So we can easily write algorithms that are uncomputable (in a finite time) as computer programs,
By definition, if an algorithm is uncomputable you can't write it as a computer program. XD
If it merely takes forever, it can still be written as a computer program, like a method to compute an irrational number in decimal form to infinitely many decimal places.
It will just never halt.
Algorithms have to take a finite amount of steps to be computable. Uncomputable algorithms don't satisfy this condition.
So what? Your claim was not "uncomputable programs are not useful". Your claim was "you can't write an uncomputable algorithm as a program". Yes, you can.
How could we even describe uncomputable problems if we couldn't write them? If we can write a description of an uncomputable problem, we can write a program that attempts to solve it, following that description. (For example, if you have two 21x21 matrices with integer entries, can you perform a multiplication using them, possibly with repetitions, so that you get a zero matrix as a result? The problem is undecidable, but you can certainly write a program that tries to find it.)
Anyways, I don't understand what this has to do with the question whether there exists a unified theory of quantum gravity or not.
Why does a magnet float over a superconductor?
I mean, I know that the floating is caused by the Meissner effect, but what I don't understand is what keeps the magnet stable. Why doesn't it simply slide to the side and fall off when it reaches the edge of the superconductor?
I heard the explanation for this a long time ago, but I don't remember much of the details now. However, I think the reason is flux pinning, where small magnetic channels form through the superconductor, much like a pincushion with needles through it.
Two questions:
1) The Heisenberg uncertainty principle states that it's not possible to know both the exact position and momentum of a particle at the same time. However, what happens at absolute zero temperature, where all motion stops?
2) I know extremely little about thermodynamics, but it sounds to me like the second law is just a consequence of the first law, and hence redundant. Please correct my understanding.
Let me explain: The first law states that energy cannot be created nor destroyed. In other words, a closed system cannot produce more energy than it contains.
The second law states that the entropy of a closed system never decreases. In other words, the amount of energy available for useful work in a closed system never increases.
This sounds to me like a simple consequence of the first law. If the amount of energy available for useful work inside a closed system could increase, that would mean that the closed system could produce more energy than it contains (by doing more work than what its available energy would allow), which would be against the first law.
Why is the second law necessary?
1) It is apparently impossible to reach absolute zero; so far, we have been able to get down to near femto-Kelvins, but the absolute zero eludes us. There is some speculation that it is due to the uncertainty principle. In college, the professors just states outright that you can't reach absolute zero.
2) You can (in principle, at least) reduce or increase the "energy available for useful work" (thereafter W) without changing the total energy of a system (hereafter E) by transforming the residual energy E - W into W; this does not violate the first law of thermodynamics. The second law of thermodynamics states that while you can transform W into E - W, you can't do the reverse -- turn E - W into W.
Two questions:
1) The Heisenberg uncertainty principle states that it's not possible to know both the exact position and momentum of a particle at the same time. However, what happens at absolute zero temperature, where all motion stops?
I believe at absolute zero it becomes impossible to acquire information about the object -- there's no way to "sense" it that wouldn't impart energy to the particle, thereby raising its temperature and rendering its momentum uncertain.
2) I know extremely little about thermodynamics, but it sounds to me like the second law is just a consequence of the first law, and hence redundant. Please correct my understanding.
Let me explain: The first law states that energy cannot be created nor destroyed. In other words, a closed system cannot produce more energy than it contains.
The second law states that the entropy of a closed system never decreases. In other words, the amount of energy available for useful work in a closed system never increases.
This sounds to me like a simple consequence of the first law. If the amount of energy available for useful work inside a closed system could increase, that would mean that the closed system could produce more energy than it contains (by doing more work than what its available energy would allow), which would be against the first law.
Entropy is more than just energy; it's energy in a useful form. My reading of the second law is that basically there is waste in any energy transformation that cannot be usefully captured (because the capture process involves its own waste).
I'm not a physicist and these are not remotely authoritative answers; just my understanding.
