6 ms·

I didn’t read the article yet but yesterday I was wondering about something: does gravity (the bending of space) bends the electromagnetic field? I guess they (

I didn’t read the article yet but yesterday I was wondering about something: does gravity (the bending of space) bends the electromagnetic field? I guess they (spacetime and electromagnetic fields) are two independent fields but maybe they influence each other ? Edit: maybe because these two forces have very different magnitude it is not possible to measure it

AnotherGoodName 5y ago
Everything obeys the curvature of spacetime. We'd be breaking the speed of light and thus breaking causality if certain fields didn't have to obey the curvature of spacetime that gravity causes. In fact gravity is even self-interacting with itself. ie. Gravitational fields themselves influence the propagation of gravitational fields. If this wasn't the case we'd observe gravitational waves from distance objects earlier than the speed of light. Which would be a problem for all our current models of physics if true.
- tzs 5y ago
  When do gravitational waves actually arrive from distant objects relative to light from those objects? Generally the space between us and distant objects isn't actually a perfect vacuum. It should have an index of refraction greater than 1, and it should vary by frequency. Light from a distant object should arrive here spread out in time by frequency, and the earliest should arrive a little later than something moving at the speed of light would arrive. Is there something like the index of refraction for gravity waves? If not then we should see gravity waves from an event before we see any light from the event. If there is, then it should be possible for gravity waves to arrive before, at the same time, or after light from the same event depending on the frequency of the gravity wave and the light.
  - gizmo686 5y ago
    Depending on frequency, the vaccumum of space is close enough to a vaccum. If the light needs to travel through something opaque, you generally just don't see it (although it may illuminate the dust) We have measured the relative speed of gravity and light. The difference is constrained to be no more that about 10^-15 times the speed of light. This us based on a signal that travelled 130 million light years. https://en.m.wikipedia.org/wiki/GW170817 https://en.m.wikipedia.org/wiki/GW170817
  - AnotherGoodName 5y ago
    Every experiment so far has detected gravitational waves a tiny bit before they detected light based evidence. Consistent with the light being slowed by the refraction in that very small amount of matter that exists in the interstellar medium and gravity passing through that dust more or less unaffected. Of course going faster than light which is being slowed by absorption and re-emission isn't the same as breaking the speed of light since light itself is going slower than the speed of light in this case. So yes you're right that it isn't exactly the same arrival time but we're not talking about curvature differences here, we're talking about physical interactions that the light undergoes that gravity doesn't.
    - piyh 5y ago
      We need to replace faster than light with faster than gravity
      - spsoto 5y ago
        I don’t have a physics background but I’ve always seen “c” as the speed of causality. The light happens to go at that speed in the absence of gravitational disturbances. Gravity and others fields should also move at this maximum speed. That said, I’m still trying to come to terms with the fact that breaking this speed limit just means that causality would be potentially broken. Isn’t that just something we axiomatically believed based on experience and we just haven’t observed otherwise?
        Twisol 5y ago
        My (mostly layperson's) understanding is that our laws of physics demand that causality would be broken; it's not taken as an axiom. Because of how the three dimensions of space and one dimension of time are put together, you can think of there being a balance or trade between motion in space and motion in time. If you aren't moving in space, you're moving through time at the maximum possible "rate". The more rapidly you move through space, the slower you move through time. This trade bottoms out at "c", at which point you're not moving through time at all. (Since motion is impossible without time passing, "c" itself is unachievable; you can only approach it asymptotically. Something about massless particles makes "motion" not a thing in the first place, I think, meaning they can actually propagate at exactly "c" as seen by an observer.) You can visualize this as a dial on an X-Y graph which starts out pointing in the Y direction, and as you speed up, it turns more toward the X direction. When you're pointing completely in the X direction, you're moving "at the speed of light", purely in space and not at all through time. If you turn the dial even further, you're trading some of that speed back for motion in time... but in the opposite direction. Of course, this is all super-handwavey; most importantly, velocity has to be measured relative to an observer, so all of this about rates has to be anchored relative to an observer. (But this is also precisely why massless particles propagate at the same rate regardless of observer -- insert timey-wimey Doctor Who reference.) Greg Egan has a lovely trilogy, Orthogonal, set in a universe where space and time don't have this trade (formally, the sign on the time variable in some critical equation is flipped to match the spatial dimensions). He has some great material on the exact physics of such a world. [0] [0] https://www.gregegan.net/ORTHOGONAL/00/PM.html https://www.gregegan.net/ORTHOGONAL/00/PM.html
  - wlesieutre 5y ago
    https://arxiv.org/abs/1710.05833 https://arxiv.org/abs/1710.05833 > On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ∼1.7 s with respect to the merger time. So there is a delay between arrival of gravitational waves and accompanying gamma ray burst, but I couldn't tell you if that's purely because light travels slower than it would in a perfect vacuum, because the gravitational waves are generated before the gamma ray burst, or a bit of both. The GRB being less than two seconds long, I would guess they both happened at close to the same time, and it does have a speed difference. Coming from an object 130 million light years away, 1.7 seconds is a very small difference in speed.
