Question about Basics of Gravity

[Mordred]

27 minutes ago, Markus Hanke said:

 

it's just that in all likelihood this would not be described by a quantum field theory. I think such a unification of forces will require us to let go of the notion of a smooth and continuous spacetime, which renders the concept of a QFT meaningless.

One quantum field theory I keep an eye in the hopes of a gravitational quantum field theory is quantum geometrodynamics. I find many of the methods of the theory promising but much like LQG has the same issues with gravity to address. 

 Granted it also has some of the same methodologies to LQG.

It's also likely one of the reasons I enjoy studying it is its a canonical field theory which I typically prefer over the conformal methods

Edited May 12, 2023 by Mordred

[Markus Hanke]

23 hours ago, Mordred said:

One quantum field theory I keep an eye in the hopes of a gravitational quantum field theory is quantum geometrodynamics.

QGD is conceptually similar to LQG (one might argue that the latter is a specific example of the more general former), but I would not consider it to be a quantum field theory in the ordinary sense since it does not involve quantised operator-valued fields on a fixed spacetime background. 

Nonetheless, I agree that this general approach to things - ie some form of quantisation of geometry itself - is probably the most promising when it comes to quantum gravity candidates.

[Mordred]

6 hours ago, Markus Hanke said:

QGD is conceptually similar to LQG (one might argue that the latter is a specific example 

Nonetheless, I agree that this general approach to things - ie some form of quantisation of geometry itself - is probably the most promising when it comes to quantum gravity candidates.

I agree, I too feel that's likely the most possible method at least as far as I have come across.

[crowman]

On 5/12/2023 at 5:29 AM, Markus Hanke said:

It's not that GR modifies the background, it's that it does not have any background. It's a fully background-independent theory - in contrast to the other interactions.

Would a roundabout way of saying that be, there is no absolute spacetime and so no frame is special?

Hence, no background dependency when it comes to spacetime.

That’s how I’m making sense of it.

Something to do with the field equations being in two parts, the movements of mass / energy dictates the spacetime geometry and vice versa?

[Genady]

3 hours ago, crowman said:

Something to do with the field equations being in two parts, the movements of mass / energy dictates the spacetime geometry and vice versa?

It sounds as if one could calculate the movement of mass / energy, and then use it to calculate the spacetime geometry. But I don't think it is generally possible. The movement of mass / energy depends on the spacetime geometry, and one cannot calculate the former without the latter. 

I think that the equality between Einstein tensor and stress-energy tensor dictates the spacetime geometry, i.e., the spacetime geometry is dictated by the equation rather than by its parts. IOW, the spacetime geometry is such that it makes these two parts equal.

[Markus Hanke]

11 hours ago, crowman said:

Would a roundabout way of saying that be, there is no absolute spacetime and so no frame is special?

Well, that’s part of it. But basically what it means is that spacetime does not exist in anything else - it’s not embedded in some kind of higher-dimensional space (=background), and the curvature that forms its geometry isn’t of the extrinsic kind, in the same way that a cylinder is extrinsically curved. IOW, nowhere in the theory is there any reference to anything that isn’t spacetime. 

This is in contrast to the Standard Model, which assumes a background spacetime - and a specific one at that - on which its fields live. You simply can’t have a quantum field without a background on which it lives.

11 hours ago, crowman said:

Something to do with the field equations being in two parts, the movements of mass / energy dictates the spacetime geometry and vice versa?

As Genady pointed out above, there are no distinct parts - a specific aspect of energy-momentum simply equals a specific aspect of spacetime geometry, up to a proportionality constant. Of course, when you are dealing with a specific scenario you can run things both ways - ordinarily you start with a distribution of energy-momentum, and calculate curvature from that. But because these are equivalent, you can do it the other way around as well - if you are given a specific geometry, you can calculate in what general way energy-momentum has to be distributed in such a spacetime.

