# Negative Gravity and Spacetime: Does this align with known physics or is it inherently flawed?

This idea is based on a convoluted understanding on space-time. I posted the idea to r/scificoncepts, and it can be found here.

The principle I’m working with is how gravity affects time. Generally, the more gravity affecting the spacetime around you, the slower you perceive time (Such as in interstellar where every minute was a hundred years or something.)

If more gravity means you perceive time slower than the rest of the universe, it stands to reason that less gravity means you perceive time faster. Currently, you can reach around 0g (but not actually 0g) in the vacuum of space. There could be a workaround with the unknown force of dark energy. Seeing as dark energy counteracts gravity, it could be interpreted as negative gravity. Following the relationship of spacetime, the more negative gravity you have, the faster you will perceive time.

The second part of this space-time relationship is time. This part is more tenuous and is potentially a correlation doesn’t equal causation scenario. If you can affect time in any way then you can also affect space. If you condense a lot of time in a certain place (so time is perceived more quickly), then the gravity would decrease. If you slowed down time perception then the gravity would increase.

Is my thinking in any way correct or have I got the wrong end of the stick?

• (1) In your own frame of reference time always flows at one second per second. Always. (2) Spacetime is not made of space and time. It is a four-dimensional continuum. (3) In the model where gravitational fields affect the flow of time, gravitation is not a force. You cannot "counteract" it with anything, because it is not a force. (In that model, gravitation is a fictitious force corresponding with the difference between the local geometry of spacetime and Euclidean geometry.) (4) Please show your math from which you deduce that negative gravity would correspond to time contraction. Jun 11, 2021 at 14:05
• I think we have an issue with the tags and their compatibility with your question. hard-science, science-based, reality-check shouldn't be used together as they are from the strictest to the most relaxed of the tags covering the same requirements reality-check being the least strict, you should pick one not all three. science-fiction definitely seems the most appropriate for your question, so I've edited them. If I've misunderstood your intention, then please feel free to revert the edit. Jun 11, 2021 at 14:34
• @AlexP if the whole universe is "down" in a gravity well, and we call that position nearly "flat space", then anything "higher" would look like "negative gravity" where time runs relatively faster.
– BMF
Jun 11, 2021 at 14:54
• how am I supposed to help you world-build. this does not belong here unless you edit the question to be more like how would people use this quirk of physics, or a this is how I set up my world check my assumptions. It's interesting, don't get me wrong but where are you going with this? Jun 11, 2021 at 14:54
• @AlexP Are you saying that negative curvature can't be embedded in positive curvature? Space should be continuous from positive->flat->negative and back again. The real question is whether something like "negative gravity" is physically real. Negative energies can lead to FTL and causality problems.
– BMF
Jun 11, 2021 at 16:49

This idea is based on a convoluted understanding on space-time. I posted the idea to r/scificoncepts, and it can be found here.

The ideas (as to be determined when put into mathematical form) are either consistent with general relativity (the Einstein equations) and special relativity (speed of light invariance and inertial invariance) or they are not.

The principle I’m working with is how gravity affects time. Generally, the more gravity affecting the spacetime around you, the slower you perceive time (Such as in interstellar where every minute was a hundred years or something.)

This is not an accurate characterization of general relativity. Gravity in General relativity is not separate from space-time but a consequence of space-time geometry. The Einstein equations are complicated to compute for even the simplest of problems but the concept behind them is quite simple. In the most reduced form the Einstein equations can be expressed as (I removed the cosmological constant because it is not relevant to the discussion at hand and/or can be incorporated into the Einstein tensor):

$$G_{\mu\nu} = T_{\mu\nu}$$

The interpretation is simple: The spacetime geometry (as understood by defining how length is computed between any two points) is determined by the magnitude of the energy-density at any given point. Mass is just one component of energy-density, but becomes the most relevant when discussing things of extreme energy-density like black-holes.

The observed time (or the rate at which things proceed) must vary between different observers ensure that the laws of physics are equivalent in the different frames of reference and that this equation is always observed as accurate.

This is not a difficult concept to envision by analogy. For example take a napkin, lay it flat on a table and draw two points and a line connecting them. Now bend the napkin. When projected onto the table the line will now be shorter than on the napkin. If you move at a constant rate from one point to the other you will go a distance L in time T (v ~ L/T) in the napkin's frame. But in the table's frame you go a distance of $$l$$ in time t, since $$l$$ is shorter than L, you will measure a different v if t = T. But if the energy (which is dependent on velocity) must be observed to be the same, then t must not be equal to T. This is NOT what is going on in the Einstein equation: it is far more complicated, however this analogy illustrates the concept.

If more gravity means you perceive time slower than the rest of the universe, it stands to reason that less gravity means you perceive time faster. Currently, you can reach around 0g (but not actually 0g) in the vacuum of space. There could be a workaround with the unknown force of dark energy. Seeing as dark energy counteracts gravity, it could be interpreted as negative gravity. Following the relationship of spacetime, the more negative gravity you have, the faster you will perceive time.

