1. In­tro­duc­tion

Fig­ure 1.1: A white Mi­ata and a non­white one.

The Mi­ata is a sports car de­vel­oped by the Japan­ese car man­u­fac­turer Mazda. Fig­ure 1.1 shows a white and a non­white Mi­ata.

The Mi­ata^1.1 was in­tro­duced in the USA mar­ket in 1990. It is def­i­nitely im­por­tant to rec­og­nize that the Mi­ata was pri­mar­ily de­signed for the USA mar­ket. How­ever, it was also very suc­cess­ful in other mar­kets. Here are some lan­guages in which the praises of the Mi­ata were sung:

Eng­lish
(Span­ish) Español
(Greek) Ελληνικά
(Russ­ian) Русский
(CJK) 中日韓
(High UTF-8) 𐑍𐑎𐑏

Con­sider what Homer had to say at the start of the Il­iad:

μῆνιν ἄειδε θεὰ Πηληϊάδεω Ἀχιλῆος
οὐλομένην, ἣ μυρί᾽ Ἀχαιοῖς ἄλγε᾽ ἔθηκε,
πολλὰς δ᾽ ἰφθίμους ψυχὰς Ἄϊδι προΐαψεν
ἡρώων, αὐτοὺς δὲ ἑλώρια τεῦχε κύνεσσιν
οἰωνοῖσί τε πᾶσι, Διὸς δ᾽ ἐτελείετο βουλή,
ἐξ οὗ δὴ τὰ πρῶτα διαστήτην ἐρίσαντε
Ἀτρεΐδης τε ἄναξ ἀνδρῶν καὶ δῖος Ἀχιλλεύς.

τίς τ᾽ ἄρ σφωε θεῶν ἔριδι ξυνέηκε μάχεσθαι;
Λητοῦς καὶ Διὸς υἱός: ὃ γὰρ βασιλῆϊ χολωθεὶς
νοῦσον ἀνὰ στρατὸν ὄρσε κακήν, ὀλέκοντο δὲ λαοί,
οὕνεκα τὸν Χρύσην ἠτίμασεν ἀρητῆρα
Ἀτρεΐδης: ὃ γὰρ ἦλθε θοὰς ἐπὶ νῆας Ἀχαιῶν
λυσόμενός τε θύγατρα φέρων τ᾽ ἀπερείσι᾽ ἄποινα,
στέμματ᾽ ἔχων ἐν χερσὶν ἑκηβόλου Ἀπόλλωνος
χρυσέῳ ἀνὰ σκήπτρῳ, καὶ λίσσετο πάντας Ἀχαιούς,
Ἀτρεΐδα δὲ μάλιστα δύω, κοσμήτορε λαῶν:
Ἀτρεΐδαι τε καὶ ἄλλοι ἐϋκνήμιδες Ἀχαιοί,
ὑμῖν μὲν θεοὶ δοῖεν Ὀλύμπια δώματ᾽ ἔχοντες
ἐκπέρσαι Πριάμοιο πόλιν, εὖ δ᾽ οἴκαδ᾽ ἱκέσθαι:
παῖδα δ᾽ ἐμοὶ λύσαιτε φίλην, τὰ δ᾽ ἄποινα δέχεσθαι,
ἁζόμενοι Διὸς υἱὸν ἑκηβόλον Ἀπόλλωνα.

Clearly then, life was not pleas­ant be­fore the com­ing of Mi­atas. It is bet­ter to drive one small Mi­ata than to sail a thou­sand ships.

Need­less to say, white was a Mi­ata color from the be­gin­ning. How­ever, early white Mi­atas had a prob­lem where the paint would peel off the cars. This was the stage at which the is­sue of Mi­ata-pho­ton in­ter­ac­tion first re­ceived sig­nif­i­cant pop­u­lar at­ten­tion. Own­ers with peel­ing paint no­ticed that their cars did not only look worse. The cars also be­came very no­tice­ably slower when the paint peeled off.

Since then, the in­creased speed of white Mi­atas be­came well known among knowl­edge­able own­ers. How­ever, some oth­ers doubted the as­so­ci­a­tion and ac­quired grey, black, and even red Mi­atas. While these Mi­atas would still drive at rea­son­able speeds, they had dif­fi­culty com­pet­ing with the white ones when max­i­mum per­for­mance was an is­sue.

Ta­ble 1.1: First-gen­er­a­tion Mi­ata col­ors pro­duced, in cars. Data com­piled by John Emer­son. Fig­ures pro­vided by Mar­ket­ing Di­vi­sion of Mazda Cor­po­ra­tion, Irvine, CA. Posted on mi­ata.net. Data are re­sorted in or­der of in­creas­ing car speed, scaled with rated en­gine power. Data for 1990-1991 white Mi­atas are ap­plic­a­ble un­til the paint peels off.

