A serious physics dilemma

[AtmaWeapon]

I thought of this a while back but forgot about it; while eating at a restaurant tonight I remembered it.

It's a common property of matter that the warmer it becomes, the less dense it is. This is the reason why hot air rises. Lava lamps work on this principle as well: the heated lava substance becomes less dense than the fluid around it and rises, then cools as it gets farther from the bulb and falls back down.

So why is it that when I get a drink at a restaurant and drink it from a straw the drink is always warm at the bottom? Even if I let it sit for 10 minutes or so it is still pretty much room temperature at the bottom. It is understandable that near the ice the drink would be cold, but everything I've been taught about thermodynamics suggests that the chilled drink should be moving to the bottom. I understand why it would be coldest near the ice but can't figure out why it doesn't eventually get that cold at the bottom of the drink.

I have two hypotheses but perhaps one of you knows another or can confirm one is correct:

Hypothesis 1: Water in the beverage does not obey the temperature/density relationship
Ice is cold water. If it displayed the aforementioned temperature/density relationship then ice would sink in warm water. In fact the opposite happens. Perhaps the water contained in Coke and other beverages causes it to display this property and the bottom of the drink will always be warmer than the top.

I don't really have a thermometer sensitive enough to test this out but I would test this by placing warm water in a rather tall (2-3 feet) container and watch the temperature at various depths.

I think I remember reading that this special property of water only holds between water/ice in that ice is still more dense than water yet it floats on water. If this is true than water itself should obey the rules like other substances and this hypothesis is wrong.

I thought perhaps the ocean was a good counterpoint to this hypothesis since the coldest water is the deepest water, but that is mainly the effect of the lack of sunlight; I don't think a temperature current could move fast enough to get warm water to the bottom of the ocean at a rate that would keep it heated.

Hypothesis 2: Environmental Interaction
The bottom of the glass has no ice, but does have warm air surrounding it. The top of the glass has warm air surrounding it, but has ice cooling it. Perhaps the movement of chilled beverage is too slow to overcome the heat of the outside air and the bottom stays warm for this reason.

Any thoughts?

[Majora]

The reason ice floats in water/liquid is because water expands as it freezes

That might help. :)

[DarkDragon]

Hypothesis 2: Environmental Interaction
The bottom of the glass has no ice, but does have warm air surrounding it. The top of the glass has warm air surrounding it, but has ice cooling it. Perhaps the movement of chilled beverage is too slow to overcome the heat of the outside air and the bottom stays warm for this reason.


This hypothesis is correct. The water near the ice *does* become more dense and sink, but not fast enough to overcome the heating of the water by the environment.

For an analogous opposite situation, consider the hot air coming out of a campfire. Air heats near the fire and then rises, as is obvious from looking at the smoke, but nevertheless the air several feet above the fire is much cooler than that right on it.

[The_Amaster]

Yeah, in this case the natural buoyancy of the ice overides the effort of the warm to rise.

[Pineconn]

Actually, I thought that was a great question, but you guys tore it apart and inserted your fancy hypotheses and apothegms. :p

Whatever happened to the good ol' science when we were taught that there were three forms of matter (http://en.wikipedia.org/wiki/State_of_matter)?

[Masamune]

Water becomes denser as it gets colder, and then becomes its densest at 4 degrees C. Then it expands from 3 to 0 degrees C.

[DarkDragon]

Sure, but the question wasn't why ice floats on water, but why water at the bottom of the glass is warmest.

[Cloral]

I can't help but think that where you live must be quite warm, because drinks I get at a restaurant are always nice and cold - even at the bottom.

Here's some interesting information on the water density question: in large bodies of water, the deepest waters will always be about 39 degrees, even in mid-summer. This is because the warmer water at the top is less dense, and so does not mix with the denser deeper water. If the deeper water gets any colder than 39 degrees, it starts to get more buoyant (because it begins to partially freeze), rises, mixes with the warmer water, and warms up (though this action is so miniscule as to not really contribute to the mixing of the body of water as a whole). This is why lakes never freeze from the bottom up.

edit:
Here's a tricky physics dilemma: A person who observes another person enter a black hole will see that person ripped to shreads by the black hole. However the person who enters the black hole will not be able to detect that anything is out of the ordinary. How can both people be correct at the same time?

