ydoaPs Posted June 22, 2008 Posted June 22, 2008 Imagine a universe in which all that exists are three balls(one red, one blue, and one yellow). Each ball has a mass of 1kg. The red and blue balls are at rest with respect to each other, but are moving with respect to the yellow ball. From a reference frame in which the yellow ball is at rest, the red ball and the blue ball are moving and thus have kinetic energy. Now, let's move our reference frame to one in which the blue ball is at rest. The red ball at rest relative to the blue ball, so has no kinetic energy(and neither does the blue ball). The yellow ball, however, is moving and thus has kinetic energy. The red ball has more energy in the reference frame of the yellow ball than it does in the reference frame of the blue ball. Thus energy is dependent on the reference frame and is not conserved from frame to frame. Mass, however is the same in every frame of reference. If we consider the three balls as a system and use the same reference frames, we get different values for the total energy of the system. As stated, each ball has a mass of 1kg. In the reference frame where the red and blue balls are at rest, the yellow ball is observed to be moving at 100m/s with respect to the red and blue balls. In the reference frame where the yellow ball is at rest, the red and blue balls are each observed to be traveling at 100m/s with respect to the yellow ball. How much [acr=Kinetic Energy]KE[/acr] does this universe have?
Mr Skeptic Posted June 22, 2008 Posted June 22, 2008 How much [acr=Kinetic Energy]KE[/acr] does this universe have? As much as it likes. Your reference frame does not need to have an object, so you could also choose a reference frame at 0.999999c. This argument is why I think that the universe's One True Reference FrameTM is the center of mass of the universe, if that can be found. Sure, any reference frame is just as good as any other, but the center of mass frame is unique, among other things it has a zero overall momentum. That would make it the reference frame of the universe, such that the universe is not moving.
Motor Daddy Posted June 22, 2008 Posted June 22, 2008 Imagine a universe in which all that exists are three balls(one red, one blue, and one yellow). Each ball has a mass of 1kg. The red and blue balls are at rest with respect to each other, but are moving with respect to the yellow ball. From a reference frame in which the yellow ball is at rest, the red ball and the blue ball are moving and thus have kinetic energy. Now, let's move our reference frame to one in which the blue ball is at rest. The red ball at rest relative to the blue ball, so has no kinetic energy(and neither does the blue ball). The yellow ball, however, is moving and thus has kinetic energy. The red ball has more energy in the reference frame of the yellow ball than it does in the reference frame of the blue ball. Thus energy is dependent on the reference frame and is not conserved from frame to frame. Mass, however is the same in every frame of reference. If we consider the three balls as a system and use the same reference frames, we get different values for the total energy of the system. As stated, each ball has a mass of 1kg. In the reference frame where the red and blue balls are at rest, the yellow ball is observed to be moving at 100m/s with respect to the red and blue balls. In the reference frame where the yellow ball is at rest, the red and blue balls are each observed to be traveling at 100m/s with respect to the yellow ball. How much [acr=Kinetic Energy]KE[/acr] does this universe have? Why are all the balls not together, like a nucleus, due to gravity?
Cap'n Refsmmat Posted June 22, 2008 Posted June 22, 2008 Gravity is weak, and unable to overcome the motion of the balls (well, it has a tiny effect, but we really don't care).
Motor Daddy Posted June 23, 2008 Posted June 23, 2008 Gravity is weak. It's weak, but the balls are the only thing in the universe, and they are close together (no?), so they should be together, yes? If the balls have motion relative to each other, what caused that motion? Did they once collide with each other?
Cap'n Refsmmat Posted June 23, 2008 Posted June 23, 2008 No. Let's suppose the balls are approximately 10 meters away from each other. That gives a gravitational force between two of them of [math]F = \frac{G \cdot m_1 \cdot m_2}{d^2} = \frac{6.67\times 10^{-11} \cdot 1 \cdot 1}{10^2} = 6.67\times 10^{-13}N[/math] That'll accelerate the two affected balls by approximately 6.67 x 10-13 m/s2: [math]6.67\times 10^{-13} = 1 \times a = a[/math] 6.67 x 10-13 meters per second squared of acceleration is a very, very tiny amount, even with another ball also contributing the same amount. They'll take a very, very long time to the velocities of the balls. [math]v = at + v_0[/math] [math]0 = -6.67\times 10^{-13} \cdot t + 100[/math] [math]t = 1.5 \times 10^{14}s[/math] That's somewhere close to five million years to slow the balls to a stop. (We're assuming a reference frame where they're moving, of course. In the frame where the balls are stationary it would take five million years to get them moving at 100m/s towards the other balls.)