Year:	1990	1991	1992	1993	1994	1995	1996	1997	all
Clas­sic red	29195	16000	11729	8415	6013	4888	4006	3950	84196
Black			4626	6111	5741	4877	4063	3702	29120
BRG green		3997							3997
Ma­rina green								3000	3000
Starlight blue							3000		3000
Mer­lot						3500			3500
Twi­light blue								1500	1500
Mon­tego blue					3003	2818	5742	4571	16134
Yel­low			1515						1515
Mariner blue	6540	3633	2096	1082					13351
La­guna blue					1788	440			2228
Sil­ver stone	3481	5802	1475						10758
Chaste white					3565	2945	2160	1929	10599
Crys­tal white	12420	8855	5195	5874		122			32466
To­tals	51636	38287	26636	21482	20110	19590	18971	18652	215364

Ta­ble 1.1 lists the var­i­ous col­ors in which the first-gen­er­a­tion Mi­ata was pro­duced. They are sorted by car speed, rel­a­tive to en­gine power. (Ta­ble 1.2 shows the same data sorted by to­tal cars pro­duced.)

At first, some fea­tures of ta­ble 1.1 may seem sur­pris­ing. For ex­am­ple, you might rea­son­able as­sume that black Mi­atas would be slower than red ones. Af­ter all, black will ab­sorb all col­ors of light, while red ab­sorbs only nonred ones. How­ever, black Mi­atas are no­to­ri­ously dif­fi­cult to keep clean. Be­cause of the great vari­a­tions in sur­face tem­per­a­tures, dirt gets baked on. So black Mi­atas re­flect a good deal of light due to the dirt.

Ta­ble 1.2: Like the first ta­ble, but sorted by to­tal cars pro­duced.

You might also won­der why the slower col­ors, and es­pe­cially red, sold quite a large num­ber of cars. The rea­son is psy­cho­log­i­cal. A sig­nif­i­cant num­ber of own­ers are some­what wary of the speed of their Mi­atas. In pri­vate com­mu­ni­ca­tions, Mi­ata own­ers have told me that it feels “some­what scary, so with­out a roof in a small, fast, car.” The re­duced speed of red Mi­atas pro­vides some sense of re­as­sur­ance. Many red Mi­ata own­ers also end up in­stalling a hard­top on a semi-per­ma­nent ba­sis.

At the other side of the list, you find the hard-core en­thu­si­asts who go for speed. (To be sure, some white Mi­ata own­ers might also be at­tracted by the fact that the white Mi­atas do not need much ef­fort to look clean. But surely, that is a small mi­nor­ity.)

An­other ob­ser­va­tion that may be sur­pris­ing at first is why a yel­low Mi­ata might best sev­eral blue ones. Af­ter all, pho­ton en­ergy in­creases from red to yel­low to green to blue. Ac­tu­ally, the yel­low Mi­ata has a lot of white thrown in. And var­i­ous blue Mi­atas are re­ally dark. While they do emit some blue, they ab­sorb col­ors of all wave­lengths.

Fig­ure 1.2: Left: Speed dif­fer­ence be­tween a white and a red Mi­ata. This uses plot units. Right: the non­lin­ear stretch­ing used to clar­ify the speed dif­fer­ence.

The left-hand graph in Fig. 1.2 com­pares the speed $v(t)$ of a red Mi­ata to that of a white one. Here $v$ is the ve­loc­ity and $t$ the time in sec­onds from rest. Sub­scripts w and r in­di­cate the white and red Mi­atas, re­spec­tively. The ve­loc­ity is taken rel­a­tive to the ter­mi­nal ve­loc­ity of the white Mi­ata. The ac­cel­er­a­tion $a(t)$, rel­a­tive to the ini­tial one $a(0)$, is also plot­ted. (The rel­a­tive ac­cel­er­a­tion is the same for the Mi­atas, al­though the ab­solute ac­cel­er­a­tion of the red Mi­ata is of course less.) For sim­plic­ity, CVT mode is as­sumed.

To clar­ify the speed dif­fer­ence, the ve­loc­ity has been plot­ted on a slightly non­lin­ear scale. The right-hand graph shows this scal­ing. In it, $v_{\rm {i}}$ is the in­di­cated speed and $v_{\rm {p}}$ the plot­ted speed. Note that this cor­rec­tion is rem­i­nis­cent of the dif­fer­ence be­tween in­di­cated air­speed and true air­speed in avi­a­tion. The plot­ted speed takes here the place of the true air­speed in avi­a­tion.

Math­e­mat­i­cally, the ve­loc­ity cor­rec­tion is given by

$$\frac{v_{\rm p}}{v_{\rm p,w}} = \frac{1+e^{1990^2(v_{\rm i}-v_{\rm i,w})/v_{\rm i,w}}}{2}$$

Note that 1990 is the model year of the first Mi­atas. For con­ve­nience, the above curve can be ap­prox­i­mated as piece­wise lin­ear.

The pur­pose of this pa­per is to shed some the­o­ret­i­cal light on the de­scribed em­pir­i­cal ob­ser­va­tions. It will be shown that spe­cial rel­a­tiv­ity com­bined with quan­tum me­chan­ics di­rectly im­plies the speed ad­van­tage of white Mi­atas. There­fore, the speed dif­fer­ence is not an ex­per­i­men­tal aber­ra­tion but a sci­en­tific fact.

Foot­notes

... Mi­ata^1.1

Mazda refers to the Mi­ata com­monly as the MX-5. The des­ig­na­tion Mi­ata has been dropped al­to­gether in re­cent years.