What’s important to remember is that the field equations are only a local constraint - they do not themselves uniquely determine geometry/energy-momentum, but merely constrain what forms these can take. To fix a unique spacetime, you need to also supply the right number and kind of initial and boundary conditions; physically these conditions usually describe the distribution of distant sources (as opposed to local ones given by the energy-momentum tensor), as well as overall symmetries of the spacetime.

Another important point is that even if the local geometry of a spacetime is uniquely determined, the Einstein equations place no constraint onto its global topology, so many solutions are topologically ambiguous.

[crowman]

On 5/16/2023 at 10:09 PM, Genady said:

I think that the equality between Einstein tensor and stress-energy tensor dictates the spacetime geometry, i.e., the spacetime geometry is dictated by the equation rather than by its parts. IOW, the spacetime geometry is such that it makes these two parts equal.

Thanks Genady, I think that’s makes it a bit more clearer for me. IOW, It’s not a leap-frog situation with one part then the other part and so on.

On 5/17/2023 at 5:53 AM, Markus Hanke said:

 To fix a unique spacetime, you need to also supply the right number and kind of initial and boundary conditions; physically these conditions usually describe the distribution of distant sources (as opposed to local ones given by the energy-momentum tensor), as well as overall symmetries of the spacetime.

 

Thank you Markus. So, that would be like ending up with the spacetime geometry around a central symmetrical mass (sphere) Schwarzschild model.

[tylers100]

I have some questions that I'm curious about before moving on:

Q: If making objects with less dense mass property alongside with perhaps a change in direction, would these be able to lift or float up (e.g. artificial anti-gravity)?

Q: If making objects with greater dense mass property alongside with a change or more concentrated direction, would these able to ground astronauts on a floor in spacecraft or space station (e.g. artificial gravity)?

Edited March 11 by tylers100

[Genady]

3 hours ago, tylers100 said:

I have some questions that I'm curious about before moving on:

Q: If making objects with less dense mass property alongside with perhaps a change in direction, would these be able to lift or float up (e.g. artificial anti-gravity)?

Q: If making objects with greater dense mass property alongside with a change or more concentrated direction, would these able to ground astronauts on a floor in spacecraft or space station (e.g. artificial gravity)?

The law of gravity is known. Try to answer your questions by applying it.

[swansont]

4 hours ago, tylers100 said:

I have some questions that I'm curious about before moving on:

Q: If making objects with less dense mass property alongside with perhaps a change in direction, would these be able to lift or float up (e.g. artificial anti-gravity)?

Q: If making objects with greater dense mass property alongside with a change or more concentrated direction, would these able to ground astronauts on a floor in spacecraft or space station (e.g. artificial gravity)?

Newtonian gravity depends on mass, and distance from that mass. There is no antigravity. “Artificial” gravity is some other force (i.e. it’s not mass attracting mass)

[tylers100]

21 hours ago, Genady said:

The law of gravity is known. Try to answer your questions by applying it.

Yeah. But the questions I brought up, are specific to see if making an object to behave differently under a condition. (e.g. trying to apply a concept or approach that is different from ordinary or convenient approach).

20 hours ago, swansont said:

Newtonian gravity depends on mass, and distance from that mass. There is no antigravity. “Artificial” gravity is some other force (i.e. it’s not mass attracting mass)

Anti-Gravity

I understand a bit; no anti-gravity but isn't sunlight, heat, or fire technically are "anti-gravity" because these go in opposite direction away from "downward" direction of gravity for some time?

Artificial Gravity

Okay, that clarifies what exactly artificial gravity is.

Questions

I am beginning to further understand my own questions a bit more; basically an augmentation.

[swansont]

1 hour ago, tylers100 said:

understand a bit; no anti-gravity but isn't sunlight, heat, or fire technically are "anti-gravity" because these go in opposite direction away from "downward" direction of gravity for some time?

Forces can oppose gravity - forces are vectors - but as they are not forms of gravity they can’t be antigravity. Gravity is an attractive force. Full stop.

[tylers100]

9 minutes ago, swansont said:

Forces can oppose gravity - forces are vectors - but as they are not forms of gravity they can’t be antigravity. Gravity is an attractive force. Full stop.