Motor Daddy Posted June 23, 2008 Posted June 23, 2008 No. Let's suppose the balls are approximately 10 meters away from each other. That gives a gravitational force between two of them of [math]F = \frac{G \cdot m_1 \cdot m_2}{d^2} = \frac{6.67\times 10^{-11} \cdot 1 \cdot 1}{10^2} = 6.67\times 10^{-13}N[/math] That'll accelerate the two affected balls by approximately 6.67 x 10-13 m/s2: [math]6.67\times 10^{-13} = 1 \times a = a[/math] 6.67 x 10-13 meters per second squared of acceleration is a very, very tiny amount, even with another ball also contributing the same amount. They'll take a very, very long time to the velocities of the balls. [math]v = at + v_0[/math] [math]0 = -6.67\times 10^{-13} \cdot t + 100[/math] [math]t = 1.5 \times 10^{14}s[/math] That's somewhere close to five million years to slow the balls to a stop. (We're assuming a reference frame where they're moving, of course. In the frame where the balls are stationary it would take five million years to get them moving at 100m/s towards the other balls.) Five million years is a drop in the bucket. How long have they existed? They could have already done the back and forth routine a few million times, no?
Cap'n Refsmmat Posted June 23, 2008 Posted June 23, 2008 Seven hours. I suggest you drop this line of questioning, as it's totally irrelevant to the main point of the thread. It's a thought experiment. Try it.
iNow Posted June 23, 2008 Posted June 23, 2008 Motor Daddy, Can you maybe not make this another 250 post thread in one day by being unnecessarily obtuse?
Motor Daddy Posted June 23, 2008 Posted June 23, 2008 Motor Daddy, Can you maybe not make this another 250 post thread in one day by being unnecessarily obtuse? I'm done.
Klaynos Posted June 23, 2008 Posted June 23, 2008 No. Let's suppose the balls are approximately 10 meters away from each other. That gives a gravitational force between two of them of [math]F = \frac{G \cdot m_1 \cdot m_2}{d^2} = \frac{6.67\times 10^{-11} \cdot 1 \cdot 1}{10^2} = 6.67\times 10^{-13}N[/math] That'll accelerate the two affected balls by approximately 6.67 x 10-13 m/s2: [math]6.67\times 10^{-13} = 1 \times a = a[/math] 6.67 x 10-13 meters per second squared of acceleration is a very, very tiny amount, even with another ball also contributing the same amount. They'll take a very, very long time to the velocities of the balls. [math]v = at + v_0[/math] [math]0 = -6.67\times 10^{-13} \cdot t + 100[/math] [math]t = 1.5 \times 10^{14}s[/math] That's somewhere close to five million years to slow the balls to a stop. (We're assuming a reference frame where they're moving, of course. In the frame where the balls are stationary it would take five million years to get them moving at 100m/s towards the other balls.) To note this is a MASSIVE underestimate as the ball is moving 100m/s relative to the others it's getting further away all the time so the acceleration due to gravity is reducing with a 1/r^2 dependence... I'm done. I wonder if you appreciate just how little you understand to be commenting on special relativity?
Motor Daddy Posted June 23, 2008 Posted June 23, 2008 I wonder if you appreciate just how little you understand to be commenting on special relativity? I wonder if you understand just how wrong SR is?
Motor Daddy Posted June 23, 2008 Posted June 23, 2008 You don't seem to. I already proved it. SR is obsolete.
Cap'n Refsmmat Posted June 23, 2008 Posted June 23, 2008 You seem to have a loose definition of proof. Try taking on yourdadonapogos' word challenge. We're already cluttering this thread with off-topic posts.
Janus Posted June 23, 2008 Posted June 23, 2008 To note this is a MASSIVE underestimate as the ball is moving 100m/s relative to the others it's getting further away all the time so the acceleration due to gravity is reducing with a 1/r^2 dependence... Actually, unless the balls are on a collision course, they will never collide or slow to a stop because 100 m/s is way more than escape velocity for these masses at these diatances (In fact, the balls would have to have started at a center to center distance of less than 1.3e-14 m for 100m/s to be less than escape velocity.)
