There are four great theories in physics in which we could find the
meaning of time: Newton's laws, thermodynamics, the relativity theory
(special and general) and quantum mechanics.
In Newton's laws, time appear to be absolute, that is to say independent
of the observer. So time, according to the Galileo's transformations, does
not depend on the system of reference, so t=to,
where to is the time measured from an absolute system of reference and t is
the time measured from another inertial system.
In addition, in Newton's laws something really strange appears: time is
invertible.In the equations there is no distinction between the past and the
future! This shows up in the equations of velocity v and acceleration a of a
mass in connection to time and space:
v=ds/dt, a=dv/dt
where ds/dt is the derivative of space in connection to time
and dv/dt is the derivative of velocity (or the second derivative of space).
In the equation of acceleration it seems clearly that we have to do with
the square of the variation of time, so there is no difference if the mass
goes from the future to the past or from the past to the future.
The first characteristic of time in Newton's laws is changed in the
relativity theory of Einstein (1905,1915). In this theory time depends on
the observer. The equation describing time (included in the transformations
of Lorentz) is:
t*t = (to - v*x/c*c)*(to - v*x/c*c)/(1 - v*v/c*c)
where to is the time in an absolute system of reference, t is the time in
another inertial system that moves with velocity v, c is the velocity of
light (300,000 km/sec) and x is the position of the movement in the absolute
system of reference. From this equation we can have some great information:
If v<<c then v*v/c*c ->0. So (1 - v*v/c*c) ->1, v/c*c ->0 and finally t=to.
That means that for small velocities compared to that of light, we go back
to the Galileo's transformations and the Newton's laws.
If v is almost equal to c (v>0.8*c), it seems that time expands, because
(1 - v*v/c*c) <1.
Finally, if v=c, it is v*v/c*c = 1 and (1 - v*v/c*c)=0, so t becomes infinite.
So if a mass could have the velocity of light, time would never pass.
With general relativity we come to the same conclusions in connection to
gravity: time passes for an observer more slowly as his weight becomes
greater. In addition, with general relativity time is not independent of
space: space and time become the four-dimensional spacetime which can be
curved by masses.
However, in the relativity theory, just like the theory of Newton, time
is invertible: the same laws appear even if a mass could go from the future
to the past.
In quantum mechanics time is seen in the aspect of the microcosm, in
contrast to Newton's and Einstein's laws. For the first time, in this theory
uncertainty appears: according to the uncertainty principle of Heisenberg,
it is
Dt*DE almost equal to h (where Dt is the uncertainty of time, DE is the
uncertainty when we count the enegy of the particle and h is the Planck
constant.
In quantum mechanics, just like the theory of relativity and the
theories of Newton, time is invertible. There are however two points in
which time seems vertible. The first is the fragmentation of a particle, the
"long-living caonium" in which the symmetry of time is splitted. The other
point is the collapse of the wave-function of Schrodinger, when the observer
finally watches the system, so the many possible results give their place to
one and unique solution. Those two points are conclusions of this theory and
they have nothing to do with its equations in which an invertible time can
be used.
The only theory in which time is vertible is thermodynamics, the first
theory that was able to connect physics and statistics. It is proved that
the entropy of a situation is proportional to the logarithm of the
probability of the existence of this situation :
S=k*lnP
where S is the entropy, P the probability of the existence of the situation
and k the constant of Boltzmann. It seems that the more probable situations
to appear are those that have the biggest entropy. So, we could say that
time passes to those situations with a biggest entropy.
So we accept a thermodynamical arrow of time. We also accept a
psychological arrow, how a human being understands time, and a cosmological
arrow, because of the expansion of the universe.
Today scientists believe that time had a beginning, that of Big Bang.
Big Bang is believed to be a spacetime irregularity (singularity).Many
scientists believe that time will finish with the Big Crunch, the opposite
of the Big Bang, others believe that the end of the universe will come with
the thermic death, a situation of maximum entropy, and others that there
will be no end of time. In addition there are scientists who are working
with imaginary time (complex spacetime) and others that believe that even
trips in time are possible.
Are we going to learn one day what is time in reality or if time really
exists (or even if "reality" has any meaning) ? Time will show...
Daphni Strintzi
Physics student at the University of Athens
Big Bang group
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More about time:
1) The quantum universe (Tony Hey, Patrick Walters)
2) The arrow of time (Peter Coveney, Roger Highfield)
3) General Physics, Optics (K.D.Alexopoulos) (in greek)
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We are apologizing for causing inconvenience with the way we have written
the mathematic formulas, but there was no other way to write them.
We are expecting your comments.
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|Big Bang group |
|Exploring the beginning of the universe |
|e-mail: yzoug@hol.gr |
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