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Author Topic:   Problem with Expanding Universe and Conservation of Energy
commike37
Inactive Member


Message 1 of 10 (177652)
01-16-2005 8:09 PM


I was thinking about the concept that the volume of the universe was proportional to how far light travels (speed of light * time, or ct). Now given conservation of energy, the total energy in a system will not change. Now if two beams of light are moving at the speed of light in opposite directions, then their kinetic energy is constant (KE=.5mv^2, v=c). However, gravitational force would decrease with distance. So my question is, what aspect of an expanding universe would create energy to balance out energy lost to the weakening of gravitation in an expanding universe? I'm just curious as to the answer.

Replies to this message:
 Message 3 by Coragyps, posted 01-16-2005 8:51 PM commike37 has replied
 Message 5 by JonF, posted 01-16-2005 9:26 PM commike37 has not replied

  
AdminNosy
Administrator
Posts: 4754
From: Vancouver, BC, Canada
Joined: 11-11-2003


Message 2 of 10 (177661)
01-16-2005 8:46 PM


Thread moved here from the Proposed New Topics forum.

  
Coragyps
Member (Idle past 734 days)
Posts: 5553
From: Snyder, Texas, USA
Joined: 11-12-2002


Message 3 of 10 (177664)
01-16-2005 8:51 PM
Reply to: Message 1 by commike37
01-16-2005 8:09 PM


Light has no mass, and no kinetic energy. Try reformulating your question.

This message is a reply to:
 Message 1 by commike37, posted 01-16-2005 8:09 PM commike37 has replied

Replies to this message:
 Message 4 by commike37, posted 01-16-2005 9:12 PM Coragyps has not replied

  
commike37
Inactive Member


Message 4 of 10 (177671)
01-16-2005 9:12 PM
Reply to: Message 3 by Coragyps
01-16-2005 8:51 PM


All right, that helps, but still, if the universe is expanding, all the particles are getting farther apart and the net force of gravitation in all of the universe would decrease, right?

This message is a reply to:
 Message 3 by Coragyps, posted 01-16-2005 8:51 PM Coragyps has not replied

Replies to this message:
 Message 6 by coffee_addict, posted 01-16-2005 9:45 PM commike37 has replied

  
JonF
Member (Idle past 168 days)
Posts: 6174
Joined: 06-23-2003


Message 5 of 10 (177676)
01-16-2005 9:26 PM
Reply to: Message 1 by commike37
01-16-2005 8:09 PM


First, your formulation of kinetic energy is Newtonian, not relativistic. When relativistic velocities are involved, you have to use the relativistic version:
which can be expanded in an infinite binomial expansion:
(I think the "approximately equals" should be "equals", since this is the infinite series, not a truncation). Anyhow, when v = 0 you get E = m0c2, which you may have seen before. When v/c is small enough, we can ignore all the terms with c in the denominator and we're always calculating differences in kinetic energy at different speeds so the m0c2 terms cancel out, and there's your classical kinetic energy: (delta E) = m0(vA2 - vB2)/2.
But that's all irrelevant; m0 is the "rest mass", and the rest mass of photons is exactly zero, so their kinetic energy is exacly zero. They do carry energy (just not in kinetic form) and they do (in manner of speaking) have and respond to gravitational fields.
Yet you could pose the question with particles that do have non-sero rest mass traveling close to the speed of light, so it's a valid question.
Consider all the ways energy can be stored in the system. Offhand I come up with electromagnetic energy (if the particles are photons), kinetic energy (if the particles have non-zero rest mass), and gravitational potential energy. As the particles separate, the gravitational potential energy increases. The kinetic energy of non-zero-rest-mass particles decreases (they slow down) or the electromagnetic energy of photons decreases (they get longer wavelength and are red-shifted). Without doing the calculations, I bet the decrease exactly equals the increase in all cases.
As an aside, this sort of thing sort of explains the idea that the Universe may be a quantum fluctuation with zero overall mass. There's some reason for assigning potential energy (which can be measured relative to any position) the value 0 when everything is an infinite distance apart. If you do that, and you already know that the act of separating things increases gravitational potential energy, it follows that the gravitational potential energy of the Universe that we see is negative*. In fact, it's not terrifically different, as such things go, from the negative of the amount of other positive energy we see ... and maybe they're exactly equal in magnitude but opposite in sign, and exactly cancel each other out. Maybe.
Be very careful of drawing new conclusions from the above; it's really a hopeless oversimplification. To draw conclusions you need the math, and I've long forgotten the math and wouldn't try to teach it here if I remembered it.
Finally, modern physicists dislike the term "rest mass" and try to avoid it. I'm just an old fart. Sylas is probably going to discredit it all.
Say, anybody seen Eta_Carinae?
-------------------------
* Say the current gravitational potential energy of the Universe is X. Getting everything infinitely far apart would increase X and make it zero, therefore X is negative now.
{edited to fix classical K.E. formula)
This message has been edited by JonF, 01-16-2005 21:30 AM