[DarkDragon]

However the person who enters the black hole will not be able to detect that anything is out of the ordinary. How can both people be correct at the same time?

Why wouldn't he detect anything out of the ordinary? I would think shredding (or at least passing out from excess force) would occur before time dilation was significant.

[Beldaran]

Yes, my limited and admittedly newtonian understanding of things leads me to believe that being crushed by the forces of unfathomable mass and gravity would alert me to a problem.

[Pineconn]

My hypothesis: Black holes are known to bend and trap light. The person viewing this will get tricked by the bending of light, thinking that the person is being slaughtered. But this is not the case. When the person enters the black hole, s/he is beyond where light bends (??) and sees nothing out of the ordinary.

^Feel free to rip that to shreds^

[DarkDragoonX]

My hypothesis: Very large amounts of LSD are involved.

[AtmaWeapon]

I think the problem is it's hard to accurately model what would happen to someone as they approach the center of the black hole. I'm going to try to explain it with my really limited (and possibly wrong) grasp of special relativity so don't go using the stuff I'm about to say as bar trivia or anything.

With current technology the situation is impossible as you would die a good while before any significant space/time effects were displayed. Supposing you had a suit or some way to survive the powers of the infinite then the problem is simply one of relativity. Relativity is fun because you get to use actors and frames of reference.

Actor one: A pot of petunias
Actor two: DarkDragoonX

The petunias have crossed the event horizon and are unable to escape the pull of the black hole. DarkDragoonX is a stationary observer outside of the event horizon.

If you assume the pull of the black hole causes a constant acceleration on the pot of petunias, it is easy to see that they will eventually accelerate towards the speed of light. As this happens, time dilation and length contraction will apply. From what I understand these forces enforce the speed limit in the universe but I'll be really simple since my understanding of the concepts isn't really that profound. As the petunias approach the speed of light, their perception of time is distorted in such a way that time passes slower for the petunias. In other words, as the petunias accelerate the amount of time they perceive passing over an interval will be less than the amount of time DarkDragoonX measures, assuming the events that define the time intervals are simultaneous.

Now a quick glance at the equation for the time dilation shows that one of the determining factors is a variable (The Lorentz Factor) defined by 1/sqrt(1 - (v^2 / c^2)). This tells us two things: at the speed of light (where v = c) this factor will be undefined due to a divide by 0. At any speeds larger than the speed of light, you end up with an imaginary number from the square root so we'll just call this behavior undefined.

This is exactly why this paradox exists. We believe that travel at the speed of light is impossible, and our equations that define motion reflect this. As the petunias approach the speed of light, their perception of time slows. The assumption that can be made is that at the speed of light perhaps time does not pass for the individual, which leads to the thought that the petunias would never sense their destruction. However, the behavior is undefined and it seems silly to suggest a paradox based on a model that does not define the situation in question.

In the end, all we know is the pot of petunia's final thoughts were "Not again." and if we understood exactly why they thought this we would know a lot more about the nature of the universe.

[DarkDragoonX]

The petunias have crossed the event horizon and are unable to escape the pull of the black hole. DarkDragoonX is a stationary observer outside of the event horizon.

Aw man, I never get to be the one who gets torn to pieces by a spatial anomaly. /pout

[Cloral]

That particular paradox was, btw, on a special on the Discovery Channel about Hawking and black holes. It isn't something I just made up.

I think it's a matter of frames of reference, as the two observers go out of causal contact as the event horizon is crossed. So if I'm right, what the outside observer views is the result of the massive distortion caused by the black hole's gravitational pull. Like when you stand next to a lake and look at a fish in the water, the fish isn't quite where it appears due to the distortion of the water surface. This would indicate that falling into a black hole wouldn't be such a bad thing, assuming that you had adequate supplies. There could even be whole worlds in the black hole, totally oblivious to their situation. This assumes though that my understanding of black holes is correct. Considering that I haven't taken any higher-level physics classes, I could very well be way off base.

