It's an article from 1962:

"After the detection of the gravitational wave GW170817, Jason T. Wright (Physics Today, 72, 5, 12, 2019) reminded the community that many of its features had been predicted by Dyson more than half a century earlier. Dyson’s article was published only once, in Cameron’s long out of print collection, though a scan may be found at the web site of the Gravity Research Foundation (https://www.gravityresearchfoundation.org). Dyson thought it had been reprinted (in his Selected Papers, AMS Press, 1996, forward by Elliot H. Lieb) but it was not. Hoping to make the article easier to find, I wrote Dyson for his permission to post it at the arXiv"

It's about using two big bodies, A and B, to accelerate objects: "The energy source of the machine is the gravitational potential between the stars A and B. As the machine continues to operate, the stars A and B will gradually be drawn closer together, their negative potential energy will increase and their orbital velocity V will also increase."

Nice idea.

I wonder if one could calculate an upper bound of the available potential gravitational energy available in the entire universe by estimating how far every massive point (baryon) is from all the others.

If space is expanding, does that also mean that gravitational potential energy is always increasing, too? I'd never thought of that before

No, it doesn't, because the concept of "gravitational potential energy" is not meaningful for an expanding universe considered as a whole. It's only meaningful for isolated systems within the universe.

Wouldn't there be meaning in saying it would take this much energy to push all the matter in the universe to one place?

Which that amount should be increasing as space-time expands.

Thought experiment, if you could place a mass of an arbitrary amount at any one point in space, how much mass would you need such that all the mass of the universe is now falling towards it.

Or could you bend space-time to a point that all mass falls into it.

Wouldn't there be meaning in saying it would take this much energy to push all the matter in the universe to one place?

No. The universe is not an isolated system that we can operate on from the outside. You can't treat it as though it is. So your thought experiments aren't meaningful.

Obviously the thought experiment requires energy that doesn't 'exist' or doesn't have meaning in the sense that it could happen literally. It's a what-if and that does have a number and that does have meaning.

So there is meaning to the previous persons question which is what the thought experiments were meant to show but obviously that's something you can't imagine.

Obviously the thought experiment requires energy that doesn't 'exist'

No, it requires energy to be added to the system from outside the system. Which is precisely what you cannot do with the universe as a whole. That's what makes such thought experiments meaningless for the universe as a whole.

How is your objection not a useless and unfalsifiable catch-all that applies to calculating any quantity over a volume?

Um, what? I can operate on an ordinary volume (say a beaker in my lab or a planet that I am in a distant orbit around) from the outside. I can't operate on the universe as a whole from the outside. How is this not an obvious difference?

Why is it not meaningful? "Isolated systems" seems meaningless - there is no objective cutoff where a gravitational system becomes "isolated", except perhaps in the sense of "non-intersecting light cones".

See my response to thx-2718 downthread, about having to add energy from outside the system.

I have read all of your comments and not one of them actually says anything concrete. It's the exact same vague objection repeated over and over again.

Please explain exactly why you think calculating the total gravitational potential energy of the entire universe or a well-defined sub-volume of it is intractable. Feel free to use arbitrarily technical mathematical or physics language, just please stop being vague.

It's not. Moreover, the total energy is actually being lost, as particles "lose" kinetic energy due to expansion (and the light is red-shifted).

If this seems to violate the law of energy conservation, you're spot on. It is indeed being violated.

This is not fundamentally problematic by itself, because the law of conservation of energy depends on time invariance. Which doesn't hold in the case of an expanding universe. But it is an unsatisfying copout, and we hope that it can be resolved by the quantum gravity.

Space in our universe has a vacuum energy and our expanding (actually, accelerating) universe is in fact gaining "dark" energy.

https://en.wikipedia.org/wiki/Dark_energy

Dyson was like George Gamow, protean in intellectual power and scope and imagination yet forever just outside the Nobel sphere.

Is that why he invented the Dyson Sphere?

Circular logic.

No, spherical logic.

I think you are being a bit Anglo-centered.

Georgiy Antonovich Gamov (Ukrainian: Георгій Антонович Гамов, Russian: Георгий Антонович Гамов) was born on March 4, 1904 in Odessa, Russian Empire (now Ukraine).

His father taught Russian language and literature in high school, and his mother taught geography and history at a school for girls. In addition to Russian, Gamow learned to speak some French from his mother and German from a tutor. Gamow learned English in his college years and became fluent. Most of his early publications were in German or Russian, but he later used English for both technical papers and for the lay audience.