This message is a reply to:
 Message 1 by commike37, posted 01-16-2005 8:09 PM commike37 has not replied

  
coffee_addict
Member (Idle past 477 days)
Posts: 3645
From: Indianapolis, IN
Joined: 03-29-2004


Message 6 of 10 (177682)
01-16-2005 9:45 PM
Reply to: Message 4 by commike37
01-16-2005 9:12 PM


Hey mike, would you explain to us why you think the net force in the universe would decrease? I think that after you have given us the reason that you will answer your own question.
Cheers

Here is something to relieve stress.
a + b = t
(a + b)(a - b) = t(a - b)
a - b = at - bt
a - at = b - bt
a - at + t/4 = b - bt + t/4
(a - t/2) = (b - t/2)
a - t/2 = b - t/2
a = b
Since all numbers are the same, math is useless.

This message is a reply to:
 Message 4 by commike37, posted 01-16-2005 9:12 PM commike37 has replied

Replies to this message:
 Message 7 by commike37, posted 01-17-2005 7:34 PM coffee_addict has replied

  
commike37
Inactive Member


Message 7 of 10 (177951)
01-17-2005 7:34 PM
Reply to: Message 6 by coffee_addict
01-16-2005 9:45 PM


Well, I didn't quite get all of that (I haven't gotten to relativity in AP Physics yet), but it looks good enough to me.
And by the way, I picked out the problem with your way to relieve stress. If a = b, then multiplying both sides by (a - b) means multiplying by zero. (ie: 1 * 0 = 2 * 0, 0 = 0)
This message has been edited by commike37, 01-17-2005 19:34 AM

This message is a reply to:
 Message 6 by coffee_addict, posted 01-16-2005 9:45 PM coffee_addict has replied

Replies to this message:
 Message 8 by coffee_addict, posted 01-17-2005 11:13 PM commike37 has not replied
 Message 9 by jsmall, posted 02-10-2005 10:23 PM commike37 has not replied
 Message 10 by Darwin Storm, posted 02-11-2005 12:19 PM commike37 has not replied

  
coffee_addict
Member (Idle past 477 days)
Posts: 3645
From: Indianapolis, IN
Joined: 03-29-2004


Message 8 of 10 (178000)
01-17-2005 11:13 PM
Reply to: Message 7 by commike37
01-17-2005 7:34 PM


Well, you are suppose to assume that a does not equal b.

Here is something to relieve stress.
a + b = t
(a + b)(a - b) = t(a - b)
a - b = at - bt
a - at = b - bt
a - at + t/4 = b - bt + t/4
(a - t/2) = (b - t/2)
a - t/2 = b - t/2
a = b
Since all numbers are the same, math is useless.

This message is a reply to:
 Message 7 by commike37, posted 01-17-2005 7:34 PM commike37 has not replied

  
jsmall
Inactive Member


Message 9 of 10 (184486)
02-10-2005 10:23 PM
Reply to: Message 7 by commike37
01-17-2005 7:34 PM


Please explain question
Are you hinting that stars should be flying apart from loss of gravity or something? I'm not sure what u mean by net gravity. It could be very well be that total gravity in the universe is decreasing, but staying strong in spots with large masses.
I'm no expert, but here's another idea:
Space is increasing between particles, but in a star, for instance, the gravitational attraction would keep the particles together. I think the expansion really only applies to open space.

This message is a reply to:
 Message 7 by commike37, posted 01-17-2005 7:34 PM commike37 has not replied

  
Darwin Storm
Inactive Member


Message 10 of 10 (184582)
02-11-2005 12:19 PM
Reply to: Message 7 by commike37
01-17-2005 7:34 PM


Commike37, I must point out a few errors in your question. First off, the conservation of energy is not the conservation of force. Gravity is a force, not energy. However, an expanding universe would signify a INCREASE, not decrease in the potential energy of the universe. For example, the further apart two gravitational objects are frome each other, the greater their potential energy. Part of this ties in the dark energy discussion. If the universe is expanding in an accererated manner, then some form of "energy" is required. This is where the dark energy arguement arises.
On the other hand, if the velocity of the objects in the universe was deccelerating with respects to our galaxy, that would be as expected. The increase of potential energy would be balanced by the decrease in kinetic energy. However, modern readinds indicate that this is not the case, and that brings up the dark energy problem.

This message is a reply to:
 Message 7 by commike37, posted 01-17-2005 7:34 PM commike37 has not replied

  
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