This is based upon a naïve understanding of what is meant by gravity. As stated above, gravity is a consequence of space-time's relationship with energy. Taking away energy therefore leaves an absence of gravitational effects. If you envisioned another force which is opposite gravity (a negative mass perhaps). This negative mass would still add energy to a system, just like two negative charges still adds energy to a system even though they repel each other. To wit, if there existed a particle which repelled matter rather than attracted it, the energy-density would still be positive.

Again this concept can be illustrated by analogy. Darkness for instance is the absence of light. The Candela for instance is a measure of luminous intensity of light, but negative Candela's do not make any physical sense. We cannot have darker than darkness. Or the second, is a measure of time, but we cannot negative seconds. The equations which describe physical laws are just a short hand way of compactly and precisely defining the laws. Making elementary changes to these equations (like adding negative signs) rarely makes physical sense.

Now dark energy is a concept which appears in Cosmology. However dark energy, rather than subtracting from the total energy of the Universe, adds to it so as to account for the hyperinflation of space which cannot occur with only the currently observed amount energy.

The second part of this space-time relationship is time. This part is more tenuous and is potentially a correlation doesn’t equal causation scenario. If you can affect time in any way then you can also affect space. If you condense a lot of time in a certain place (so time is perceived more quickly), then the gravity would decrease. If you slowed down time perception then the gravity would increase.

Space is not separate from Time in General Relativity. Likewise Time is not separate from Space. Spacetime is determined by the distribution of energy; of which mass is a component. The relationship is a complex mathematical expression which cannot be characterized by saying "More gravity == expanded time, reduced time == less gravity". This is not a valid interpretation of the Einstein equations as I detailed above.

(EDIT)

I saw mentioned in the comments to the question the idea of simply choosing a spacetime curvature which could have the desired effect.

The issue here is violating the geodesic equation. Additionally and ultimately the consequence here is the violation of energy conservation. Energy, whether potential or kinetic represents the ability to move objects through space: the higher the energy the faster the motion through space (the higher the energy transferred -> the greater the force -> and the faster the object accelerates).

If an object had a property which produced a net negative energy density; this that would mean that this object would simply remove energy from the system. This clearly violates the conservation of energy.

Now I am aware of the idea of the Alcubierre drive, Quantum fluctuation..etc. This is very different however, since the Alcubierre drive produces a negative energy density, with a corresponding positive energy density elsewhere so the total energy change remains zero.

Additionally, negative energy densities in Casimir effect are only the effects of virtual particle interactions. Off-shell interactions are not interpreted as physical since they cannot be directly observed and are simply the result of the mathematics required to perform calculations in QFT. Simply put, net negative energy densities do not appear in on-shell calculations, nor is General Relativity compatible with QFT rendering conjecture of this nature immaterial.

• Can you elaborate a bit on the math behind your claim that negative energy density violates conservation of energy/the geodesic equation? The argument you gave in the edit seems a bit vague and like you could twist it around to also say that positive energy densities violate conservation of energy because they add energy to the system, which clearly isn't true-- the point of conservation of energy is that the total energy has to be constant, not that it's zero. Jun 12, 2021 at 15:35
• (cont) Also, total energy is a difficult concept to define in GR-- the local statement of energy conservation $\nabla_{\alpha}T^{\alpha \beta} = 0$ relies on the connection and thus choice of coordinates, so you have to be pretty careful what you're talking about when talking about conservation of energy in GR. The usual quantities we use often aren't globally conserved for this reason, and when you can find energy-like quantities that are globally conserved they're much less intuitive than your definition as the ability to move objects through space. Jun 12, 2021 at 15:38
• (cont) Finally, I'm pretty sure you can have negative mass/energy densities if we're talking about $T^{00}$ as our definition. For instance, the cosmological constant term $\Lambda g_{\alpha \beta}$ in the EFE looks exactly like the stress energy tensor for a perfect fluid with negative mass density $\rho = -\Lambda$ when taken in a comoving, inertial frame. All that being said, it's been a while since I studied GR so if you're able to address these points with more precise language it's definitely possible I'm wrong or misinterpreting you. Jun 12, 2021 at 15:46
• @elduderino Yes, I was trying to keep my post accessible. Certainly the conservation of energy is about net energy exchange. But specifically the issue of dark energy producing negative gravity centers around the $T^{00}$ component of the Stress-Energy Tensor. This term is dependent on relativistic mass. However, the conservation of energy requires the dispersion relation (assuming mass-energy equivalence which is at the crux of general relativity and which also arises naturally in the Dirac formulation of QM). (1) Jun 13, 2021 at 1:41
• @elduderino The dispersion relation in turn requires the mass (even negative mass) contribute a positive value to the total energy of a particle. The only mathematically consistent way is to have imaginary mass, but what does this mean physically? This is also precisely why I avoided too much discussion of the Cosmological constant which is not compatible with current QFT and is currently an open question in physics. (2) Jun 13, 2021 at 1:49