He was educated at the Institute of Physics and Mathematics in Odessa[2] (1922–23) and at the University of Leningrad (1923–1929). Gamow studied under Alexander Friedmann in Leningrad, until Friedmann's early death in 1925, which required him to change dissertation advisors. At the university, Gamow made friends with three other students of theoretical physics, Lev Landau, Dmitri Ivanenko, and Matvey Bronshtein. The four formed a group they called the Three Musketeers, which met to discuss and analyze the ground-breaking papers on quantum mechanics published during those years. He later used the same phrase to describe the Alpher, Herman, and Gamow group.

Upon graduation, he worked on quantum theory in Göttingen, where his research into the atomic nucleus provided the basis for his doctorate. He then worked at the Theoretical Physics Institute of the University of Copenhagen from 1928 to 1931, with a break to work with Ernest Rutherford at the Cavendish Laboratory in Cambridge. He continued to study the atomic nucleus (proposing the "liquid drop" model), but also worked on stellar physics with Robert Atkinson and Fritz Houtermans.

In 1931, Gamow was elected a corresponding member of the Academy of Sciences of the USSR at age 28 – one of the youngest in its history. During the period 1931–1933, Gamow worked in the Physical Department of the Radium Institute (Leningrad) headed by Vitaly Khlopin [ru]. Europe's first cyclotron was designed under the guidance and direct participation of Igor Kurchatov, Lev Mysovskii and Gamow. In 1932, Gamow and Mysovskii submitted a draft design for consideration by the Academic Council of the Radium Institute, which approved it. The cyclotron was not completed until 1937.

Defection

Gamow worked at a number of Soviet establishments before deciding to flee the Soviet Union because of increased oppression. In 1931, he was officially denied permission to attend a scientific conference in Italy. Also in 1931, he married Lyubov Vokhmintseva (Russian: Любовь Вохминцева), another physicist in Soviet Union, whom he nicknamed "Rho" after the Greek letter. Gamow and his new wife spent much of the next two years trying to leave the Soviet Union, with or without official permission. Niels Bohr and other friends invited Gamow to visit during this period, but Gamow could not get permission to leave.

Gamow later said that his first two attempts to defect with his wife were in 1932 and involved trying to kayak: first a planned 250-kilometer paddle over the Black Sea to Turkey, and another attempt from Murmansk to Norway. Poor weather foiled both attempts, but they had not been noticed by the authorities.

In 1933, Gamow was suddenly granted permission to attend the 7th Solvay Conference on physics, in Brussels. He insisted on having his wife accompany him, even saying that he would not go alone. Eventually the Soviet authorities relented and issued passports for the couple. The two attended and arranged to extend their stay, with the help of Marie Curie and other physicists. Over the next year, Gamow obtained temporary work at the Curie Institute, University of London, and the University of Michigan.

https://en.wikipedia.org/wiki/George_Gamow

how exactly is energy extracted from such a system?

A large mass is dropped on the right trajectory between the two, the gravitational forces slingshot it back at higher velocity, which can be captured with some sort of electromagnetic regenerative braking mechanism. Just a toy idea for how energy can be extracted.

When a (perfect) ball is thrown at a (perfect) car, it will bounce off with the same velocity, v, but with its direction reversed. If the car is moving with some velocity -V, when the ball bounces off it will have a velocity -v - 2V, gaining an extra -2V. (This is easier to understand from the car's passenger's point of view, who will see the ball arriving with a relative velocity v + V and bouncing with -v - V, or -v - 2V relative to the ground).

In the ball-car collision the electromagnetic forces are the ones responsible for changing the direction of the ball. But in the binary system, it is gravity. In particular as the shuttle enters orbit around the "incoming" star, the star's gravity will pull it forward mostly when it completed half orbit.

I hope I make sense.

Overall, such a joy to read this paper. With basic physics it makes you dream of sci-fi...

EDIT: typos

In a similar vein, John Kraus (Of Antennas... textbook fame) described a gravitational transmitting and receiving system as a fun (?) diversion near the end of the book.

It has been a few years, but I seem to recall that the transmitter was a 500T steel bar spun at very close to the maximum RPM the tensile strength of steel allowed; the radiated energy was something like a fraction of an attowatt. (An attowatt = 1*10^-18W)

There are more efficient transmitting schemes out there.

It is kind of wild that we stumbled upon transmitting information via electromagnetic waves so early on. They seem to be hard to beat.

Fortunately for us we can see them.

Gravity waves are much harder to observe.

You can also argue that we can see them because they are stronger and are evolutionary important.

