@Let's consider the behavior of a low-mass test body in vacuum, at which it does not change the vacuum state. Then the gravitational potential at the location of the test body will be equal to the square of the speed of light in the absence of a gravitational field, and the gravitational energy of the test body is equal to the product of its mass by the square of this velocity. Let's start increasing the mass of the test body. This will lead to a decrease in the speed of light at its location, that is, to a decrease in the gravitational potential. At the same time, the gravitational energy of the test body will remain unchanged. That is, the gravitational energy of the test body will not be zero. Therefore, the zero on the right side of your equations must be deleted!

Valery Borisovich Morozov

When considering the law of conservation of energy in systems involving gravitational fields, it's essential to account for the signs of energy appropriately. The law of conservation of energy states that the total energy of a closed system remains constant over time. In your scenario, where ε_g represents the energy of the gravitational field and ε_s represents the energy of the substance, we need to consider the signs of these energies.

If both ε_g and ε_s are positive, the conservation law can be written as:

δε_s + δε_g = 0

However, in the case where the energy of a stationary gravitational field is negative, we need to adjust our understanding of energy conservation accordingly. Negative energy in the gravitational field represents a potential energy decrease, which is balanced by an increase in the energy of the substance.

So, in this case, the appropriate conservation law would be: δε_s - δε_g = 0

This equation suggests that as the energy of matter decreases (δε_s < 0), the absolute value of the gravitational field energy (|δε_g|) also decreases.

Thus, part of the energy from the substance is converted into gravitational potential energy, resulting in a decrease in the absolute value of the gravitational field energy.

To answer this question effectively, you can explain the concept of negative energy in the gravitational field and how it relates to the conservation of energy. Emphasize that energy conservation still holds true, but the signs of energy must be considered carefully to account for the contribution of both the substance and the gravitational field to the overall energy balance of the system.

Negative energy might even be necessary for the Law of Conservation of Energy, otherwise positive energy cannot be explained. In order to explain the existence of positive energy, there must be an equal amount of negative energy so that total energy is zero. Zero energy does not have to be explained. The Law should be amended to "NET energy cannot be created or destroyed."

The thread question

“Is the law of conservation of energy true if the energy is negative?”

- looks as is physically rather strange – really, by definition of “energy”, there cannot be some negative energy, energy is only positive parameter of everything in Matter.

Though formally such strange thing can be introduced and used, say, когда лошадь тянет телегу, лошадь действует на телегу с силой F, совершая работу W=Fs, потому телега движется со скоростью V, преодолевая силы трения. При этом лошадь передает телеге энергию E=W;

В то же время телега действует на лошадь с силой -F, совершая работу W=-Fs,. При этом телега передает лошади совсем отрицательную энергию E=-W;

- however this “really negative” energy is rather evidently quite useless in physics.

Nonetheless the thread question is quite legitimate in mainstream physics, since in the standard mainstream theory of really nothing else than some fundamental Gravity force - GRT, gravitational fields contain just negative energies.

What looks as rather strange, however in this case the postulate that Gravity field - and fields of other Forces – have some energy at all, looks is even more strange. When introducing of “negative energy” at analysis of interactions of some bodies is only useless, the postulates that Forces fields contain some energy simply vulgarly and brutally violate the energy conservation law, what is fundamentally never happens really in Matter, besides some too exotic things that are outside physics.

Really, as that is rigorously scientifically shown in the Shevchenko-Tokarevsky’s 2007 Planck scale informational physical model of Gravity [and Electric] Forces, more see https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces

- any fields of any Forces fundamentally don’t contain any energy at statics, and really in this case the real problem is - what happens in this case at motion of bodies. Though that isn’t unique problem at developing of based on the SS&VT model above really scientific theory of Gravity, more see the section “Conclusion” in the link.

Cheers

Stefan Bernhard Rüster ,

Correct description of the plot of energy to the power of the tensor energy pulse ьса. I need a lot of stationary support.

Warren Frisina

I do not dispute the existence of negative gravitational field energy. However, the conservation law assumes that energy increments are always positive.

