In 1905, Albert Einstein showed in his Special Theory of Relativity that space is intimately connected to time via the cosmic speed limit of light and so, strictly speaking, we live in a Universe with four dimensions of space-time. For everyday purposes however, we think of the Universe in three dimensions of space (north-south, east-west, up-down) and one dimension of time (past-future). In that case, a fifth dimension would be an extra dimension of space.

Such a dimension was proposed independently by physicists Oskar Klein and Theodor Kaluza in the 1920s. They were inspired by Einstein’s theory of gravity, which showed that mass warped four-dimensional space-time. Since we’re unable to perceive these four dimensions, we attribute motion in the presence of a massive body, such as a planet, not to this curvature but to a ‘force’ of gravity. Could the other force known at the time (the electromagnetic force) be explained by the curvature of an extra dimension of space?

Kaluza and Klein found it could. But since the electromagnetic force was 1,040 times stronger than gravity, the curvature of the extra dimension had to be so great that it was rolled up much smaller than an atom and would be impossible to notice. When a particle such as an electron travelled through space, invisible to us, it would be going round and round the fifth dimension, like a hamster in a wheel. Kaluza and Klein’s five-dimensional theory was dealt a serious blow by the discovery of two more fundamental forces that operated in the realm of the atomic nucleus: the strong and weak nuclear forces.

But the idea that extra dimensions explain forces was revived half a century later by proponents of ‘string theory’, which views the fundamental building blocks of the Universe not as particles, but tiny ‘strings’ of mass-energy. To mimic all four forces, the strings vibrate in 10-dimensional space-time, with six space dimensions rolled up far smaller than an atom.

String theory gave rise to the idea that our Universe might be a three-dimensional island, or ‘brane’, floating in 10-dimensional space-time. This raised the intriguing possibility of explaining why gravity is so extraordinarily weak compared with the other three fundamental forces. While the forces are pinned to the brane, goes the idea, gravity leaks out into the six extra space dimensions, enormously diluting its strength on the brane.

There is a way to have a bigger fifth dimension, which is curved in such a way that we don’t see it, and this was suggested by the physicists Lisa Randall and Raman Sundrum in 1999. An extra space dimension might even explain one of the great cosmic mysteries: the identity of ‘dark matter’, the invisible stuff that appears to outweigh the visible stars and galaxies by a factor of six.

In 2021, a group of physicists from Johannes Gutenberg University in Mainz, Germany, proposed that the gravity of hitherto unknown particles propagating in a hidden fifth dimension could manifest itself in our four-dimensional Universe as the extra gravity we currently attribute to dark matter. Though an exciting possibility, it’s worth pointing out that there’s no shortage of possible candidates for dark matter, including subatomic particles known as axions, black holes and reverse-time matter from the future!

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In Runs 1 and 2, as the accelerating gradient was increased at the beginning of the runs, SPL's were the first of these luminous phenomena to be observed. In Run 2, the onset of observable SPL's was found to be at a gradient of ~3MV/m. And various SPL's remained in view throughout these runs whenever there was an adequate accelerating gradient in the cavity. As one would expect, the amount of light emission from these sites tends to correlate with the magnitude of the accelerating gradient, and hence they are a useful indicator of the gradient. 

While we attribute these SPL's to a field emission process, the specific physics involved or their relationship to the MLO phenomenon is not clear. In this regard, it is relevant to note that there are two intriguing sequences involving SPL's described in Sec. 5.4. These sequences support the notion that (some of) the flashes and the SPL's are specifically associated with field emission sites. They also imply the possibility that (some) flashes, SPL's, and MLO's are related phenomena. 