Okay, thanks for answering.

[Genady]

1 hour ago, tylers100 said:

But the questions I brought up, are specific to see if making an object to behave differently under a condition. (e.g. trying to apply a concept or approach that is different from ordinary or convenient approach).

How your questions are different from ordinary or conventional approach to behavior of objects under gravity?

[tylers100]

6 hours ago, Genady said:

How your questions are different from ordinary or conventional approach to behavior of objects under gravity?

Augmentation and a change in direction function.

Since I answered augmentation is what close to what questions are about. Making an object heavier (dense geometry or augmented, hypothetically grounding astronauts on a floor). I thought that and then a change in direction in particular in order to produce an artificial anti-gravity (launching spacecraft more easily).

Augmentation would be good for grounding astronauts on floor in spacecraft or space station.

Changing direction would be good for launching spacecraft. But in practical, I don't know if it can be accomplished. It is like trying to produce an object such as ball and expect it to fly upwardly up in air indirectly defying physics laws..? It would be still retain its weight load but its motion direction is changed (it would still structurally and functionally within or obeying physics law, just going in a different direction).

[falkor1995]

im very curious about how time symmetry plays a role in gravity since mass bends light........

[Mordred]

Time symmetry doesn't bend light nor does time. Time is just a property of a state/object etc that describes a rate of change. Spacetime however is a geometric mathematical process that uses the interval (ct). This gives dimensionality equivalence of length via a vector. It is the interactions of the particle fields via its energy/mass density relations that curves spacetime. For example spacetime without particles to generate a mass term has zero curvature.

Gravity under GR is a pseudo-force that results from that spacetime curvature.

Hope that helps

[Markus Hanke]

9 hours ago, Mordred said:

For example spacetime without particles to generate a mass term has zero curvature.

Careful here - the field equations emit many vacuum solutions without the presence of particles. For example, the standard Schwarzschild solution represents a spacetime that is everywhere vacuum (T=0 at all points), yet not flat.

In general terms, the EFE states a local (!) equivalence between the Ricci tensor and a source term - but a vanishing Ricci tensor does not necessarily imply a flat manifold.

[Mordred]

point taken in so far as the Schwartzchild is a static spherically symmetric mass solution lol setting static in terms of the stress tenser though may be a bit too high level for the discussion. As static also requires the metric to not depend on time and its pressure and energy/density terms must also only depend on radius using curvilinear coordinates

 

Edited April 4 by Mordred

[Markus Hanke]

23 hours ago, Mordred said:

point taken in so far as the Schwartzchild is a static spherically symmetric mass solution lol

I was referring to the exterior metric, which has T=0 everywhere. The main point I am trying to make is that the EFE is a purely local constraint on the metric - but one must also account for sources that are distant in space and/or time, which happens via boundary conditions when solving the equations. To put it differently, the metric isn’t in general determined solely by local energy-momentum alone, but also by distant sources (and cosmological constant).

[Mordred]

Agreed, on that I tend to think more on global distributions lol which makes sense as that's my field as a cosmologist lol so oft forget to recall some of the metrics of localized spacetimes when replying to threads

[Markus Hanke]

On 4/5/2024 at 6:53 AM, Mordred said:

Agreed, on that I tend to think more on global distributions lol

I understand

Just as a side remark though, it is interesting to note that the EFE also admits cosmological vacuum solutions. An example is the Kasner metric; this kind of universe is completely empty (no energy-momentum and no cosmological constant), yet still not Riemann-flat in general, and metrically expands in an anisotropic manner. One can contrast this against the case of FLRW, and finds that it is precisely the presence of matter/radiation that enables an isotropic expansion.

Obviously this is purely academic, but nonetheless instructive.

[Mordred]

Not too familiar with the Kasner metric I will have to look into that one. Lol it will give me something new to study do thanks for that. Though I have run into a few papers on it. Hadn't put a lot of time studying it 

Edited April 7 by Mordred