Pyrel - an open-source rewrite of the Angband roguelike game in Python.
1) The Heisenberg uncertainty principle states that it's not possible to know both the exact position and momentum of a particle at the same time. However, what happens at absolute zero temperature, where all motion stops?
Actually, all motion does not stop, all particles just collapse to lowest possible energy state.
And due to Heisenberg uncertainity principle, that energy state does not have zero energy. So there is still motion.
My physics teacher explained the second law to us in that it means that all forms of energy will be turned to heat eventually. And you can never reverse that.
It's a very different message from the first one, but they sound similar.
I thought the reason behind the Heisenberg uncertainty is because in order for a wave to be measured, it has to represent some form of motion, while knowing the exact position of a particle requires to consider it completely still.
In other words, as the time function approaches zero, the graph starts looking like a dot, and not a arc, so you can't extract the form of the wave from the dot.
But couldn't you obtain the particle's position as the limit from the wave function as time approaches 0?
I know some sciencists said they were able to measure both things at once by projecting two exact copies of a beam and measuring the exact position of a particle in one of them, and the wave form on the other, but I don't quite understand the utility of that achievement.
In quantum mechanics particles are not described by a single set of coordinates, but instead by an amplitude at every point in space, called the wave function. For example, in one dimension, it could look like this:
If you measure the position of this particle, you are most likely to measure it between 4 and 5, but you are also quite likely to measure it at 3 or 6. Similarly to a particle not having a single position, but an amplitude at every possible position, the same applies to momentum. So if you imagine replacing the position x with the momentum p on the graph above, you would have an example of a possible momentum wavefunction.
The uncertainty principle comes about because position and momentum turn out not to be independent quantities, but instead the fourier transforms of each other. A fourier transform basically means that you try to build up the function using sines and cosines at various frequencies as building blocks, and measure how much you need to add of each of them to get back the function you want:
The point now is that the sharper you want to make your position wavefunction, the more high frequencies you need to include in the fourier transform, which means that the momentum wavefunction will get broader. Thus, there is a tradeoff between sharpness in position and momentum.
Regarding temperature, as Ilari says, motion does not stop at absolute zero, but particles instead all occupy the lowest possible energy state. A gas of such particles is called degenerate, and there are two possible cases here. If the particles are fermions (ex: protons, electrons, neutrons), they cannot all be in the true lowest energy state, since each energy state only can be occupied by one particle. So some particles will end up having pretty high energies even though the temperature is practically zero. For a large enough gas, the particles may in fact be moving close to the speed of light and still be in the lowest energy state they can be. An important example of degenerate gases from nature is neutron stars. These are actually quite hot by our standards, but due to the huge density and number of particles involved, they still behave as if the temperature were almost zero, and are very degenerate.
The other possibility happens when the particles are bosons (ex: photons). In that case they are all allowed to occupy the same lowest energy state, and so you won't end up with any high-energy particles. A degenerate gas of this kind is called a Bose-Einstein condensate.
At high temperatures, the average kinetic energy per particle is proportional to the temperature (for noninteracting particles without internal degrees of freedom it is 3/2*k*T, where k is the Boltzmann constant). I guess this is why people think that motion will stop at zero degrees. But at low temperatures this approximation breaks down, and the average kinetic energy per particle becomes independent of the temperature (again for noninteracting particles without internal degrees of freedom it becomes 3/5*Ef, where Ef depends on the density of the gas).
Regarding the first and second laws of thermodynamics: With just the first law, you would have no reason to think that heat should flow from a hot object to a cold object, and not the other way around. The second law tells you that it will flow from hot to cold because the entropy would decrease otherwise (it is still possible to make a cold object colder, but only with work from the outside). Without the second law, you could make a perpetuum mobile, a machine that runs forever without external power. According to the first law it would not be able to produce energy from nothing, but you could still make things like an elevator that needs no power input as long as as many people take it up as take it down during the day. Basically, any process could be infinitely efficient.