- goatlover 5y ago
  How does this work with whatever (dark energy?) caused Inflation?
  - AnotherGoodName 5y ago
    Again everything obeys it. If there was something that didn't obey fundamental changes to spacetime itself we'd observe things like gravitational waves in a completely different location and time to their visual counterparts. We do not see any evidence of this. So for any theory that states a change in the fabric of spacetime itself you can guarantee that everything must conform to that change.
- raattgift 5y ago
  LIGO, Virgo, and other gravitational wave observatory collaborations forthcoming in our solar system are expected to see the gravitational wave component of a https://en.wikipedia.org/wiki/Multi-messenger_astronomy https://en.wikipedia.org/wiki/Multi-messenger_astronomy event precede that event's electromagnetic (gamma rays, light, radio waves) component. Why? Both the electromagnetic wave and the gravitational wave obey the massless wave equation, for which there is the free parameter "c". This parameter is the wave's propagation speed in vacuum. But electromagnetism couples much more strongly with interstellar and intergalactic gas and dust than gravitation does, so such intervening media slows the electromagnetic wave compared the gravitational one. This is a handy feature, since when a high-redshift candidate event is detected by LIGO or Virgo, various telescopes can search the inferred location on the sky, looking for a trailing component. A neutron star-black hole merger, for instance, will have a such a component. So will a star falling apart in proximity to a black hole (a "tidal disruption event"). The spread for closer events isn't so big: detection of the LIGO/VIRGO G298048 (sourced about 140 million light years away, so very low redshift) event's gamma rays trailed by about about 1.7 seconds after the gravitational waves. We can draw a direct comparison with neutrinos. Although they are not massless, and thus obey a different wave equation, they are very very very light, so we in multi-messenger astronomy we can treat them as if they effectively move at the speed of light. (In fact, supernova multi-messenger astronomy is a strong constraint on the difference between the speed of light and the speed of neutrinos). Neutrinos also couple with gas and dust very very weakly, and so a neutrino signal and a gravitational wave signal will arrive at nearly the same time, with the electromagnetic components arriving later. > ... curvature ... curvature of spacetime ... Gravitational fields themselves influence the propagation of gravitational fields While you're right that different solutions of the Einstein Field Equations of General Relativity do not superpose linearly (around a Schwarzschild black hole, a very low-mass particle behaves very differently from a one with enough mass to have a gravitational self-force: https://arxiv.org/abs/0902.0573 https://arxiv.org/abs/0902.0573 for gory details) it's probably easy to be misled by mixing a field view of General Relativity ("GR") with a geometry ("curvature") view. We can take an effective field theory view of GR and say that there is some chosen background (e.g. Minkowski spacetime) that is perturbed by a non-rotating point mass, the combination of the two (Minkowski + perturbation) generates the Schwarzschild spacetime. We can then add another mass, a second perturbation, and see what the combination of three (Minkowski + perturbation_1 + perturbation_2) does. This is the approach of https://en.wikipedia.org/wiki/Post-Newtonian_expansion https://en.wikipedia.org/wiki/Post-Newtonian_expansion and as can be seen in the diagram on that page, it is only valid when the two masses are fairly far apart. It is hard not to think of the perturbations as fields in the sense that you seem to be thinking about. Unfortunately this has its limits. As you bring the masses closer together (increasing compactness, moving downwards on the Y axis in the diagram), obviously wrong predictions tend to creep in, destroying one's confidence in the idea that in a system with multiple gravitating masses, each generates its own independent gravitational field which can somehow be combined (or which somehow propagate through some background). In the most popular General Relativity reference book, Misner, Thorne & Wheeler's Gravitation, the authors discuss the expression "prior geometry", meaning some aspect of the curvature which is externally fixed or non-dynamical. General Relativity is a theory with "no prior geometry", and they make a brief argument about this. While some decades later we are much better with post-Newtonian expansion approaches (which do fix a prior geometry, which is then studied using perturbation methods), and can ignore "no prior geometry" as much more than a slogan in many cases, unfortunately we cannot do so for all of them. For highly relativistic problems (objects moving near c; "escape velocities" near c), one must resort to the full theory of General Relativity, either solving the exact form, a good approximation (see https://pos.sissa.it/081/015/pdf https://pos.sissa.it/081/015/pdf), or a numerical solution where neither of the previous two forms are known or to "hide" divergences in analytical approaches. Additionally, for speculative modelling of highly relativistic systems we may wish to require that the model enjoy the manifest https://en.wikipedia.org/wiki/Background_independence https://en.wikipedia.org/wiki/Background_independence of the full theory of General Relativity, which in a practical sense means that all possible observers will agree on the point-coincidences of the system independent of the choice of observer's system of coordinates or relative motion (object "A" and object "B" are in contact at the same point in spacetime for all observers; you don't have fast-moving observers calculate them never to have been in contact; you don't have rotating observers calculating them as never-in-contact; you don't have observers in deep space disagreeing with planet-bound observers about whether "A" and "B" come into contact, etc). Approximations instead fix some aspect(s) into a background, and in some strongly relativistic systems, one may have to introduce counter-terms ("ghosts") for families of observers that are not ideal Eulerian observers within that background. (Einstein has a good argument about this in Chapter XXXII ("The Structure of Space According to the Theory of General Relativity") in his 1934 book, https://www.ibiblio.org/ebooks/Einstein/Einstein_Relativity.pdf https://www.ibiblio.org/ebooks/Einstein/Einstein_Relativity.... whose "not-even-quasi-Euclidean" argument is extended in Appendix 4 and accompanied by a further fourteen pages as Appendix Chapter 5 ("Relativity and the Problem of Space") in the (not-as-freely-available) 2nd edition https://doi.org/10.4324/9780203518922 https://doi.org/10.4324/9780203518922 )
- z3t4 5y ago
  What if we had an object massive enough that gravity could not escape? Would it become weightless?
  - astrange 5y ago
    You can't construct such an object. An already-existing black hole might be one, but one that gets created in the universe never actually completes from the perspective of someone outside it, because its time slows down infinitely. … or something like that.
sega_sai 5y ago
Yes it does. Because the light bending by the Sun (predicted and measured in early 20th century) is bending of electromagnetic waves.
- jpgvm 5y ago
  Specifically this phenomena is called gravitational lensing and it's incredibly cool.
  - herlitzj 5y ago
    Yep. Predicted by Einstein in 1912 https://en.wikipedia.org/wiki/Einstein_ring https://en.wikipedia.org/wiki/Einstein_ring
- javajosh 5y ago
  It does but in the same way it's true that Jupiter's gravity affects you, personally. For all practical purposes GR has no effect on our planet, fun observations of Mercury's perihelion and GPS signal-beaming satellites aside. GR matters a tiny little bit for certain specialized engineering problems like doing precise inter-planetary transits. It matters a bit more for long-term position prediction of highly eccentric bodies, and really only starts to really matter at the cosmological scale. It's a matter of perspective. Our Solar System's mass is 98% in the Sun. Earth is tiny and small and, as a GR object, is moving very slowly, and that only according to how its particles were set in motion at the beginning of time. As others have said, gravitational lensing is a real thing, but that is a cosmological effect, and we are completely at the whim of the Initial Conditions for these opportunities. (If there are real engineering applications for GR, especially in optics, I would be delighted and grateful to learn more!)
