SR and the earth, sun, and galaxy.

by aychamo
Tags: earth, galaxy
 P: 273 Arcon, Your statements are very interesting. I gradually figured that your arguments with DW seems to focus on whether the gravity mass is the same as inertial mass and the measured mass is a gravity mass. Any way, I need some times to read them. DW, you seem to believe that the inertial mass described by E/c^2 not the same as gravity mass. In one place, you said that g=GM/R^2 and the M is the rest mass. By the way, I am confused, proper time is the time of the mover's own time. How about proper mass? Straightly, it seems to be the rest mass. But you seem to say that's the E/c^2. Please help me with the terms. . Thanks.
 P: 273 DW, Arcon, If the argument focused on whether gravity mass is the same as inertial mass. I would like to ask another question. If you noticed, some people are trying to capture a light in a confinement. Let's say if I am able to keep some photons bouncing inside a confinement, will this confinement exihibit any gravity from the mass by E/c^2 of the lights inside the confinement to the objects nearby? What will your predict? If I know a little bit about laser, maybe we can do some experiemnts with lasers.
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 Originally posted by Sammywu Your statements are very interesting.
We have Einstein to thank for that. :-)

By the way, the terms proper mass and rest mass are synonyms. I choose to use the term proper mass because the term rest mass can easily be interpreted to mean the relativistic mass when v = 0. However that is not always true since relativistic mass is also a function of the gravitational potential so you there can be a difference. I.e. for v = 0 relativistic mass, m, and proper mass, m0 are related as

$$m = \frac {m_0}{\sqrt{1 + 2\Phi/c^{2} }}$$

 Let's say if I am able to keep some photons bouncing inside a confinement, will this confinement exihibit any gravity from the mass by E/c^2 of the lights inside the confinement to the objects nearby?
Yes. But even a straight beam of light can generate a gravitational field sicne it has energy and energy has mass. John Archibald Wheeler once showed that it's possible for light was able to form an object and act as a gravitating body even with no confining walls. That object is called a geon. Its unstable though so it wouldn't last long.
 P: 273 Arcon, DW, How about this one? Since higher temperature means a group of molecules moving in higher average speed against us. Will they be measured with higher inertial mass and gravity mass?
 P: 273 DW, Arcon, How about these two: When an electron in a atom absorbed a photon and elevated to a higher state, will the atom show higher inertial mass and gavity mass? If I spin a top to very high spin speed, not only now we have angular mometum also will it be measured with higher mI and mG?
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Sammywu - You do understand that there are two commonly used terms in relativity regarding mass right? These term terms are relativisitic mass and proper mass. In all cases when I use the term "mass" it means "relativisitic mass. It is in this sense of the term that I'm answering your questions. In the present case it makes no difference.

 Originally posted by Sammywu Since higher temperature means a group of molecules moving in higher average speed against us. Will they be measured with higher inertial mass and gravity mass?
Yes.
 When an electron in a atom absorbed a photon and elevated to a higher state, will the atom show higher inertial mass and gavity mass?
Yes.
[quote]

If I spin a top to very high spin speed, not only now we have angular mometum also will it be measured with higher mI and mG?

Yes. In fact I worked out a similar question this past week regarding a rotating cylinder. See
http://www.geocities.com/physics_wor...g_cylinder.htm
 P: 273 Arcon, DW, Actually I like the term proper mass. It's better than rest mass. Put it simple, there is no such thing as rest mass. An electron in an atom has different mass from a free electron as we already show, if Arcon is right and DW agreed. The elctron has a spin of 1/2, so its true rest-rest mass shall be smaller than our published figure if you can stop its spin. This is my stupid thought. Do not bother that much. DW, can we show that stress energy tensor or the mass energe tensor changed due to the spin of the top with your modern SR? Arcon, when I have time, I will browse your explanation of spinning of cylinders. Thanks.
 P: 273 DW, Arcon, About relativistic mass, I can't say what I agree. Let's examine another case. Let two objects A and B with the same mass m, moving toward each other in 2/3c relative to me, the observer. The threes are all in its own inertial reference frames. Agreed? Now, two objects collide and lump together as one. What is the mass when they lump as one? What were they before lumped together, relative to me, A or B? Can we apply this to the phenomenon of an electron and a positron lumped together as a gamma photon for a short period? Is there a term. for apparent mass? Is it the same as relativistic mass? By the way, I think DW does have good intention in puclishing the modern relativity formulae in another thread. I think we can show our difference in thinking and theory. Actually DW shall make his formulae even more clearer. Discussion of how they were derived will be even better. Thanks
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 Originally posted by Sammywu DW, Arcon, About relativistic mass, I can't say what I agree. Let's examine another case. Let two objects A and B with the same mass m, moving toward each other in 2/3c relative to me, the observer. The threes are all in its own inertial reference frames. Agreed?
Im sorry but I don't understand what you mean by "The threes". Please clarify. Do you mean you and the other two particles are each in an inertial frame of referance?
 Now, two objects collide and lump together as one. What is the mass when they lump as one?
Let the proper mass of each particle before collision be m0. Let the proper mass of the final lump be M0. The mass of each particle before collision is

$$m = \gamma m_{0}$$

The total mass, mtotal, before the collision is the sum of the two masses

$$m_{total} = 2\gamma m_{0}$$

Since this is a closed system mass is conserved and therefore

$$M_{0} = m_{total} = 2\gamma m_{0}$$
 Can we apply this to the phenomenon of an electron and a positron lumped together as a gamma photon for a short period?
No. If you did then the momentum of the system would not be conserved. Look at this from the viewpoint of the zero momentum frame of reference. When there were the electron and positron then there was no momentum. When these particles appear and only one photon appears there will now be momentum since one single photon always has momentum. But you can have them anihilate and yield two photons moving in opposite directions as obeserved in the zero momentum frame of reference.
 P: 273 Arcon, Yes. When I say the three, I mean looking from the three different objectss points of view. Can we show the 4 vector momentum conservation and energy conservation from the three different observers. About the other statement, I oversimplified that, there needs to be a subvelocity 2/3c in both particles toward the screen. so, their true velocity will be c*sqrt(8/9) with an angle toward the middle of teh seceren. Sorry about that.
 P: 273 Arcon, Any way this went far away from our original topic. Let's try to resolve my question about a free falling object in a gravity field in your equations. Your gamma is dt/dt'. Since dt/dt' is a not constant here, this gamma is not constant either. OK, I stuck here and don't know how to continue. Want to help me. Thanks. My object is try to derive the clock difference when the object returns to the initial falling point in your formulae.
 P: 273 Arcon, This is the test case for you in case you do not know what test I was up to. Making a device like a donut with a connecting tunnel through one of the diameters. With an open end at the joint of the tunnel and the donut, you can shoot an object in with certain speed. Put a comparable significant mass in the middle; now this is a artificial Sun experiment that you can let objects orbiting through the donut and objects falling through the tunnel. You can perform a true comparison of clocks between free falling objects and orbiting objects. YOu can assume the middle mass is a evenly densed sphere of M0 with a radius of RM. Apparently your formula will only deal with detail gravity density.
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