If you kept the first law the same, but reversed the second law, you would end up with a universe behaving much as if time went backwards. Heat would flow from cold objects to warm ones, the air molecules in a room might suddenly all concentrate in one end of the room, and a shattered glass might spontaneously reassemble. On the other hand, mixing things and making them more homogeneous would require energy from the outside.
Speaking of neutron stars, what happens if eg. a companion star keeps adding material to a nearby neutron star until its mass exceeds the degeneracy pressure and it collapses? Does it behave like a supernova, or something else?
amaurea wrote:
The second law tells you that it will flow from hot to cold because the entropy would increase otherwise
I think you mean decrease.
If you kept the first law the same, but reversed the second law, you would end up with a universe behaving much as if time went backwards. Heat would flow from cold objects to warm ones, the air molecules in a room might suddenly all concentrate in one end of the room, and a shattered glass might spontaneously reassemble.
You lost me on that last one. Why would that be? What does thermodynamics have to do with the shattering of a glass? I don't see the connection to temperature.
If the second law of thermodynamics is reversed, then you would lose entropy on each "energy transaction"; the easiest way to imagine a universe bound by those rules would be to have one just like ours except that time flows backwards.
Pyrel - an open-source rewrite of the Angband roguelike game in Python.
If the second law of thermodynamics is reversed, then you would lose entropy on each "energy transaction"; the easiest way to imagine a universe bound by those rules would be to have one just like ours except that time flows backwards.
"Most people think time is like a river, that flows swift and sure in one direction. But I have seen the face of time, and I can tell you - they are wrong. Time is an ocean in a storm."
Surprisingly, there might be more truth to this fictive statement than one might think.
In GR the concept of time is complicated. Time passes at different speeds in different frames of reference, and in different gravitational potentials. Also, time is more related to the geometry of space than in classic physics.
In quantum mechanics the concept of time is... even more complicated. Cause-and-effect relationships get muddled, reversed and pretty confusing. Effect may, seemingly, precede cause (such as in the delayed choice quantum eraser experiment, where a choice made after measurement affects the measurement... seemingly from the future).
More related to the quote, AFAIK in some interpretations of quantum mechanics there's no "arrow of time". (Of course this is probably a vast oversimplification. As said, the subject is complicated.)
I used to think that time could flow backwards or stand still, then forwards again and we wouldn't notice since our brains get rewinded as well. To even perceive that change in direction in the flow of time you'd have to be a being outside of our known universe. But does that idea even make sense, if you take into account that time is relative? Could all relative flows of time still be reversed or slowed down at once or does that idea make absolutely no sense at all, since it's assuming there'd be another flow of time outside of our known concept of time to compare it to? If that makes any sense.
Speaking of neutron stars, what happens if eg. a companion star keeps adding material to a nearby neutron star until its mass exceeds the degeneracy pressure and it collapses? Does it behave like a supernova, or something else?
I am not totally sure, but I think it will directly collapse into a black hole without any explosion. Let me try to explain my reasoning. There are two main types of supernova: Core collapse and thermonuclear runaway. In the core collapse supernova, the pressure of the core of the star becomes too small to sustain the weight of the star once the nuclear fuel there is spent, and the core collapses. During this process the electrons and protons react to form neutrons, and the core becomes a neutron star, which is kept up by a strong form of pressure called neutron degeneracy pressure. This is strong enough to stop the collapse, and the in-falling matter bounces, causing a shockwave to travel outwards. This eventually (the exact mechanism is uncertain) causes the star to blow up, leaving a neutron star or possibly a black hole, if even the neutron degeneracy pressure was not enough.
In the thermonuclear runaway supernova, called type 1a, the star is a white dwarf which is accreting matter from another star. The star is supported by electron degeneracy pressure, which has the property that the pressure does not increase even if the temperature does so. Once the white dwarf becomes massive and dense enough it starts becoming able to fuse the carbon it consists of. This releases energy and causes the temperature to rise. But due to the strange properties of the degeneracy pressure, the pressure does not respond to this, and stays the same, which in turn means that the density also stays the same. So the star still has the same high pressure, but the temperature has increased. This makes it even easier for it to fuse carbon, which makes the temperature increase faster, which causes more fusion, and so on. A violent burst of nuclear fusion spreads through the star, and the energy released is enough to blow it up.
