Space Engine

Propulsion Disk wrote:

default0.0player wrote:

Source of the post If a civilization is powerful enough to create a universe, could they do entropy reduction to survive the Heat Death?

Let's first take a look at what entropy is. let's start with an example, say it's winter and it's freezing outside, so, you turn your heater on (or up). the tempertures are now different inside and outside and therefore the entropy is low outside, and high inside. the hot air molecules in your house give off their heat energy to the cold air molecules outside, and over time the heat energy is evenly distributed amongst the two systems, and they have reached thermodynamic equilibrium, this is the increase in entropy. Therefore entropy is the movement towards thermodynamic equilibrium, and since energy is always conserved, hence the first law of thermodynamics, entropy must increase, hence the second law. Now back to your statement, as Stellarator said, "Increasing entropy overtime in a system is the natural result of that system existing." because of the particles' energies within a closed system, in this case that closed system is the entire universe, but the universe isn't very closed, in fact, it's infinite, therefore all the energy in the universe will eventually be evenly spread out amongst an infinitely huge universe, even to this day on it's way to higher infinities, and since any elementary particle, massive or massless is an energy wave, hence QFT and the mass-energy equivalence E = mc2, they will too be smeared across our universal plane, that is the heat death of the universe, or rather cool death because the energy will be smeared out amongst an infinite universe and therefore be infinitely low, or as low as it can be, but i'm getting off track. Now you should see, that there is no way to reverse entropy like that, all we could do is ether make a giant cold substance for the energy to go into, still increasing entropy, or make a giant hot substance that would lose it's energy to the cold and once again increase entropy, but nothing that would stop our demise, no matter how advanced we, or other civilizations might be.

PS sorry for all the "amongst"'s "hence"'s and "infinite"'s, this post was way to redundant.  

I have something that I cannot understand. Just after a Big Bang. The universe is very small and hot. It would reach thermodynamic equilibrium long long before today. One probable explanation is that the Universe spend most of its time in a Heat Death. However anything could happen in a very very long time, so after a sufficient time the entropy decreased to a extent to allow civilization to survive

default0.0player wrote:

Source of the post Just after a Big Bang. The universe is very small and hot. It would reach thermodynamic equilibrium long long before today.

Aye, it was very hot and dense and low in entropy.  But it was also expanding very rapidly.  That expansion combined with gravity are what we need to think about here.

The universe actually did reach an equilibrium very quickly, with the photons in thermal equilibrium with matter up to a point of "decoupling", when the universe became transparent and light was free to stream through it and become what we now see as the CMB.  The CMB radiation is very well fit by a Planck spectrum, which shows us that it was in thermal equilibrium when it was released.  Nowadays the radiation is far from equilibrium with matter, since the CMB temperature is only ~2.7 Kelvin while a lot of matter is much hotter.

But in terms of reaching maximum entropy, the universe was (and still is) very far away from that.  This is because maximizing entropy depends not only on thermal equilibrium (how kinetic energy is distributed among the particles), but also by how the particles themselves are distributed in space.  As the universe expands the matter on large scales becomes more dilute, but on smaller scales regions that are denser than average can collapse to make galaxy clusters, stars, planets, and so forth.  These processes are irreversible, meaning useful energy is irretrievably lost (often radiated away as heat), and the entropy of the universe increases as a consequence.

So as long as stars shine, planets form, life evolves, and so on, the entropy increases towards some theoretical maximum at heat death.  Actually the most significant source of increase in entropy in the universe occurs with the formation of black holes -- especially supermassive ones.

Here's a nice paper showing how the entropy of the universe changes over time, from the Big Bang to the very distant future and heat death.  Heat death itself isn't an event that strikes at a particular instant, but rather is a very slow asymptotic process.  The evaporation of the last supermassive black holes ties in very closely with the entropy of the universe approaching its maximum, some 10¹⁰⁰ years from now.  Even after they evaporate the entropy continues to increase a little, because the Hawking radiation can continue to become more uniformly mixed through the universe.  After that, the universe becomes quite boring... an ever-expanding sea of ever-more dilute and uniform radiation and the faint hum of gravitational waves.

