General thoughts:
Difference of heat and work is minimized in entropy? Analogous to difference of kinetic energy and potential energy?
Quantum mechanics literally originated from a lightbulb moment, a dude name Max Planck was thinking how he could maximize the energy output of a lightbulb. He realized that the distribution of emitted colours and the intensity of those colours made bad predictions. He had to alter the distribution.
Is the lagrangian not actually about finding the smallest difference between the slope of an angle and the differance in distance between the jumps?
What if you make a small line segment and rotate it around a point, while calculating the lagrange of it around at all those points?
Why doesn’t light dissipate as heat, just like everything? Because it is heat
No aether needed because light is particles. Actually nothing needs an aether because of fields.
But quantum theory shows us that not only do electromagnetic waves display some properties of matter, but “matter” (e.g. elec-trons, protons, etc.) may be represented by waves of a field. In the end, only fields exist, distributed over space and at the same time shaping that space (or more accurately, space-time).
Thus, the phenomena of time dilation and length contraction are manifestations, in different reference frames, of the same phenomenon. They are the same, just like magnetism and electricity and space and time itself.
Is there also an action associated with space, such as S=L dx instead of S=L dt
What would happen if we go at lighstpeed?
One of the striking features of the phenomena of time dilation and length contraction is that both become catastrophic when the relative speed of the frames of reference is c. In this case all time intervals are dilated to infinity, which is to say that nothing happens! On the other hand, all lengths are contracted to zero, which implies that there is no finite world for things to happen in anyway. These comments are pertinent to the famous question which Einstein purportedly asked himself when he was a 15-year old schoolboy, a question which, he said, set him on the train of thought which was to culminate in the special theory of relativity: what would the world look like if one could travel on a beam of light? The answer appears to be that time and space would cease to exist.
Because of the equivalence of gravitational and inertial masses, it is a logical consequence of this statement that energy also is a source of gravitational fields. This fact creates the complications of Einstein’s theory of gravitation, with which we shall deal later. All fields, including the gravitational field, contain energy. The energy of the gravitational field can be the source of more gravitational fields. This situation sharply distinguishes the gravitational field from the electromagnetic one. The sources of the electromagnetic field are charges, but charges do not produce more charge. Electromagnetic fields are not themselves charged, and thus cannot produce further electromagnetic field
Is space isotropic inside an event horizon? No? Angular momentum?
Entropy:
This energy is disordered in that it is the energy of incoherent motion; because the motions are as likely to be in one direction as another, no work can be done using them. Heat motion carries net kinetic energy, but no net momentum because momentum is a vector. This is why heat energy cannot be utilized.
Since heat appears to be more or less inadvertently produced in all energy transformations in which it is used to do useful work for specific purposes, to what extent can heat energy itself be exploited to do such work? This question attracted the attention of Sadi Carnot (1796-1832), eldest son of Napoleon’s ministry of war. He wrote down in 1823 for the first time in history the Second Law.
The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperature of the bodies between which it is effected — by the transfer of caloric.
Important question in thermodynamics:How can we make a continually working machine?
A difference in temperature has made it possible for the system to do work
Entropy vector:
The ratio of kinetic energy of a bunch of molecules versus the net direction of the other three momentum vectors is the entropy.
The capability to do work is in the ith direction is p,i/|E|
Carnot cycle:
How can we make a continually working heat engine?
Start with a flywheel attached to a gas chamber with a piston.
State 1: Equilibrium, no motion.
State 2: Gas chamber gets heated, piston will move to the right, work gets done on the wheel.
What happens at the end of the stroke, i.e. when the wheel is completely to the right? The flywheel will do work on the gas chamber. When there is no heat loss or friction, this work will equal the
Incoherent motion is absolute.
On entropy and order:
Something that is “ordered”, or “orderly”, is not disordered or random. Randomness is the converse of order. What do we mean, for example, by saying that the positions, or the motions, of the molecules of a gas are random? We mean that the positions and motions of the molecules are as likely to have any value as any other. The state of any molecule is independent of the states of any other; there are no correlations between them. (We must remember, however, that the equal probability of all configurations is subject to obvious macroscopic constraints; all gas molecules stay in the container, and their total energy is fixed.)
Because of the accuracy of the statistical physics of macroscopic phenomena, we find ourselves in a strange situation: we understand the macroscopic world if we discard all microscopic information. It is precisely the impossibility of explaining the macroscopic world in terms of microscopic determinism that makes it appear deterministic. We have come a long way from Laplace’s mechanistic model of the physical world. Quantum mechanics will take us even further in revealing the element of chance at the core of things, in the behaviour of matter at the atomic and subatomic levels.
The heat of an object divided by its entropy is its temperature.
Two systems: 1 & 2. They exchange energy.
System 2 to system 1. For each system: dS=dQ/T,
The heat flow in an object divided by the temperature of that object will be its change in entropy.
A writing place. 