Ok, with that in place, what should happen to a neutron star? The scenario is similar to the last case: The white dwarf is supported by electron degeneracy pressure, while the neutron star is supported by neutron degeneracy pressure, and both are accreting matter. However, where the white dwarf had the potential energy source of carbon and oxygen fusion left, the neutron star has no energy source left. So when it becomes too massive, it won't blow up, it will just collapse. And unlike the core collapse scenario above, there is no known form of matter to stop the collapse and cause a bounce either. So it should end up as a black hole with no explosion.
The wikipedia articles on supernovas are good, and are worth a read if you want to know more.
Warp wrote:
amaurea wrote:
The second law tells you that it will flow from hot to cold because the entropy would increase otherwise
I think you mean decrease.
Yes.
Warp wrote:
If you kept the first law the same, but reversed the second law, you would end up with a universe behaving much as if time went backwards. Heat would flow from cold objects to warm ones, the air molecules in a room might suddenly all concentrate in one end of the room, and a shattered glass might spontaneously reassemble.
You lost me on that last one. Why would that be? What does thermodynamics have to do with the shattering of a glass? I don't see the connection to temperature.
Entropy corresponds to how ordered a system is. If one counts the number of microscopic states of a system that correspond to various macroscopic properties, one finds that there are many more unorderly states than others, and thus random perturbations of the system are much more likely to push the system towards a chaotic state than an ordered one.
I'll give you a simple example to illustrate. Imagine that you have a blob of matter where the molecules can be in one of two states: 0 or 1, and that each of these states is equally likely per se, but that the number of 0s vs. 1s in the blob as a whole determines its color, with 100% 0 being black and 100% 1 being white, and 50/50 being gray, and so on. Which color is the most likely to observe, assuming that the molecules do not interact? If there are N molecules, the chance of having 100% white is 2^(-N), since every molecule must be 0 to get it, and so is the chance of having 100% black. So both of these chances are really tiny for realistic values of N. Even something like 75% black turns out to be extremely unlikely: For large N, the only state with any large probability will be 50%. So how is this connected to the entropy? The entropy is just a way of expressing how likely these states are. The 50% state will have a high entropy, while the 100% and 0% states have very low entropies. So entropy doesn't need to be defined in terms of temperature and heat flow, entropy can be regarded as more fundamental, and used to define temperature.
So what does this have to do with a shattering glass? Well, why do you often see glasses fall down from tables and shatter, but never pieces of glass start bouncing towards each other and just happen to meet in the right way to fuse into a glass which proceeds to jump up to come elegantly to rest at the table? The first is natural, but the second is absurd, but why? It is not because the laws of physics prohibit the last one. In fact, the fundamental laws of physics like both of them equally well. I'll try to describe how the reverse glass fall and breakage can come about without any antigravity or other violations of the laws of physics:
What exactly happens when the glass falls down and shatters? Let us go through the scenario in detail: You accidentally push over the glass, which falls down and hits the ground. A shockwave spreads out through the glass, exciting the molecules causing them to vibrate and in some locations lose contact with each other. This causes cracks with grow into fissures, and the glass shatters. The remains of the shockwave is translated into individual motions of the pieces, which fly off into the air, where they are slowed slightly by air resistance, and dissipate the rest of their energy into heat and vibrations in the ground when they finally fall down.