Edit:  added some clarification on the difference between thermodynamic equilibrium and maximum entropy or heat death, where the former does not necessarily imply the latter, especially in cosmology.

default0.0player wrote:

Source of the post I have something that I cannot understand. Just after a Big Bang. The universe is very small and hot. It would reach thermodynamic equilibrium long long before today. One probable explanation is that the Universe spend most of its time in a Heat Death. However anything could happen in a very very long time, so after a sufficient time the entropy decreased to a extent to allow civilization to survive

Sorry, I should have said that's a part of entropy, another thing that is probably stronger than the first claim is well, you know how air, steam, or any gas expands, well this is a property of increasing entropy, the energy must take up as much space as possible in the limits of the space it occupies, and if strong enough, it will try to break through the barriers to get to an even higher entropy state, so the amount of entropy can be measured by calculating the volume of a system, therefore although in thermodynamic equilibrium, the hot, dense, universe before the big bang had very low entropy. the universe would rather take up all the space that it can with it's energy than have it be the same everywhere, so high entropy has the same temperature same everywhere and, more importantly, IS everywhere at it's limit.

Propulsion Disk wrote:

Source of the post so the amount of entropy can be measured by calculating the volume of a system

Not necessarily, and in fact this doesn't work with the expansion of the universe.  Let's look in a bit more detail. 

In some cases, such as gas expanding to fill its container, it is true that the expansion is associated with increasing entropy, and volume will appear in the expression for the entropy of the system.  This is because that particular expansion process is not reversible.  That system "wants" the gas to expand, and not the other way around, because the expanded gas has many more microstates for that macrostate.  There are many more ways to arrange the molecules uniformly throughout the entire container than to have all the molecules bunched together on one side.  So naturally the system evolves that way.

For the universe, however, the expansion is isentropic (keeps the entropy the same)!  The increase in entropy as the universe evolves is not because of the increase in volume (which is a reversible process), but rather because of irreversible processes taking place within the universe, such as star and black hole formation.  A cloud of gas may naturally collapse into a star, but a star will not naturally revert back into a cloud of gas.  (It can explode as a supernova, but this isn't a mirror image of the collapse since it releases a lot of light, neutrinos, and new heavy elements.)

Consider a universe with enough matter to halt the expansion and collapse again in a Big Crunch.  In this case, the entropy of the universe continues to increase during the collapse phase!  Again because of irreversible processes happening within the universe, while the expansion and collapse themselves do not change the entropy.

Black holes provide another example:  The entropy of a black hole is not related to its volume, but rather its surface area.

Watsisname wrote:

Source of the post Not necessarily, and in fact this doesn't work with the expansion of the universe.  Let's look in a bit more detail. In some cases, such as gas expanding to fill its container, it is true that the expansion is associated with increasing entropy, and volume will appear in the expression for the entropy of the system.  This is because that particular expansion process is not reversible.  That system "wants" the gas to expand, and not the other way around, because the expanded gas has many more microstates for that macrostate.  There are many more ways to arrange the molecules uniformly throughout the entire container than to have all the molecules bunched together on one side.  So naturally the system evolves that way.For the universe, however, the expansion is isentropic (keeps the entropy the same)!  The increase in entropy as the universe evolves is not because of the increase in volume (which is a reversible process), but rather because of irreversible processes taking place within the universe, such as star and black hole formation.  A cloud of gas may naturally collapse into a star, but a star will not naturally revert back into a cloud of gas.  (It can explode as a supernova, but this isn't a mirror image of the collapse since it releases a lot of light, neutrinos, and new heavy elements.)Consider a universe with enough matter to halt the expansion and collapse again in a Big Crunch.  In this case, the entropy of the universe continues to increase during the collapse phase!  Again because of irreversible processes happening within the universe, while the expansion and collapse themselves do not change the entropy.Black holes provide another example:  The entropy of a black hole is not related to its volume, but rather its surface area.

How do irreversible processes relate to entropy on a microscopic scale? I'm having trouble visualizing this on a universal scale.
PS I said that you CAN (in some cases) measure entropy by the amount of volume, so unless this still wrong and I need to watch through the Space Time episodes on entropy again, then yeah...

