Class notes
Applied physics notes
- Course
- Modern physics mechanics
- Institution
- Stanford Lake College (SLC)
In this document 2 lectures are available about Applied physics mechanics and in detail
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Lecture 1 | Modern Physics: ClassicalMechanics (Stanford)
Stanford
Classical mechanics is the basis for all of physics. the conservation of
energy. The conservation of momentum. The principles by which all
systems evolve in nature is the same set of rules. in order to understand
that we have to understand the principles in a fairly general context. Let
's begin with the very very simple kinds of systems that we can think of.
what kind of laws can you imagine for this extremely simple world. we 're
coming for that all right. be our first kind of question for tonight. So our
first concept is the space of states in this case, just heads in tails. It 's
just two points, heads and tails so two points in an abstract space is
called the phase space of a system.. we have a large variety of different
laws of physics that we could have. For example, we could simply have.
We could label these one two, three, four, five and six, which one is one
and one is six is not very important, but the there are six of them. we
could have a law of physics, which says 1 goes to 2, 2 goes to 3-3. Goes
to 4. 4. Goes to 5, 5. Goes to 6 and 6 goes back to 1..
Where you happen to be? You know exactly where to go next? So it 's
deterministic and deterministic into the future meaning to say wherever
you start you know where you will be arbitrarily. if you start here and you
go a hundred thousand times. You 'll just wind up writing up some where
you stay there. these are all acceptable laws of physics, but what does it
fail? It fails to be deterministic in the past.. classical mechanics would be
basically the same thing, but with the arrows turned in the opposite
direction. All arrows reversed here. I have a problem not going into the
past, but I have problem going into future.. can not work my way
backward with uniqueness. I can work my. way forward. there 's an
infinite number of possible states a state corresponding to every integer
positive and negative a particle on a position. On a line where the
position could be any integer value. in the same order, you can have
slightly more interesting situations. There 's no reason why the number
of states has to be finite..
All the known laws of physics fit into this class of information conserving
laws even those which are quantum mechanical. information
Conservation is perhaps the most fundamental law of basic classical
physics that you don't lose information about now why that why is that so
it 's not written into the laws of. physics, Why they are what they are.
The analog of a state is just a location of a particle, where is it but is it
enough to know where a particle is in order to say what happens next
now what else do you need to know its velocity. the state in the same
, sense that i used it does not just consist of the location of the particle,
but you can say it two ways. In practice, classical systems do n't really
have the property that you can predict endlessly where they're going to
be and exactly what they'll do, but you can always say given a time
interval. I want to be able to predict exactly for the next 30 seconds,
where every molecule in this room will be. in principle given any length of
time. In classical physics, there exist a degree of precision, which allows
you to extrapolate..
You need to know both the position and the velocity in classical theory in
the physics in order to predict what happens next reflects itself in the
structure of the equations of mechanics. the equations of motion
Newton's equations in this case are what are called secondorder
equations instead of firstorder. equations are deterministic. If you know
the initial conditions are. deterministic are predictable infinitely
predictable.. systems are less predictable and get out of control very
quickly. if we know the position of the particle at any instant of time,
then we know where it 's going to be in the next instant. The next two
instance the next three instants it completely predicts the motion, but
this is not the character of Newton 's equations. in order to predict I have
to tell you the position as well as the velocity. I can then predict the
acceleration the next. to a third derivative, the fourth derivative. both of
these laws require only knowledge of where you are at one instant to tell
you where you 'll be next.. If you know that you're at heads, then you
know you ''ll be next at heads, if you know tails if you 're at tails you
know yourself, but so you only need the piece of information heads or
tails that does it that tells you everything now..
A single heads or tails was not a complete specification of information
involved two pieces of information and once we recognized that we were
able to to to write this down as a law of physics, which is deterministic
and reversible okay so you could go beyond this. You could say I need to
know the first three things in order to know what happens next. You can
do that. it would mean you would need positions velocities and
accelerations to represent the phase space as it happens. that is not the
case for classical mechanics that 's an experimental fact. it would n't stop
us. If we did need accelerations. We would just write third order
equations and we will make our phase space threedimensional..
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