timo

I don´t really have an answer for you but my guess would be that it´s due to the sudden change in pressure. When you open the bottle, the pressure inside the bottle suddenly changes to room pressure (I´d guess it was less before that). Maybe someone who has a phase diagram of water at hand or who has a less rusted memory of thermodynamics than me can help you more.

With "spherical symmetric" I meant the planet, of course. You don´t really expect the gravitational force of a human body on itself to have much influence, do you? I´m not sure if it will impress you much but please let me state the following: I can only keep such a posting frequency as we have it now because I have actually done such calculations to quite some extend during my first two years of studying (gravity and electrostatics are quite similar for these kind of problems). I wouldn´t be so quick with my responses if I wasn´t quite certain about what I say. So please take a moment to think about the physical situation a bit. I´ll also think about whether I maybe misunderstood your posts. Try to forget the gravitational attraction of the human body on itself. Then, consider each atom of the human body as seperate. Hopefully, you´ll see that the net gravitational force on that atom is zero. Then, try to understand that it´s zero for each and every atom of the human body.

No. That´s what I was trying to tell you. The net force on each and every particle -regardless whether it´s the whole body, an arm or just an atom- is zero. There was a thread about the gravitational field of a spherical symmetric mass a few days age where Swansont and me were topping each other with details a bit. Maybe I´ll find it and you believe this thread more than my words.... EDIT: There you go: http://www.scienceforums.net/forums/showthread.php?t=15720 Your position is at a certain radius. As long as the problem is spherical symmetric, the only matter relevant for gravitational attraction is that which is in the volume with a radius smaller than yours as the rest cancels out. Since you were talking about a hollow core, this mass is zero. This is true for both your head and your leg.

^^ Ok, I seem to have misunderstood you. Actually, it was the following statement that made me think you´re on the wrong track:

Oh, I only read the initial post before replying so I forgot this important one: You´re wrong YT. The only force relevant when "infinite trucks pull on everysingle particle of you all pulling in opposite directions" is the net force (the sum). If it´s zero for every single particle, then every single particle experiences zero force. As a matter of fact, it is a very important property of forces that you can arbitrarily split them up or sum them up as long as the sum of them remains unchanged. The prime example for an application is a ball rolling down a ramp where you split up the gravitational force into one parallel to the ramp and one perpendicular to it. Take for example the classical electromagnetic force: Humans consist of a whole lot of electrons and protons. We´d probably blast each other over the distance from here to england if the attraction of my protons on your electrons wasn´t cancelled out by my electrons (might be a funny calculation, btw).

I dunno. Analysis of shock waves play a role in that, afaik. But then, I didn´t even know the core was solid. Yes. Nope. Just because there´s no gravitational force working you can´t conclude that there´s no pressure. Spacecrafts would be a very unhealthy place if there was no pressure in them, for example. In the case of spacecrafts the pressure is due to the walls that won´t let the air escape into void. In the case of your earth core it´s the mass around the center of earth (which experiences a gravitational force) that excerts pressure on it.

^^ Which of both? And in case my point didn´t become clear before: I don´t think it´s a good idea to judge people on one´s assumptions of what they might have wanted to say rather than on what they actually did say.

I´m not a native english speaker so correct me if I´m wrong: Isn´t he saying that all actions taken were according to the law instead of saying that everything they do was ok because it´s for a "good cause"? My reading of the passage you provided is the former while your comment on it seems to imply the latter.

Perhaps it would help if you could simply explain why you are talking about a uniform gravitational field at all. I can´t see any reason for doing so because you mainly seem to consider non-uniform fields. And why do you plug your result for a uniform field [3] into an equation for an escape velocity [4,5] - a quantity inherently bond to non-uniform fields? EDIT: The keyword in my comment about the patchwork of internet sources was "patchwork", not "internet sources". It´s imho not a fluent read. It reads as if you plug things in the equations because the letters are equal. That´s how reading your text makes me feel. No, I´m afraid I can´t be more specific about it.

- The point is that you are giving a movement equation for a uniform gravitational field. The problem is that you are not dealing with a uniform gravitational field. - eq [3] seems unjustified at first glance because the reason you obtain it is "substituting [2] in [19]" with [19] standing in a block of other uncommented equations. It´s simply not enough for me to understand what you are doing there. It simply makes the impression as if the reason for doing it was that the letters match. - the natural units are definitely not the problem in reading the text. The formatting and the writing style that seems like a patchwork of different internet sources are the problems - at least for me.

The link does work if you remove the "confused" stemming from the smiley at the end.

I don´t really understand your problem. You are given 100 positive real numbers and take the 11 smallest ones. No, I meant the set of 11 of those hundred numbers which gives the smallest product of all possible sets of 11 of those hundred numbers (because they are the smallest numbers). Sorry, I didn´t understand that part at all.

It is the displacement of the particle´s postition from the point you rotate around or -to avoid the usage of the term "displacement"- the particle´s position relative to the center of rotation.

