Virtual Mass of Empty Space Provides Gravity
Raising Rotation Rates in M33 Galaxy
Our preference for a continuous rather than quantized spacetime may explain our surprise on finding in 1998 (1,2) that 95% of the mass-energy of the universe was hidden from us. Beyond the 4% of energy we thought was the totality in the universe, 26% of the hidden energy appears to provide invisible extra mass, such as that found in galaxy clusters by Fritz Zwicky in 1932 (3). The remaining 70% has not been identified but may be involved in expansion of the universe.
Extra Mass in Galaxies
Zwicky observed galaxies in the Coma cluster moving too fast to be restrained by their visible mass. He concluded they were bound together by the extra mass of invisible dark matter. In 1999 Vera Rubin (4), found gravity from a comparable extra mass prevented fast-moving stars from escaping their galaxies.
In continuous spacetime, cold dark matter (CDM) particles are the leading candidate for invisible extra mass in galaxies (5). These particles are assumed to produce a gravitational field but do not otherwise interact with any form of radiation, matter or themselves. None have been detected. But this is not unusual in the search for a newly proposed particle.
Virtual Mass
In Quantized Spacetime (more details in QST paper), empty spacetime quanta provide extra mass in galaxies and elsewhere. As the smallest fragment of spacetime, the spherical quantum has three length dimensions and one time dimension. 10182 of these quanta are packed randomly into a spacetime matrix that fills the visible universe. Each quantum can give a particle within it three space dimensions and one time dimension. Expressed in the matrix as positions in spacetime, the dimensions define the relative locations and velocities of particles and empty quanta.
Even though tightly packed, the spherical quanta remain surrounded by gaps, because QST quanta are rigid except when penetrated by a gravitational field. When this occurs, the quantum shrinks in the direction of the field but not completely until the field intensity reaches that of a black hole. Below this intensity, the gaps remain. And as the dimensions of spacetime are expressed only within a quantum, the gaps between quanta are beyond spacetime. They form an interconnected labyrinth, amounting to a second universe about 30% the size of spacetime.
As such, the gaps have enough volume to contain the hidden 95% of energy in the universe. But being outside of spacetime quanta, the bulk of the energy has no spacetime dimensions. So, although it has the dimension of energy, it can have no mass or gravity, making it hard to detect except by indirect means.
There can be an exception to this lack of mass at some regions where the bulk surface forms an interface with spacetime, if this yields direct contact with spacetime dimensions. From the perspective of bulk energy, spacetime quanta are bubbles of spacetime within it. And although spacetime and the bulk are separated by a spherical surface, the surface has zero thickness (like air bubbles in water). So the bulk may gain surface dimensions via its interface with spacetime. But only if a spacetime quantum is empty.
If there is a particle present, the quantum dimensions are assigned to the particle. It there is no particle, the quantum's dimensions are available to the second universe through its interface with spacetime. Then, a local surface region of bulk energy gains two space dimensions and one time dimension. Combined with bulk energy, this creates a localized surface mass unrelated to a matter or radiation particle. As such it is virtual mass.
The local gravitational field from a patch of bulk virtual mass crosses into the quantum and the spacetime matrix. By this means, a galaxy gains an increment of mass at each quantum within it that has no matter or radiation particle. The sum of the virtual mass fields produced by trillions upon trillions of empty quanta around every star in a galaxy can provide sufficient virtual mass to raise its rotation speed.
Triangulum Galaxy M33
An opportunity for comparison of CDM and virtual mass is provided in the local M33 galaxy by the measurements of its rotation rates made by Edvige Corbelli and Paolo Salucci and published in 2000 (6). They point out that M33 is well situated for investigating extra mass. It is a typical disk galaxy that is near enough to Earth to be a reference marker for distances beyond it. And its partial face-on orientation facilitates optical and doppler radio measurement of its rotation rates.