In no step in this process is energy lost, it is just transformed from potential energy, into kinetic energy of the glass as a whole, into vibrational energy, into kinetic energy in the pieces, and finally into sound waves and eventually heat. Microscopically, we can just as well run all of these backwards. It would go something like this:
Pieces of glass are lying scattered on the ground, at rest. But gradually, the random motion of the molecules in the ground just happen to move in phase in such a way as to cause a sound wave to travel inwards towards each shard, the movements just happening to line up so that the amplitude increases as the sound wave gets closer to the shard. When it reaches it, the shard is launched into the air by the ground's vibrations, and this just happens to be in the right direction for it to head towards all the other shards that just happened to exhibit the same phenomenon at the same time. Similarly, when traveling through the air, the random motions of the air molecules just happen to align to cause a localized light breeze which slightly accelerates each shard (this is the reverse of air resistance). The shards all just happen to meet their matching partners at just the right place, angle and time. By now, the random thermal motions of the molecules in the pieces of glass just happen to come into phase, causing the shard to begin to vibrate. The vibrating edges of neighboring pieces of glass are lucky enough to swing in phase, and the molecules on each side matches so well that the molecules stick to each other through the edge, creating a whole glass. This glass is vibrating violently, but the different vibrating modes in the glass randomly line up to become a shockwave traveling down to one part of the glass, leaving the rest of the glass traveling upward to compensate for the motion of the shockwave. At the same time, the glass is falling and just about to hit the ground. Meanwhile, in the ground, the motions of the molecules in the ground again just happens to align to create a large wave which happens to concentrate at the spot where the part of the glass with the shockwave is about to hit. By happenstance, the shockwave in the glass and the vibrations in the ground cancel out, leaving the glass travelling upwards. It is then gradually slowed by gravity so that it just clears the edge of the table, where it gently hits the receding back of your hand, and is elegantly brought to rest.
As I said, the fundamental laws of physics do not distinguish between these scenarios - they are all equally valid. But notice that the first one does not rely on any special coincidences, while the last one needs a long chain of extremely unlikely coincidences to line up in order to work. So the first one will happen all the time, while the last one will never happen. This is the essence of the second law of thermodynamics. It says that some processes that are fundamentally allowed will nevertheless not happen because the would require amazing coincidences at the microscopic level.
Maybe in a very rough sense. I thought entropy is the measurement of how much energy available for useful work there is in the system.
There are many examples of situations where the stabilization of temperature (ie. energy flowing from a hot place to a colder one, completely in accordance to thermodynamics) actually increases order. For example a chunk of lava, which is just an amorphous blob of molten rock material, cools down to ambient temperature, and inside the blob crystals form, which are very highly-ordered arrangements of molecules. Or you could have a droplet of water, which is just an amorphous blob of water molecules: It freezes and forms a highly-ordered, multiple-axis-symmetrical snowflake.
Increasing entropy does not always mean increasing chaos. There are many, many situations where order increases instead. This does not violate the laws of thermodynamics. The increase in chaos might be true for most gaseous materials, as entropy in them increases, but it's certainly not true in all other cases as well. I don't really know where this notion is coming from.
(I know that Stephen Hawking put up the notion in his famous book. He probably didn't invent the notion, but he certainly made it popular. Hawking is an absolutely brilliant scientist, but even as a layman I would question his competence as a popularizer of science, ie. explaining science to the lay public. His latest book, for example, was quite a disappointment.)
Well, why do you often see glasses fall down from tables and shatter, but never pieces of glass start bouncing towards each other and just happen to meet in the right way to fuse into a glass which proceeds to jump up to come elegantly to rest at the table?
Because of gravity.
The first is natural, but the second is absurd, but why?
Because of gravity. It overwhelms any chemical or quantum-mechanical effect the glass may be experiencing.
(Ok, it may be that there's an astronomically minuscule chance that due to quantum fluctuations all of the molecules of the glass would spontaneously move to the right places at the same time, re-forming the glass. However, I don't think this has anything to do with thermodynamics and all to do with quantum mechanics. Anyways, the chances are so small that it just doesn't happen.)
Anyways, I just don't see how reversing entropy would make pieces of glass spontaneously re-form the original shape. Entropy doesn't "know" what the "original shape" was, how can it form it? Reversing entropy does not reverse gravity, how could it defy it? It makes no sense.