δ ε_s + δ ε_g = 0

and the total energy if the energy of the gravitational field is negative

ε = ε_s - ε_g

To all!

Energy is a quantity that has no direction. therefore, the energy sign can be chosen depending on the context. Introducing the energy of the gravitational field into the Einstein equation, part of the Ricci vector asymptotically coincides with the energy-momentum tensor of the gravitational field, but the sign of the tensor is opposite.

Preprint Energy of space in the gravitational field equation v.2

the total energy is conserved:

ε = ε_s - ε_g

Stefan Bernhard Rüster ,

I was trying to figure out how negative energy works. And I discussed this topic without connecting it with your remark.

The sign of energy is a very conditional thing. everything depends on the conditional level of zero-point energy. the FLOW of energy has a certain direction.

I'm a little confused on this issue. This is really important for the conservation law. That's the only thing I cared about at work.

Preprint Energy of space in the gravitational field equation v.2

All the time, the conservation law was obtained in the form

0 = δε_s - δε_g

Now I see that this is correct, the components of the equation should be considered as energy flows having a direction.

I'm going to use LL-2 § 106. Equations of motion of a system of bodies in the second approximation.

Best regards Valery

“…Preprint Energy of space in the gravitational field equation….”

- again – see SS post on page 1, any assumptions [in the GR real postulate] that Forces fields, contain some – either positive or negative - energy, including yet quite mystic but postulated in the standard in mainstream physics GR, “Energy of space”, simply vulgarly and brutally violate the energy conservation law,

- what fundamentally never happens really in Matter, besides some too exotic things that are outside physics;

- and how the energy conservation law, which, of course, really acts at interactions in gravitationally coupled systems, acts in fundamental Nature Gravity force case [and at action of all other Forces cases in Matter], see Shevchenko-Tokarevsky’s 2007 Planck scale informational physical model of Gravity in the link in the pointed above SS post.

Recent SS post in https://www.researchgate.net/post/Does_string_theory_have_enemies_both_from_high_energy_physics_as_well_as_from_cosmology_unification_guards_of_criteriaToE is relevant to this thread question.

Cheers

Valery Borisovich Morozov

Your equations seems to be applicable to a specific system where the total system energy change is assumed to be = 0

A general equation would be

δ ε_s + δ ε_g = δ ε_system

Now use your logic. Let us see what happens.

Regards

Ist doch nicht schlimm.

Negative Feldenergie muss der Grund für das Auftreten sein. Aber niemand hat das drängende Gravitationsfeld gesehen. Das bedeutet, dass das Vorzeichen der Feldenergie keine Rolle spielt und wir positive Feldenergie in die Feldgleichung einsetzen müssen. Dann verschwindet das Paradoxon mit der Nichterhaltung der Energie in der Schwerkraft. Und Sie können die Gravitationsfeldgleichung ohne lächerliche Singularitäten in den Lösungen erhalten.

Preprint Energy of space in the gravitational field equation v.2

Preprint Элементарный вывод уравнения гравитационного поля

The law of conservation of energy applies even with negative energy, but it's important to understand how the "negative" sign is used in physics.

Here's the breakdown:

• Total Energy Conservation: The core principle is that the total amount of energy in an isolated system stays constant. It can't be created or destroyed, only transformed between different forms (kinetic, potential, thermal, etc.).
• Negative Sign as Reference Point: Sometimes, energy is assigned a positive or negative value depending on a chosen reference point. This doesn't mean there's negative energy out there, but rather it reflects a difference from that reference.
• Example: Gravity: Gravitational potential energy is a classic example. It's negative because it represents the potential for an object to fall towards another object due to gravity. As the objects get closer (energy decreases), the gravitational potential energy becomes more negative. However, at infinite separation, the potential energy is defined as zero (reference point).

So, the law of conservation of energy holds true even with negative energy values. It just means the total sum, considering positive and negative contributions, remains constant.

I hope this clarifies how negative energy works within the law of conservation of energy!