Figure 1. Photo of the Triangulum Galaxy (M33) taken by the Hubble Space Telescope, showing bright star clusters, clouds of gas and dust, and glowing red gas clouds in the spiral arms. The stars visible here extend out to about 5 kpc radius from the M33 center, while smaller stars, dust and gases detectable by radio emissions extend out at least for another 12 kpc and probably further. (Credit: NASA)
Methods
In their paper, Corbelli’s and Salucci’s Figure 6 (Figure 2 here) shows the variation in rotation speed of M33’s main components across its disk from 0.4 kpc to 16 kpc. 'Gas' includes galactic dust. At inner radii the peripheral speed, marked by small black dots, comes from starlight observations. Beyond 4 kpc radius, where starlight fades, the larger dots show speeds recorded by doppler measurements at Arecibo of M33 21-cm radio emissions from atomic hydrogen. The curve for cold dark matter was derived from a mathmatical model.
With a special interest in the center regions, Corbelli and Salucci plotted their measured rotation speeds from the center to a radius of 3 kpc at approximately 0.25 kpc intervals. Beyond 3 kpc to 16 kpc, the interval became about 1 kpc.
Figure 2: Rotation speed curve for the M33 galaxy disk and its components, published by Corbelli and Salucci in 2000. Solid line, M33 galaxy rim; short dashes, star matter; long dashes, gaseous matter, including dust ; alternating dashes, estimated Cold Dark Matter component (extra mass).
1 kiloparsec (kpc) equals 3,262 light years.
Corbelli and Salucci Model
Supplementing their measurements with data from star and gas mass-distribution models, Corbelli and Salucci estimated M33 rotation speeds of stars and gases (Figure 2) by assuming M33 is an exponential stellar disk, a gaseous disk and a massive dark halo. They found that with a suitable choice of parameters, the speed variations they obtained match those of hierarchical clustering models of the type developed by Navarro, Frank, and White (7) and by Kravtsov, Klypin, and Khokhlov (8). On this basis they calculated the CDM rotation curve shown in Figure 2.
QST Model
Based on the most sensitive measurements of M33 rotation rates before Arecibo was damaged beyond repair, and consistent with hierarchical clustering models, the rotation rate curves in Figure 2 are well suited for examining virtual mass as an alternative to dark matter and for calculating its effective density. Therefore the Corbelli and Salucci curves were used in a QST model of M33 to calculate virtual mass density and compare its distribution with that of cold dark matter.
The QST mass model used an approximation that treats a galaxy disk as a circular slab through the equator of a sphere of the same radius, with rotation speeds at various radii in the slab assumed to be governed by Newton’s expression for within a sphere. From Newton’s gravitational constant G, Equation 1 provided the rotational velocity, V meters/second, of a disk mass of M kilograms extending out to a radius R meters from the galaxy center. Disk velocities were calculated at successive steps of 1 kpc to obtain the velocity of a ring at that radius. At each radius, V represented the local disk rotation speed
Shuffling the elements of this equation produced Equation 2, which
provided the mass of a disk of radius R rotating at a known velocity, V. From this the mass of individual rings within the disk were gained by successive subtraction.
From the speeds measured by Corbelli and Salucci in Figure 2, Equation 2 gave the masses of baryonic matter components (stars and gas) in each of their rings and the total mass of the whole disk given by the rotation rate of the M33 periphery. Subtracting the total baryonic massin the rings within M33 from the total mass within the galaxy disk provided the variation of extral-mass within the disk, whether it was CDM or virtual mass.
Because QST views extra mass as coming from empty spacetime quanta, less is expected at the center of M33 and more in its low-density outer regions. This is the opposite of expectations for cold dark matter, which, if it is matter, will be distributed in the way seen in stars and gases, with higher densities at the inner regions. To cover both regions with equal resolution, calculations were carried out and displayed at 1 kpc intervals, starting at 1 kpc.
