Is it possible that the speed of transfer of information increases to infinity as curvature of spacetime decreases to zero? I know Special Relativity says no. But how would we know for sure since all our measurements take place in the gravity well of our star, our galaxy, etc.? If the speed of information did approach Infinity in very flat spacetime (e.g. between galaxies), how would that change our current understanding of physics?
I believe the simple answer is:
Special Relativity is a special case of General Relativity. In particular it is that special case of General in flat space time. So assuming General Relativity is correct, then Special Relativity is correct and Special relativity says information can’t be transmitted faster than the speed of light.
If information could be transferred at ~ infinity, then GR would be wrong so we wouldn’t have a good theory with which to answer your question.
I was suggesting that GR is accurate describing curved spacetime, but do we know GR accurately describes very flat spacetime?
Relativity is a classical geometric theory of space and time and gravitation, not formulated in terms of “information”. In any case, ISTM that any reasonable definition of information, that is, measure of uncertainty, being transmitted should reduce to considerations of causality, so you are back to checking that two spacelike separated measurements do not depend on each other, or that an effect cannot precede its cause.
The observable universe is pretty flat, and gravitational theory has been tested by astronomers.
What does this have to do with information?
Why would one even think otherwise?
Yes, all of the observations we’ve ever made have been in curved space. But we’ve made observation in regions of space of very different curvature. If the speed of information varied with curvature in any sort of smooth way, then all of our calculations would be very badly off.
From the wiki page ‘Galaxy rotation curve’
“A significant discrepancy exists between the experimental curves observed, and a curve derived from theory. The theory of dark matter is currently postulated to account for the variance.[3]”.
If information from stars located near the edge of a galaxy arrived faster than information from stars closer to the center then wouldn’t it seem (if you assumed the speed of information is constant) that the outer stars are rotating faster than they actually are?
It sounds like you are referring not to “information” (what information are you talking about?) but to some modified theory of gravity, which people have toyed with to try to account for the orbital speeds of stars in galaxies. This possibility is mentioned in the article you linked to.
If you could send a signal (information) faster than c, it would go backwards in time, so a reply could arrive before the message was sent, violating causality. My question concerns the possibility that c could increase in very flat space. Earth is about half way between our galaxy’s core and the outer rim, so we can’t do direct experiments in very flat space. If c does increase in flat space, a message sent in flat space traveling much faster than we measure the speed of a photon locally (it exceeds our local c), wouldn’t exceed c in the local flat space or violate causality. If we assume c is constant and it’s actually not, our perception of the universe might be inaccurate and confusing.
We are in very flat space. It takes extremely precise measurements to be able to even detect the local curvature at all. And the propagation of information works the same way here as it does right next to black holes, where it’s not remotely flat at all, as evidenced by our observations of the gravitational waves from black hole mergers.
There it is: Our perception of the Universe is not confusing, and so it makes sense to assume that it’s accurate. If it worked like you suggest, then our perception of the Universe would be very confusing.
Step 1 before proposing a theory like this: Fully understand Special and General Relativity. And that doesn’t mean some dumbed-down pop-science version for the general public.
Without step 1 there is no step 2.
Pop-science is like the simplified explanations you give to small kids to explain things at their level.
Your theory is like a small kid coming up with a funny solution to a complex problem in the adult world. If you want anybody to take you seriously, you need to understand the adult version first.
How can we be in the gravity well of a galaxy and still be in very flat space? It takes extremely precise measurements to detect gravitational waves too.
We have to invoke ‘dark matter’ to explain galaxy rotation. Maybe GR is accurate until you reach the extremes; near a black hole c starts to decrease, and near intergalactic space it increases. Given our current level of science and technology, do we really know for sure c is a universal constant?
The earth is spherical. But for almost all daily purposes, we can take the surface of the earth in our vicinity to be a very flat area.
Galaxies are not that dense when you consider the whole thing. You only have to worry about significant curvature when up close and personal with something like a black hole.
Also note that (in relativity) the geometric “speed of light” that converts between length and time is a constant (which people measure), even though there are (predicted and observed) phenomena like light being deflected by gravity/spacetime curvature (ie “c” varying). GR predicts and quantifies this phenomenon- it is a triumph rather than a failure of the theory.
OK, what do you calculate the effects of this would be?
I did not mean to mislead anybody by implying that curvature of space-time can be treated as though it were exactly zero or not observed at all, it’s just that in most situations, even of light grazing the Sun, the field of gravity is “weak”.
If you could take good optical photographs of black holes and stars orbiting nearby it would make an excellent test of the theory of gravitation. Deviation from GR would result in observable effects.
Weather systems spin over the “very flat areas” on Earth and release release impressive amounts of energy in the process. You need a better analogy.
And as far as those weather systems are concerned, yes, those areas of the Earth are flat. Nothing wrong with the analogy.