Watsisname wrote:

Stellarator wrote:

Source of the post Entropy in a system will always increase, as per the Second Law of Thermodynamics. Increasing entropy overtime in a system is the natural result of that system existing.

Entropy of a closed system can also be constant.  Example:  An expanding universe filled with photons is isentropic, or has a constant entropy.  Why?  Because expanding a sea of photons is a reversible process -- no useful energy is lost and the system could evolve the other way just as easily.  To be precise, the entropy of a sea of photons is proportional to its volume times its temperature cubed.  But its temperature is inversely proportional to the size (scale factor "a" of the universe), while volume is proportional to scale factor cubed.   So the entropy is proportional to VT³ ∝ a³/a³ = constant.

The layman's interpretation of the 2nd law really should not be that "entropy of a closed system always increases", but rather that "entropy of a closed system cannot decrease."  Actually, even that is wrong.  It can decrease, too!  It's just vastly less probable for it to decrease, especially if the size of the system (and number of particles it contains) is very large.

To make sense of this, and what entropy means in a rigorous statistical mechanics sense, I like to use an analogy with coins, such as here where I also use it as a way to understand the concept of negative temperature.  For a bunch of coins, the entropy is the logarithm of the number of ways the individual heads and tails could be arranged (the microstates of the system) to yield the same total number of heads and tails (the particular macrostate of the system).  Then the 2nd law here states that if you have a large number of coins, and start flipping them randomly, then you are statistically more likely to trend toward the macrostate that has the largest number of microstates.  That would be half of them being heads and half of them being tails.  

There's nothing mysterious about why the system evolves in that direction.  There are simply many more ways for it to evolve in that direction!  If all ways have equal probability (this is the "fundamental assumption of statistical mechanics"), then you expect the system to evolve in the direction that has the most ways of getting there, and thus increases the entropy.  Getting all heads or all tails out of coin flips isn't impossible, it's just very unlikely if you have a lot of coins.

Thanks for this nice explanation Wat and also for the one about the connection between galactic black holes and overall galactic mass.  When you talked about groups of galaxies that are exceptions to the rule, I yearned for an H-R diagram for galaxies that would neatly fit all the different types into a biaxial chart.
About entropy, an artificial civilization that was sufficiently advanced should be able to make that reverse entropy condition more likely I would think?  Coming back empty is a "natural" way around it, I'm sure that an extremely high level civilization could come up with others.  Of course they would be godlike compared to us (and may even have created our own universe.)
I thought about dumping entropy into another universe but that seems like a very dirty way of decreasing it in ours, sort of like littering.  Surely a godlike civilization would not do that!  Then again, we have Asimov's The Gods Themselves (have you read it?)

Wat if the entropy of a black hole relates to its surface area, may that indicate that our universe can be described as existing on the surface of a black hole?

Propulsion Disk wrote:

Source of the post How do irreversible processes relate to entropy on a microscopic scale? I'm having trouble visualizing this on a universal scale.

Irreversible processes involve changes that can't be undone (go in reverse) as easily as they happened forwards, which is equivalent to saying that they increase the entropy of the system and its environment.  

Microscopically, this happens when the process transforms energy (ultimately) into heat, instead of purely between potential energy.  Conversion to thermal energy can increase entropy for two reasons:  one is that each particle in the system may gain more units of thermal energy, which increases the number of microstates of the system.  For analogy, if I have a bunch of boxes (representing particles), then the entropy of that system of boxes is a minimum because there is no additional information for which box contains.  But if I add some marbles to them (representing units of energy), then the entropy increases because now there is additional information about how many marbles are in each box.

Another way that conversion to heat can increase the entropy is that the heat may be radiated to the environment, which increases the number of microstates since then there are photons to account for, or vibrations in surrounding molecules if the transfer involves conduction or convection.  Macroscopic examples include exothermic chemical reactions, or the plastic deformation of a structure (as opposed to elastic deformation).  Another good example is friction vs. frictionless movement.
  