  - raattgift 5y ago
    > If there are real engineering applications for GR, especially in optics Large-frame optical Sagnac gyroscopes for precision geodesy: https://www.frontiersin.org/articles/10.3389/fspas.2020.00049/full https://www.frontiersin.org/articles/10.3389/fspas.2020.0004... And some detail on the GINGER project, "Sagnac Effect, Ring Lasers, and Terrestrial Tests of [post-Newtonian] Gravity" (clarification mine), https://www.mdpi.com/2075-4434/3/2/84/htm https://www.mdpi.com/2075-4434/3/2/84/htm I imagine there is some literature on higher order modes in dispersion compensating fibre spools placed over underground flows (magma, water) but don't really have time to think about what decade practical engineering problems might emerge. Of possible interest to you, quoting preface of following: "These few words should make it clear that quantum optics, experimental gravitation and measurement theory are not nearly as far apart as one might first have thought. However, there has traditionally been little contact between physicists working in these various fields." (which is a little less true now because of e.g. LIGO) https://link.springer.com/book/10.1007%2F978-1-4613-3712-6 https://link.springer.com/book/10.1007%2F978-1-4613-3712-6 Next, I'm pretty sure that the emissions spectra of galactic magnetars (https://en.wikipedia.org/wiki/SGR_1935%2B2154 https://en.wikipedia.org/wiki/SGR_1935%2B2154 , one of Arecibo's last big detections, §2.1 of https://arxiv.org/abs/2103.06052v1 https://arxiv.org/abs/2103.06052v1 ) are far from the cosmological scale (see https://arxiv.org/abs/1507.02924 https://arxiv.org/abs/1507.02924 n.b. figure 24). > gravitational lensing ... is a cosmological effect Also pretty sure the Magellanic Clouds, other non-naked-eye Milky Way satellites, and some galactic targets aren't "cosmological", https://en.wikipedia.org/wiki/Gravitational_microlensing#Observing_microlensing https://en.wikipedia.org/wiki/Gravitational_microlensing#Obs... Finally, it strikes me as unfair to to invoke Initial Conditions as a way to discount the relevance of gravitational observations. What, if not Intial Conditions, determines the frequency of your HeNe laser? Where did the neon in particular come from? (spoiler: https://en.wikipedia.org/wiki/Neon#Occurrence https://en.wikipedia.org/wiki/Neon#Occurrence) And that helium is mostly a cosmological effect! ("The vast majority of helium was formed by Big Bang nucleosynthesis one to three minutes after the Big Bang. As such, measurements of its abundance contribute to cosmological models.")
tsimionescu 5y ago
A field is, by definition, a physical quantity in space and time. The key idea of GR is that gravity is the curvature of space time. The electromagnetic field is not bent, light for example always travels in perfect "straight lines" in the curbed space time created by mass/energy (more specifically, light always follows the shortest possible length of space-time between two points, which, in un-curved space-time is a straight line, but is a curved line if space-time is curved). Do note that current quantum field theories do not work in curved space-time, so this may turn out to be wrong in certain crucial ways.
- raattgift 5y ago
  > quantum field theories do not work in curved space-time In general curved spacetimes. But that includes a lot of obvious unphysicality. Modelling our universe, QFT in CS (the subject of textbooks, after all, like Birrell and Davies) works just fine away from strong curvature, all of which as far as we can tell is shrouded behind an event horizon or not-practically-observable in the very early universe. You don't have to take my word for it. See https://en.wikipedia.org/wiki/Robert_Wald https://en.wikipedia.org/wiki/Robert_Wald 's first three slides (after the title slide) at http://gravity.psu.edu/events/abhayfest/talks/Wald.pdf http://gravity.psu.edu/events/abhayfest/talks/Wald.pdf ) tl;dr: it is a fine effective theory, but not a good candidate for a fundamental theory. (Also in your first paragraph you are implicitly carving up spacetime in to space + time, and not taking that into account in what you write about "straight lines". However, you've got one part right namely (paraphrasing the start, up to the second comma, of your parenthetical) the spacetime interval of a null geodesic).