It makes sense that the easiest to implement would also be the easiest to learn. It's more shocking just how much harder every other option is.

What other options are there apart from mentioned gravity? I mean there are waves in materials like sound but that seem to be easier than EM.

Neutrinos, perhaps.

I always wondered how you might be able to extract energy from the expansion of space. It's particularly interesting because conservation of energy does not hold on such large scales.

It's particularly interesting because conservation of energy does not hold on such large scales.

IMHO, conservation of energy still applies, so Big Bang model is just wrong. Use Occam's razor when in doubt.

I'm not in doubt on this question. Please refer to https://www.preposterousuniverse.com/blog/2010/02/22/energy-... for a digestible piece on this topic.

Think about harpooning a galaxy at, say, 100 megaparsecs, with a long rope attached to the harpoon. In the Milky Way, loop the rope around the rotor of an electric generator. In the distant galaxy, have the harpoon-end of the rope fall into its central supermassive black hole. Ignoring proper motions (the black hole and the electric generator are likely to move within their host galaxies, and their host galaxies within their galaxy cluster), this gives one about 72 kilometres per second per megaparsec of linear speed on the rope as the space between us and the distant galaxy increases.

Of course, you need a lot of rope, for the rope to be indestructible (and ideally of low mass), for lucky aim when harpooning, and for the harpoon to be able to carry rope all the way to the target, and for the target and far end of the rope to be impossible to separate.

The more local model for this is to erect a scaffolding well above an object in hydrostatic equilibrium (so anything from a round planet to a supermassive black hole) and fix electric generators to the scaffolding, driven by ropes dropping onto the scaffold-surrounded object. There are a lot of physics questions that can be explored using that model; it's a good exercise in all of them. (Some coursework uses this setting to explore the dominant energy condition of general relativity, since that imposes a maximum tensile strength on non-exotic matter rope or wire or filament: there is a speed limit on the operation of intermolecular/interatomic binding forces; c.f. Bell's rope-spaceship "paradox" in special relativity.)

energy is not conserved

Carroll's point is that there is a generalization of conservation of energy in curved Lorentzian spacetimes, where changes in the motion of matter and changes in the spacetime geometry are exactly related. That applies in the harpoon-a-distant-galaxy model as well. The rope (and stresses within it) and power produced by the electric generator are all forms of moving matter, creating a geometrical change which (depending on the properties of the rope) may become non-negligible. A rope that is strong enough (and implicitly having much more mass per cm^3 than empty space) to connect two megaparsec+-separated galaxies (driving a generator at one end for appreciable time and feeding a black hole at the other for appreciable time) forces one into some calculating to answer the question: does the rope slow the metric expansion along its length?

Next, how do you get the generator to turn rather than be carried out of our galaxy? (We can sharpen this somewhat by dispensing with a generator, and throwing each end of our megaparsecs-long rope into a megaparsecs-separated galactic centre black hole. What happens if there is a large mass-ratio (heavy:light) between the black holes, or their surrounding galaxies? Does the lighter black hole get pulled out of its galaxy by the heavier? What happens as the mass ratio goes to 1?

Carroll's link above, showing \Nabla_{\mu}T^{\mu\nu} = 0 says that as long as we don't introduce further degrees of freedom we can calculate the equations of motion in the systems above. That is, it's fine for an expanding space with nonzero vacuum energy, and for that plus noninteracting (except by gravity) dusts. However, our very long rope cannot be non-interacting (it must be at least self-interacting) and its extra degrees of freedom are liable to become important under extreme tension (e.g., it might get hot and radiate a ~blackbody spectrum), so a somewhat different covariant equation would apply.

Said rope is part of the expanding Universe i.e. it also expands, just the right amount, doesn't it?

I think this idea is essentially an example of a "gravitational slingshot".

I found it interesting that such a system could be used to "accelerate delicate and fragile objects to a velocity of 2000 km/sec at an acceleration of 10,000 g, without doing any damage to the objects. ... So a large space ship with human passengers and normal mechanical construction could easily survive the 10,000 g acceleration." This seems counterintuitive, but since the object is in freefall the entire time, I guess it makes sense.

The 10,000g would be approximately uniform through the entire volume of the ship, so no damage. In a regular rocket, the acceleration would have to be transmitted to passengers and cargo through the normal force, and that would crush you.

Makes sense, though if you'd asked me before your explanation, I'd have thought the idea of accelerating at high speed without leaving free fall impossible.

Of course there are also more mundane ways of utilizing gravity such as Tidal and Hydroelectric power, or just walking (controlled falling) for that matter.