Cosmologically, the expansion doesn't change entropy for two reasons.  First, because the expansion is adiabatic (by definition).  No thermal energy is lost to the surroundings because there are no surroundings.  The second condition is that the expansion doesn't rearrange the distribution of internal energy or matter.  This is unlike the free expansion of a gas to fill a container, because the container originally has information about what bits of volume within it contain atoms or not.  Free expansion of a gas to fill the container leads to more microstates being occupied, but the expansion of the universe does not lead to occupying more microstates.  The universe is not filling in an originally empty space as it expands!

So instead of the entropy of the universe increasing by expansion, it increases only because of irreversible processes happening within -- stars forming, black holes growing, life evolving and doing its thing, and so forth.  This is what I wanted to emphasize after your description of the universe's increasing entropy.  It isn't because of expansion.  It's completely independent of expansion!  We cannot use the free expansion of a gas as an analogy for it.

A-L-E-X wrote:

Source of the post Wat if the entropy of a black hole relates to its surface area, may that indicate that our universe can be described as existing on the surface of a black hole?

Not literally, but describing it that way can lead to some useful insights about the nature of information and spacetime.  PBS Spacetime has some good description -- I'll refer to them.

Watsisname wrote:

Source of the post Another way that conversion to heat can increase the entropy is that the heat may be radiated to the environment, which increases the number of microstates since then there are photons to account for, or vibrations in surrounding molecules if the transfer involves conduction or convection.

One thing to say about this is that, conduction and, on a more mechanical level convection, are caused by radiation, the photoelectric effect tells us this. in fact, almost all transfers of energy are due to radiation according to QFT, and even more so with QED because that's where Feynman's diagrams lye.

Watsisname wrote:

Source of the post So instead of the entropy of the universe increasing by expansion, it increases only because of irreversible processes happening within -- stars forming, black holes growing, life evolving and doing its thing, and so forth.  This is what I wanted to emphasize after your description of the universe's increasing entropy.  It isn't because of expansion.  It's completely independent of expansion!  We cannot use the free expansion of a gas as an analogy for it.

I was not using it as an analogy, I was using it to describe what was really going on, but yeah, your right, I've gotten pretty rusty...

Watsisname wrote:

Source of the post Microscopically, this happens when the process transforms energy (ultimately) into heat, instead of purely between potential energy.  Conversion to thermal energy can increase entropy for two reasons:  one is that each particle in the system may gain more units of thermal energy, which increases the number of microstates of the system.  For analogy, if I have a bunch of boxes (representing particles), then the entropy of that system of boxes is a minimum because there is no additional information for which box contains.  But if I add some marbles to them (representing units of energy), then the entropy increases because now there is additional information about how many marbles are in each box.Another way that conversion to heat can increase the entropy is that the heat may be radiated to the environment, which increases the number of microstates since then there are photons to account for, or vibrations in surrounding molecules if the transfer involves conduction or convection.  Macroscopic examples include exothermic chemical reactions, or the plastic deformation of a structure (as opposed to elastic deformation).  Another good example is friction vs. frictionless movement.  Cosmologically, the expansion doesn't change entropy for two reasons.  First, because the expansion is adiabatic (by definition).  No thermal energy is lost to the surroundings because there are no surroundings.  The second condition is that the expansion doesn't rearrange the distribution of internal energy or matter.  This is unlike the free expansion of a gas to fill a container, because the container originally has information about what bits of volume within it contain atoms or not.  Free expansion of a gas to fill the container leads to more microstates being occupied, but the expansion of the universe does not lead to occupying more microstates.  The universe is not filling in an originally empty space as it expands!

Yeah I get it now, it really just took some remembering though, because PBS space time did go over this if i'm not mistaken, but I am having trouble with the whole thing about "the universe not filling in originally empty space as it expands", mainly because you didn't state why "the universe doesn't rearrange the distribution of internal energy or matter". but anyway, thank you once again WHN!

Propulsion Disk wrote:

Source of the post but I am having trouble with the whole thing about "the universe not filling in originally empty space as it expands", mainly because you didn't state why "the universe doesn't rearrange the distribution of internal energy or matter".