DJBruce Posted June 23, 2008 Posted June 23, 2008 I have posted my answer to the question. I have no idea if this is even close but heres my best shot at this. Please do not read if you do not want a POSSIBLE spoiler. The total kentic energy of the system is 15000. E[math]_{}K[/math]=1/2MV[math]^{2}[/math] So when yellow is my refrence the energy of my system is 1/2(1)(100[math]^{2}[/math])+1/2(1)(100[math]^{2}[/math])=10000 but this doesnt mean that the yellow ball is not moving so when we use the red ball is the reference it the energy of my system is 1/2(1)(100[math]^{2}[/math])=5000 If you add these you would be able to find the Kinetic energy of the system. As I said I have no idea if this is right but thats my best shot.
ydoaPs Posted June 23, 2008 Author Posted June 23, 2008 I have posted my answer to the question. I have no idea if this is even close but heres my best shot at this. Please do not read if you do not want a POSSIBLE spoiler. The total kentic energy of the system is 15000. E[math]_{}K[/math]=1/2MV[math]^{2}[/math] So when yellow is my refrence the energy of my system is 1/2(1)(100[math]^{2}[/math])+1/2(1)(100[math]^{2}[/math])=10000 but this doesnt mean that the yellow ball is not moving so when we use the red ball is the reference it the energy of my system is 1/2(1)(100[math]^{2}[/math])=5000 If you add these you would be able to find the Kinetic energy of the system. As I said I have no idea if this is right but thats my best shot. You're mixing frames. Swansont is on the right track, though
nstansbury Posted June 28, 2008 Posted June 28, 2008 That gives a gravitational force between two of them of [math]F = \frac{G \cdot m_1 \cdot m_2}{d^2} = \frac{6.67\times 10^{-11} \cdot 1 \cdot 1}{10^2} = 6.67\times 10^{-13}N[/math] Ahem... apologies but I believe.... [math]F=G(\frac{m_1\cdot m_2}{r^2})[/math]
Cap'n Refsmmat Posted June 28, 2008 Posted June 28, 2008 That's essentially the same thing, but you changed d to r.
Farsight Posted July 2, 2008 Posted July 2, 2008 Imagine a universe in which all that exists are three balls(one red, one blue, and one yellow). Each ball has a mass of 1kg. The red and blue balls are at rest with respect to each other, but are moving with respect to the yellow ball. From a reference frame in which the yellow ball is at rest, the red ball and the blue ball are moving and thus have kinetic energy. Now, let's move our reference frame to one in which the blue ball is at rest. The red ball at rest relative to the blue ball, so has no kinetic energy(and neither does the blue ball). The yellow ball, however, is moving and thus has kinetic energy. The red ball has more energy in the reference frame of the yellow ball than it does in the reference frame of the blue ball. Thus energy is dependent on the reference frame and is not conserved from frame to frame. Mass, however is the same in every frame of reference. If we consider the three balls as a system and use the same reference frames, we get different values for the total energy of the system. As stated, each ball has a mass of 1kg. In the reference frame where the red and blue balls are at rest, the yellow ball is observed to be moving at 100m/s with respect to the red and blue balls. In the reference frame where the yellow ball is at rest, the red and blue balls are each observed to be traveling at 100m/s with respect to the yellow ball. How much [acr=Kinetic Energy]KE[/acr] does this universe have? None of the balls "have" any kinetic energy. They only have kinetic energy in relation to something else with a different relative motion. The kinetic energy is "in the motion", not in the balls. You can simplify matters by talking about a universe consisting of only two balls, one yellow, and the other red & blue with a mass of 2kg, and you can work out 5000 and 10000 joules for each. But this is only the kinetic energy of one ball with respect to the other. To obtain the kinetic energy of "the universe" you have to treat the universe as an absolute frame and ascertain the velocity of the balls with respect to it. This is not defined, so the answer is indeterminate.
Cap'n Refsmmat Posted July 2, 2008 Posted July 2, 2008 I think that's part of the point of this exercise.
Pete Posted July 2, 2008 Posted July 2, 2008 (edited) Thus energy is dependent on the reference frame and is not conserved from frame to frame. Conservation means does not change with time while invariance means does not change upon change in coordinates. Energy is conserved but not invariant. How much [acr=Kinetic Energy]KE[/acr] does this universe have? It seems as if you're thinking of an absolute rest frame in which kinetic energy is to be evaluated. That is not the case. There are no absolute frames of rest. I already proved it. SR is obsolete.What is this proof that you're referring to? Pete Edited July 2, 2008 by Pete multiple post merged
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