ninepoints 5y ago
Look up "gravitational lensing"

AnotherGoodName 5y ago

Everything obeys the curvature of spacetime. We'd be breaking the speed of light and thus breaking causality if certain fields didn't have to obey the curvature of spacetime that gravity causes. In fact gravity is even self-interacting with itself. ie. Gravitational fields themselves influence the propagation of gravitational fields. If this wasn't the case we'd observe gravitational waves from distance objects earlier than the speed of light. Which would be a problem for all our current models of physics if true.

tzs 5y ago
When do gravitational waves actually arrive from distant objects relative to light from those objects? Generally the space between us and distant objects isn't actually a perfect vacuum. It should have an index of refraction greater than 1, and it should vary by frequency. Light from a distant object should arrive here spread out in time by frequency, and the earliest should arrive a little later than something moving at the speed of light would arrive. Is there something like the index of refraction for gravity waves? If not then we should see gravity waves from an event before we see any light from the event. If there is, then it should be possible for gravity waves to arrive before, at the same time, or after light from the same event depending on the frequency of the gravity wave and the light.
- gizmo686 5y ago
  Depending on frequency, the vaccumum of space is close enough to a vaccum. If the light needs to travel through something opaque, you generally just don't see it (although it may illuminate the dust) We have measured the relative speed of gravity and light. The difference is constrained to be no more that about 10^-15 times the speed of light. This us based on a signal that travelled 130 million light years. https://en.m.wikipedia.org/wiki/GW170817 https://en.m.wikipedia.org/wiki/GW170817
- AnotherGoodName 5y ago
  Every experiment so far has detected gravitational waves a tiny bit before they detected light based evidence. Consistent with the light being slowed by the refraction in that very small amount of matter that exists in the interstellar medium and gravity passing through that dust more or less unaffected. Of course going faster than light which is being slowed by absorption and re-emission isn't the same as breaking the speed of light since light itself is going slower than the speed of light in this case. So yes you're right that it isn't exactly the same arrival time but we're not talking about curvature differences here, we're talking about physical interactions that the light undergoes that gravity doesn't.
  - piyh 5y ago
    We need to replace faster than light with faster than gravity
    - spsoto 5y ago
      I don’t have a physics background but I’ve always seen “c” as the speed of causality. The light happens to go at that speed in the absence of gravitational disturbances. Gravity and others fields should also move at this maximum speed. That said, I’m still trying to come to terms with the fact that breaking this speed limit just means that causality would be potentially broken. Isn’t that just something we axiomatically believed based on experience and we just haven’t observed otherwise?
      - Twisol 5y ago
        My (mostly layperson's) understanding is that our laws of physics demand that causality would be broken; it's not taken as an axiom. Because of how the three dimensions of space and one dimension of time are put together, you can think of there being a balance or trade between motion in space and motion in time. If you aren't moving in space, you're moving through time at the maximum possible "rate". The more rapidly you move through space, the slower you move through time. This trade bottoms out at "c", at which point you're not moving through time at all. (Since motion is impossible without time passing, "c" itself is unachievable; you can only approach it asymptotically. Something about massless particles makes "motion" not a thing in the first place, I think, meaning they can actually propagate at exactly "c" as seen by an observer.) You can visualize this as a dial on an X-Y graph which starts out pointing in the Y direction, and as you speed up, it turns more toward the X direction. When you're pointing completely in the X direction, you're moving "at the speed of light", purely in space and not at all through time. If you turn the dial even further, you're trading some of that speed back for motion in time... but in the opposite direction. Of course, this is all super-handwavey; most importantly, velocity has to be measured relative to an observer, so all of this about rates has to be anchored relative to an observer. (But this is also precisely why massless particles propagate at the same rate regardless of observer -- insert timey-wimey Doctor Who reference.) Greg Egan has a lovely trilogy, Orthogonal, set in a universe where space and time don't have this trade (formally, the sign on the time variable in some critical equation is flipped to match the spatial dimensions). He has some great material on the exact physics of such a world. [0] [0] https://www.gregegan.net/ORTHOGONAL/00/PM.html https://www.gregegan.net/ORTHOGONAL/00/PM.html
- wlesieutre 5y ago
  https://arxiv.org/abs/1710.05833 https://arxiv.org/abs/1710.05833 > On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ∼1.7 s with respect to the merger time. So there is a delay between arrival of gravitational waves and accompanying gamma ray burst, but I couldn't tell you if that's purely because light travels slower than it would in a perfect vacuum, because the gravitational waves are generated before the gamma ray burst, or a bit of both. The GRB being less than two seconds long, I would guess they both happened at close to the same time, and it does have a speed difference. Coming from an object 130 million light years away, 1.7 seconds is a very small difference in speed.