Corbelli’s and Salucci’s CDM curve in Figure 2 represents their estimate of the variation of M33 extra mass rotation speed with radius in continuous spacetime. To investigate the M33 extra mass in quantized spacetime, Corbelli’s and Salucci's periphery, star, and gas rotation curves were used in Equation 2 of the QST model to calculate the variation with radius of the chief mass components of M33. In this way, curves for the M33 total mass, M33 gas mass and of M33 star mass were obtained.
In this process, a mass discrepancy appeared in the region beyond the transition from optical to doppler radio observation. After 8 kpc for the stars and 11 kpc for the gases, the cumulative mass instead of continuing to increase, or remaining at a constant final value, declined slightly (for the stars) or it declined and then rose again (for the gas). As loss of mass in this way is physically impossible, it was considered an error attributable to the approximation used in the QST model.
To correct this, the star mass was stabilized at the maximum reached at 8 kpc. The gas mass was corrected by continuing a slight rise in gas central mass to the level reached at 13 kpc and continuing it to 16 kpc. Recalculation of the rotation curves (Figure 3) showed a very slight affect on star rotation and a negligible effect on the CDM (extra mass) rotation. So the calculation with masses continued with the revized rotation rate curves.
Figure 3. The CDM rotation rate curve of Figure 2 as a result of small revisions made in star and gas masses to correct apparent decreases in central mass after 8 kpc. The new curves show this correction had little effect on the CDM curve of Figure 2. The error may have resulted from approximations made in the simple model.
Results
The adjusted masses were used to calculate the variation with radius of the individual ring masses of each component and the cumalative rise in component mass with radius from the center (Figure 4).
Figure 4: Variation of the central mass within each baryonic component disk with radius from the center and within the M33 disk as a whole.
The variation of QST extra mass with radius was calculated as the difference in Figure 4 between the total mass of the M33 disk and the total mass of its baryonic stars and gases. The result is shown in Figure 5.
Figure 5: The variation of QST extra mass with radius from M33 center, obtained by subtraction of star and gas total masses from the total central masses of M33 galaxy.
Based on the 0.5 kpc disk thickness assumed by Corbelli and Salucci, the variation of QST extra mass cumulative density with radius from the M33 center was calculated. Figure 5 shows the result.
Figure 5: The variation of the density of virtual mass with radius from the center.
The closest estimate available for virtual mass density comes at the outermost radius of 16 kpc where the presence of stars and gases is at a minimum. There, the density of virtual mass is 8.11 x 10-21 kg m-3
Discussion
Discussing one aspect of a galaxy made up of billlions of stars and their various companions and end states, dust, gases, and extra mass involves approximations, because galaxies are the most complicated objects in the universe, with complex interactions between their components at all levels, from electrons and protons, to black holes, stars, gas and dust clouds, and star clusters. In Figure 5, for example, the causes in the small semi-regular variations in the overall envelope of rise and fall in virtual mass density are unknown. They may arise from spiral arms, random amounts of ordinary matter from stars and gases, or variations in gravitational and magnetic fields emerging from central regions. Until a galaxy is mapped star-by-star, a certain amount of uncertainty is to be expected.
Obtaining accurate rotation speeds for extra mass in outer regions of galaxies is difficult, due to the weak strength of the doppler signals from hydrogen of very low density. In the central regions uncertainties arise in the distribution of stars and gases when assessed by visual means, even when supported by established models. And magnification of errors can occur when seeking a value for extra mass that is the difference between two large quantities, as in this paper where the difference between total galaxy mass and the total mass of its baryonic compoents reveals the size of virtual mass.
But galaxies are where the presence of a massive amount of unexplained extra mass was first recognized, followed later by an effort by every specialist science to explain it in its own specialist terms. And as this has not been succesful to date, it is worth asking whether adherence to continuous spacetime by these sciences conceals the source of extra mass in galaxies.
