Timeline for How to explain apparent acceleration due to the expansion of the universe and inertial reference frames?
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| Feb 28, 2021 at 22:03 | comment | added | Dale | @timm ah, yes, understood. Then we are thinking of the same stress energy tensor. The pressure would be purely electrostatic. I am not sure it would be stable, but maybe it would. | |
| Feb 28, 2021 at 21:48 | comment | added | timm | @Dale I am talking about the "perfect fluid model" on which the Friedmann equations are based, see en.wikipedia.org/wiki/Friedmann_equations . The pressure (p in the stress energy tensor) in our actual universe is negative due to the dark energy/cosmological constant resp. which is the cause of the accelerated expansion of our universe und thus the tidal force I mentioned. This pressure which you call "fluid pressure" isn't a positive pressure exerted by a fluid as you seem to mean. Its sign isn't fixed but depends on the ingredients of the universe. | |
| Feb 28, 2021 at 20:26 | comment | added | Dale | @timm you wouldn’t want to use a perfect fluid model because the fluid pressure would be a third interaction. You would want to use a charged dust so that there was no fluid pressure. The only “pressure” would be due to the electromagnetic stress energy tensor. It seems that such solutions should exist, but they might be unstable. | |
| Feb 28, 2021 at 20:18 | comment | added | timm | It may seem obvious to discuss such a gedanken experiment based on the perfect fluid model, so no local inertial systems. The balance of the forces should be possible if A and B are charged accordingly. However only for a short period of time because the tidal force which pulls A and B apart is not constant. | |
| Feb 28, 2021 at 17:48 | comment | added | Dale | @timm I was talking about local (non-tidal) gravity. I haven’t thought about your idea enough. It may be possible to have such an arrangement, I don’t know. It would certainly not be as simple as two point masses/charges. | |
| Feb 28, 2021 at 17:29 | comment | added | timm | @Dale Do you say that the tidal force due to a positive value of the second derivative of the scale factor can - in principle - not be balanced by an electrostatic force? | |
| Feb 28, 2021 at 14:42 | history | edited | Dale | CC BY-SA 4.0 |
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| Feb 28, 2021 at 3:54 | comment | added | Dale | Not in an inertial frame, no. You can only do it using non-inertial frames. Then gravity shows up as a fictitious force | |
| Feb 28, 2021 at 3:26 | comment | added | Eoin | Thank you for your help clearing my confusion. Are you saying that there is no configuration of charge and mass which would ensure that two objects initiated near each other at rest would remain at rest with respect to each other? | |
| Feb 28, 2021 at 3:05 | comment | added | Dale | You are trying to use Newtonian gravity in cosmology. It doesn’t work. They are not compatible. At cosmological scales you have to describe gravity using general relativity and in GR gravity is locally a fictitious force. It doesn’t exist in local inertial frames. Part of your confusion is due to failing to respect that incompatibility. | |
| Feb 28, 2021 at 3:00 | comment | added | Eoin | $\frac{kQ_1Q_2}{r^2}=\frac{m_1 m_2 G}{r^2}$. If $\frac{Q_1Q_2}{m_1m_2}=\frac{G}{k}$ then there is no force between the two. We may initialize them together at rest, they stay at rest (until expansion is observed) and an outside observer would say they exert no net force upon the other. Surely they would also say no net force is observed? | |
| Feb 28, 2021 at 2:54 | comment | added | Dale | There is no gravitational force in an inertial frame. So there is nothing to balance the electrostatic force. A 0 force cannot balance any non-0 force. Inertial frames are not predicated on no net force between the objects, only on having accelerometers. Ideally the accelerometers would read zero, but even if they don’t you can do a little math and still use them to define an inertial frame. | |
| Feb 28, 2021 at 2:53 | comment | added | Eoin | I am having trouble understanding your comment that it is not possible to balance the gravitational and electrostatic force. What if we change the scenario slightly, so that we are object A and we wish to be in an inertial reference frame with object B. If our ratios of mass to charge are just right, then the equations of Newtonian physics tell us that there should be no net-force acting upon us, and thus no net motion. Thus we observe no force acting upon us, so we are together in the same inertial frame. Yet, as time passes, our distance separates. | |
| Feb 28, 2021 at 2:13 | history | answered | Dale | CC BY-SA 4.0 |