The Science of Magical Energy
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Open Access

Sunburst¹

¹ National Research Laboratory, 7 Tourmaline Lane, Crystal Empire 

How to cite this article: Sunburst. (2023). The Science of Magical Energy. Journal of Arcana, 4(2), 6-9.

Abstract

According to the laws of thermodynamics, energy cannot be created or destroyed in an isolated system; it can only be converted from one form to another. However, the emission of magic from a user (e.g. directed via a unicorn’s horn) or a magical artifact results in the emission of light, heat, kinetic and other forms of energy. Although many researchers throughout antiquity have avoided discussion on the origins of magic from a being or an artifact, or its relationship with physics, this paper herein seeks to demonstrate the necessary relationship between magic and energy. Specifically, magic is merely another form of energy that is converted to useful and non-useful forms of energy. Through empirical studies and statistical analysis, the quantification of constants in the energy-magic equation will be distilled as an argument for this relationship. 

Introduction 

The first law of thermodynamics states that energy cannot be created or destroyed in an isolated system. Consider a thought experiment where a unicorn is placed into some hypothetical box. When they cast a simple illumination spell, light energy is generated without the explicit conversion of energy from one form to another. In this case, some scholars would argue that the unicorn’s chemical potential energy (from food) would be converted to light energy. However, chemical potential energy is not a direct causation of light energy in this context.

In an attempt to address this, a new form of energy should be introduced, magical energy, which would cover the intermediary step between chemical potential energy and light energy. However, based on metrological studies and studies of magic, the quantity of magic is measured in motes [1], which is not dimensionally consistent with the unit for energy. Therefore, a new mathematical expression should be introduced to ensure the validity of this hypothesis. 

To ascertain this hypothesis, empirical studies will be conducted. The effect of magic on energy will be tested in an ordinary least square regression model, which standard error will enable the computation of test statistics for its p-value, and hence its significance. 

Methodology

Magically attuned crystals of equal weight (10.0 g, 20.0 g, 50.0 g, 100.0 g) are used to store a consistent amount of motes (1.00, 2.00, 5.00 and 10.0) for testing. To charge the crystals, the author directed magic into them till magic diffraction and then reflection occurs. To emit the energy contained within these crystals, magic from a smaller, charged magical attuned crystal (2.0 g) acts as a seed catalyst (0.20) to the magical photoluminescence/photoexcitation conducted in a dark room. The intensity of the light emitted is measured using a lux meter. 

Results and Discussion 

After conducting experiments in line with Table 1, a linear relationship between the light emitted and the magic is observed from Figure 1. A trendline using ordinary least square regression analysis was plotted with the consideration of all data points, revealing a explained regression ratio of 0.9966 (Table 2).

The test statistic for the effect of magic on the light emitted was found to be 24.29, yielding a p-value using the student t-distribution of 0.002. Coupled with the 95% confidence interval of 3.150451 to 4.5071, it is very unlikely for a nil relationship between magic and light energy emitted. However, from Figure 1, it is observed that there is a greater than expected light emission from the crystals. This is likely due to the greater percentage uncertainty introduced from the seed catalyst (Table 1) for Experiment 1. To further explore the relationship, data from the first experiment is omitted for a second round of regression analysis. 

There is an improvement in the explained proportion (0.9999) and the test statistic has increased to 122.55 (Table 3). Despite this, a higher p-value of 0.005 was recorded due to a smaller sample size (n = 3) in the student t-distribution. Nonetheless, the small p-value observed in both circumstances highlights the fact that there is a strong link between the amount of magic and the intensity of light emitted. 

To formulate the equation between magic M and light energy E emitted, consider E = 𝜷₀ + 𝜷₁M (Table 4) as it is most suitable from Figure 1. For dimensional consistency, [𝜷₀] = Joules and [𝜷₁] = Joules/Motes. The low p-values observed for 𝜷₁ and the higher p-values for 𝜷₀ enables a conservative estimate of the empirical equation to be E  ≅ 3.9M + c, where c is a constant for further determination. 

Conclusion

In this study, by conducting empirical studies and employing statistical analysis, the quantification of constants within the energy-magic equation (i.e. E  ≅ 3.9M) has been distilled, presenting a compelling argument for the existence of the relationship between magic and energy. Magic itself is a form of energy that can be stored (in a similar fashion to chemical potential energy) in objects or analogously in beings of varying levels of sapience. Hence, this seeks to add a layer of understanding to understand the relationship and causality between the conversion of magical energy to light energy. The high p-value for the parameter 𝜷₀ and its relatively high deviations indicate that some energy has been lost to other forms, such as heat (when 𝜷₀ is negative), or experimental error (when 𝜷₀ is positive). Nonetheless, this reflects the validity of the first law of thermodynamics and the need for further study in more stringent experimental conditions. 

Declaration 

The author declares no conflict of interest.

References
[1] Equestrian Standards Bureau. Correlation and Regression Standards Workbook—A Standardized Standards Guide, 8.

Year in which published: what happened 2,023 years ago in Equestria?

Introduction: "standard error" is a procedure or formula that can be expressed as a computation? I thought standard error was a measure of the uncertainty inherent in measurements and an estimate in the confidence in the validity of a claim. My memory of applied statistics is way fuzzy.

N = only three trials? That is incredibly low for a simple energy experiment! I think only behavioral and medical papers get by on such low numbers of observations (I recall reading a paper making guesses about fostering and thief suckling in fawns based on one observation in the field! 8^D).

Magic itself is a form of energy that can be stored (in a similar fashion to chemical potential energy) in objects or analogously in beings of varying levels of sapience

Citation missing. The experimental design depended on crystals that had been demonstrated to store Motes at a rate of 1 Mote/10g of attuned crystal (source of crystals ought to have been stated), but stating that sapient beings also _store_ magic, rather than just channel it or create it from nothing sounds like a blanket statement borne out by empirical analysis. That is to say, somepony somewhere demonstrated storage capacity in magically capable organisms. That paper should be cited, otherwise it's hearsay or an intuitive leap without a foundation.

The deviations in 𝜷₀ plus the N = 3 is giving me cold fusion flashbacks. 8^D

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Welcome back!

1. Yeah, standard error of a regression can be calculated in a formula by using feasible statistics.
2. Of course N = 3 is horrible! It was a usual silly article I wrote again after a hiatus, and yes, I was lazy to make out more observations.
3. Should have cited Twilight for that one.

You should be a peer reviewer for some journals!

Twilight would have made a good source. Peer reviewer! Never! Just skimming over all the graphs and statistics reminds me how much I do not want to do research!

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Actually, what do you mean by "cold fusion" flashback?

I recall that the minuscule success of the cold fusion experiments was due to measurement errors, kind of like the minuscule deviations from the theoretical output from your crystal storage things. Ergo, the difference between actual cold fusion and 'ha ha nope, not cold fusion after all' is really small, as were the number of trials.