If I understood you correctly, then the product of the 11 smallest numbers is >1.

Can you explain what you mean by that? It doesn´t sound as if it´s correct.

They are two of the four fundamental forces in physics (I think I´d prefer the term "intercations"). As usual for such a rather broad question, wikipedia is a good start: http://en.wikipedia.org/wiki/Fundamental_force.

You probably found the only place where I wrote "velocity" instead of "4-velocity". I did this to get in touch with LazerFazers post. 4-veocity is the relativistic analogon to what you know as velocity (3-velocity) and it´s restriction is simply that the magnitude described in my previous post is one... except for photons (see below). This constraint on the magnitude of the 4-velocity directly translates into the constraint that the magnitude of the 3-velocity has to be <c (=c if the magnitude of the 4-velcity is 0). An exception are massless particles. The magnitude of massless particles´ 4-velocity is zero. This is also a reason why you cannot switch to the photon´s frame of reference. The 4-velocity of a particle is always a base vector in a particle´s frame of rest (the base vector of the time component). It is not possible to construct a useful base with a base vector of magnitude 0. Well, the point is: There is no frame of reference in which a photon was at rest. The red point might move across moon´s surface faster that c. The photons making up that red dot move from the laser to the moon at c. For the "movement of information" part. I have yet to see a definition of "information" I understand. You can argument in a way that the information didn´t travel with more than the speed of light. But in the end, I personally see little sense in talking about abstract terms like "information" at all. All particles are bound to have a 3-velocity <= c. That´s sufficient for me to know and therefore that´s also all I know and can say here.

I´d like to add that the mass/charge distribution doesn´t have to be uniform. It is sufficient if it´s spherical symmetric (each shell gives a contribution as if the mass was at the center of the sphere and so does the total force, then). Still, you have to be outside of the mass distribution (=the body). Assuming the mass of earth remains unchanged, then "yes" (just added this remark because there seemed to be a bit of confusion).

Hi LazerFazer and welcome to these forums. The idea of your previous post, namely that every body moves through spacetime with a velocity of magnitude c, is correct. However, your assumption on how to calculate the magnitude of the velocity -and therefore probably also your proof- is at least not conform to the standard notation used in relativity. To stay within your naming convention, the magnitude of the 4-velocity is calculated by c² = t² - x² - y² - z². Therefore, if either the magnitude of x, y or z increases, t must also increase to "compensate" for it. For relativistic calculation, one usually uses the so-called "natural units" with c=1. I´ll take the freedom to also use them to save me from headaches caused by units transformations. So for a moving particle, you have a 4-velocity of for example (t>1, x>0, y=0, z=0). Now, how does this translate to time dilatation? Well, within one unit of the particles eigentime (the time measured by the particle), it moves t units of coordinate time (4-position = original position + 1* 4-velocity). Since t>1, the cooridnate time passed "during" this one eigentime unit is >1. Therefore, coordinate time "passes" faster than eigentime. In other words: Eigentime -which is the time measured by the particle- passes slower than coordinate time -which is the time measured by the "outside observer". The object which causes this strange magnitude of t²-x²-y²-z² is called the Minkowsky Metric. It really is a bit strange and it takes a bit of time to get used to this metric (which strictly speaking isn´t even a metric). But it plays an essential -perhaps even THE essential- role in the formulation of relativity.

Uh, oh, ... in this case another "I can imagine that ..." correction would be needed, too. I was actually thinking that it´s pretty obvious that I was making fun of it. I get the strange feeling that my posts are prone to misunderstandings, lately.

If you throw a ball into the air it will be at rest at the uppermost point of its trajectory. Surely, you are not going to tell me that there´s no force acting on it at this point. Exaclty. It isn´t wrong. Again: An upwards velocity doesn´t mean upwards acceleration. You´re giving the explanation yourself in the following sentences:

Seeing the chaos that broke out in this thread, I think it´s a good idea to emphazise the answer which came closest to the intend of the original question: @others who want to measure temp in celsius or fahrenheit and heat in calories: That´s possible of course. You can as well measure energy in snickers and mass in pizzas. But neither of them are conform with the international standard units (see links in quote above or http://en.wikipedia.org/wiki/SI_base_units).

Yes, you are pretty confused. Thinking it´s 3E is a mistake I can understand up to some point. But why did you change your mind from (originally) 3B to 3A now? Perhaps you should slowly go through 1 to 5 in order and give your anwer with an explanation why you think this is the answer.

Some people sell you crystals that catch these positive energy waves created of the solar system´s eigenfrequency and therefore increase your overall health and life expectancy (and in this case also your mental capabilities since they match the frequency of the brain). EDIT: On topic: I have never head of it. I´d also not know what the frequency of the solar system should be. It sounds like a pretty much made-up statement to me. Did you notice that when you count the sun as a planet, the number of planets equals the number of your fingers? Too bad, I won´t be able to sell crystals with this wisdom.