Genady

More specific situation, for example: if a satellite is held at rest with respect to Earth, it will certainly experience acceleration. While if it free falls toward Earth, the Earth free falls toward it, and both feel nothing. I'm sure your opinion will change after learning GR. Here is how Penrose - who knows something about gravity - describes the situation: Previously, an inertial motion was distinguished as the kind of motion that occurs when a particle is subject to a zero total external force. But with gravity we have a difficulty. Because of the principle of equivalence, there is no local way of telling whether a gravitational force is acting or whether what ‘feels’ like a gravitational force may just be the effect of an acceleration. Moreover, as with our insect on Galileo’s rock or our astronaut in orbit, the gravitational force can be eliminated by simply falling freely with it. And since we can eliminate the gravitational force this way, we must take a different attitude to it. This was Einstein’s profoundly novel view: regard the inertial motions as being those motions that particles take when the total of non-gravitational forces acting upon them is zero, so they must be falling freely with the gravitational field (so the effective gravitational force is also reduced to zero). Thus, our insect’s falling trajectory and our astronauts’ motion in orbit about the Earth must both count as inertial motions. On the other hand, someone just standing on the ground is not executing an inertial motion, in the Einsteinian scheme, because standing still in a gravitational field is not a free-fall motion. To Newton, that would have counted as inertial, because ‘the state of rest’ must always count as ‘inertial’ in the Newtonian scheme. The gravitational force acting on the person is compensated by the upward force exerted by the ground, but they are not separately zero as Einstein requires. On the other hand, the Einstein inertial motions of the insect or astronaut are, according to Newton, not inertial. Penrose, Roger. The Road to Reality (pp. 393-394). Knopf Doubleday Publishing Group.

Gravitational acceleration is. As per equivalence principle.

The answer depends on your frame of reference, i.e. an observer. In the first scenario, as we consider an orbit around the Sun, yes it will get tighter. In the second scenario, wherever you put an observer, the Earth will be free falling toward it (plus the initial velocity.) There is no absolute frame of reference to give an absolute answer.

Thank you. I know about chirality - in the Standard Model, in chemistry, in biochemistry (e.g. DNA), in biology, too. Most examples in biology I know of have explanations, e.g. chirality of snails. Those are not applicable to corals. Looking for new ideas ...

Yes, the actual calculation should be done from the Friedman equations. The result is the same - a uniform infinite mass density causes deceleration. It is one of the components. The total result - positive, negative, or zero - depends on other components, specifically, on the current rate of expansion and on cosmological constant (or, dark energy, if you prefer.)

The acceleration is relative to an observer. If an observer is attached to the mass, it does not accelerate anywhere. To any other observer, it accelerates - free falls - toward them with G*M/(R^2), where R is the distance from the observer and M is the mass of the stuff inside a ball of radius R.

With all due respect, we are going circles for some time already. The answers to all these objections are in the Susskind lecture 1, I've linked earlier. The math is simple and the result is calculable. The outcome is that the uniform infinite distribution of mass causes it to shrink. All points toward all points. If it started with expansion, this distribution causes the expansion to decelerate.

Some years ago while diving around the island where I live I've noticed that this coral always makes a right-handed helix. I wonder if it might be an adaptive feature or, more generally, what could cause it. I mean, I saw dozens of them and never one turning left...

I hope you will enjoy this video as well. Susskind presents an example of dark matter mass calculation starting at about 31st minute. (Only stuff inside an orbit has gravitational effect on the orbit.)

R in this calculation stands for distance from origin. Which of course is arbitrary. As Susskind has shown in his derivation, the final result does not depend on R. No, that calculation doesn't have such flexibility. The observable effects of dark matter lead to calculation of not only it's mass - positive - but also of its amount and distribution. The only observable effect of dark energy is acceleration of the universe expansion.

Correct again. All effect for the smaller R's add up. All effect s for the larger R's cancel.

Right, it doesn't have an effect inside the sphere, it does have the effect outside it.

