According to the principle that force is an exchange of "virtual particles", the "graviton" appears only when an object enters the gravitational field, how does it appear? Where is the "graviton" when only isolated matter carries its own gravitational field?
According to the principle that space-time is "curved" by matter, and curved space-time is gravity, is the "graviton" a part of matter? Does it also participate in the bending of space-time? Or is it the bending of space-time that produces the "graviton", and must the graviton also propagate along the geodesic?
a) Space-time is a kinetic "background medium "* that we should consider as a universal energy-momentum form. It can be transferred and exchanged like any other form of energy-momentum, and thus has the ability to change, and to be changed. Any elementary particle possesses an intrinsic spacetime parameter, which is where SR's "Length Contraction and Time Dilation" manifests itself, and why GR matter is able to change spacetime. Any interaction must be transmitted and exchanged through spacetime.
b) Different forms of energy-momentum can cause spacetime "bending", which must reflect the unity of energy-momentum [1]. The only thing that can cause spacetime to bend is spacetime. That is to say, energy-momentum, matter can only rely on its own spacetime to change other spacetime. Therefore, one of the properties that matter carries is the "curved" state of spacetime around it [2].
c) The essence of the "curvature" of spacetime is the unequal change of the components of the four-dimensional spacetime intrinsic metric Δs={Δt,Δx,Δy,Δz}† . This can be expressed as (ds)^2=-(a0*dt)^2+(a1*dx1)^2+(a2*dx2)^2+(a3*dx3)^2, with a0~a3 unequal. Such a definition is concise and physically complete, and is able to unify all spacetime-related concepts under the Minkowski spacetime framework. Consider spacetime as consisting of arbitrarily small-sized elements ΔV, which are of the same size, but in which the metric components Δt,Δx,Δy,Δz can be different. This requires the existence of two different properties of spacetime, an absolute positional coordinate and a relative metric between positions. This is equivalent to giving spacetime the concept of "metric density". Obviously it presents the media role of spacetime in a more vivid way.
d) This kind of definition of curvature can bring many convenient and reasonable explanations:
It guarantees the continuity of the whole spacetime and the global orthogonality of the three-dimensional space; it perfectly matches the "Length Contraction and Time Dilation" effect of SR and the Riemannian spacetime concept of GR✧.
Light does not change spacetime in free space, but participates in energy momentum to change spacetime in curved spacetime. Light changes spacetime in the same way that it is changed, e.g. gravitational redshift [4], violet shift, cosmological redshift, what actually happens is that its spacetime metric {Δt,Δx,Δy,Δz} is changed.
According to GR's causality, and reversibility, the energy-momentum causes the spacetime {Δt,Δx,Δy,Δz} to change, and then the energy implied by spacetime itself should be a function of Δt, and the momentum a function of Δx,Δy,Δz. This is the most direct and final expression, and the only possible choice!
Since the "geodesic" is the shortest path caused by energy-momentum L=∫ds=∫√gμν-dxμ-dxν, it is of course equivalent to the expression of energy-momentum. Therefore, this metric expression of distance has only a nominal meaning. In reality it should be the lowest "metric density" (lowest energy) path.
It is commonly believed that gravity is not a real force [5][6]. Objects move instinctively along geodesics, just as force is not required for inertial motion in free space. This interpretation is not in place††. It is the maintenance of energy-momentum conservation of the interacting system in a changing spacetime metric {Δt,Δx,Δy,Δz} that is the root cause of the "gravitational force" that leads to accelerated motion!
Criterion: What can change spacetime can only be spacetime. To change Δs={Δt,Δx,Δy,Δz}, another Δs'={Δt',Δx',Δy',Δz'} must join it, whether it is carried by a mass or arrives by a gravitational wave [7].
e) If the force is still defined according to the concept of exchanging virtual particles [10], then such a "graviton" does not exist‡. We must find a direct correlation between the so-called exchange of virtual particles and the exchange of energy-momentum. A "graviton "** exists if one considers the smallest unit of spacetime metric change due to the smallest unit of energy-momentum to be a "graviton". It consists only of the smallest spacetime metric {Δt,Δx,Δy,Δz} and must be dispersive. This is unlike any other elementary particle.
f) One of the symmetry manifestations of gravity should be the existence of positive and negative. If the theory has only gravity and no repulsion, then it must be deficient. Even if the repulsive force does not normally exist, a reason for its absence should be given.
g) When an interaction occurs, the energy-momentum involved is strong, the force presented is strong. In contrast to the electromagnetic force, the gravitational force is weak because it is not the main body of energy-momentum, but rather a spatio-temporal concomitant of the energy-momentum of matter, or an " residual " ♬.