goatlover 5y ago
How does this work with whatever (dark energy?) caused Inflation?
- AnotherGoodName 5y ago
  Again everything obeys it. If there was something that didn't obey fundamental changes to spacetime itself we'd observe things like gravitational waves in a completely different location and time to their visual counterparts. We do not see any evidence of this. So for any theory that states a change in the fabric of spacetime itself you can guarantee that everything must conform to that change.
raattgift 5y ago
LIGO, Virgo, and other gravitational wave observatory collaborations forthcoming in our solar system are expected to see the gravitational wave component of a https://en.wikipedia.org/wiki/Multi-messenger_astronomy https://en.wikipedia.org/wiki/Multi-messenger_astronomy event precede that event's electromagnetic (gamma rays, light, radio waves) component. Why? Both the electromagnetic wave and the gravitational wave obey the massless wave equation, for which there is the free parameter "c". This parameter is the wave's propagation speed in vacuum. But electromagnetism couples much more strongly with interstellar and intergalactic gas and dust than gravitation does, so such intervening media slows the electromagnetic wave compared the gravitational one. This is a handy feature, since when a high-redshift candidate event is detected by LIGO or Virgo, various telescopes can search the inferred location on the sky, looking for a trailing component. A neutron star-black hole merger, for instance, will have a such a component. So will a star falling apart in proximity to a black hole (a "tidal disruption event"). The spread for closer events isn't so big: detection of the LIGO/VIRGO G298048 (sourced about 140 million light years away, so very low redshift) event's gamma rays trailed by about about 1.7 seconds after the gravitational waves. We can draw a direct comparison with neutrinos. Although they are not massless, and thus obey a different wave equation, they are very very very light, so we in multi-messenger astronomy we can treat them as if they effectively move at the speed of light. (In fact, supernova multi-messenger astronomy is a strong constraint on the difference between the speed of light and the speed of neutrinos). Neutrinos also couple with gas and dust very very weakly, and so a neutrino signal and a gravitational wave signal will arrive at nearly the same time, with the electromagnetic components arriving later. > ... curvature ... curvature of spacetime ... Gravitational fields themselves influence the propagation of gravitational fields While you're right that different solutions of the Einstein Field Equations of General Relativity do not superpose linearly (around a Schwarzschild black hole, a very low-mass particle behaves very differently from a one with enough mass to have a gravitational self-force: https://arxiv.org/abs/0902.0573 https://arxiv.org/abs/0902.0573 for gory details) it's probably easy to be misled by mixing a field view of General Relativity ("GR") with a geometry ("curvature") view. We can take an effective field theory view of GR and say that there is some chosen background (e.g. Minkowski spacetime) that is perturbed by a non-rotating point mass, the combination of the two (Minkowski + perturbation) generates the Schwarzschild spacetime. We can then add another mass, a second perturbation, and see what the combination of three (Minkowski + perturbation_1 + perturbation_2) does. This is the approach of https://en.wikipedia.org/wiki/Post-Newtonian_expansion https://en.wikipedia.org/wiki/Post-Newtonian_expansion and as can be seen in the diagram on that page, it is only valid when the two masses are fairly far apart. It is hard not to think of the perturbations as fields in the sense that you seem to be thinking about. Unfortunately this has its limits. As you bring the masses closer together (increasing compactness, moving downwards on the Y axis in the diagram), obviously wrong predictions tend to creep in, destroying one's confidence in the idea that in a system with multiple gravitating masses, each generates its own independent gravitational field which can somehow be combined (or which somehow propagate through some background). In the most popular General Relativity reference book, Misner, Thorne & Wheeler's Gravitation, the authors discuss the