superconductor loses its
superconductive properties.
-
- Trojan points
-
- L4 and L5, the two dynamically stable
Lagrange points (under certain conditions).
-
- Trojan satellites
-
- Satellites which orbit a body at one or the
other
Trojan points relative to a secondary body. There are several examples
of this in our own solar system: a group of asteroids which orbit in the the
Trojan points of Jupiter; daughter satellites which orbit in the Trojan
points of the Saturn-Tethys system, and an additional satellite (Helene)
which orbits in the forward Trojan point of Saturn and Dione.
-
- twin paradox
-
- One of the most famous "paradoxes" in history,
predicted by A. Einstein's special theory of relativity. Take two twins,
born on the same date on Earth. One, Albert, leaves home for a trip around
the Universe at very high speeds (very close to
that
of light), while the other, Henrik, stays at home at rests. Special
relativity predicts that when Albert returns, he will find himself much
younger than Henrik.
That is actually not the paradox. The paradox stems from attempting to
naively analyze the situation to figure out why. From Henrik's point of view
(and from everyone else on Earth), Albert seems to speed off for a long
time, linger around, and then return. Thus he should be the younger one,
which is what we see. But from Albert's point of view, it's Henrik (and the
whole of the Earth) that are travelling, not he. According to special
relativity, if Henrik is moving relative to Albert, then Albert should
measure his clock as ticking slower -- and thus Henrik is the one who should
be younger. But this is not what happens.
So what's wrong with our analysis? The key point here is that the
symmetry was broken. Albert did something that Henrik did not -- Albert
accelerated in turning around. Henrik did no accelerating, as he and all the
other people on the Earth can attest to (neglecting gravity). So Albert
broke the symmetry, and when he returns, he is the younger one.
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