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Side note / question to real physicists: I am curious, for example, why general relativity does not break conservation of momentum in 3D, given that it seems li

Side note / question to real physicists: I am curious, for example, why general relativity does not break conservation of momentum in 3D, given that it seems like warped space time (to my lay perspective) violates 3D translational symmetry. For example, how do wormholes or the Alcubierre drive not violate conservation of momentum? Edit: Removed my own confused interpretation of the article’s confused interpretation and correction footnote.

auntienomen 7y ago
Energy and momentum are in general _not_ conserved in general relativity. This is a well-known feature of the theory, not a mistake made by the article's author. In field theories like GR, energy is generator of time translations. It's conserved if time translations leave the system invariant, but this only occurs in very special cases in general relativity (static spacetimes). So in general, in Gr, energy is not conserved. Same thing goes for momentum, which generates spatial translations.
- electrograv 7y ago
  Thank you! Another question on a tangentially related topic: Could you perhaps shed more light on why there so much pessimistic skepticism towards any claims of working reaction-less propulsion drives (violating conservation of momentum), for example? I understand the experience-based reasons for skepticism (since there have been many claims that don’t replicate), but why do there also seem to be so many physicists claiming with 100% confidence that no such thing could ever work, according to current physics theory? I’m referring for example to skepticism about things like “EMDrive” from a theoretical perspective (e.g. the posts from physicists here: https://www.reddit.com/r/EmDrive/ https://www.reddit.com/r/EmDrive/) as opposed to focusing on experimental failures to replicate.
  - auntienomen 7y ago
    I'm not an expert in these things. But my recollection is that the solutions of general relativity that behave like warp drives all violate various energy conditions and hence are only possible in the presence of what physicists politely refer to as "exotic matter". The Alcubierre drive, for example, requires matter with a negative energy density. We're reasonably certain that the class of quantum field theories we use to describe matter (QED, QCD, the Standard Model itself,..) are not compatible with these requirements.
  - cygx 7y ago
    why do there also seem to be so many physicists claiming with 100% confidence that no such thing could ever work Because it would violate conservation of momentum. Now wait a minute, you might think, haven't we just learned that such conservation laws don't hold in GR? It's more complicated than that. An analogy would be doing mechanics in a rotating reference frame. To make this work out, you have to account for things like centrifugal forces, with energy contributions that come 'out of nowhere' - as in, if you go to the non-rotating, inertial frame, they vanish: There's no real physical source providing that energy. Something similar happens in general relativity, where you can get conservation laws via Noether's second theorem even if your spacetime is not static (or rather stationary, to be pedantic). You will generally get a contribution from the gravitational field, which cannot be localized, but also - in contrast to the previous example - cannot be made to vanish because global inertial frames do not exist in general. One should perhaps also mention that reactionless motion supposedly is possible in classical physics: It's been claimed that a body can change its position without ejecting any propulsive mass through a series of deformations in an inhomogeneous gravitational field. There's a cute name for this, 'swimming in spacetime'.
- contravariant 7y ago
  That's only if you view the metric separate from the rest of the physics though, when you include it the resulting (classical) field theory is invariant under time translations (see Hilbert-Einstein equations). The fact that energy isn't conserved for a fixed metric is basically just what makes flybys capable of increasing the kinetic energy of a projectile.
deleted 7y ago
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auntienomen 7y ago

Energy and momentum are in general _not_ conserved in general relativity. This is a well-known feature of the theory, not a mistake made by the article's author. In field theories like GR, energy is generator of time translations. It's conserved if time translations leave the system invariant, but this only occurs in very special cases in general relativity (static spacetimes). So in general, in Gr, energy is not conserved. Same thing goes for momentum, which generates spatial translations.

electrograv 7y ago
Thank you! Another question on a tangentially related topic: Could you perhaps shed more light on why there so much pessimistic skepticism towards any claims of working reaction-less propulsion drives (violating conservation of momentum), for example? I understand the experience-based reasons for skepticism (since there have been many claims that don’t replicate), but why do there also seem to be so many physicists claiming with 100% confidence that no such thing could ever work, according to current physics theory? I’m referring for example to skepticism about things like “EMDrive” from a theoretical perspective (e.g. the posts from physicists here: https://www.reddit.com/r/EmDrive/ https://www.reddit.com/r/EmDrive/) as opposed to focusing on experimental failures to replicate.
- auntienomen 7y ago
  I'm not an expert in these things. But my recollection is that the solutions of general relativity that behave like warp drives all violate various energy conditions and hence are only possible in the presence of what physicists politely refer to as "exotic matter". The Alcubierre drive, for example, requires matter with a negative energy density. We're reasonably certain that the class of quantum field theories we use to describe matter (QED, QCD, the Standard Model itself,..) are not compatible with these requirements.
- cygx 7y ago
  why do there also seem to be so many physicists claiming with 100% confidence that no such thing could ever work Because it would violate conservation of momentum. Now wait a minute, you might think, haven't we just learned that such conservation laws don't hold in GR? It's more complicated than that. An analogy would be doing mechanics in a rotating reference frame. To make this work out, you have to account for things like centrifugal forces, with energy contributions that come 'out of nowhere' - as in, if you go to the non-rotating, inertial frame, they vanish: There's no real physical source providing that energy. Something similar happens in general relativity, where you can get conservation laws via Noether's second theorem even if your spacetime is not static (or rather stationary, to be pedantic). You will generally get a contribution from the gravitational field, which cannot be localized, but also - in contrast to the previous example - cannot be made to vanish because global inertial frames do not exist in general. One should perhaps also mention that reactionless motion supposedly is possible in classical physics: It's been claimed that a body can change its position without ejecting any propulsive mass through a series of deformations in an inhomogeneous gravitational field. There's a cute name for this, 'swimming in spacetime'.
contravariant 7y ago
That's only if you view the metric separate from the rest of the physics though, when you include it the resulting (classical) field theory is invariant under time translations (see Hilbert-Einstein equations). The fact that energy isn't conserved for a fixed metric is basically just what makes flybys capable of increasing the kinetic energy of a projectile.

deleted 7y ago

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