expression "prior geometry", meaning some aspect of the curvature which is externally fixed or non-dynamical. General Relativity is a theory with "no prior geometry", and they make a brief argument about this. While some decades later we are much better with post-Newtonian expansion approaches (which do fix a prior geometry, which is then studied using perturbation methods), and can ignore "no prior geometry" as much more than a slogan in many cases, unfortunately we cannot do so for all of them. For highly relativistic problems (objects moving near c; "escape velocities" near c), one must resort to the full theory of General Relativity, either solving the exact form, a good approximation (see https://pos.sissa.it/081/015/pdf https://pos.sissa.it/081/015/pdf), or a numerical solution where neither of the previous two forms are known or to "hide" divergences in analytical approaches. Additionally, for speculative modelling of highly relativistic systems we may wish to require that the model enjoy the manifest https://en.wikipedia.org/wiki/Background_independence https://en.wikipedia.org/wiki/Background_independence of the full theory of General Relativity, which in a practical sense means that all possible observers will agree on the point-coincidences of the system independent of the choice of observer's system of coordinates or relative motion (object "A" and object "B" are in contact at the same point in spacetime for all observers; you don't have fast-moving observers calculate them never to have been in contact; you don't have rotating observers calculating them as never-in-contact; you don't have observers in deep space disagreeing with planet-bound observers about whether "A" and "B" come into contact, etc). Approximations instead fix some aspect(s) into a background, and in some strongly relativistic systems, one may have to introduce counter-terms ("ghosts") for families of observers that are not ideal Eulerian observers within that background. (Einstein has a good argument about this in Chapter XXXII ("The Structure of Space According to the Theory of General Relativity") in his 1934 book, https://www.ibiblio.org/ebooks/Einstein/Einstein_Relativity.pdf https://www.ibiblio.org/ebooks/Einstein/Einstein_Relativity.... whose "not-even-quasi-Euclidean" argument is extended in Appendix 4 and accompanied by a further fourteen pages as Appendix Chapter 5 ("Relativity and the Problem of Space") in the (not-as-freely-available) 2nd edition https://doi.org/10.4324/9780203518922 https://doi.org/10.4324/9780203518922 )
z3t4 5y ago
What if we had an object massive enough that gravity could not escape? Would it become weightless?
- astrange 5y ago
  You can't construct such an object. An already-existing black hole might be one, but one that gets created in the universe never actually completes from the perspective of someone outside it, because its time slows down infinitely. … or something like that.

sega_sai 5y ago

Yes it does. Because the light bending by the Sun (predicted and measured in early 20th century) is bending of electromagnetic waves.

jpgvm 5y ago
Specifically this phenomena is called gravitational lensing and it's incredibly cool.
- herlitzj 5y ago
  Yep. Predicted by Einstein in 1912 https://en.wikipedia.org/wiki/Einstein_ring https://en.wikipedia.org/wiki/Einstein_ring
javajosh 5y ago
It does but in the same way it's true that Jupiter's gravity affects you, personally. For all practical purposes GR has no effect on our planet, fun observations of Mercury's perihelion and GPS signal-beaming satellites aside. GR matters a tiny little bit for certain specialized engineering problems like doing precise inter-planetary transits. It matters a bit more for long-term position prediction of highly eccentric bodies, and really only starts to really matter at the cosmological scale. It's a matter of perspective. Our Solar System's mass is 98% in the Sun. Earth is tiny and small and, as a GR object, is moving very slowly, and that only according to how its particles were set in motion at the beginning of time. As others have said, gravitational lensing is a real thing, but that is a cosmological effect, and we are completely at the whim of the Initial Conditions for these opportunities. (If there are real engineering applications for GR, especially in optics, I would be delighted and grateful to learn more!)