Dark matter and dark energy are separable in a variety of ways. Dark matter attracts, dark energy repulses. Dark matter density falls off with a cube of expansion, dark energy density doesn't change with expansion. Dark matter non-uniformities accelerate clamping of regular matter, dark energy doesn't have such effect. ...

By the Newton's theorem, a particle inside an empty massive sphere doesn't feel any gravity from the sphere. It holds the same for positive and for negative gravity. Neither positive nor negative mass homogeneously distributed outside galaxy have any gravitational effect on the galaxy.

Sorry for the misunderstanding. I was kidding. Such headlines, I guess, are just click baits. Thought about it because the thread topic mentions impressing scientists. I don't enjoy claiming that scientists are easily shocked but rather enjoy making fun of popular science reports.

Evidently, scientists are easily shocked: Scientists Shocked by Discovery of Enormous, Healthy Coral (futurism.com) Climate scientists shocked by scale of floods in Germany | Flooding | The Guardian Scientists 'shocked' by high levels of microplastic pollution in London's Thames (nbcnews.com) Scientists shocked by Arctic permafrost thawing 70 years sooner than predicted | Climate crisis | The Guardian Scientists shocked by mysterious deaths of ancient trees - BBC News Scientists shocked to discover how much lightning may clean the atmosphere | CBC Radio Scientists Shocked By Rare, Giant Sunfish Washed Up On California Beach : NPR Italian scientists shocked by earthquake devastation | Nature Scientists ‘shocked’ to find life in extreme depths under Antarctic ice - National | Globalnews.ca Scientists 'shocked' after second coral bleaching at Great Barrier Reef in two years - CNN ... the list goes on and on.

A friend has sent this question to me. I have it solved with linear algebra (and some hand waving). Can you find a shorter way to the answer? (It's not a homework, not mine anyway. My homework times long gone.) A gardener collected 17 apples. He finds that each time he removes an apple from his harvest, he can share the remaining fruit in two piles of equal weight, each containing 8 apples. Show that all apples are the same weight.

No, position and time are described by real numbers in QM.

It is true. For observer 1, a particle P is at rest and a particle Q accelerates toward it. For observer 2, Q is at rest and P accelerates toward it. Susskind answers exactly this question in the lecture that I've linked in the post above yours.

An easy derivation, with answers to the audience's questions relevant to the above discussion, can be found here, starting about 30 minutes into the lecture:

The center is just an origin of coordinates. Of course, the premise is homogeneity and isotropy of the entire space. For any coordinate system, a particle in its origin does not move anywhere, but all other particles accelerate toward it. The same as in the Hubble expansion.

Each particle is attracted equally from all directions, and these will cancel indeed. But, each particle attracts all other particles and they will all accelerate toward it. This is so for all particles and thus all particles accelerate toward each other. So, the entire thing homogenously and isotropically contracts, or slows its expansion. For a bit more precise treatment, take any particle as a center and consider particles on a sphere of radius R around it. Each particle on the sphere, according to the old Newton's theorem that holds in GR as well, is attracted to the center as if the mass of the entire ball of radius R is in the center, and effect of each larger sphere on it is 0. This holds for any point picked as a center. The fully precise result in GR follows from increasing mass density in Friedman equation.

Yes, it would cause a net gravitational attraction and that would cause slowing of the universe expansion.

Not proved, according to this: "In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero-point energies of quantum fields are “real.” On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents. … I have presented an argument that the experimental confirmation of the Casimir effect does not establish the reality of zero-point fluctuations. Casimir forces can be calculated without reference to the vacuum ... . The vacuum-to-vacuum graphs (See Fig. 1) that define the zero-point energy do not enter the calculation of the Casimir force, which instead only involves graphs with external lines. So the concept of zero-point fluctuations is a heuristic and calculational aid in the description of the Casimir effect, but not a necessity." Casimir effect and the quantum vacuum R. L. Jaffe Phys. Rev. D 72, 021301(R) – Published 12 July 2005

If there were much more of it around, it would affect the cosmological expansion. Perhaps it could be detected this way.