You're not alone with having trouble with it!  This is tricky stuff to think about.  I think the challenge is how to not imagine the expansion of the universe to be like a sphere expanding into some external space.  We're used to objects having boundaries, where that boundary is a part of the space.  But the universe is not like that.

So, to help try to understand this better, let's start with the two most important cosmological principles, which are known by observation:

• The universe is homogeneous.
• The universe is isotropic.

Homogeneous means that the distribution of matter and energy is, on large enough scales (at least a few hundred million light years), the same everywhere.  You can pick out any large chunk of space that you like, and you'll find basically the same stuff with the same density as anywhere else.

Isotropic means that the universe looks, (again on large enough scales), the same in every direction.  

These two principles might sound like they are equivalent, but it is important to recognize both.  For example, being inside a regular pattern of rectangular bricks would be a situation where things are homogeneous, but not isotropic.  Everywhere is the same arrangement of bricks, but if you look in one direction you may see more bricks along a given distance than if you look in a different direction.  We could also have a situation that looks isotropic but is not homogeneous, such as being at the center of a bunch of concentric spheres.


Now, if the expansion of the universe involved material filling some previously empty space, then that would contradict homogeneity and isotropy.  It would mean there's some boundary where on one side things look different than on the other side.  No such boundary exists in the universe.  No matter where you are, things look the same all around you.

So we must recognize that the cosmic expansion is not a volume increase in the same way that a gas expands as it fills a container, or even the expansion of a gas after popping a balloon in space.  The distribution of particles is also (again on large scales) not changing.  It remains homogeneous and isotropic!  Each particle (representing perhaps a cluster of galaxies) is basically motionless in the space.  It's instead the space itself that is expanding.  I'm sure you've encountered that idea before, but it can still be tricky to grasp what it really means.  

Together (the lack of particles expanding into new territory, and the lack of the expansion rearranging it into some new distribution) means that there is no change in entropy.  But, I've said that these conditions only apply on very large scales.  On smaller scales, matter does collapse into structures, and things do start looking non-homogeneous and non-istropic.  As we covered, that is what leads to an increase in entropy, since those processes aren't reversible.

I hope that helps!

Watsisname wrote:

Source of the post I hope that helps!

Yes, this concludes the entropy saga. Thank you again WHN! i'll keep reading more and more about this, and all the other fields of physics, and maybe someday, be just as smart as you. Maybe...

Watsisname wrote:

Propulsion Disk wrote:

Source of the post but I am having trouble with the whole thing about "the universe not filling in originally empty space as it expands", mainly because you didn't state why "the universe doesn't rearrange the distribution of internal energy or matter".

You're not alone with having trouble with it!  This is tricky stuff to think about.  I think the challenge is how to not imagine the expansion of the universe to be like a sphere expanding into some external space.  We're used to objects having boundaries, where that boundary is a part of the space.  But the universe is not like that.

So, to help try to understand this better, let's start with the two most important cosmological principles, which are known by observation:

• The universe is homogeneous.
• The universe is isotropic.

Homogeneous means that the distribution of matter and energy is, on large enough scales (at least a few hundred million light years), the same everywhere.  You can pick out any large chunk of space that you like, and you'll find basically the same stuff with the same density as anywhere else.

Isotropic means that the universe looks, (again on large enough scales), the same in every direction.  

These two principles might sound like they are equivalent, but it is important to recognize both.  For example, being inside a regular pattern of rectangular bricks would be a situation where things are homogeneous, but not isotropic.  Everywhere is the same arrangement of bricks, but if you look in one direction you may see more bricks along a given distance than if you look in a different direction.  We could also have a situation that looks isotropic but is not homogeneous, such as being at the center of a bunch of concentric spheres.


Now, if the expansion of the universe involved material filling some previously empty space, then that would contradict homogeneity and isotropy.  It would mean there's some boundary where on one side things look different than on the other side.  No such boundary exists in the universe.  No matter where you are, things look the same all around you.

So we must recognize that the cosmic expansion is not a volume increase in the same way that a gas expands as it fills a container, or even the expansion of a gas after popping a balloon in space.  The distribution of particles is also (again on large scales) not changing.  It remains homogeneous and isotropic!  Each particle (representing perhaps a cluster of galaxies) is basically motionless in the space.  It's instead the space itself that is expanding.  I'm sure you've encountered that idea before, but it can still be tricky to grasp what it really means.  