Maybe in a very rough sense. I thought entropy is the measurement of how much energy available for useful work there is in the system.
You are right that the term "ordered" or "chaotic" aren't totally clear. But I did go on to give you two example of precisely what is meant here, which is the number of microscopic states corresponding to a macroscopic property. This is the fundamental definition, the measurement of how much useful work is available in a system is a derived property which follows from this, and which is less useful because it doesn't tell you *why* it is like that.
Warp wrote:
There are many examples of situations where the stabilization of temperature (ie. energy flowing from a hot place to a colder one, completely in accordance to thermodynamics) actually increases order. For example a chunk of lava, which is just an amorphous blob of molten rock material, cools down to ambient temperature, and inside the blob crystals form, which are very highly-ordered arrangements of molecules.
The entropy of the lava does decrease when it cools down. However, the air around the lava gets heated up. And there are many more combinations of individual air molecule momentums that together correspond to, say, 400 K than to 300 K. That is why the total entropy of the lava + air system increases. The same applies to the freezing water.
Warp wrote:
Increasing entropy does not always mean increasing chaos.
It does if you interpred a more "chaotic" state as meaning one with more microscopic states corresponding to it, like the gray state in my example in the previous post, compared to the white and black states.
Warp wrote:
Well, why do you often see glasses fall down from tables and shatter, but never pieces of glass start bouncing towards each other and just happen to meet in the right way to fuse into a glass which proceeds to jump up to come elegantly to rest at the table?
Because of gravity.
Please don't skim the post the next time. I explained how the glass gets back up on the table without needing reverse gravity. The glass vibrates, which means that the molecules are moving backwards and forwards. By an improbable stroke of luck they can end up moving in phase, such that the molecules in the top part of the glass are moving upwards at the speed at which the glass was falling originally. Of course, total momentum must be conserved, so these molecules must push off from something, which is the molecules below, which in turn push off from the molecules below them again, until they reach the ground, where enough downwards momentum is deposited to make up for the upwards motion the glass got.
If there is a step of this process you don't think is possible, think about how exactly that step happens in the normal direction, when the glass falls down, and which forms of energy turn into what, and where that energy goes. In your case, you seem to think that the "jumping back up on the table" step is impossible. To see that it is possible (but extremely unlikely because it requires lots of coincidences), just consider what happens to the downward momentum and kinetic energy at the microscopic level when the glass hits the ground. When you have track of where all the energy goes, you will also know how to play the process backwards.
Warp wrote:
The first is natural, but the second is absurd, but why?
Because of gravity. It overwhelms any chemical or quantum-mechanical effect the glass may be experiencing.
(Ok, it may be that there's an astronomically minuscule chance that due to quantum fluctuations all of the molecules of the glass would spontaneously move to the right places at the same time, re-forming the glass. However, I don't think this has anything to do with thermodynamics and all to do with quantum mechanics. Anyways, the chances are so small that it just doesn't happen.)
I think you're misunderstanding what sort of unlikely happenstances are needed here. I am not talking about any quantum effect here, like the glass molecules' quantum mechanical uncertainty in position and momentum just happening to make them all tunnel into the right positions to be a whole glass again. You are right that that sort of example wouldn't be relevant at all.
Warp wrote:
Anyways, I just don't see how reversing entropy would make pieces of glass spontaneously re-form the original shape. Entropy doesn't "know" what the "original shape" was, how can it form it?
You're right, and this is the point. The second law of thermodynamics says that systems will move towards more likely configurations, just like you will tend to roll 7 more often than 2 when rolling two dice, because there are more ways of getting 7 (1+6,2+5,3+4,4+3,5+2,6+1) than ways of getting 2 (1+1). Trying to reverse this would be like demanding that it should suddenly be more likely to get 2 than 7. And you can't do that without loading the dice. And in loading the dice, you are making an arbitrary choice of which way to load them, just as I did with the example where the glass comes together again.