[Beldaran]

Maybe our whole universe is a black hole in some other retarded universe full of stupid fuckers.

[Pineconn]

:eyebrow:

Anyway.

So, I was more or less correct, without the long post, knowledge of physics, and the mathematical equations. :rolleyes:

[The_Amaster]

And do these petunias happen to be the reincarnation of some poor fool who keeps getting sucked back into life, only to be killed by the same man?

*Ahem* sorry.
What I don't get, though is, if we're in a black hole-proof suit,


which leads to the thought that the petunias would never sense their destruction.

how do the petunias get destroyed at all?

[AtmaWeapon]

That particular paradox was, btw, on a special on the Discovery Channel about Hawking and black holes. It isn't something I just made up.

Oh OK I was thinking maybe it was that one but it seemed like the big deal with his Information Paradox was the disappearance of information once the black hole collapsed. I know he eventually decided the theory was wrong but honestly I couldn't watch that show all the way through because it was an hour of blue balls. It went something like this:

Stephen Hawking is a smarty man and came up with a theory so profound, so shocking, that he faced ridicule from all of his peers. *biographical information*

But despite the success of his early years, Hawking would go on to be attacked for a theory that shocked the world's physicists. More when we return.

Commercials

*biographical information*

But Hawking was about to discover something that was so chilling, the entirety of his peers mocked him for decades.

Commercials

*biographical information*

Hawking was very close to discovering a theory that would rock physics...

Commercials

*Information Paradox*

Commercials

When we left off... *recap of previous material*

Commercials

When we last left, *shorter recap*
*More Information Paradox*

Commercials

*aftermath*

Commercials

But Hawking would soon discover a flaw in his theory...

Commercial

At this point I decided I had had enough. It was a 10 minute program spread over an hour or longer and I was getting pretty ill.

*edit* also no one saw what I did there with the petunias :(

[Cloral]

Maybe our whole universe is a black hole in some other retarded universe full of stupid fuckers.

You know I seriously had that thought. I was thinking about what it would be like to fall into a black hole, and the result I got was remarably like our observations of the universe. It would explain, among other things, how parts of the universe could be out of causal contact with us. It would also explain why the universe seems to be expanding. So who knows. Maybe there was no big bang after all. But again, I don't know enough about physics to even begin to figure whether there is any basis to this idea. Really I'm probably just missing some fact of the way black holes work that would prove that this couldn't be the case.

[The_Amaster]

Interesting theory. It would possibly explain the Big Bang. I mean, it's acceptd that the universe was a infantismle speck of matter that blew up into massive proportions, but how did it get so tiny. Possibly either crushed by a black hole, or else somthing entered a black hole, got crushed, exited the other side and blew up again.

[Pineconn]

Actually, I think that the universe is just fake. Like, similar to Beld's theory, that we may be an exhibit in a glass dome at a museum, with people pointing and laughing at us. I will prove, during my lifetime, that there is a glass wall at the end of the universe.

[AtmaWeapon]

When both the question and the answer are known, the universe will be destroyed and immediately replaced with one even more confusing.

For more information that proves this see this interesting clip (http://youtube.com/watch?v=oHg5SJYRHA0).

[The_Amaster]

When both the question and the answer are known, the universe will be destroyed and immediately replaced with one even more confusing.

Another theory states that this has already happened.

The closest we'll probably ever get is "What do you get if you multiply 6 by 9?"

[AtmaWeapon]

HOW DID YOU GET THAT AND MISS THE PETUNIAS I WAS MORE PROUD OF THAT ONE :mad:

[The_Amaster]

And do these petunias happen to be the reincarnation of some poor fool who keeps getting sucked back into life, only to be killed by the same man?

I didn't. I wonder how many other people get these referances were spitting back and forth.

[deathbyhokie]

I didn't. I wonder how many other people get these referances were spitting back and forth.

Exactly 42