Questions
1) How to define the concept of orthogonality of " intrinsic curvature " of spacetime between three spatial dimensions? How to realize its rationality?
(2) In the "curved spacetime", the "geodesic" is the shortest path, is its metric process essentially different from the "Length Contraction and Time Dilation" of SR?
3) Is the "graviton" currently sought by physics a detectable entity with a fixed form?
4) Doesn't it make sense that the positive or negative spacetime metric gradient determines whether an "attractive" or "repulsive" force is generated?
4) Photons are quantized, mass is quantized, and mass-induced "spacetime bending" should certainly be quantized. "Space-time bending" is equivalent to gravity. Doesn't the cause of space-time bending tell us what a "graviton" is? Aren't gravitational waves a collection of gravitons? Why do we have to search for "quantum gravity" through various assumptions，structures that are more fundamental than elementary particles [11]? Why should GR match the quantum framework and not the other way around?
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Notes
* "The main insight of Einstein's general relativity was the change of the role of space and time from a passive 'arena', in which physics takes place, to an active dynamical entity that is shaped by matter and acts back on it; but space-time remained a sharply defined classical object"[9]. However, space-time is not the same as matter in many ways, for example, it is universal, flat free space-time contains no energy-momentum, it can only be modified by the addition of energy, it can change nothing else. g = g0 + h, g0 is background metric (coordinate spacetime), contains no energy-momentum; h is modulation metric (relative spacetime), with energy-momentum. Therefore, it is appropriate to call this view of spacetime an upgraded version of the "Aether" doctrine [3].
✧ Einstein never argues for the spacetime bending premise in GR, but takes Gaussian coordinates directly, which seems to be the only option. In fact, in SR, point-particle states vary equally in each component of the measure, g00 = g11 = g22 = g33, and the other gμν = 0; when there is a scale for the object, it changes only in the direction of motion. In GR the static Schwarzschild spacetime g00, g11, g22, g33 is not 0, and the other gμν = 0. Forcing the other gμν = 0 does not lead to complete failure of GR.
† Expressing spacetime bending in a deformed "3D mesh" animation [14], although more graphically expressing Δs={Δt,Δx,Δy,Δz}, may result in definitional conflicts: can spacetime be locally and infinitely stretched or extruded, resulting in spacetime tearing, or overlapping? Can the bending directions of neighboring spacetimes conflict? Does the endowed bending of spacetime conflict with the external bending of the overall spacetime? How is the orthogonality of the overall 3D spacetime manifested? How do field representations reflect spacetime curvature when other fields are in curved spacetime?
§ As when light passes through a medium with different refractive indices n, resulting in a decrease in the speed of light. This actually reflects the change in spacetime density in the path.
†† We need to focus on why there is motion, not whether there are "forces". An ant and a bee both know the shortest path to their nests, but if the ant loses its legs, it will not be able to return to its nest, and if the bee loses its wings, it will fall free along the geodesic and will not return to its nest.
‡ The essence of exchanging "virtual particles" is to exchange fields; the essence of exchanging fields is to maintain the conservation of energy-momentum; maintaining the conservation of energy-momentum is manifested as "force".
¶ The energy-momentum itself is a function of space-time and manifests itself internally. When energy-momentum is exchanged with the outside world, there must be external motion to balance the exchange. In fact, the relationship between energy-momentum and space-time is reflected in both rest and motion.
** Defined in this way, the essence of the graviton is the minimum spacetime metric. Because the constituents of matter and energy-momentum that lead to the curvature of spacetime are different, the metric of spacetime curvature they lead to is also different. We need to note one thing, energy quantization is derived from the theory of blackbody radiation. It is not correct to generalize that the photon is the smallest energy quantum, it is simply the smallest energy quantum at a particular frequency E=hν. the same is true of the graviton.
