GBW1: Chris Capon – Entropy and the Shape of The Universe
This is the first ‘Guest Blog Week’ to be run on Dreams in Vitro – click the banner above to find out more about it. Finally this week is Chris Capon an engineering student from the University of Queensland. This is the last guest blog for the first guest blog week – I hope you enjoyed it. Normal blogs by me will resume soon (maybe).
Entropy and the Shape of The Universe
By: Chris Capon
Ok, after a reasonable bit of pressure from Myles, I have finally written this guest blog entry and it’s a little different from Myles’s own entries due to a deffernce in interests. I’m currently studying first year engineering, majoring in mechanical and aerospace at the University of Queensland and am tossing up between doubling with physics. As such, things that I write will most likely be based on new technologies, ideas for technologies or physics (though physics will most likely feature in them all XD). Hope you enjoy.
In science there are laws and theories. The difference between them is that laws have been deemed unbreakable, while a theory can be disproven with a single contradictory event. Taking this into account, it got me thinking about the about the three laws of thermodynamics, more specifically though the second law, which is:
A process in a system will always tend to increase the entropy of the universe.
The entropy of the universe tends towards a maximum.
There are many ways the law may be phrased or for a thermodynamically reversible system you can take the time derivative of entropy, where it is greater than 0. This law is thought to be one of the only unbreakable laws in physics, indeed a certain physicist named Albert Einstein famously stated:
A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts.
Another, perhaps less well known person named Seth Lloyd, a Professor of Mechanical Engineering at MIT stated:
Nothing in life is certain except death, taxes and the second law of thermodynamics. All three are processes in which useful or accessible forms of some quantity, such as energy or money, are transformed into useless, inaccessible forms of the same quantity. That is not to say that these three processes don’t have fringe benefits: taxes pay for roads and schools; the second law of thermodynamics drives cars, computers and metabolism; and death, at the very least, opens up tenured faculty positions.
Now, I didn’t started questioning this law to put myself against these minds, I was just thinking about the law itself and it came to me that it makes some assumptions about the universe that as of yet haven’t been conclusively proven and as such the validity of this law cannot be ascertained as of yet but I’ll get to that later. Firstly though, what is entropy?
Entropy is quantitative measure of disorder in a system. A nice little analogy I came up with is sitting a class down in a lecture and making them listen to increasingly discordant violin music. As time goes on the not only does the music become more discordant but so does the class, which becomes increasingly restless. Their energy is no longer as useful as it was at the start of the class and requires an addition on energy from the lecturer to silence the room and reduce disorder; the usefulness of energy with time decreased. So perhaps a good way to think of entropy is the measure of the usefulness of energy in the system. I would like to note that the increasingly discordant violin music was not a good example of entropy…but that’s just my opinion.
Now you may be thinking, “hey but he just said you can put energy into a system to decrease entropy! Gasp, entropy decreased, second law = broken :O” This is not true because the entropy of a non-adiabatic (an adiabatic system is isothermal…no heat flows) system may decrease through heat flows out of the system. I’m not entirely sure about the validity of inputting energy into a system to decrease entropy but I would assume that it is acceptable because an ordered system has a higher internal energy than a disordered system. Though that does lead to the question why a decrease in energy would result in an increase order as well (decrease in entropy)? It is really a balance of energy flows, if you imagine a ground state atom; it’s in its most ordered and stable state. If energy is input, its electrons jump up energy levels, so in order to return to its preferred state ordered state it must release energy and thus a heat flow out of this system increases microscopic order. Hmm now that I think about it, input energy that increases order must simply allow a heat flow out of the system because I can’t think of an example that would allow entropy to decrease via an energy input in the form of heat. Entropy could decrease with electrical or chemical energy though through the formation of crystal structures in a liquid resulting in a solid.
Ok so now that you have a general understanding of entropy, whereby it can decrease in a system but must always increase according to the second law, can we find any way to break it? As I mentioned before, I believe the second law makes some interesting assumptions that, if incorrect, would break it. The first is that it assumes the universe is infinite. As I stated early, a way of expressing entropy is to take it’s time derivative because the only factor that entropy seems to be dependent on is time. If you were to increase time into infinity, the only way for the value of the entropy gradient (think of a graph) to remain greater than zero is for space also be infinite. If space is not infinite then after an infinite amount of time, the entropy gradient across the universe would be equal zero and therefore the second law is broken because it cannot equal zero. This is to say that there would be no more useful energy in the universe because it would be distributed everywhere equally. Despite this though, even this assumption also contains its own assumption that the universe is flat.
Einstein himself provide conclusively that the universe could just as easily be curved as flat and indeed, I’m sure all readers have seen graphically representations of classic space-time under the influence of gravity, which definitely does not look flat (this isn’t exactly the same as what I’m talking about because that’s local warping of space-time and not the entire sheet of space-time as it were). Now we have already said that the only factor that entropy is dependent on is time, which at first thought is constant/straight. Yet at the same time, using the laws or general or even special relativity it can be shown that time is dependent on an observers frame of reference and whether they are accelerating or not. Therefore isn’t it also fair to assume that there will be natural fluctuations in the fabric of the universe due to a combination of both gravity and accelerating frames of reference? If these two assumptions (finite universe & warped space time) hold, what does it do to the second law though?
If parts of the universe are aging at different rates and we set time to infinite in our entropy derivative, you get an interesting occurrence whereby the second law holds. This is because you would essentially get a Swiss cheese sort of distribution of entropy, where the holes are points where entropy has decreased to zero (perfect order, massive amounts of energy) and increased to infinite because, unlike with a flat universe, the higher ordered system can still undergo processes, which would result in a transfer of excess entropy that (what I shall call our entropy hill) cannot contain.
Thus in order for the second law to hold in both a infinite and finite universe, the finite universe must at the very least be curved.
Hope you enjoyed and would love to hear any opinions, everything I have written, aside from the quotes of course, is stuff that I came up with is not necessarily correct and it’d be interesting to hear any opposing views or flaws in my logic (or if not flaws, perhaps things that I need to explain better).