The entropy of systems

I honestly don't think we can avoid calculus. Let's take a brief look at it to see why. Start with y = x^2 Now we want to make that x just a teeny weeny bit bigger, and obviously that will make y just a smidge bigger as well. So, y + dy = (x + dx)^2

We expand the right hand side y +dy = x^2 + 2x*dx + (dx)^2

What does that dx^2 mean? It's a little bit of a little bit, so we just throw it out as being totally inconsequential. Then we've got y + dy = x^2 + 2x*dx

But y = x^2 so we can subtract that from our expression, to give us dy = 2x*dx divide that through by dx to give us dy / dx = 2x

Okay, jenny Graviton and Billy photon are bright young students and read this and do the sums, they both come up with 2x. Though billy Photon looks rather pet lipped about it. "Hang about," he says to Jenny, "your dx isn't teeny weeny at all! It's 2.998E 8 metres. That's huge!" Jenny Graviton pats him on the head, "that is tiny, something we girls have known about you boys for ages." Billy pulls a face at this cheap sexual joke but is still looking doubtful. "okay then, your dy / dx is a tiny triangle on the curve x^2. To me that is still ginormous."

Jenny pretends to think about it for a moment "To me the hypotenuse of that tiny triangle is a straight line, I've just worked out the tangent for some point on a curve. Now you keep telling me that you can only go at the speed of light, so your admittedly bigger hypotenuse is a straight line as well."

GD: 29 Jul 2009 : 22:00:19<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">How does your theory explain changing forces acting on a changing mass (for example: the sun)?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote"><b>In the non-relativistic case,</b> force is mass times acceleration (f = ma), and that is the same as the rate of change of momentum (f = dp/dt).

As for the force acting on the sun's changing mass, I suppose you must mean the gravitational pull of the planets. In that case, the laws enacted by Newton and Keppler and amended by Einstein are correct, provided they are plugging in the correct value of the suns mass, and including the mass of light inside the sphere whose radius is the same as the planet's distance from the sun.

According to Wikipedia-sun , the mass of the sun is decreasing at the rate of 4.26 x 10^9 kg/s, not because of relativistic speed, but because of nuclear fusion. In the sun's core, hydrogen is converted to heavier elements up to iron. These are exothermic processes, and the energy released radiates into space mainly as light (the solar wind's kinetic energy being a small fraction of that total).

According to Wikipedia-solar-wind , the solar wind carries away about 1.85 x 10^9 kg/s. (Actually, I am confused by the two Wikipedia articles; read my comments in the talk section of the solar wind article .)

I could be wrong, but I think those who claim light has no mass would say that the gravity of the sun decreases the instant the light is emitted. What I am saying is that, as a spherical shell of light is emitted each second and expands at the speed of light, the gravity of light in that shell continues to pull us toward the sun until the second we are inside that expanding spherical shell. I calculate that the sunlight inside the mean radius of Earth's orbit has a mass of 4.26 x 10^9 kg/s x 499 s = 2.125 x 10^12 kg. Inside the mean radius of Neptune's orbit (30.104 AU), the mass of sunlight is 5.80 x 10^15 kg. The sun's mass is 1.9891 x 10^30 kg. So the mass of the sun and sunlight for determining Earth's orbit is less than that for determining Neptune's orbit by a factor of about 1 - (3.43 x 10^-14). In other words, Neptune feels the gravity of the sun's mass as it was 6 hours ago, while Earth feels the gravity of the sun as it was 8 minutes ago. I think GR uses the mass of the sun as it is now. The difference is probably undetectable, but conceivably it might affect long-term predictions of planetary orbits calculated with at least 15 significant digits. (Note that I have omitted the mass of solar wind, since I'm not sure of its magnitude.)

<b>In the relativistic case,</b> force is still the rate of change of momentum, but that is no longer the same as mass times acceleration because some of the force goes into the increasing mass. I propose the following formulas:
f = dp/dt = m dv/dt + v dm/dt
In plain English, force is the rate of change of momentum, and that is equal to mass times the rate of change of velocity plus velocity times the rate of change of mass. My memory has faded after four decades, but I seem to remember that force wasn't even mentioned in general relativity classes at U. of Richmond, Va. Anyone reading this who has studied GR at a decent University, please tell me; is force even defined in GR, nowadays?