Please don't misunderstand. I am not trying to argue that a universe with a reverse second law of thermodynamics would make sense - just the opposite! I am trying to illustrate *why* the second law exists, and I think the glass is a good example of this. Going forwards requires no special circumstances, while going backwards needs heaps and heaps of unlikely coincidences. This is the essence of the second law of thermodynamics.
I hope you see how the examples with the dice, the colored blob, the air molecules in the room and the falling glass all show the same effect. And how going backwards breaks no fundamental laws, but are very unlikely because you are going from a very general state into a very specific state.
On that topic, how can a star collapse further through degeneracy pressure?
The pauli exclusion principle states that no two fermions can occupy the same state, not cannot occupy the same state unless pushed hard enough.
So what exactly happens if you add more mass? How can the star compress further without violating the pauli exclusion principle?
With more pressure, electrons must move to higher energy levels to compress further. When they're energetic enough, they may combine with protons to neutrons, which can be compressed further (assuming there are protons present, but if we're talking about star remnants there are).
After that, I can only see a lot of handwaving with "oh, then they probably split up into quarks. Then preons. And then they just form a black hole, screw Pauli!".
Is that the current state of research, or is there an explanation that might remove the handwaving?
On that topic, how can a star collapse further through degeneracy pressure?
AFAIK you can get two particles arbitrarily close to each other, just not exactly on the same place. It's just that the closer you try to get them, the more force it requires. When density is high enough, gravity provides that force, and when the certain critical density is surpassed, the event horizon will appear. Then there's no way out.
The point now is that the sharper you want to make your position wavefunction, the more high frequencies you need to include in the fourier transform, which means that the momentum wavefunction will get broader. Thus, there is a tradeoff between sharpness in position and momentum.
Regarding temperature, as Ilari says, motion does not stop at absolute zero, but particles instead all occupy the lowest possible energy state. A gas of such particles is called degenerate, and there are two possible cases here. If the particles are fermions (ex: protons, electrons, neutrons), they cannot all be in the true lowest energy state, since each energy state only can be occupied by one particle. So some particles will end up having pretty high energies even though the temperature is practically zero. For a large enough gas, the particles may in fact be moving close to the speed of light and still be in the lowest energy state they can be. An important example of degenerate gases from nature is neutron stars. These are actually quite hot by our standards, but due to the huge density and number of particles involved, they still behave as if the temperature were almost zero, and are very degenerate.
The other possibility happens when the particles are bosons (ex: photons). In that case they are all allowed to occupy the same lowest energy state, and so you won't end up with any high-energy particles. A degenerate gas of this kind is called a Bose-Einstein condensate.
At high temperatures, the average kinetic energy per particle is proportional to the temperature (for noninteracting particles without internal degrees of freedom it is 3/2*k*T, where k is the Boltzmann constant). I guess this is why people think that motion will stop at zero degrees. But at low temperatures this approximation breaks down, and the average kinetic energy per particle becomes independent of the temperature (again for noninteracting particles without internal degrees of freedom it becomes 3/5*Ef, where Ef depends on the density of the gas).
Regarding the first and second laws of thermodynamics: With just the first law, you would have no reason to think that heat should flow from a hot object to a cold object, and not the other way around. The second law tells you that it will flow from hot to cold because the entropy would decrease otherwise (it is still possible to make a cold object colder, but only with work from the outside). Without the second law, you could make a perpetuum mobile, a machine that runs forever without external power. According to the first law it would not be able to produce energy from nothing, but you could still make things like an elevator that needs no power input as long as as many people take it up as take it down during the day. Basically, any process could be infinitely efficient.
If you kept the first law the same, but reversed the second law, you would end up with a universe behaving much as if time went backwards. Heat would flow from cold objects to warm ones, the air molecules in a room might suddenly all concentrate in one end of the room, and a shattered glass might spontaneously reassemble. On the other hand, mixing things and making them more homogeneous would require energy from the outside.