A basic feature of continuous spacetime is that it allows two points to be infinitely close together. Richard Feynman has questioned this assumption as threatening the legitimacy of the renormalization process essential in getting rid of unwanted infinities in particle physics.(He received a Nobel prize as a co-inventor of this.) In 1985 he wrote ". . . perhaps the idea that two points can be infinitely close together is wrong . . . If we make the minimum possible distance between two points as small as 10-100 centimeters . . .the infinities disappear, alright -- but other inconsistencies arise, such as the total probability of an event adds up to slightly more or less than 100%, or we get negative energies . . . " (9)
So, although an estimate of the mass of empty quanta is inevitably tainted by other influences in the galaxy, it is worth pursuing it to the edge of the galaxy where the taint is least. In addition, a useful comparison between CDM and QST virtual mass can be gained from the M33 rotation curves obtained by Corbelli and Salucci.
Figure 4 shows the rise and fall of familiar sources of mass -- stars and gases -- indicating that few empty quanta are to be expected in more central regions but many more towards the periphery. The two sources of mass also show the characteristic rise and fall of ordinary matter with radius in a galaxy. One would expect CDM to follow a similar curve if extra mass is indeed matter, but this is clearly not the case, unless its curve begins to fall some distance beyond the 16 kpc radius of the present data.
While Figure 4 shows a steady rise in extra mass that is consistent with evidence of a growing population of empty quanta beyond the congested central region of the galaxy, the density curve for extra mass is still falling at 16 kpc, indicating that the edge of the galaxy may be as far out as 25 kpc radius from the M33 center, where the ultimate density of virtual mass may be orders of magnitude lower than at 16 kpc. The disk rotation speeds obtained by Corbelli and Salucci for M33 were at radii that taxed the limit of Arecibo’s capability. After its loss, future measurement of extra mass in galaxies at greater radii must weight for the higher sensitivities of interferometer arrays currently coming online.
In the meantim, a clear distinction between the behavior of CDM and virtual mass appears in the behavior of high energy gas clouds that become stalled between colliding galaxies, as seen in mergers in the Bullet and other galaxy clusters (10, 11, 12). When two galaxies collide, particles in the cloud that forms are close together, and interact strongly. Observation of the track of distant galaxy light grazing the cloud shows little or no deflection attributable to gravity from extra mass, which remains evident in the departing galaxies.
Energetic interactions within the cloud, involving turbulence and bow shocks, raise the cloud to x-ray temperatures, releasing larger numbers of photons that occupy previously empty spacetime quanta. In essence, a string of real particles with four dimensions beats a virtual mass with three dimensions in a contest for occupancy of a spacetime quantum. But there is no energy deficit due to the loss of virtual mass, because that part of localized bulk surface energy simply returns to the bulk.
A similar suppression of empty spacetime quanta, and so of virtual mass, can be expacted at various regions at the center of galaxies where energetic systems such as supernova, shock waves, accretion disks, active black holes, and jets occupy quanta that might otherwise be empty. Variation of the level and pattern of suppression would account for different forms of rotation curves observed in galaxies, such as the occasional appearance of an anomalous cusp in rotation rate near the center, observed by Rubin (4) and others and still awaiting explanation.
There is also a marked difference in CDM and virtual mass behavior in the formation of black holes, or black shells as they are described in QST. This is described elsewhere on this site, but cold dark matter might be expected to contribute to the mass of the black hole, while virtual mass would return to bulk energy and make no contribution.
7 Conclusion
Recognizing that spacetime is quantized rather than continuous may account for a quarter of the universe’s unexplained 95% of mass-energy (1, 2). Stored in gaps between spacetime quanta, this energy is dimensionless. It gains two length dimensions and one time dimension at its interface with each empty spacetime quantum. This creates a virtual mass whose gravitational field crosses into spacetime and becomes the source of extra mass in galaxies and galaxy clusters, except where empty spacetime quanta are lacking --- in dense central regions of galaxies and in energetic gas clouds stalled by galaxy collisions. From M33 rotation rates obtained by Corbelli and Salucci, the QST simple model of M33 predicts a density of virtual mass at 16 kpc from the center as 8.11 x 10-21 kg m-3.
8 References
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