Fractal Foam Model of Universes: Creator

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by PhilJ</i>

As for the force acting on the sun's changing mass, I suppose you must mean the gravitational pull of the planets.

<b>In the relativistic case,</b> force is still the rate of change of momentum, but that is no longer the same as mass times acceleration because some of the force goes into the increasing mass. I propose the following formulas:
f = dp/dt = m dv/dt + v dm/dt

In plain English, force is the rate of change of momentum, and that is equal to mass times the rate of change of velocity plus velocity times the rate of change of mass.

<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Thanks Philj !

Your equation looks great. The rate change of mass is a consequence of the second law of thermodynamics (example:Coupling forces decreasing with time)

I think the the sun's changing mass is somewhat affected by the gravitational pull of the planets, but the main reason is that gravitation is produced by the fusion reaction taking place: converting mass into energy.

This action of converting mass into energy produces a force. This force then causes motion. (do you agree?)
For example: the combined action of the atoms in the earth's interior, slowly converting mass into energy is what causes gravity. This motion is mainly in one direction: towards the center of the earth.

Now we are moving into statistical mechanics... I will try to find some force equations modified for relativistic motion.

GD: 30 Jul 2009 : 22:50:59<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Now we are moving into statistical mechanics... I will try to find some force equations modified for relativistic motion.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

You really need to learn how to walk before you enter the starting gate at the Olympics, GD. Retake any science and math courses that you failed; then advance thru the more advanced courses in the proper sequence. And take the math at least one semester ahead of the physics that depends on it. Your problem is that you are challenging well established physics concepts that you don't understand. Get the understanding first; if you still think you can do better, more power to you.


Fractal Foam Model of Universes: Creator

<b>[Philj] " ... because some of the force goes into the increasing mass."</b>

That is in fact the way they used to teach it. Of course the physical world is independent of our perception, and sometimes that forces us to change our ideas about it.

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For a while SR made the claim that mass was a function of velocity. But over the years experimantal evidence accumulated that failed to support this, and they gradually adjusted the theory. These days it is momentum, not mass, that increases with relative velocity. Mass itself is now recognized as an "invariant" quantity, and they (big science) are trying to erase the old concepts of rest mass and relativistic mass.

Problem is, the math of those concepts works fine for solving certain kinds of real world problems. People are creatures of habit and many of the credentialed investigators that were taught SR in the "dark early days" are reluctant to turn lose of these tools. They know the equations do not describe the <u>real</u> real world. But they give you the right answer anyway, with less effort and less confusion, so why not use them?

Eventually these guys will retire, and the problem will "go away". The tipping point was in the mid to late 80s, just a few years after I got my sheepskins.

===

Moral of the story? Math is very useful in the doing of physics, but it is not physics. Additional constraints apply - your mileage may vary.

Larry: 31 Jul 2009 : 09:26:11<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Mass itself is now recognized as an "invariant" quantity, and they (big science) are trying to erase the old concepts of rest mass and relativistic mass.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Thanks, Larry. I was aware that relativistic mass was <i>passe</i>, but I really am surprised to hear that mass is invariant. It makes perfect theoretical sense to me---especially in the context of my own model---that mass should increase with relativistic speed. It'll take a while to wrap my brain around this new info. I guess I better take some of those " Great Courses " on DVD for subjects that I thought I already knew.

By the way, my profs, back in the mid '60s were "old school" even for those days. A lot of the garbage they tried to teach me didn't sink in, and I didn't understand why until I did independent reading on relativity in the '80s. A word of advice to students: Don't worship your profs; they often don't know what they're talking about. Also, don't go on faith that your textbook is up to date--- expecially if the copyright is more than a year old. If something doesn't sound right to you, research it on the internet.

Fractal Foam Model of Universes: Creator