♬ Wilczek said, "The apparent feebleness of gravity results from our partiality toward the perspective supplied by matter made from protons and neutrons ." [13]. Concerning the question of the order of magnitude of forces, why don't we first see that different forces are located in different structures, and why don't we analyze them structurally?
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References
[1] https://www.researchgate.net/post/NO10_Can_different_forms_of_energy_be_unified;
[2] https://www.researchgate.net/post/NO5_How_Fermions_combine_four_properties_in_one;
[3] Whittaker, E. (1910). A History of the Theories of Aether and Electricity, Courier Dover Publications（1989）;
[4] Will, C. M. (2018). Theory and experiment in gravitational physics, Cambridge university press.
[5] Ashtekar said,“Gravity is a manifestation of spacetime geometry”：Ashtekar, A. and E. Bianchi (2021). "A short review of loop quantum gravity." Reports on Progress in Physics 84(4): 042001. “”
[6] Kiefer said,“All manifestations of the gravitational field known so far can be understood from a classical theory—Einstein's theory of general relativity (GR), also called geometrodynamics. It is defined by the Einstein–Hilbert action." Kiefer, C. (2007). Lecture Notes in Physics-Approaches to fundamental physics, Springer. Why quantum gravity?: 123-130.
[7] Abbott, B., S. Jawahar and etl. (2016). "LIGO scientific collaboration and virgo collaboration (2016) gw150914: first results from the search for binary black hole coalescence with Advanced LIGO." PHYSICAL REVIEW D Phys Rev D 93: 122003.
[8] Why Should We Study Quantum Gravity? What Are Prima Facie Questions? Isham, C. J. (1994). Prima facie questions in quantum gravity. Canonical gravity: From classical to quantum, Springer: 1-21.
[9] Kiefer, C. (2007). Lecture Notes in Physics-Approaches to fundamental physics, Springer. Why quantum gravity?: 123-130.
[10] Cowan, G. (2012). "Review of particle physics." Phys. Rev. D 86(010001): 390.
[11] Mielczarek, J. and T. Trześniewski (2018). "Towards the map of quantum gravity." General Relativity and Gravitation 50(6): 68.
[12] https://www.researchgate.net/publication/373877548_Convergent_and_Disperse_Cyclic_Multiverse_Model_CDCMM；
[13] Wilczek, F. (2005). "Nobel Lecture: Asymptotic freedom: From paradox to paradigm." Reviews of Modern Physics 77(3): 857.
[14] Schutz, B. (2009). A first course in general relativity. China, Cambridge university press.
The graviton deecribes the gravitational field in a similar way that the photon describes the elrctromagnetic field. The coupling of matter to the electromagnetic field is through the electric current of the matter fields and the
coupling of matter to the gravitational field is through the energy-momentum tensor of the matter fields. This is the way it's possible to compute the flux 9f radiation, in both cases.
In order not to write too long posts, I'll address the further questions separately.
It should be stressed, however, that it is not correct to talk about individual gravitons, in the sense that it is possible to describe gravitational radiation and gravitational waves are the superposition of a large number of gravitons, that can't be resolved individually, just like electromagnetic waves are the superposition of a large number of photons, that can't be resolved individually. The difference between the two is that, while it is possible to describe theoretically and measure experimentally the ``shot noise'' of photons, which describes the number fluctuations of photons, it isn't known how to describe theoretically the ``shot noise'' of gravitons, nor to measure it experimentally.
It is possible to describe the properties of individual gravitons in a certain approximation, that doesn't, however, allow the description of their ``shot noise''.
The graviton isn't part of matter, any more than the photon is a part of matter.
The difference between the two is that the photon isn't a source of the electromagnetic field, since it doesn't carry electric charge; however the graviton-in the approximation that it can be described at all-is a source of the gravitational field, because it does carry energy and momentum-and anything that carries energy and momentum, produces a gravitational field and, therefore, curves spacetime.
So yes, gravitons, that are massless particles of spin 2, do propagate along geodesics, just like photons, that are particles of spin 1 do.
Indeed this is the content of the measurement of the propagation of gravitational waves produced by the merger of two neutron stars and of the electromagnetic waves produced during the same process.