Together (the lack of particles expanding into new territory, and the lack of the expansion rearranging it into some new distribution) means that there is no change in entropy.  But, I've said that these conditions only apply on very large scales.  On smaller scales, matter does collapse into structures, and things do start looking non-homogeneous and non-istropic.  As we covered, that is what leads to an increase in entropy, since those processes aren't reversible.

I hope that helps!

You put it very elegantly!  It helps people I believe if they think of space and time as properties of our universe only because as a matter of fact what we consider space and time could only exist in our physical universe (excluding alternate timeverses of course.)  Anything that exists that isn't in our own universe would have its own dimensions and so our space and time wouldn't have anything to do with it.  As a matter of fact, the concept of boundary wouldn't even be applicable since with its own dimensions it could even be superimposed on ours.  Of course this doesn't mean there couldn't be ANY interaction between universes, as "dark flow" gravity interactions may still be possible.

And thanks for the reference to The Holographic Principle!

Just a quick question about the values of mathematics (yet still a physics question). Are there mathematical descriptions for all physical properties? or are quantitative descriptions limited by how much they can present without the use of words. And what about qualitative descriptions? I feel that they would have that capability more so than the quantitative ones, but I wouldn't know.   

This is a very good question.  An important combination of physics and philosophy.

In my view, I think there must be the capacity to make mathematical descriptions of all physical properties. A physical property is (in principle) a measurable one.  It is some aspect of nature that is present has some measurable effect on something else.  Then we define a unit for that property, so that we can describe the amount that is present.  Generally, the more of it there is, the stronger the effect will be.

Example:  We hang a spring from the ceiling, and then attach a weight to the end of the spring.  The spring stretches a little.  Add another weight, and the spring stretches a little more.  We can do this for many weights and measure the amount of stretching that results.  We recognize this phenomenon and ascribe several physical properties to it.  The "weights" we are adding possess a property of mass.  The more mass they have, the more force that is required to suspend them in the Earth's gravitational field, and thus the more the spring stretches when the masses are hung on it.

There is another property which is fundamental to the spring.  It is the relationship between the amount of force applied to the spring and the amount of stretching that results.  We define a spring constant for it.  If 10 Newtons of force causes 2cm of stretch, then the spring constant is 5 Newtons per centimeter.  This property depends on the structure of the spring itself.

At the end of the day, I think all physical properties must be defined in such a way that we could measure the amount of it with some instrument, according to the effects it has on something else.  An instrument could also be said to be some calibrated tool which is sensitive to that property.  A ruler is a calibrated instrument for measuring lengths.  Many scales for measuring masses are simply springs, which take advantage of Hooke's law as in the example above.

I can't really think of anything which could be called a physical property in any meaningful sense, and not be described in this way.  If it can't be described through quantitative relationships in principle, I would consider it unphysical and irrelevant.  At best, we may say there can be physical properties that we haven't discovered yet, because we so far lack the observations and instruments to be sensitive to their effects.  Or we may have detected it, but not yet have worked out a quantitative understanding of how it behaves, whether due to insufficient precision of measurements or by insufficient advancement of mathematics.  

Watsisname wrote:

Source of the post I can't really think of anything which could be called a physical property in any meaningful sense, and not be described in this way.  If it can't be described through quantitative relationships in principle, I would consider it unphysical and irrelevant.  At best, we may say there can be physical properties that we haven't discovered yet, because we so far lack the observations and instruments to be sensitive to their effects.  Or we may have detected it, but not yet have worked out a quantitative understanding of how it behaves, whether due to insufficient precision of measurements or by insufficient advancement of mathematics.  

I was really just wondering how far mathematics could delve into the field of science, it seems to me that there's almost no limit about how far the two subjects can go together! and mathematics does it so elegantly to, I've been studying about it and that's why I asked this question, and that's the answer I was hoping to get for it! So thanks WHN!

Read The Mathematical Universe- it's fascinating!