- raattgift 5y ago
  > If there are real engineering applications for GR, especially in optics Large-frame optical Sagnac gyroscopes for precision geodesy: https://www.frontiersin.org/articles/10.3389/fspas.2020.00049/full https://www.frontiersin.org/articles/10.3389/fspas.2020.0004... And some detail on the GINGER project, "Sagnac Effect, Ring Lasers, and Terrestrial Tests of [post-Newtonian] Gravity" (clarification mine), https://www.mdpi.com/2075-4434/3/2/84/htm https://www.mdpi.com/2075-4434/3/2/84/htm I imagine there is some literature on higher order modes in dispersion compensating fibre spools placed over underground flows (magma, water) but don't really have time to think about what decade practical engineering problems might emerge. Of possible interest to you, quoting preface of following: "These few words should make it clear that quantum optics, experimental gravitation and measurement theory are not nearly as far apart as one might first have thought. However, there has traditionally been little contact between physicists working in these various fields." (which is a little less true now because of e.g. LIGO) https://link.springer.com/book/10.1007%2F978-1-4613-3712-6 https://link.springer.com/book/10.1007%2F978-1-4613-3712-6 Next, I'm pretty sure that the emissions spectra of galactic magnetars (https://en.wikipedia.org/wiki/SGR_1935%2B2154 https://en.wikipedia.org/wiki/SGR_1935%2B2154 , one of Arecibo's last big detections, §2.1 of https://arxiv.org/abs/2103.06052v1 https://arxiv.org/abs/2103.06052v1 ) are far from the cosmological scale (see https://arxiv.org/abs/1507.02924 https://arxiv.org/abs/1507.02924 n.b. figure 24). > gravitational lensing ... is a cosmological effect Also pretty sure the Magellanic Clouds, other non-naked-eye Milky Way satellites, and some galactic targets aren't "cosmological", https://en.wikipedia.org/wiki/Gravitational_microlensing#Observing_microlensing https://en.wikipedia.org/wiki/Gravitational_microlensing#Obs... Finally, it strikes me as unfair to to invoke Initial Conditions as a way to discount the relevance of gravitational observations. What, if not Intial Conditions, determines the frequency of your HeNe laser? Where did the neon in particular come from? (spoiler: https://en.wikipedia.org/wiki/Neon#Occurrence https://en.wikipedia.org/wiki/Neon#Occurrence) And that helium is mostly a cosmological effect! ("The vast majority of helium was formed by Big Bang nucleosynthesis one to three minutes after the Big Bang. As such, measurements of its abundance contribute to cosmological models.")

tsimionescu 5y ago

A field is, by definition, a physical quantity in space and time. The key idea of GR is that gravity is the curvature of space time. The electromagnetic field is not bent, light for example always travels in perfect "straight lines" in the curbed space time created by mass/energy (more specifically, light always follows the shortest possible length of space-time between two points, which, in un-curved space-time is a straight line, but is a curved line if space-time is curved). Do note that current quantum field theories do not work in curved space-time, so this may turn out to be wrong in certain crucial ways.

raattgift 5y ago
> quantum field theories do not work in curved space-time In general curved spacetimes. But that includes a lot of obvious unphysicality. Modelling our universe, QFT in CS (the subject of textbooks, after all, like Birrell and Davies) works just fine away from strong curvature, all of which as far as we can tell is shrouded behind an event horizon or not-practically-observable in the very early universe. You don't have to take my word for it. See https://en.wikipedia.org/wiki/Robert_Wald https://en.wikipedia.org/wiki/Robert_Wald 's first three slides (after the title slide) at http://gravity.psu.edu/events/abhayfest/talks/Wald.pdf http://gravity.psu.edu/events/abhayfest/talks/Wald.pdf ) tl;dr: it is a fine effective theory, but not a good candidate for a fundamental theory. (Also in your first paragraph you are implicitly carving up spacetime in to space + time, and not taking that into account in what you write about "straight lines". However, you've got one part right namely (paraphrasing the start, up to the second comma, of your parenthetical) the spacetime interval of a null geodesic).

ninepoints 5y ago

Look up "gravitational lensing"