Any interaction must and is transmitted through spacetime. The question is how much it actually affects spacetime. The answer is provided by Einstein's equations, where matter appears on the RHS and the ``coupling constant'' is Newton's constant. So it turns out that for the interactions other than gravity, the energies are so small that the deviation from flat spacetime is negligible. And for masses much less than that of the Earth, also: Electromagnetic waves that propagate to and from GPS satellites from the Earth are sensitive to the curvature of spacetime produced by the Earth, for instance.
Spacetime is ``bent'' by matter, not by spacetime. Empty spacetime is flat. The ``vacuum'' solutions to Einstein's equations, that do not describe flat spacetime, describe spacetime that is ``asymptotically flat'' but had some matter, nonetheless. So the Schwarzschild solution to Einstein's equations describes the spacetime outside a massive body. The boundary conditions describe the way in which the presence of a massive body implies that spacetime isn't flat.
Dear Stam Nicolis
Thank you very much for your answers and the perspective you bring. While some of the questions will take time to mull over, there are some comparable questions that can still continue the discussion.
1) Photons do not disperse, do gravitons have to disperse？ This would be an important difference between photons and gravitons. Electromagnetic waves traveling to great distances scatter into discrete photons in all directions. A gravitational wave traveling to any distance will remain continuous, in other words will it decay infinitely until it converges to free space-time？
2) A photon carries no electric charge, but we should note that the electric field E carried by an electric charge is the same physical quantity as the E of an electromagnetic wave; an electron carries an electric charge as well as a magnetic moment, and magnetism in this case is the same physical quantity as the H of an electromagnetic wave.
3) "Any interaction must and is transmitted through spacetime." My deeper meaning is that all interactions are interactions with spacetime, not just through spacetime. The point here is to identify the existence of spacetime parameters within elementary particles. For example, when inertial motion occurs, it can be seen as an interaction of an object with spacetime.
4) "Spacetime is ``bent'' by matter, not by spacetime." This is true according to GR, but if we consider the root cause, we need to analyze the "orthogonality" between matter and spacetime. ". The question remains, what makes matter change spacetime? My point is that only matter itself has a spacetime parameter through which it changes the spacetime around it, just as the electric field of an electron extends through space.
Best Regards, Chian Fan
Dear Chian Fan
Regarding the latest questions:
1) Yes, gravitons can disperse, though this is hard to detect directly. However electromagnetic waves don't ``scatter into individual photons''-that's, just, wrong. Gravitational waves don't ``decay'', either. They describe
classical perturbations of a spacetime background.
2) Electromagnetic waves are produced by electric charges, that, at some moment in time, were moving nonuniformly. And they can't be produced in the absence of matter. That's nothing new.
3) No, all interactions are definitely not interactions with spacetime, the three, besides the gravitational interaction, describe the properties of matter in a fixed spacetime background. And the reason they don't affect the spacetime geometry is quantitatively described by Einstein's equations.
Inertial motion means that a particle follows a geodesic of flat spacetime.
4) What makes matter change spacetime starts with the property of spacetime of being invariant under general coordinate transformations. Then in noticing that the only way matter can, on the one hand, be described as moving in spacetime is if matter couples to the spacetime geometry through the fields that define it. In general relativity the only field that defines the spacetime geometry is the metric and the only way the equations of motion of matter can take the metric into account in a way that is consistent with invariance under general coordinate transformations is if matter is coupled to the metric through the energy-momentum tensor of matter. This can be generalized if additional fields describe the spacetime geometry, as is the case for so-called scalar-tensor theories or, in the most general case, supergravity.
As is, always, the case, the interactions follow from the symmetries. It's the discovery of what the symmetries of spacetime are, that determines what are the ways in which matter can affect it.
Dear Stam Nicolis
Thank you very much for the extremely informative points.
"As is, always, the case, the interactions follow from the symmetries. It's the discovery of what the symmetries of spacetime are, that determines what are the ways in which matter can affect it." This is a really important issue regarding symmetry, so a separate topic is set up to show this. https://www.researchgate.net/post/Symmetry_Invariance_and_Conservation_1-Who_is_the_Primary
Looking forward to your review！
Best Regards, Chian Fan
Dear Chian Fan
Thank you for these discussions! Indeed the issue of symmetries has become the most important issue for setting up the description of natural phenomena.