MLO's are the most intriguing of the luminous phenomena observed in this series of runs, and they are the major focus of our interest. The intrigue derives from the challenge to find a proper physics understanding of the MLO phenomenon. These MLO's occurred with cavity accelerating gradients in the range of 2 to 4.4 MV/m, but this phenomenon was actually quite episodic. Often, the MLO's would appear subsequent to a flash of light, or FoL (discussed in more detail below). Usually, the tracks of the MLO's (if they appeared) would last only a few frames. However, there were three video tape segments in which the continuous existence of MLO's was observed in a sequence of frames (orbits) of more than 10 s duration: two (single MLO orbits) in the single-cell data, and one (containing three contemporaneous MLO orbits) in the five-cell data. In these segments it appears that the MLO's were orbiting the axis of the cavity without any wall contact. Fig. 6, which reproduces Fig. 5a from Ref. [1], is an early frame the (only) orbit 7 sequence in Run 2. 

In this sequence (which appeared right after a flash), there initially appear to be three orbiting MLO's (note the three track segments indicated in Fig. 6: Orbits 11, 12, and 13, as listed below in Table IV), soon reduced to two, both of which disappeared at about the same time ~11 s later. Another category of MLO behavior was also observed in Run 1; that is, there were examples of MLO's bouncing off of the cavity walls. Reflections of these tracks in the cavity walls concurrent with the directly viewed MLO tracks assisted in the analysis of these events. 

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Physics challenges In the course of this paper we have noted various difficulties in formulating a physics explanation of the luminosity associated with five luminous phenomena: SPL's, CID's, the flash, the semi-flash, and MLO's. (Possible avenues for explanation have also been indicated.) Of these five phenomena, MLO's appear to be the most complicated and the most perplexing. Not only do they emit light, but they also appear to be small discrete stable objects, capable of independent motion in the cavity vacuum for extended periods of time. We have observed two distinct modes of their behavior: Mode I, or ballistic, and Mode II, or macromolecular. (We make the tacit assumption that the internal structure and composition of the MLO's in these two modes are the same, or very nearly so.) While there are numerous questions of detail, in overview, salient general questions include: How are MLO's related to SPL's and FoL's? How are MLO's formed? What are they made of? What is their mechanism for light emission? What forces give them their self-coherence and internal stability? What are the long-range forces that enable them to move for long periods of time without wall contact in stable closed orbits in the vacuum space of the superconducting cavities? What forces enable them to maintain the observed quasi-stable (centimeter sized) multi-MLO macromolecular configurations away from the cavity walls, which configurations can settle into quasi-stable at-rest locations away from the cavity walls? And we have seen that there can be several such locations (orientations) available for a given MLO configuration. Is it possible that we are seeing a new dynamical force regime? 

An intriguing question A review of the literature reveals that the MLO's observed in these data do not at all resemble the usual low pressure gas discharges. (See also Ref. [1].) On the other hand, several important qualitative features of the observed MLO's are similar to those of ball lightning (BL). Could it be that the MLO is a "little brother" to BL? That is, are MLO's and BL governed in general by the same physics principles, but at significantly different spatial scales? (BL varies in size from a cm to >1 m [27], in contrast to the ≤ 1.5 mm for MLO's.) The similarities are striking. BL forms stable, relatively long-lived balls of luminosity that move about in air (implying that they are of low density) without any apparent source for the radiated energy (actually the MLO has an obvious source: the cavity RF field, but the mechanism for the conversion of that energy into radiation is not clear) and are often devoid of any contact with nearby material objects [27, 28]. And more interestingly, multi-BL formations have been observed [27, p. 36; 29] that resemble the Mode II MLO behavior. (It is also relevant to observe that both phenomena appear to elude a proper physics explanation within the realm of established physics.) Hence, it would seem appropriate to consider looking into BL for a possible explanation of the cavity lights phenomena. Along these lines, Ref. [30] discusses a BL model based upon a kind of electromagnetic monopole that offers the possibility to explain many of these perplexing questions, e.g., the essential nature of the orbiting objects, their interactions, their internal stability, their orbital stability, and their ability to form quasi-stable macromolecular formations. Based upon this model, some experimental predictions can be made, which we plan to explore in future runs.